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2016

Effects of Hydrostatic Pressure on Critical Current Density & Pinning Effects of Hydrostatic Pressure on Critical Current Density & Pinning

Mechanism of Iron Based Superconductors and MgB2 Mechanism of Iron Based Superconductors and MgB2

Babar Shabbir University of Wollongong

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Recommended Citation Recommended Citation Shabbir, Babar, Effects of Hydrostatic Pressure on Critical Current Density & Pinning Mechanism of Iron Based Superconductors and MgB2, Doctor of Philosophy thesis, Institute for Superconducting and Electronic Materials, University of Wollongong, 2016. https://ro.uow.edu.au/theses/4637

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Institute for Superconducting and Electronic Materials

Effects of Hydrostatic Pressure on Critical Current Density & Pinning Mechanism of Iron Based Superconductors and MgB2

Babar Shabbir

This thesis is presented as part of the requirements for the Award of the Degree of Doctor of Philosophy

of the University of Wollongong

December 2015

Declaration

I, Babar Shabbir, declare that this thesis, submitted in partial fulfilment of the

requirements for the award of Doctor of Philosophy, in the Institute for

Superconducting & Electronic Materials (ISEM), Faculty of Engineering,

University of Wollongong, Australia, is wholly my own work unless otherwise

referenced or acknowledged. This document has not been submitted for a

qualification at any other academic institution.

Babar Shabbir

December 09, 2015

i

ABSTRACT

The iron based superconductors have revealed distinctive superconducting

properties, including reasonable critical temperature (Tc ≈ 56 K), extremely

high upper critical field (Hc2) on the order of 100 T, high intrinsic pinning

potential, low anisotropy values, generally between 1-8, high irreversibility

field (Hirr), and high critical current density (Jc), which is of vital importance

for low and high field application. Enhancement of Jc or flux pinning has

always been an important focus of superconductor research over the past

decade. Usually, three approaches have been used to increase the Jc in cuprates,

MgB2, and iron based superconductors:

• Texturing processes to reduce the mismatch angle between adjacent grains and

thus overcome the weak-link problem in layer-structured superconductors;

• High energy ion implantation or irradiation to introduce point defect pinning

centres; and;

• Chemical doping, which can induces more point pinning centres.

Weak-links and weak flux pinning are the predominant factors causing low Jc

values, specifically at high fields and temperatures in pnictide polycrystalline

bulks, and these problems must be overcome. In order to enhance the Jc in

granular superconductors, we have to increase/improve: i) grain connectivity;

ii) point defects inside grains; and iii) Tc enhancement, which can increase the

effective superconducting volume as well as Hirr and Hc2. Furthermore,

elimination of weakly linked grain boundaries (GBs) is a prerequisite for

improving the Jc values. Moreover, the nature of the pinning mechanism plays

an important role in obtaining good Jc field dependence values along with a

ii

suitable pinning force, which can boost pinning strength and, in turn, leads to

higher values of Jc. Although chemical doping and high energy particle

irradiation can induce point defects, they can only enhance Jc either in high

fields or low fields, with degradation of Tc. Therefore, the most ideal approach

should be one which can improve grain connectivity (in the case of

polycrystalline bulks and wires/tapes), induce more point defects, increase

superconducting volume and Tc, and especially enhance Jc, at both low and

high fields.

It has been reported that hydrostatic pressure has a positive effect on Tc in

cuprates and pnictide superconductors. Hydrostatic pressure can reduce

anisotropy, improve the grain connectivity (in the case of polycrystalline bulks

and wires/tapes), induce more point pinning centres, and increase the

superconducting volume, Hirr, and Hc2. Therefore, the hydrostatic pressure

approach was chosen for investigation of its effects on Jc and the pinning

mechanism in granular superconductors, single crystals, and tapes.

We found that hydrostatic pressure up to 1.2 GPa can not only significantly

increase Tc from 15 K (underdoped) to 22 K, but also significantly enhances the

irreversibility field, Hirr, by a factor of 4 at 7 K, as well as the critical current

density, Jc, by up to 30 times at both low and high fields for Sr4V2O6Fe2As2

polycrystalline bulks. It was found that pressure can induce more point defects,

which are mainly responsible for the Jc enhancement. In addition, pressure can

also transform surface pinning to point pinning in Sr4V2O6Fe2As2.

Hydrostatic pressure can also significantly enhance Jc in NaFe0.972Co0.028As

single crystals by at least tenfold at low field and more than a hundredfold at

iii

high fields. Significant enhancement in the in-field performance of

NaFe0.972Co0.028As single crystal in terms of pinning force density (Fp) is found

at high pressures. At high fields, the Fp is over 20 and 80 times higher than

under ambient pressure at12 K and 14 K, respectively, at P = 1 GPa. We have

discovered that the hydrostatic pressure induces more point pinning centres in a

sample, and the pinning centre number density found at 1 GPa is almost twice

as high as under ambient pressure at 12 K and over six times as high at 14 K.

We also demonstrated strong flux pinning over a wide field range under

hydrostatic pressure in optimally doped Ba0.6K0.4Fe2As2 crystal by enhancing

the pinning force via the formation of giant vortexes, which can, in turn, cause

significant enhancement of the critical current density in both low and high

fields. Additionally, we also discuss a fundamental mechanism related to Jc

enhancement with unchanged superconducting critical temperature values

under hydrostatic pressure. The pressure of 1.2 GPa improved the Fp by nearly

5 times at 8, 12, 24, and 28 K, which can increase Jc by nearly two-fold at 4.1

K and five-fold at 16 K and 24 K in both low and high fields, respectively. This

study also revealed that such an optimally doped superconductor’s performance

in both low and high fields can also be further enhanced by pressure.

Finally, the impact of hydrostatic pressure of up to 1.2 GPa on the Jc and the

nature of the pinning mechanism in MgB2 have been investigated within the

framework of the collective theory. We found that the hydrostatic pressure can

induce a transition from the regime where pinning is controlled by spatial

variation in the critical transition temperature (𝛿𝑇c) to the regime controlled by

spatial variation in the mean free path (δℓ). Furthermore, Tc and low field Jc are

iv

slightly reduced, and the Jc drops more quickly at high fields than at ambient

pressure. The hydrostatic pressure can reduce the density of states [Ns(E)],

which, in turn, leads to a reduction in the Tc from 39.7 K at P = 0 GPa to 37.7

K at P = 1.2 GPa.

v

Dedicated to my family and

friends

vi

ACKNOWLEDGEMENTS

I cannot express enough thanks to my supervisor, Prof. Xiaolin Wang, who

offered me this interesting project. I would also like to thank him for his

kind cooperation, guidance, encouragement, and continuous support

throughout my PhD. His way of research thinking is highly unique, picking up

different research angles to which we have never paid much attention. I have

enjoyed his company and outstanding supervision. He is definitely a role model

for students. I would also like to thank my co-supervisor, Prof. Shi Dou, for his

advice and support during my study. I am also thankful to discovery Project

(ID: DP1094073) under Project Title: Materials science and superconductivity

in the new iron based high temperature superconductors.

I am pleased to thank Prof. Reza Ghorbani at Ferdossi University, Iran, for his

guidance and Dr. T. Silver for her kind help in correcting the English in this

thesis.

I would also thank all of my friends, colleagues, staff members at ISEM,

especially Nasir, Mislav, Fexiang, Kinkie, Munir, Nazrul, Dr. Md. Shariar, G.

Peleckis, Deepak, Mathew, Franklin, Sujeeva, Ashkan, and Faiz for the

friendly atmosphere at ISEM and their help in my research work.

How can I forget my Pakistani friends at this special moment, who keep me

smiling with their memories and jokes. Special thanks to Nadeem, Shakeel,

Mehmood, Jehnazeb, Kamran, Ishtiaq, Husnain, Adnan, Asad, Imran, Adil,

Irfan, Behram, Mohsin, Faheem and Fawad.

vii

Completion of this project could not have been accomplished without the

support of my family. Special thanks to my parents, sisters, brothers, sisters-in-

law, brothers-in-law, father-in-law, and mother-in-law, especially for their

prayers and love.

Finally, to my caring, loving, and supportive wife, Adeeba: my deepest

gratitude. Your encouragement when times got rough is much appreciated and

duly noted. It was a great comfort and relief to know that you were willing to

provide management of our household activities and look after our children

while I completed my work. My heartfelt thanks. Special thanks to my little

angels Adam and Lala, who make me smile all the time.

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TABLE OF CONTENTS

ABSTRACT .................................................................................................................. i

ACKNOWLEDGEMENTS ......................................................................................... v

TABLE OF CONTENTS ............................................................................................. 1

LIST OF FIGURES ..................................................................................................... 4

LIST OF TABLES ..................................................................................................... 11

CHAPTER 1: Introduction ......................................................................................... 12

1.1 References .................................................................................................. 19

CHAPTER 2: Literature Review ............................................................................... 23

2.1 History of Superconductivity ..................................................................... 23

2.2 Pinning Mechanism .................................................................................... 28

2.3 Iron based Superconductors (FeSCs) ......................................................... 29

2.3.1 Crystal structure and phase diagram ..……………………………………31

2.3.2 Superconducting Properties of FeSCs ..................................................... 33

2.3.3 Effects of Chemical doping on SC Properties of FeSCs…...………......40

2.3.4 Effects of Irradiation on SCs Properties of FeSCs……………………..42

2.3.5 Effects of Pressure on SCs Properies of FeSCs...……………………...44

2.3.6 Conclusion ............................................................................................. 47

2.4 MgB2 .......................................................................................................... 49

2.4.1 Crystal structure and two gap conductivity…………………………….49

2.4.2 Superconducting (SC) Properties of MgB2 ........................................... 51

2.4.3 Effects of Chemical doping on SC Properties of MgB2 ......................... 53

2.4.4 Effects of Irradiation on SCs Properties of MgB2……………………..57

2.4.5 Effects of Presuure on SC Properties of MgB2 ...................................... 59

2.4.6 Conclusion ............................................................................................. 61

2.5 References .................................................................................................. 62

CHAPTER 3: Experimental ....................................................................................... 82

3.1 Fabrication of samples ............................................................................... 82

3.1.1 Sr4V2O6Fe2As2 Polycrystalline Bulks…………………………………… 82

3.1.2 NaFe0.7Co0.3As Single Crystal ................................................................... 82

3.1.3 Ba0.6K0.4Fe2As2 Single Crystal ................................................................... 83

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3.1.4 MgB2 .......................................................................................................... 83

3.2 Experiemental Equipment………..……………………………………….83

3.2.1 Vibratory Sample Magnetometer ……………………………………...83

3.2.2 Hydrostatic Pressure Cell...……. ……………………………………...85

CHAPTER 4: Hydrostatic pressure, a very effective approach to significanly enhance

Jc in granular iron pnictide superconductors .............................................................. 96

4.1 Introduction ................................................................................................ 96

4.2 Results and Discussion ............................................................................. 100

4.3 Conclusion ............................................................................................... 107

4.4 Experiment ............................................................................................... 108

4.5 References ................................................................................................ 109

CHAPTER 5: Giant enhancement in Jc, upto hundred fold, in superocnducting

NaFe0.7Co0.3As single crystals under hydrostatic pressure ...................................... 112

5.1 Introduction .............................................................................................. 112

5.2 Results and Discussion ............................................................................. 113

5.3 Conclusion ............................................................................................... 122

5.4 Experiment ............................................................................................... 123

5.5 References ................................................................................................ 124

CHAPTER 6: Observation of strong flux pinning and possible mechanism for critical

current enhancement under hydrostatic pressure in optimally doped (Ba,K)Fe2As2

Single Crystals ......................................................................................................... 126

6.1 Introduction .............................................................................................. 126

6.2 Results and Discussion ............................................................................. 129

6.3 Conclusion ............................................................................................... 138

6.4 Experiment ............................................................................................... 139

6.5 References ................................................................................................ 140

CHAPTER 7: Hydrostatic pressure induced transition from δTc to δℓ pinning

mechanism in MgB2 ................................................................................................. 143

7.1 Introduction .............................................................................................. 143

7.2 Results and Discussion ............................................................................. 144

7.3 Conclusion ............................................................................................... 151

7.4 Experiment ............................................................................................... 152

7.5 References ................................................................................................ 153

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CONCLUSIONS ...................................................................................................... 156

PUBLICATION FROM THIS WORK .................................................................... 158

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LIST OF FIGURES

Figure 2-1: Resistance versus Temperature plot for mercury obtained by Kamerling

Onnes (Left Side). Photograph of Kamerlingh onnes (Right side)………………....23

Figure 2-2: The Periodic Table classified by all known elemental superconductors and their Tc (DOI: 10.1038/419569a)…………………………………….…………….24

Figure 2-3: Meissner effect, the expulsion of external magnetic field from inside the

superconductor in the superconducting state by creating surface current. The field is

applied at (a) T > Tc and (b) T < Tc (Image taken from

Wikipedia)…………………………………………………………………………...24

Figure 2-4: Response of Type I and II superconductors in external magnetic fields

(Image taken from http://fhc80.com.br/superconductivity-of-metals-and-

alloys.htm).……………..………………………………………………..………….26

Figure 2-5: A) Magnetic flux line penetrating in a type-II superconductor in form of

vortices B) Current Swirls around the core of each vortex (Picture taken from book

Superfluids)……………………………………………….……………………...…26

Figure 2-6: The Tc of some known superconductors versus the year of discovery as

compiled by ASG, University of Geniva, Switzerland……………………………..27

Figure 2-7: Crystal structures (tetragonal with the c-axis pointing up) of FeSCs: FeSe, LiFeAs, LaOFeAs and Sr2VO3FeAs crystallize in space group P4/nmm, BaFe2As2 in I4/mmm. Iron atoms: dark grey spheres, Arsenic(selenium):black spheres and cations: Light grey balls [29]…………............………………………..31 Figure 2-8: Phase diagrams for different families of FeSCs [30, 38-40]…………………………………………………………………………………...32

Figure 2-9: Hc2 values for different families of FeSCs [62, 64-66]…………………35

Figure 2-10: Field dependant Jc values for 1111, 122, 111 and 11 crystals [212-217]………………………………………………………………………………….37

Figure 2-11: Transport Jc as a function of field for Sr0.6K0.4Fe2As2 tapes..……........39

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Figure 2-12: Jc values for different polycrystalline bulks [32-35]…..........................39

Figure 2-13: Tc as a function of doping concentrations [105]………………………41

Figure 2-14: Tc as a function of doping concentrations for sulphur doped FeSe

[107]…………………………………………………………………………………42

Figure 2-15: Comparison of Jc for un-irradiated and irradiated SmFeAsO1-xFx

[110]…………………………………………………………………………………43

Figure 2-16: Comparison of Jc for un-irradiated and irradiated Co doped 122

compound [113]…………………………………………………………………..…44

Figure 2-17: Pressure dependence of Tc for under-doped, optimally-doped and over-doped LaFeAsO1-xFx [119]………………………………………….……..………45

Figure 2-18: Pressure dependence of Tc values for SrFe2As2 [126]………..……….46

Figure 2-19: The crystal structure of MgB2 superconductor [13]……….…………50

Figure 2-20: MgB2 Fermi surface along with symmetry directions of Brillouin zone [34]…..........................................................................................................................51

Figure 2-21: (Left) Tc dependence on carbon concentration. (Right) Field dependence of Jc at different temperatures for undoped and carbon doped samples [217]…………………………………………………………………………………54

Figure 2-22: Transformation of δTc to δℓ pinning mechanism by graphene oxide doping [257]……………………………………………………………………...….56

Figure 2-23: Reduction of Tc by irradiation for MgB2 [258]…….…………………57

Figure 2-24: Tc suppression under neutron irradiation [272]…...…………………..58

Figure 2-25: Pressure dependence of Tc for MgB2 [276]….………………………..60

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Figure 2-26: The Tc as a function of pressure through different pressure mediums as

compiled by Buzea et all [154] and the references therein……….…………………60

Figure 3-1: Schematic drawing of VSM linear motor and its sample puck………...84

Figure 3-2: Pressure cell construction………………………………………………85

Figure 3-3: Cutting the teflon tube…………………………………………………86

Figure 3-4: Setting the Teflon cap to one end of the Teflon tube…..………………86

Figure 3-5: Inserting Teflon tube + cap in center cyclinder…..……………………87

Figure 3-6: Inserting sample and inserting second Teflon cap..……………………88

Figure 3-7: Teflon tube is centred and setting the pistons.....………………………89

Figure 3-8: Applying teflon powder, piston backup, side cylinders and pressurizing

nuts……………………………………………………………………………….…89

Figure 3-9: Final assembly before pressurizing ….…………………………………90

Figure 3-10: Measuring compression and inserting pressure cell into a

clamp…………………………………..……………………………………………91

Figure 3-11: Setting the pressure spanners…………………………………………91

Figure 3-12: Typical sample pressure and vs. sample

compression…………………………………………………………………………94

Figure 3-13: Pressure cell threaded to VSM sample rod

adopter………………………………………………………………………………95

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Figure 4-1: Temperature dependence of ZFC and FC moments at different pressures

for Sr4V2O6Fe2As2. The inset shows the pressure dependence of Tc…………..….100

Figure 4-2: Field dependence of Jc under different pressures at 3, 4, 6, and 7

K……………………………………………………………………………………101

Figure 4-3: Comparison of Jc at 0 and 1.2GPa at 4 and 6 K. The inset shows

d(lnJc)/dP versus temperature, indicating enhancement of Jc at a rate of 1.08GPa-1 at

zero field…………………………………………………………………………...101

Figure 4-4: Pressure dependence of Jc (logarithmic scale) at 0, 2, and 4 T at the

temperature of 6 K…………………………………………………………………102

Figure 4-5: Hirr vs. T for different pressures……………………………………….102

Figure 4-6: Logarithmic plot of Jc as a function of reduced temperature at different

pressures and fields………………………………………………………………..103

Figure 4-7: Plots of fp vs. H/Hirr at different pressures (0, 0.75, and 1.2 GPa) for 4

(left) and 6 K (right) temperature curves. The experimental data is fitted through the

Dew-Hughes model, and the parameters are shown……………………………….105

Figure 5-1: Temperature dependence of magnetic moment at different applied

pressures in both ZFC and FC runs for NaFe0.97Co0.03As………………………….113

Figure 5-2: Field dependence of Jc at different pressures (0, 0.45 and 1GPa) at

different temperatures……………………………………………………………..114

Figure 5-3: Plot of 𝐽𝑐1𝐺𝐺𝐺/𝐽𝑐0𝐺𝐺𝐺 versus field at 12K and 14K. There is a giant

enhancement in Jc values at P =1GPa. The inset shows the plot of d(lnJc)/dP versus

temperature, which demonstrates enhancement in lnJc at a rate of nearly 3GPa-1 at

14K…………………………………………………………………………………115

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Figure 5-4: Plot of Hirr versus temperature at different pressures. Inset shows Hirr as a

function of reduced temperature …………………………………….…………….115

Figure 5-5: Logarithmic plot of critical current density as a function of reduced

temperature at different pressures and magnetic fields…………………………….116

Figure 5-6: Top panel shows normalized temperature dependence (t = T/Tc) of

normalized measured Jc at 0.1T and 0T, in good agreement with δℓ pinning. Lower

panel shows plots of Fp vs. H/Hirr at P=0GPa and P= 0.45GPa at 14K. The

experimental data is fitted through D. Dew Hughes model………..........................118

Figure 5-7: Pinning force density (Fp) as a function of field at P=0GPa and P=1GPa

at 12K and 14K. The inset shows the temperature dependence of the pinning centre

number density at the different pressures………………………………………….120

Figure 5-8: Reduced field dependence of the normalized Jc at 14K for different

pressures. The inset shows the same plot for 12K at P=0GPa and

P=0.45GPa…………………………………………………………………………121

Figure 6-1: Magnetic moments versus temperature at P = 0 GPa and P = 1.2

GPa…………………………………………………………………………………129

Figure 6-2: M-H loops at 4.1, 8, 12, 16, 20, 24, 28, and 32 K for P = 0, 0.75, and 1.2

GPa………..……………………………………………………………………….130

Figure 6-3: Jc as a function of field at P = 0 GPa and 1.2 GPa at 4.1 K, 16 K, and 24

K……………………………….…………………………………………………..131

Figure 6-4: Fp versus field at 8 K, 12 K, 24 K, and 28 K at different

pressures…………………..……………………………………………………….132

Figure 6-5: Fp for different superconductors………………...................………….132

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Figure 6-6: Jc-Fp ratios at P = 1.2 GPa and P = 0 GPa. The relative change of Jc with

pressure as a function of T is given in the

inset………………………………………………………………………………..133

Figure 6-7: Fp ∝ Np holds where P < P0 (the threshold pressure value) and the size of

defects, L0 ≈ ξ….…………………………………………………………………..134

Figure 6-8: lnJc versus reduced temperature at different fields and

pressures..………………………………………………………………………….136

Figure 6-9: Jc as a function of T/Tc. Experimental data points are in agreement

with 𝛿ℓ pinning…………………………………………………………………….137

Figure 7-1: XRD Pattern of MgB2 ………..………………...................………….144

Figure 7-2: Temperature dependence of magnetic moment under different applied

pressures in both ZFC and FC runs. The inset shows the pressure dependence of the

Tc for MgB2. Tc is found to decrease with a slope of dTc/dP = -1.37

K/GPa………………………………………………………………………………145

Figure 7-3: Field dependence of Jc under different pressures measured at 5 K, 8 K,

20 K, and 25 K…………………………………………………………………….146

Figure 7-4: Comparison of Jc at two pressures (0 GPa and 1.2 GPa) for 8 K and 20 K

curves. The inset shows the plot of ΔJc/Jc0 versus field, illustrating the trend towards

the suppression of Jc with increasing field, nearly at a same rate of ~ -0.97 T-1 for 8 K

and 20K……...…………………………………………………………………….147

Figure 7-5: Hirr as a function of temperature………………………………………148

Figure 7-6: Jc as a function of reduced temperature (𝜏 = 1 − 𝑇 𝑇𝑐⁄ ) at 0, 2.5, and 5 T

for pressures of 0, 0.7, and 1.2 GPa. The solid lines are fitted well to the data

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according to the power law in the framework of Ginzburg-Landau

theory………………………………………………………………………………148

Figure 7-7: Double logarithmic plot of –log[Jc(B)/Jc(0)] as a function of field at 12 K

and 20 K……………………………………………………………………………149

Figure 7-8: Plots of Bsb(T)/ Bsb(0) vs. T/Tc at different pressures (0, 0.7. and 1.2 GPa).

The red fitted line is for δTc pinning, the black fitted line is for 𝛿ℓ pinning, and the

green fitted line is for mixed δ(𝑇c + ℓ) pinning …………………………………..150

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LIST OF TABLES

Table 1-1: Pressure investigations on Jc and Tc of some superconducting

materials…………………………………………………………………………….16

Table 2-1: Scaling parameters for core pinning according to Dew Hughes

Model………………………………………………………………………………..29

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1 INTRODUCTION

The discovery of iron-based superconductors (FeSCs) in 2006 brought new

motivation to the field of high-temperature superconductivity and strongly

correlated electron systems [1, 2]. The FeSCs consist of FeAs layered

structures alternating with spacer or charge reservoir blocks. The FeSCs can

thus be classified into the pnictide “1111” system for RFeAsO (R: a rare earth

element), including LaFeAsO, SmFeAsO, PrFeAsO, etc.; into the “122” type

for BaFe2As2, SrFe2As2, or CaFe2As2; into the “111” type for

LiFeAs, NaFeAs, LiFeP, and chalcogenides; or into the “11” type such as

FeSe, etc. [3-15]. The parent compound of pnictides is semimetallic, in contrast

to the cuprates, as their parent compounds are Mott insulators. The pnictide

superconductors exhibit distinctive superconducting properties, including

reasonable critical temperature (Tc ≈ 56 K), extremely high upper critical field

(Hc2) on the order of 100 T, high intrinsic pinning potential, low anisotropy

values, generally between 1-8, high irreversibility field (Hirr), and high critical

current density (Jc), which is the predominant limiting factor for low and high

field applications [16-20]. Strong pinning has been observed in pnictides,

which gives rise to high Jc values in both single crystals and thin films. The

oxypnictide SmFeAs(O,F) superconducting films show high Jc values (~106

A/cm2 at 4.2 K) in low fields [21]. Similarly, SmFeAsO0.7F0.25 single crystals

reveal a promising combination of high Jc values (> 106  A cm−2 at 5 K) and

nearly isotropic critical current densities along all crystal directions [22]. The Jc

for SmFeAsO0.8F0.15 crystals has been enhanced up to 107 A cm−2at 5 K [23].

High critical current density Jc of 4 MA/cm2 at 4 K was obtained in Co-doped

BaFe2As2 (BaFe2As2:Co) epitaxial films [24]. Jc of 5 MA/cm2 at low fields and

13

temperatures is reported for Ba0.6K0.4Fe2As2 crystals [25].

BaFe2(As0.66P0.33)2 films exhibited nearly isotropic critical current densities in

excess of 1.5 MA cm−2 at 15 K and 1 T, which are seven times higher than

previously reported for BaFe2As2 films [26]. The point defects induced by

heavy-ion and proton irradiation in Ba0.6K0.4Fe2As2 single crystal increased the

Jc up to 5 MA/cm2 at 5 K and 7 T [27]. A Jc value of 106A/cm2 has also been

found in FeSe films at 2 K [28]. Usually, Jc values in polycrystalline bulks and

tapes/wires are lower as compared to single crystals and films due to weak flux

pinning. Jc values of nearly 104 - 105 A/cm2 have been obtained at high fields

and temperatures for polycrystalline bulks and tapes/wires, although they are

lower than what are required for practical applications [29]. At 4.2 K and low

fields, transport Jc of 104 A/cm2 has been found in Sn-added Sr1-xKxFe2As2

superconducting tapes [30]. Similarly, (Sr,K)Fe2As2 superconducting wire

prepared by the powder-in-tube (PIT) method combined with a hot isostatic

pressing (HIP) technique provided a transport Jc value of 105 A/cm2 at 4.2 K

under self-field [31]. Jc as a function of applied magnetic field at 4.2 K for the

K-doped wire exhibited Jc values of nearly 105 A/cm2 at low fields [32].

Although Jc values at low fields and temperatures are high to some extent, the

major drawbacks are that Jc decays rapidly in high fields, especially at high

temperatures. Enhancement of Jc or flux pinning has always been a leading area

of research over the past decade. Usually, three approaches have been used to

increase the Jc in cuprates, MgB2, and iron based superconductors:

• Texturing processes to reduce the mismatch angle between adjacent grains and

thus overcome the weak-link problem in layer-structured superconductors;

14

• Irradiation to introduce point defect pinning centres; and;

• Chemical doping, which can induce more point pinning centres.

Weak-links and weak flux pinning are the predominant factors causing low Jc

values, specifically at high fields and temperatures in pnictide polycrystalline

bulks, so these problems must be overcome. In order to enhance the Jc in

granular superconductors, we have to increase/improve: i) grain connectivity;

ii) point defects inside grains; and iii) Tc enhancement, which can increase the

effective superconducting volume as well as Hirr and Hc2.

We have taken into account the following facts regarding the flux pinning

mechanism in polycrystalline pnictide superconductors. Elimination of the

weakly linked grain boundaries (GBs) is a prerequisite for improving the Jc

values, as the coherence length for pnictides is very short (ξ of a few nm) [33].

Furthermore, the nature of the pinning mechanism plays an important role in

improving the Jc field dependence values along with the pinning force, which

can boost the pinning strength and, in turn, leads to higher values of Jc. The

ideal size of defects for pinning should be comparable to the coherence length

[34]. Therefore, point defect pinning is required for high Jc values in contrast to

surface pinning, because its pinning force is stronger than that for surface

pinning at low and high field, according to the Dew-Hughes model [35]. Thus,

it is desirable to induce more point defects. Although chemical doping and high

energy particle irradiation can induce point defects and enhance Jc, especially

in high field, Tc and low field Jc deteriorate greatly for various types of

superconductors. Therefore, the most ideal approach should be one which can

improve grain connectivity (in the case of polycrystalline bulks and

15

wires/tapes), induce more point defects, and increase the superconducting

volume and Tc.

It has been reported that hydrostatic pressure has a positive effect on Tc in

cuprate and pnictide superconductors. High pressure of 150 kbars can raise the

Tc of Hg-1223 significantly, from 135 K to a record high 153 K [36]. The Tc of

hole-doped (NdCeSr)CuO4 has been increased from 24 to 33 K at 3 GPa [37].

The enhancement of Tc for Y2B4C7O14 is more than 10 K at 2 GPa [38]. It

should be noted that pressure also shows positive effects on Tc for various

pnictide superconductors. Pressure can result in improvement of Tc from 28 K

to 43 K at 4 GPa for LaOFFeAs [39]. For Co doped NaFeAs, the maximum Tc

can reach as high as 31 K from 16 K at 2.5 GPa [40]. Pressure can enhance the

Tc of La doped Ba-122 epitaxial films up to 30.3 K [41]. A huge enhancement

of Tc from 13 K to 27 K at 1.48 GPa, with even a high value of 37 K at 7 GPa,

has also been reported for FeSe [42, 43]. In addition, pressure can 1) reduce the

lattice parameters and cause the shrinkage of unit cells, giving rise to reduction

of the anisotropy; 2) improve the grain connectivity because of compression of

both grains and grain boundaries (GBs); 3) induce more point pinning centres,

as the formation energy of point defects decreases with increasing pressure.

Pressure can also cause low-angle GBs to migrate in polycrystalline bulk

samples, resulting in the formation of giant grains and leading to the sacrifice

of surface pinning centres thereafter. Therefore, a higher ratio of point pinning

centres to surface pinning centres is expected due to the formation energy and

migration of GBs under pressure. The significant enhancement in Tc under

pressure means that superconducting volumes should be increased greatly

compared to Tc without pressure. Therefore, it was expected that hydrostatic

16

pressure would increase superconducting volume, Hirr, and Hc2 due to Tc

enhancement, increase the pinning centre number density by inducing more

point defects, improve grain connectivity (in the case of polycrystalline bulks

and wires/tapes), and reduce the anisotropy in pnictide superconductors. There

is some evidence for Jc enhancement (not more than one order of magnitude)

under pressure for some conventional and unconventional superconducting

materials, which are listed in Table 1-1. The origin of the Jc enhancement is

still unclear, however. Therefore, detailed investigations are required to

examine pnictide Jc under pressure (especially to obtain the maximum in-field

performance) and reveal the cause of Jc enhancement.

No Material Pressure effect on Jc Pressure

effect on Tc

Reference

1 Nb-Zr Alloys 15% enhancement for 1.75 GPa

Tc not changed [44]

2 Nb3Sn Negative Negative [45]

3 TI2CaBa2Cu20 Bulk

Twofold enhancement Positive [46]

4 YBazCu,Og Bulk Fivefold enhancement Positive [46] 5 YBaCuO rings Positive Positive [47] 6 YBCO Bulk Positive No effect [48]

7 YBCO Bicrystalline ring

+20%/GPa Positive [49]

8 Bi-2223 Superconducting Wire

Negative (0.9 GPa) Negative [50]

9 FeSe0.5Te0.5 Enhanced by one order of magnitude

Enhanced by 7 K at 1 GPa

[51]

Table 1-1: Pressure investigations on Jc and Tc of some superconducting materials.

We have used the hydrostatic pressure approach to investigate its effects on Jc

and pinning mechanisms in granular superconductors and single crystals, which

are systematically discussed in Chapters 4, 5, and 6. We also propose that the

pressure approach can be used, even when all the other approaches used are

17

exhausted, to further improve the Jc in superconductors. Moreover, we have

also investigated pressure effects on pinning in MgB2 (Chapter 7). The

following are the summaries of our main results:

A) We found that hydrostatic pressure up to 1.2 GPa can not only significantly

increase Tc from 15 K (under-doped) to 22 K, but also significantly enhances

the irreversibility field, Hirr, by a factor of 4 at 7 K, as well as the critical

current density, Jc, by up to 30 times in both low and high fields for

Sr4V2O6Fe2As2 polycrystalline bulks. It was found that pressure can induce

more point defects, which are mainly responsible for the Jc enhancement. In

addition, pressure can also transform surface pinning to point pinning in

Sr4V2O6Fe2As2.

B) Hydrostatic pressure can significantly enhance Jc in NaFe0.972Co0.028As single

crystals by at least tenfold at low field and more than a hundredfold at high

fields. Significant enhancement in the in-field performance of

NaFe0.972Co0.028As single crystal in terms of pinning force density (Fp) is found

at high pressures. At high fields, the Fp is over 20 and 80 times higher than

under ambient pressure at 12 K and 14 K, respectively, at P = 1 GPa. We have

discovered that the hydrostatic pressure induces more point pinning centres in a

sample, and the pinning centre number density found at 1 GPa is almost twice

as high as under ambient pressure at 12 K and over six times as high at 14 K.

C) We also demonstrated strong flux pinning over a wide field range under

hydrostatic pressure in optimally doped Ba0.6K0.4Fe2As2 crystal by enhancing

the pinning force via the formation of giant vortexes, which can, in turn,

cause significant enhancement of the critical current density in both low and

high fields. Additionally, we also discuss a fundamental mechanism related to

18

Jc enhancement with unchanged superconducting critical temperature values

under hydrostatic pressure. The pressure of 1.2 GPa improved the Fp by

nearly 5 times at 8, 12, 24, and 28 K, which can increase Jc by nearly two-fold

at 4.1 K and five-fold at 16 K and 24 K in both low and high fields,

respectively. This study also revealed that such an optimally doped

superconductor’s performance in both low and high fields can also be further

enhanced by pressure.

D) The impact of hydrostatic pressure of up to 1.2 GPa on the Jc and the nature of

the pinning mechanism in MgB2 have been investigated within the framework

of the collective theory. It has been demonstrated that hydrostatic pressure can

induce a transition from the regime where pinning is controlled by spatial

variation in the critical transition temperature (𝛿𝑇c) to the regime controlled by

spatial variation in the mean free path (δℓ). Furthermore, Tc and low field Jc are

only slightly reduced, although the Jc drops more quickly at high fields than at

ambient pressure. The hydrostatic pressure can reduce the density of states

[Ns(E)], which, in turn, leads to a reduction in the critical temperature from

39.7 K at P = 0 GPa to 37.7 K at P = 1.2 GPa.

19

1.1 References 1. Kamihara Y, et al. Iron-Based Layered Superconductor:  LaOFeP. J. Am.

Chem. Soc. 128, 10012-10013 (2006). 2. Wang X, Ghorbani SR, Peleckis G, Dou S. Very High Critical Field and

Superior Jc-Field Performance in NdFeAsO0.82F0.18 with Tc of 51 K. Adv. Mat. 21, 236-239 (2009).

3. Kamihara Y, Watanabe T, Hirano M, Hosono H. Iron-Based Layered

Superconductor La[O1-xFx]FeAs (x = 0.05−0.12) with Tc = 26 K. J. Am. Chem. Soc. 130, 3296-3297 (2008).

4. Chen XH, Wu T, Wu G, Liu RH, Chen H, Fang DF. Superconductivity at 43K

in SmFeAsO1-xFx. Nature 453, 761-762 (2008). 5. Ren Z-A, et al. Superconductivity and phase diagram in iron-based arsenic-

oxides ReFeAsO1−δ (Re = rare-earth metal) without fluorine doping. EPL 83, 17002 (2008).

6. Rotter M, Tegel M, Johrendt D. Superconductivity at 38 K in the Iron Arsenide

(Ba1-xKxFe2As2). Phys. Rev. Lett. 101, 107006 (2008). 7. Sasmal K, et al. Superconducting Fe-Based Compounds (A1-xSrx)Fe2As2 with

A=K and Cs with Transition Temperatures up to 37 K. Phys. Rev. Lett. 101, 107007 (2008).

8. Shirage PM, Miyazawa K, Kito H, Eisaki H, Iyo A. Superconductivity at 26 K

in (Ca1- xNa x)Fe2As2. Appl. Phys. Exp. 1, 081702 (2008). 9. Wang XC, et al. The superconductivity at 18 K in LiFeAs system. Solid State

Commun. 148, 538-540 (2008). 10. Pitcher M J, et al. Structure and superconductivity of LiFeAs. Chemical

Commun., 5918-5920 (2008). 11. Tapp JH, et al. LiFeAs: An intrinsic FeAs-based superconductor with Tc=18K.

Phys. Rev. B 78, 060505 (2008). 12. Chu CW, et al. The synthesis and characterization of LiFeAs and NaFeAs.

Physica C 469, 326-331. 13. Parker DR, et al. Structure, antiferromagnetism and superconductivity of the

layered iron arsenide NaFeAs. Chemical Commun. 2189-2191 (2009). 14. Zhang SJ, et al. Superconductivity at 31 K in the "111"-type iron arsenide

superconductor Na1−xFeAs induced by pressure. EPL 88, 47008 (2009). 15. Deng Z, et al. A new "111" type iron pnictide superconductor LiFeP. EPL 87,

37004 (2009).

20

16. Wu G, et al. Superconductivity at 56 K in samarium-doped SrFeAsF. J. Phys.: Condens. Matter 21, 142203 (2009).

17. Prakash J, Singh SJ, Samal SL, Patnaik S, Ganguli AK. Potassium fluoride

doped LaOFeAs multi-band superconductor: Evidence of extremely high upper critical field. EPL 84, 57003 (2008).

18. Wang X-L, et al. Very strong intrinsic flux pinning and vortex avalanches in

(Ba,K)Fe2As2 superconducting single crystals. Phys. Rev. B 82, 024525 (2010). 19. Yuan HQ, et al. Nearly isotropic superconductivity in (Ba,K)Fe2As2. Nature

457, 565-568 (2009). 20. Lee S, et al. Weak-link behavior of grain boundaries in superconducting

Ba(Fe1−xCox)2As2 bicrystals. Appl. Phys. Lett. 95, 212505 (2009). 21. Iida K, et al. Oxypnictide SmFeAs(O,F) superconductor: A candidate for high-

field magnet applications. Sci. Rep. 3, 2139 (2013). 22. Moll PJW, et al. High magnetic-field scales and critical currents in

SmFeAs(O, F) crystals. Nat. Mater. 9, 628-633 (2010). 23. Fang L, et al. Huge critical current density and tailored superconducting

anisotropy in SmFeAsO0.8F0.15 by low-density columnar-defect incorporation. Nat. Commun. 4, 2655 (2013).

24. Katase T, Hiramatsu H, Kamiya T, Hosono H. High Critical Current Density 4

MA/cm2 in Co-Doped BaFe2As2 Epitaxial Films Grown on (La,Sr)(Al,Ta)O3 Substrates without Buffer Layers. Appl. Phys. Exp. 3, 063101 (2010).

25. Fang L, et al. High, magnetic field independent critical currents in

(Ba,K)Fe2As2 crystals. Appl. Phys. Lett. 101, 012601 (2012). 26. Miura M, et al. Strongly enhanced flux pinning in one-step deposition of

BaFe2(As0.66P0.33)2 superconductor films with uniformly dispersed BaZrO3 nanoparticles. Nat. Commun. 4, 2499 (2013).

27. Kihlstrom KJ, et al. High-field critical current enhancement by irradiation

induced correlated and random defects in (Ba0.6K0.4)Fe2As2. Appl. Phys. Lett. 103, 202601 (2013).

28. Wen-Hao Z, et al. Direct Observation of High-Temperature Superconductivity

in One-Unit-Cell FeSe Films. Chin. Phys. Lett. 31, 017401 (2014). 29. Ma Y. Progress in wire fabrication of iron-based superconductors. Supercond.

Sci. Technol. 25, 113001 (2012). 30. Gao Z, et al. High transport critical current densities in textured Fe-sheathed

Sr1−xKxFe2As2+Sn superconducting tapes. Appl. Phys. Lett. 99, 242506 (2011).

21

31. Pyon S, et al. Enhancement of critical current densities by high-pressure sintering in (Sr,K)Fe2As2 PIT wires. Supercond. Sci. Technol. 27, 095002 (2014).

32. Weiss JD, et al. High intergrain critical current density in fine-grain

(Ba0.6K0.4)Fe2As2 wires and bulks. Nat. Mater. 11, 682-685 (2012). 33. Stewart GR. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589-

1652 (2011). 34. Su H, Welch DO, Wong-Ng W. Strain effects on point defects and chain-

oxygen order-disorder transition in 123 cuprate compounds. Phys. Rev. B 70, 054517 (2004).

35. Dew-Hughes D. Flux pinning mechanisms in type II superconductors. Phil.

Mag. 30, 293-305 (1974). 36. Chu CW, Gao L, Chen F, Huang ZJ, Meng RL, Xue YY. Superconductivity

above 150 K in HgBa2Ca2Cu3O8+δ at high pressures. Nature 365, 323-325 (1993).

37. Murayama C, Mori N, Yomo S, Takagi H, Uchida S, Tokura Y. Anomalous

absence of pressure effect on transition temperature in the electron-doped superconductor Nd1.85Ce0.15CuO4- δ . Nature 339, 293-294 (1989).

38. Yuh Yamada TM, Yoshinari Kaieda, Nobuo Mōri. Pressure Effects on Tc of

Superconductor YBa2Cu4O8. Jpn. J. Appl. Phys. 29, L250-L253 (1990). 39. Takahashi H, Igawa K, Arii K, Kamihara Y, Hirano M, Hosono H.

Superconductivity at 43 K in an iron-based layered compound LaO1-xFxFeAs. Nature 453, 376-378 (2008).

40. Wang AF, et al. Pressure effects on the superconducting properties of single-

crystalline Co doped NaFeAs. New J. Phys. 14, 113043 (2012). 41. Katase T, Sato H, Hiramatsu H, Kamiya T, Hosono H. Unusual pressure effects

on the superconductivity of indirectly electron-doped (Ba1-xLax)Fe2As2 epitaxial films. Phys. Rev. B 88, 140503 (2013).

42. Mizuguchi Y, Tomioka F, Tsuda S, Yamaguchi T, Takano Y.

Superconductivity at 27K in tetragonal FeSe under high pressure. Appl. Phys. Lett. 93, 152505 (2008).

43. Margadonna S, et al. Pressure evolution of the low-temperature crystal

structure and bonding of the superconductor FeSe (Tc=37K). Phys. Rev. B 80, 064506 (2009).

44. Brandit NB, aPapp E., The effect of hydrostatic pressure on the critical current

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46. Diederichs J, Reith W, Sundqvist W, Niska J, Easterling KE, Schilling JS.

Critical currents in Tl-2122 and Y-124 sintered under high hydrostatic pressure. Supercond. Sci. Technol. 4, S97 (1991).

47. Tomita T et al., Enhanced superconducting properties of bicrystalline

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23

2 LITERATURE REVIEW

2.1 History of Superconductivity Superconductivity is a macroscopic quantum phenomenon of infinite electrical

conductivity or zero electrical resistance and exclusion of magnetic fields, occurring

in different elements, as well as intermetallic alloys and compounds,

when cooled below a specific temperature, which is well-known as the critical

temperature, Tc. This phenomenon was discovered by the Dutch physicist Heike

Kamerlingh Onnes (Figure 2-1: Right) on April 8, 1911 in Leiden, while he was

measuring the electrical resistance of mercury and found that it suddenly drops to

zero at a temperature of 4.2 K, as shown in Figure 2-1: Left [1].

Figure 2-1: Resistance versus Temperature plot for mercury obtained by Kamerling Onnes (Left). Photograph of Kamerlingh Onnes (Right).

It has been found that twenty-one metallic elements and many different alloys and

compound materials exhibit superconductivity. The Periodic Table in Figure 2-2

shows all known elemental superconductors and their Tc.

24

Figure 2-2: Periodic Table classified by all known elemental superconductors and their Tc (Adopted from Hemley, R. J. & Mao, H.-K in Proceedings of the International School of Physics 'Enrico Fermi': High Pressure Phenomena (eds Hemley, R. J., Bernasconi, M., Ulivi, L. & Chiarotti, G.) (Italian Phys.

Soc., Bologna, in the press).

There are the two characteristics of all superconductors, i.e., zero resistivity and the

Meissner effect. In 1933, the German physicists Walther Meissner and Robert

Ochsenfeld discovered a unique property of superconductors, that a superconductor

can completely expel magnetic field from its interior during its transition to the

superconductivity state from the normal state [2].

Figure 2-3: Meissner effect, the expulsion of external magnetic field from inside the superconductor in the superconducting state by creating surface current. The field is applied at (a) T > Tc and (b) T < Tc

(image taken from Wikipedia).

25

In 1935, the macroscopic London theory explained the electrodynamics of

superconductors by introducing two new equations in addition to Maxwell equations

[3]. These equations can explain the experimental observations, i.e., the Meissner

effect and zero resistance. Another macroscopic phenomenological theory,

Ginzburg–Landau (GL) theory (1950), thoroughly explained the macroscopic

properties of superconductors [4]. Nevertheless, neither theory (the London theory

and the GL theory) described the microscopic origins of the superconducting

properties. The first microscopic theory was proposed by Bardeen, Cooper, and

Schrieffer (BCS) in 1956 [5]. Later on, Bardeen, Cooper, and Schrieffer were

awarded the Nobel Prize for it. A significant contribution was also made by N. N.

Bogolyubov [6]. BCS theory is based on the electron-electron attraction resulting in

what is generally known as Cooper pairs (total spin of Cooper pair is zero), which

occurs below Tc through phonons (emitted from the vibrations of ions). L. P. Gorkov

elaborated the microscopic theory further by showing that BCS theory can be

interrelated to GL theory in the vicinity of Tc [7]. It is noteworthy that BCS theory

can only explain the pairing mechanism in conventional superconductors. A. A.

Abrikosov (1957) categorized superconducting materials into two groups, depending

on their behaviour in magnetic fields: type I and type II superconductors [8]. The

magnetization response of type I and type II superconductors are shown in Figure 2-

4.

For H > Hc, superconductivity is completely destroyed in type-I superconductors,

where H is the strength of the applied field and Hc is a critical field. In contrast, the

response of type II superconductors to H is different. Rather, the formation

of magnetic vortices occurs in a certain applied magnetic field range, i.e., between

Hc1 and Hc2. Below Hc1, the magnetic field cannot penetrate inside the material, and

26

superconductivity disappears above Hc2. The magnetic vortex can be imagined as a

cylinder which is aligned to the applied field. The superconducting order parameter

is zero inside the cylinder. These vortices are surrounded by a superconducting

region.

Figure 2-4: Response of Type I and II superconductors in external magnetic fields (image taken from

http://fhc80.com.br/superconductivity-of-metals-and-alloys.htm).

The GL coherence length, ξGL, can be estimated from the radius of the cylinder [2].

The vortices arrange themselves into a regular pattern known as a vortex lattice. The

vortex pattern depends mostly on the structure of the material. The vortexes can be

pinned by defects (due to grain boundaries, impurity particles, and or crystal

imperfections) in the material, a phenomenon known as flux pinning. To prevent flux

creep/motion, which can generate resistance and reduce the Jc and Hc2, flux pinning

plays an important role in terms of applications. The pinning effect is not effective at

a certain magnetic field, commonly known as the irreversibility field, Hirr.

Figure 2-5: A) Magnetic flux line penetrating in a type-II superconductor in form of vortices B)

Current Swirls around the core of each vortex (Picture taken from book Superfluids).

27

In 1962, the British physicist Brian David Josephson discovered the tunnelling

property of superconducting Cooper pairs and was awarded the Nobel prize in

Physics [9, 10]. He demonstrated that without any voltage being applied, a current

can flow indefinitely long through a Josephson junction (JJ), which consists of

two superconductors separated by a thin insulating barrier (weak link). Josephson

junctions have many applications, especially in superconducting qubits,

superconducting quantum interference devices, and in rapid single flux quantum

digital electronics.

In 1986, the IBM researchers Bednorz and Müller achieved the first milestone in

modern era of superconductivity by discovering superconductivity in a lanthanum-

based cuprate perovskite material (Tc ≈ 35 K) [11]. Soon after, the replacement of

lanthanum by yttrium (i.e., yttrium barium copper oxide, YBCO) increased the Tc to

92 K, which is above the maximum of 30 K predicted by BCS theory [12]. Their

noble discovery was aroused great hopes and motivated scientists to achieve more

milestones in the field of superconductivity.

Figure 2-6: Tc of some known superconductors versus the year of discovery, as compiled by the Applied Superconductivity Group, University of Geneva, Switzerland

28

Another conventional superconductor, MgB2 (which could be explained by BCS

theory) with Tc of 40 K, was discovered in 2001 [13], Recently, Hideo Hosono of the

Tokyo Institute of Technology, Japan discovered superconductivity in iron based

compounds, generally known as iron based superconductors [14, 15].

2.2 Pinning Mechanism

Generally, the fundamental interactions between pinning centres and vortices are the

magnetic and core interactions in high Tc superconductors. The interaction of

surfaces between superconducting and non-superconducting material parallel to the

applied field results in magnetic interactions, which are commonly very small in

type-II superconductors with a high Ginzburg-Landau (GL) parameter, κ. The core

interaction arises from the coupling of the locally distorted superconducting

properties with the periodic variation of the superconducting order parameter, which

is significantly more effective in type-II superconductors due to the high κ value.

There are two predominant mechanisms of core pinning, i.e., 𝛿𝑇c pinning, which is

associated with spatial fluctuations of the Tc and 𝛿ℓ pinning, which is associated with

fluctuations in the charge carrier mean free path, ℓ [16-22].

The Dew Hughes model provides a good explanation of the pinning mechanism in

terms of the vortex pinning force FP = Jc × B [23]. D. Dew.Hughes proposed a

scaling law, i.e. 𝐹𝑝 ∝ ℎm(1 − ℎ)n to determine the nature of the pinning mechanism,

where h is the reduced field, h = B/Birr (where Birr is the irreversibility field, and m

and n are two basic parameters), which can indicate the origin of the pinning

mechanism. In case of 𝛿ℓ pinning, m = 2 and n = 2 with no hmax implies volume pins;

m = 0.5 and n = 2 with hmax = 0.2 for surface/grain boundary pinning; and m = 1 and

n = 2 with hmax = 0.33 for point pinning. Similarly, in the case of δTc pinning, m =

29

n=1 with hmax = 0.5 corresponds to volume pins; m = 3/2 and n = 1 with hmax = 0.6

relates to surface/grain boundary pinning; and m = 1 and n = 1 with hmax = 0.67

indicates point pinning. D. Dew Hughes summarized his work on the nature of the

pinning mechanism in a tabular form. As discussed earlier, the core pinning

mechanism is more significant in type II superconductors, so only scaling parameters

(i.e., m and n) along with hmax for core pinning need to be presented in Table 2-1.

.

Types of Interaction

Geometry of Pin

Type of centre

scaling parameters

Position of maximum

Core

Volume δℓ m=2 n=2

Not defined

δTc m=1 n=1

h=0.5

Surface δℓ m=0.5 n=2

h=0.2

δTc m=3/2 n=1

h=0.6

Point δℓ m=1 n=2

h=0.33

δTc m=2 n=1

h=0.67

Table 2-1: Scaling parameters for core pinning according to the Dew Hughes Model [23].

2.3 IRON BASED SUPERCONDUCTORS (FeSCs)

Superconductivity in FeSCs was discovered by Kamihara [14, 15]. Although

superconductivity in iron related compounds (such as U6Fe: Tc ≈ 3.9 K and

Lu2Fe3Si5: Tc ≈ 6.1 K) have been known to the scientific community for some time

[24, 25], but due to the strong local magnetic moment of iron, they didn’t attract

30

much attention at that time. This ground-breaking discovery by Kamihara has led to

the discovery of other iron based superconducting families. The iron pnictides (FePn,

where Pn is As or P), including iron chalcogenides (FeCh, where Ch includes S, Se,

and Te) have been widely investigated over the last few years [26]. High Tc values of

around 56 K have been found in 1111 type structures (discussed later), which is high

in comparison with other superconductors, except for the cuprates [27]. Tc around 38

K, 20 K and 14 K are also reported for 122, 111, and 11 type structures, respectively,

which can be further enhanced by hydrostatic pressure, doping, etc. [26]. The

superconducting pairing mechanism may be related to the coexistence of magnetism

with superconductivity in the phase diagram. In FeSCs, it is generally believed that

phonon mediation does not play a role in pairing. Theoretical assumptions include

several electronic instabilities that could mediate the superconducting pairing, e.g.,

spin fluctuations or interorbital pair hopping. Besides some similarities, the

properties of the FeSCs are basically different from those of the cuprates. Both have

layered structure and unconventional, high values of Jc and Hc2. In contrast, FeSCs

are semimetallic, whereas the parent compounds of cuprates are Mott-insulators.

Furthermore, FeSCs have less anisotropy as compared to cuprates. FePn forms the

FeAs layered structure, with a spacer or charge reservoir block. The compounds can

be classified as belonging to the “1111” system of RFeAsO, where R is a rare earth

element (such as LaFeAsO, SmFeAsO and PrFeAsO etc). the “122” type, including

BaFe2As2, SrFe2As2, or CaFe2As2; the “111” type of LiFeAs, NaFeAs, LiFeP, etc.

and iron chalcogenides categorized as “11” type, such as FeSe, etc. [28].

31

2.3.1 Crystal Structure and Phase Diagram

Figure 2-7 shows the crystal structures of the different families of FeSCs. The

elementary constituent is a quasi-two-dimensional layer consisting of a square lattice

of iron atoms with tetrahedrally coordinated ionic bonds to either phosphorus,

arsenic, selenium, or tellurium anions that are positioned above and below the iron

lattice, forming a common blocking layer.

Figure 2-7: Crystal structures (tetragonal with the c-axis pointing up) of FeSCs: FeSe, LiFeAs, LaOFeAs, and Sr2VO3FeAs crystallize in space group P4/nmm, and BaFe2As2 in I4/mmm. Iron atoms: dark grey spheres, arsenic (selenium):black spheres, and cations: light grey balls [29].

The FeAs layer is an arrangement of Fe-As covalent bonding and Fe-Fe metallic

bonding [30]. It is widely believed that superconductivity emerges from the iron

layers. The Fe and As/Se atoms forms Fe(As/Se)4 tetrahedra, whereas the Tc of

FeSCs mostly depends on the angle between the FeAs/Se bonds and the height of the

tetrahedra [30-32]. The 1111 compounds such as LaFeAsO, LaFePO, etc. are

considered as belonging to the ZrCuSiAs type crystal structure with space group

P4/nmm [33]. It comprises negatively charged FePn layers, where the Fe atoms form

32

a planar square lattice, and positively charged rare earth oxide (REO) layers, with RE

a rare earth element. The 122 compounds have the ThCr2Si2 type structure with

space group I4/mmm [34]. The 111 compounds are categorized as the anti-PbFCl

type [35]. The 11-FeCh compounds simply have the α-PbO type structure with space

group P4/nmm and contain a stack of FeCh4 tetrahedral layers [36] . Finally, the

structures of the more complicated compounds such as Sr2VO3FeAs are found to be

of Sr2GaO3CuS-type [37].

Figure 2-8: Phase diagrams for different families of FeSCs [30, 38-40].

The phase diagrams for different families of FeSCs are shown in Figure 2-8. For

LaO1−xFxFeAs (1111 type compounds), 100% superconducting volume fraction

appears as soon as the orthorhombic distortion and the spin density wave (SDW)

magnetism are suppressed. The antiferromagnetic (AFM) and superconducting (SC)

phases do not overlap for different doping concentrations, which is not the case for

others FeSCs. High Tc values found for around x = 0.08 and 0.10 [38]. An

experimental phase diagram for the Ba-based 122 system has been compiled by

33

Paglione et al. [30]. It consists of an AFM state that is eliminated with substitution

and a superconducting dome that is nearly centred near the critical concentration

where the AFM order is eliminated. The coexistence of the AFM and SC phases is

considered as an intrinsic property of the generic FeSC phase diagram. The

coexistence of AFM and SC over a region of x that is less than 0.025 has been found

for 111 type compounds. A concentration of nearly 0.03 provides high values of Tc

[40]. For 11 compounds, superconductivity appears through the Se doping, with Tc

increasing gradually up to 16 K for x = 0.5, by suppressing AFM [39].

2.3.2 Superconducting Properties of FeSCs

FeSCs have revealed remarkable properties in recent times. Great progress has been

made in further enhancing their superconducting properties so that they can be used

in practical applications, by replacing other conventional superconductors such as

NbTi, etc., which have much lower Tc values than FeSCs. Having layered structures,

FeSCs are less anisotropic than cuprates and reveal high values of Tc, Jc, and Hc2.

Details are as follows.

2.3.2.1 Critical Temperature (Tc)

High Tc values of nearly 56 K were found in FeSCs soon after the discovering of this

new family. The Tc of FeSCs mostly depends on the angle between the FeAs/Se

bonds and the height of the tetrahedra in most cases [30]. Kamihara et al., found

superconductivity (Tc = 26 K) in LaFeAsO after fluorine doping [15]. Takahashi et

al. increased the Tc of this compound up to 43 K at P = 4 GPa [41]. Soon after,

researchers found high values of Tc (above 50 K) in compounds with the same

34

structure [RFeAs(O1-xFx)] by doping with lanthanides such as Sm, Nd, Pr, Gd, etc.

[42-45]. Researchers also reported Tc values of 56 K in non-oxypnictides [46].

The superconductivity that emerges in 122 compounds is due to

hole/electron/isovalent doping or by applying external pressure [47].

Superconductivity at 38 K is reported in Ba0.6K0.4Fe2As2 [48], which is the highest

among the 122 compounds. In addition, Tc values of 32 K, 26 K, 26 K, and 22 K

have also been reported for Sr0.6K0.4Fe2As2, Sr0.6Na0.4Fe2As2, Ca0.6Na0.4Fe2As2, and

BaFe1.8Co0.2Fe2As2, respectively [49-51]. Superconductivity has been found in

undoped 111 compounds such as LiFeAs at 18 K [52], and between 9-25 K for

NaFeAs [53, 54]. Scientists also have discovered superconductivity in simple

structured FeSe compounds at Tc ≈ 8 K [55, 56]. Furthermore, Tc values of 14 K and

31.5 K have also been reported for FeTe0.5Se0.5 and K0.82Fe1.63Se2 [57, 58].

2.3.2.2 Hc2 and Hirr

FeSCs reveals extremely high Hc2 values as compared to other superconductors

(Figure 2-9). Different groups have estimated Hc2 to be between 100 and 300 T by

using the Werthamer–Helfand–Hohenberg (WHH) model [59, 60] for different

FeSCs. Details for the WHH model are found elsewhere [61]. Besides high values of

Hirr, the 𝐻𝑐2𝑎𝑎 (T = 0 K) ≈ 304 T and 𝐻𝑐2𝑐 (T = 0 K) ≈ 62–70 T have been found in

single crystals of NdFeAsO0.82F0.18 along with anisotropy < 6, which is less than that

of YBCO [60]. Hc2 (T = 0) values of 150 T and Hirr (15 K) ≈ 25 T have also been

reported for polycrystalline SmFeAsO0.85F0.15 samples [62]. The value of 𝐻𝑐2𝑎𝑎 is

estimated to be well above 100 T for fluorine doped LaFeAsO, with anisotropy

around 2.3 for 5% fluorine doping and above 50 T for bulks [63].

35

Figure 2-9: Hc2 values for different families of FeSCs [62, 64-66].

The nearly isotropic nature of superconductivity in the hole doped compound

(Ba1−xKx)Fe2As2 has been reported [64]. The Hc2 increases linearly with decreasing

temperature for H//c and vice versa for H//ab. Both curves are nearly the same,

suggesting an isotropic Hc2 in (Ba1−xKx)Fe2As2 which is a unique property for a

layered superconductor. The Hc2 along the ab and c planes for the electron-doped

compound Ba(Fe1−xCox)2As2 follows same trend as the hole-doped (Ba1−xKx)Fe2As2,

and an almost isotropic Hc2 is found in the limit of zero temperature [67, 68].

Among the FeSCs, LiFeAs shows a relatively low value of μ0Hc2(0), which has been

reported to be 15 T for H//c and 26 T for H//ab [66]. In spite of their low Tc (~14 K),

11 compounds such as Fe1.11Te0.6Se0.4 shows a high Hc2 of 45 T at zero temperature

[65]. Furthermore, Hc2 values above 100 T and Hirr (9 K) ≈ 6 T have also been

reported for FeSe0.5Te0.5 [69].

36

2.3.2.3 Critical current density (Jc)

High values and weak field dependence of Jc are desirable for potential applications.

Jc values of ~106 to 107 A/cm2 have been found in FeSCs, which are almost field

independent at low temperature in many cases. Generally, Jc can be obtained for a

rectangular shaped crystal with dimensions c < a < b and B//c by using Bean’s

model, which is as follows;

Jc = 20∆M/ [a (1-a/3b)]………. (2-1)

where a and b are the sample dimensions perpendicular to the applied field and ∆M

is the height of the magnetization loop. Flux jumping has been observed in different

superconductors. Our team reported flux jumping for the first time in FeSCs, i.e.

(Ba1-xKx)Fe2As2. Generally, flux jumps can be found for large-size samples with high

Jc values, small specific heat, and a sufficiently fast ramp rate of the magnetic field

[70]. Flux jumping has also been reported for LiFeAs [71]. It is important to mention

here that 111 type compounds have not been widely investigated in terms of Jc.

A. Jc in Single Crystals

High Jc values have been reported in different single crystals, as can be seen in

Figure 2-10. An in-plane Jc (almost field independent up to 7 T at 5 K) of 106 A/cm2

at 5 K for a SmFeAsO1−xFx crystal (1111 family) has been reported [72, 73]. 122

compounds show isotropic and high Jc in crystals. Significant fishtail peak effects

and high current carrying capability up to 5·× 106 A/cm2 at 4.2 K have been reported

for K-doped Ba0.6K0.4Fe2As2 single crystal [74]. The fishtail effect at low

temperature has also been reported for the other 122 compounds [75, 76]. As for the

11 compounds, Jc of FeTe0.61Se0.39 crystals was found to be well above 105 A/cm2 at

37

low temperatures. Jc of nearly 105 A/cm2 at 5 K (field independent up to 6 T) has

also been found in 111 compounds [77]

Figure 2-10: Field-dependent Jc values for 1111, 122, 111 and 11 crystals [212-217].

B. Jc in Thin Films

Thin films have not been easy to fabricate, especially in the case of the 1111 FeSCs

where F and O are main dopants, as both are volatile and effectively uncontrolled in

the final films [78]. Because they are free from grain boundaries and strong pinning

centres, such as inclusions, surface roughness, and defects related to the growth

mode, high values of Jc have been found in thin films. Lida et al. reported high Jc

values of nearly 106 A/cm2 at 45 T and 4.2 K for both main field orientations, a

feature that is favourable for high-field magnet applications [79]. Jc > 106 A/cm2 at

4.2 K has also been reported for 122 compounds [80]. High Jc values of up to 4

MA/cm2 at 4 K have been also found in Co-doped BaFe2As2 epitaxial films grown

38

directly on (La,Sr)(Al,Ta)O3 substrates by pulsed laser deposition [37]. High Jc

values are also reported for BaFe2(As0.66P0.33)2 films with uniformly dispersed

BaZrO3 nanoparticles [81]. Jc of about 105 A/cm2 was found for FeTe0.5Se0.5 films at

4.2 K in self-field, and the same value is retained up to 8 T [82]. In general, the Jc

values in thin films are higher than those of single crystals.

C. Jc in wires/tapes

Superconductors can be used in applications in the form of wires/tapes. Ma’s group

fabricated LaFeAsO1-xFx, SmFeAsO1-xFx and Sr1-xKxFe2As2 wires by using the

powder-in-tube (PIT) method [83-85]. For 1111 compounds, transport Jc of

104A/cm2 in self-field at 4.2 K has been reported in Sn-added ex-situ SmFeAsO1-xFx

tapes [86]. Usually, 122 compounds reveal high values of Jc [87]. At 4.2 K, transport

Jc of nearly 4000 A/cm2 in self-field was found for an ex-situ PIT processed Sr1-

xKxFe2As2 + Ag/Pb wire with an Fe/Ag double sheath. The transport Jc of

Ba1−xKxFe2As2/Ag tapes is greatly improved by a combined process of cold flat

rolling and uniaxial pressing. At 4.2 K, Jc exceeds the practical level of 105 A/cm2 in

magnetic fields up to 6 T and maintains a high value of 8.6 × 104 A/cm2 in 10 T [88].

Ding et al., have fabricated (Ba, K)Fe2As2 superconducting wires through an ex-situ

powder-in-tube method. The transport Jc reached 1.3 × 104 A/cm2 and 104 A/cm2 at

4.2 K under self-field in the wires with and without Ag addition [89]. Togano et al.

have reported large transport Jc in Ag-added (Ba,K)Fe2As2 superconducting wires of

104 A/cm2:0 T and nearly 103 A/cm2:10 T at 4.2 K [90]. A transport Jc of 8.5 × 103

A/cm2 at 4.2 K, 10 T was also found for Cu/Ag-cladded Ba1-xKxFe2As2 wires [91].

Recently, a record high transport Jc of up to 0.1 MA/cm2 at 10 T and 4.2 K has been

found in Sr0.6K0.4Fe2As2 tapes, as can be seen in Figure 2-11. The Jc exceeded

1 MA/cm2 in Sr0.6K0.4Fe2As2 tapes at 4.2 K [91].

39

Figure 2-11: Transport Jc as a function of field for Sr0.6K0.4Fe2As2 tapes.

D. Jc in Polycrystalline bulks

Jc values in polycrystalline bulks have been found to be lower due to weakly linked

grains.

For 1111 compound, Wang et al. reported Jc ≈ 104A/cm2 at 5 K in self-field [92] .

Similar results have been found by Ding et al. [93]. At 5 K, Jc values of around 104

A/cm2 in self-field has been obtained in K doped 122 compounds [94]. Jc for FeTe1–

xSex polycrystals, as estimated from M–H curves, is around 104 A/cm2 at 5 K under

zero field [95]. Jc values for different polycrystalline bulks can be seen in Figure 2-

12.

Figure 2-12: Jc values for different polycrystalline bulks [32-35].

40

Low values of Jc are due to weak flux pinning. Koblischka et al. have compiled the

results on the pinning mechanisms for FeSCs in details [96]. The δTc-pinning is

mostly dominant in the 122- and 1111-families, whereas, the 11 and 111 compounds

shows 𝛿ℓ pinning. Pinning force analysis for FeSCs was conducted by using the

scaling approaches of Dew-Hughes and Kramer [23, 97]. The resulting peak

positions, h, were found at ~ 0.3 for the 11-type materials, at ~ 0.48 for the 111-type

materials, between 0.32 and 0.5 for the 1111-type materials, and between 0.25 and

0.71 for the 122-type materials. Details can be found elsewhere [236].

2.3.3 Effects of chemical doping on SC Properties of FeSCs

Chemical doping is also a useful technique for FeSCs for enhancing their

superconducting properties. The parent compounds of some of the FeSCs such as

SmFeAsO are not superconducting. Superconductivity appears when the AFM order

is suppressed. With Co-doping in the FeAs planes, the AFM order is destroyed, and

superconductivity occurs at 15.2 K [98]. Fluorine doped NdFeAsO shows superior

Jc-field Performance of 106 A/cm2 at 5 K [99]. High Jc values (i.e. > 105 A/cm2) at

45 T and 4.2 K have been obtained for epitaxial SmFeAs(O,F) thin films in both field

orientations [79]. Similar results are also reported for SmFeAs(O,F) films [100].

Fluorine doped SmFeAsO single crystals showed a high and isotropic Jc (> 2 × 106 

A/cm2) along all crystal directions [73].

Ag and Pb have been used as dopants in the development of 122 pnictide wires/tapes

in order to enhance Jc by improving the intergranular coupling of the

superconducting grains [85]. Chemical doping with Ag of polycrystalline Sr-122

superconductor can improve grain connectivity, as it can effectively suppress the

formation of the glassy phase as well as the amorphous layer. In addition, improved

41

Jc values have also been found in Ag doped 122 wires [101]. Similarly, chemical

doping with Pb can improve the grain connectivity as well [102]. It should be noted

that Pb addition can predominantly increase low field Jc, while Ag addition can

enhance the high field Jc in 122 wires/tapes. Some groups have used both Ag and Pb

as a dopants and found a slightly better result in the determination of transport Jc in

K doped 122 pnictide tapes, although weakly-linked grain boundaries still existed

[103]. Although Jc is improved to some extent by these approaches, the major

drawback is degradation of Tc in many cases. The Jc found at 2 K and 0 T reaches 4.7

× 106 A/cm2, and Jc at 5 K remains more than 1 × 106 A/cm2 at 9 T for potassium

doped 122 compounds [74]. Over-doping with K has a negative effect on the Tc [94].

High Jc of 4 MA/cm2 at 4 K was also obtained in Co-doped BaFe2As2 [104]. Similar

results are also found elsewhere [80]. Miura et al. introduced controlled amounts of

uniformly dispersed BaZrO3 nanoparticles into carrier doped BaFe2As2, which can

improves its Jc values and only has a slight effect on Tc [81]. Cu and Co substitution

in LiFeAs has resulted in suppression of the Tc value [105]. Tc suppression due to

doping concentrations can be seen in Figure 2-13.

Figure 2-13: Tc as a function of doping concentrations [105]

42

Si et all., have found Jc ~ 106 A/cm2 in tellurium doped FeSe films [106]. Tc values

of sulphur doped FeSe are significantly suppressed by high doping levels, as can be

seen in Figure 2-14 [107].

Figure 2-14: Tc as a function of doping concentrations for sulphur doped FeSe [107]

2.3.4 Effects of irradiation on SC Properties of FeSCs

Although the irradiation technique can enhance Jc in FeSCs, significant degradation

of Tc is a major disadvantage. Furthermore, it is unsuitable for large-scale

applications. There have been numerous reports on how irradiation can cause Jc

enhancement, especially for 122 compounds, as they are more convincing in terms of

their properties.

For 1111 compounds, Moore et al. studied the effects of heavy ion irradiation on the

Jc and the flux dynamics of polycrystalline NdFeASO0.85 irradiated with 2 GeV Ta

ions. A little increase in Jc of up to ~105 A/cm2 (factor of 3 to 4) at 10 K has been

observed through the formation of continuous collinear columnar defects [108].

Recently Fang et al. planted a low density of correlated nanoscale defects into

SmFeAsO0.8F0.15 by heavy-ion irradiation, resulting in an increase in Jc values up to

43

greater than 107 A/cm2 at 5 K [109]. Eisterer et al. obtained enhanced Jc values,

together with Tc deterioration, by irradiating SmFeAsO1−xFx in a fission reactor with

a fast (E > 0.1 MeV) neutron fluence of 4 × 1021 m−2 (Figure 2-15) [110]. Reduction

in Tc was also observed for a neutron irradiated LaO0.9F0.1FeAs polycrystalline

sample [111].

Figure 2-15: Comparison of Jc for un-irradiated and irradiated SmFeAsO1-xFx [110].

High intrinsic pinning strength has been reported in K doped 122 single crystals due

to small anisotropy (i.e. γ ≈ 1-3) [64, 70]. Jc values can be enhanced by irradiation

through improvement of flux pinning. For example, light ion C4+ irradiation can

increase Jc in BaFe1.9Ni0.1As2 single crystal from 0.61 × 105 up to 0.94 ×

105 A/cm2 at T = 10 K and H = 0.5 T, but along with reduction in the Tc value [112].

Nakajima et al. have introduced columnar defects into Co-doped BaFe2As2 single

crystals by heavy ion irradiation, resulting in enhancement of Jc values from 6.4 ×

105 A/cm2 to 4.0 × 106 A/cm2 at T = 5 K and 0 T, as can be seen in Figure 2-16

[113]. Similarly, Kim et al. investigated the effects of heavy ion irradiation on Co

and Ni doped Ba-122 compounds [114]. High Jc values of nearly 1.0×107 A/cm2 at 5

44

K under self-field in (Ba,K)Fe2As2 single crystals after irradiating with Au ions were

also reported [115].

Figure 2-16: Comparison of Jc for un-irradiated and irradiated Co-doped 122 compound [113], with

the insets showing the magnetic hysteresis loops at different temperatures.

Neutron irradiation can lead to a decrease in Tc and increase in Jc values by a factor

of 3 in Co doped Ba-122 FeSCs [116]. Karkin et al. investigated the effects of

neutron irradiation on the properties of FeSe compound and also found a reduction in

Tc values [117]. Haberkorn et al. studied the influence of random point defects

planted by proton irradiation into Co-doped BaFe2As2 crystal and found little

enhancement in Jc [118].

2.3.5 Effects of pressure on SC Properties of FeSCs

Hydrostatic pressure effects have been mostly studied with respect to Tc. Pressure has

been revealed to have a positive effect on Tc in FeSCs. Generally, Tc versus pressure

shows a dome-like behaviour: it increases with pressure, reaches a certain high value,

45

and then decreases with the application of further pressure applied, in a way which

mostly depends on the doping concentration. The pressure effects (less than 5 GPa)

on Tc in LaFeAsO1-xFx are positive for under-doped, optimally doped, and over-

doped samples, as can be seen in Figure 2-17 [119]. The optimally and over-doped

samples show nearly the same response to pressure, and Tc reaches up to 43 K at 4

GPa, but decreases with increasing pressure. Low Tc values were found in the under-

doped sample.

Figure 2-17: Pressure dependence of Tc for under-doped, optimally-doped and over-doped LaFeAsO1-

xFx [119].

Okada et al. measured Tc under pressure for LaNiPO and LaNiAsO, and found that

Tc increased up to 3.78 K at 1.67 GPa and 3.14 K at 0.75 GPa, respectively [120].

Takeshita et al. reported the negative effect of pressure on different compositions of

NdFeAsO1-y [121]. Similar results are also found elsewhere [122]. Lorenz et al.

found that Tc improves with pressure for un-doped material and is suppressed with

pressure for an over-doped compound in the case of SmFeAsO1-xFx [123]. Selvan et

al. measured a GdFe0.9Co0.1AsO sample under pressure and found that Tc decreased

46

from 16.7 to 10.5 K at 2.9 GPa [124]. Pressure induces superconductivity in

BaFe2As2. For example, Alireza et al. found superconductivity at 29 K, 4.5 GPa [47].

Kimber et al. found their maximum Tc in BaFe2As2 under pressure, where the FeAs4

tetrahedra are regular, with an angle of 109.47° [125]. Igawa et all., measured Tc as a

function of pressure for SrFe2As2 with different set-ups (Figure 2-18) and found

almost the same response to pressure [126].

Figure 2-18: Pressure dependence of Tc values for SrFe2As2 [126].

Gooch et al. found a positive pressure effect on Tc for under-doped K1-xSrxFe2As2

and a negative effect for their over-doped sample, whereas the Tc response to

pressure for the optimally doped sample was not significant [127]. Uhoya et al. found

a rapid increase of Tc up to 41 K at 10 GPa for EuFe2As2 [128]. Pressure of 0.69 GPa

also -induced superconductivity in CaFe2As2 at Tc ≈ 11 K [129]. Park et al.

investigated the pressure effect for Ba0.6K0.4Fe2As2 thin films and found that Tc of

47

the thin film with optimal potassium concentration gradually increased to 40.8 K at

1.18 GPa [130].

The 111 compounds have not been widely investigated under pressure. Tc was

reduced linearly with a pressure coefficient of 1.5  K/GPa for LiFeAs [131], similar

to LiFeP [132]. Zhang et al. reported that the Tc increased from 26 K to a maximum

of 31 K as the pressure increased from ambient pressure to 3 GPa for Na1−xFeAs

[133]. Wang et al. measured Co doped NaFeAs under pressure and found that the

maximum Tc enhanced by pressure in both under-doped and optimally-doped NaFe1-

xCoxAs is almost 31 K and 13 K with pressure of 2.3 GPa [134].

So far, a huge enhancement in Tc by pressure has been obtained in 11 compounds.

Margadonna et al. (2009b) found that the hydrostatic pressure can raise Tc up to 37 K

at 7 GPa from nearly 14 K [135]. Tc was also found enhanced for tellurium doped

FeSe [136].

Little work has been done on how pressure affects Jc in FeSCs. Pietosa et al. found

enhancement in Jc of one order of magnitude in 11 compounds [137]. The pinning

mechanism under pressure has not been investigated at all. Therefore, detailed

investigations are required in this regard.

2.3.6 Conclusion

The combination of reasonable values of Tc, extremely high Hc2 on the order of 100

T, high intrinsic pinning potential, and low anisotropy (generally between 1-8) makes

FeSCs worthy of investigation for applications, whereas the Jc is a major limiting

factor [73, 81, 91, 99, 104, 106, 109, 138-144]. Improvement in Jc by using various

methods has also been one of the most important topics in the field of

superconductivity. Although Jc can be improved by texturing procedures, ion

48

implantation/irradiation, and chemical doping, the major drawbacks are i) Jc decays

rapidly in high fields at high temperatures, or low field Jc deteriorates in some cases;

ii) these methods can cause degradation of Tc. Taking into account the positive

effects of pressure, we anticipated that pressure could be used to enhance Jc in

FeSCs. Our detailed investigations are reported in Chapters 4-6.

49

2.4 MgB2

The superconductivity of MgB2 (Tc ≈ 39 K) was discovered by Akimitsu in 2001

[13], although this compounds was first fabricated in 1953 [145]. Generally, MgB2 is

categorized as a conventional superconductor with a unique electronic structure.

MgB2 has a low anisotropy, in contrast to the cuprates, strongly linked grains, high

coherence length values, low fabrication costs, a multiple band structure, and has

especially high critical current density (Jc) values of 105-106 A/cm2, which makes it a

significant superconductor for applications [146-153]. Furthermore, MgB2 can easily

be drawn into wires and tapes, further supporting its potential to can replace NbTi

and NbSn3 in industry.

2.4.1 Crystal structure and two-gap conductivity

MgB2 is a simple ionic binary material possessing a simple hexagonal AlB2-type

structure (space group P6/mmm). Figure 2.19 shows the MgB2 crystal structure

[154]. It contains graphite-type boron layers, which are sandwiched between

hexagonal close-packed layers of magnesium. The lattice parameters obtained for

MgB2 are a = 3.09 Å (equal to the in-plane Mg-Mg distance), and c = 3.52 Å (the

distance between Mg- layers). Kortus et al. found that Mg s states are pushed up by

the B pz orbitals and completely donate their electrons to the boron-derived

conduction bands. The electrons donated to the system are distributed over the whole

crystal [155].

MgB2 has a strong anisotropy in the B-B distances: the distance between the boron

planes is larger than the in-plane B-B distance [156, 157]. There is no structural

transition found for MgB2 down to 2 K, even under high pressure of 40 GPa [154].

50

Figure 2-19: The crystal structure of MgB2 superconductor [13].

Numerous experiments based on heat capacity, Raman scattering, point contacts, and

optical and magnetic properties measurements of polycrystalline samples or single

crystals have revealed that MgB2 is a multi-gap superconductor [158-165]. The sp2

boron orbitals overlap, forming σ-bonds between the neighbouring atoms in the

plane, whereas the rest of the p orbitals spread above and below the plane and

produce π- bonds in MgB2. The electronic structure of MgB2 contains two types of

electrons at the Fermi level with different behaviours: the sigma-bonding is stronger

than the pi-bonding. Figure 2-20 illustrates the Fermi surface of MgB2. Г, L, M, and

A are sites in the Brillouin zone. The σ-bands form two hole-like coaxial cylinders

along the Г-A line, and the π-bands form two hole-like tubular networks near K and

M, and an electron-like tubular network near H and L [155]. The anomaly of the

charge distribution in the σ-bonding with respect to the in-plane boron atoms

provides strong coupling of the σ-bonding state to the in-plane vibration of boron

atoms, which is responsible for the superconductivity in MgB2 [166]. Electrons at

these different Fermi levels join into pairs with different bonding energies. Each π-

bond and σ-bond has certain energy gaps at the Fermi surface. The average values of

the gaps are 6.8 meV for σ-bonds and 1.8 meV for π–bonds.

51

Figure 2-20: MgB2 Fermi surface along with symmetry directions of the Brillouin zone [34].

2.4.2 Superconducting Properties of MgB2

The magnetic and transport measurements show that MgB2 is free of weakly linked

grain boundaries, which is in contrast to high temperature superconductors (HTSCs),

providing nearly the same Jc values in high magnetic fields for polycrystalline bulk

samples [167]. Therefore, MgB2 can be used in form of wires/tapes for practical

application with no degradation of Jc values. Jc values can also be enhanced by

improving the flux pinning properties.

2.4.2.1 Critical temperature (Tc)

The Tc of MgB2 is found to be almost 39 K (-234 ºC), which is the highest amongst

the conventional superconductors [13]. It is widely believed that the Tc of MgB2 is

52

crystal structure dependent. Hydrostatic pressure, neutron irradiation, and chemical

doping can change the lattice volume or structure, affecting Tc values [154].

2.4.2.2 Critical fields and Hirr

MgB2 behaves like a type-II superconductor under magnetic field. Being a layered

structure, MgB2 is an anisotropic material. The variations in the critical field values

can be observed from the planes parallel (Hc1(c2)║ab) to and perpendicular (Hc1(c2)┴

ab) to the ab-plane [168]. The anisotropy ratio γ = Hc2║ab/ Hc2┴ ab, is found

between 1.1 and 1.7 for textured bulks and partially oriented crystallites, 1.2–2 for c-

axis textured material, 1.7-2.7 for single crystals, and around 2 for thin films [169-

177].

At 5 K, Hc1 is 0.25 T and 0.125 T parallel to the ab-plane and c-axis, respectively,

and Hc2║ab ≈ 18 T, Hc2║c ≈ 3.5 T are found for single crystal [178]. For

polycrystalline materials, Hc1 is found to be 425 Oe at 5 K [179]. An Hc2 value of 16

T at 0 K has been reported for polycrystalline MgB2, and it is up to 74 T in thin films

and up to 55 T in fibres [180-184]. The Hc2 values for MgB2 can be improved by

tuning of ratio of intraband to interband scattering rates through suitable doping on

both Mg and B sites, which can also reduce the anisotropy of the critical fields.

Furthermore, the values of Hirr at 10 K range between 5 and 20 T for MgB2 bulks,

films, wires, tapes, and powders [154, 185]. Note that Hc2 in MgB2 is almost two

times greater than Hirr [186].

2.4.2.3 Critical current density (Jc)

Jc is a key parameter in superconducting applications. The Jc in MgB2 is mostly

determined by its flux pinning, as it is free of weak links. The flux pinning is field

dependent, especially in high fields, providing a quick drop of Jc with increasing

field. In polycrystalline MgB2, Jc ≈ 106 A/cm2 at 0 T, Jc ≈ 104A/cm2 at 6 T, and Jc ≈

53

102 A/cm2 at 10 T have been reported by different groups [154]. Due to weak

pinning, Jc in single crystal is nearly 105 A/cm2 at low temperatures in self-field and

drops quickly at high fields [184, 187]. Jc > 107 A/cm2 has been reported in thin

films, which are higher than for single crystals under self-field and low temperatures

due to strong pinning at the grain boundaries [184].

At 4.2 K, the transport Jc obtained for wire is above 106 A/cm2 in self-field and

around 104 A/cm2 at 8 T [186]. Another study shows that the Jc values at low fields

and temperatures in MgB2 wires are on the order of 105 A/cm2, but drops to the order

of 103 A/cm2 at around 10 T [188-190]. In contrast, MgB2 tapes show better results

for Jc at relatively high magnetic fields because of their geometrical shielding

properties. At 4.2 K, H Yamada et al. found Jc to be ~32000 A/cm2 and 14000 A/cm2

for SiC doped MgB2 in ethyltoluene at 10 T and 12 T, respectively [191].

Furthermore, Jc values for MgB2 tapes on the order of 104 A/cm2 have been found at

4.2 K and 10 T [192-196]. It was reported that factors such as porosity of the sample,

grain boundaries, impurities, homogeneity, and fabrication and sintering conditions

strongly affect Jc values in MgB2 [184].

2.4.3 Effects of Chemical Doping on Superconducting (SC) Properties of MgB2

Chemical doping can enhance Hc2, Hirr, and Jc by improving the flux pinning

mechanism in MgB2. Usually, significant enhancement in Jc has been found with

carbon source doping [146, 180, 197-200], but it comes along with degradation of Tc.

Different dopants have been used to enhance Jc values. Effects of dopants on

superconducting properties, especially Jc and Tc, which have similar properties, can

be explained as follows:

Tc values have been reduced by chemical doping with alkali metals such as Na and

Li [201], and Cs and Rb [202], alkaline earth metals such as Ba [203], poor metals

54

such as Al [204, 205] and Zn [206], and transition metals such as Ir [207] and Ni

[208], although a slight enhancement in Jc was found in some of these cases. Doping

of Al into Mg sites caused significant degradation of Tc with increasing Al content

resulting in the loss of superconductivity in MgB2 [209].

Jc at high fields in MgB2 can be improved by doping with silicides such as

elementary Si [210], ZrSi2 [194], WSi2 [211], Si3Ni4 [212], and SiO2 [193], although

reduction of Tc is a major drawback.

Carbon-containing composites or compounds, such as nano-C, B4C, carbon

nanotubes (CNT), hydrocarbons, carbohydrates, and SiC, have pronounced effects on

Jc, although Tc values are greatly degraded in a few cases [213-216]. The Jc in

magnetic field increases significantly, but Tc decreases much more slowly with

carbon doping for MgB2 films (Figure 2-21) [217]. Nano-C doping can also enhance

Jc in MgB2 tapes. Xianping Zhang et al. found that Jc reached 2.2 × 104 A/cm2 in

their 8% C doped samples at 4.2 K, 10 T [218]. Dou et al. have studied the effect of

carbon nanotube (CNT) doping of MgB2 on Tc and Jc. The Jc was found to be more

than 10 000 A/cm2 at 20 K and 4 T, and 5 K and 8.5 T, respectively [219]. Similar

results are also reported by other groups [220, 221].

Figure 2-21: (Left) Tc dependence on carbon concentration. (Right) Field dependence of Jc at different

temperatures for undoped and carbon doped samples [217].

55

Graphite, diamond, and carbide compounds improve the Jc in high fields by

improving flux pinning, but with some effect on Tc [222-224]. Silver doping can also

degrade Tc values [225].

Jc in MgB2 at high field can also be improved by doping with rare earth

elements/oxides. For instance, elemental La doped MgB2 can react with B and forms

LaB6 nanoparticle inclusions, which can serve as pinning centres, leading to high Jc

values [226, 227]. Addition of Y2O3 nanoparticles can give Jc ≈ 2 × 105  A/cm2 at 2

T and 4.2 K, but Jc drops to ~8 × 104 A/cm2 at 20 K. Hirr was also reported, i.e. 11.5

T at 4.2 K and 5.5 T at 20 K [228]. Similarly, Dy2O3 doped MgB2 can show

improved flux pinning, hence Jc [229]. Doping with Ho2O3 can form pinning centres

in the form of HoB4 impurities, which can improves high field Jc and Hirr, with Tc

and Hc2 unchanged [230]. Similar results were also obtained for transition metals,

such as Wb [231], Zr [232, 233], Cu [234], Ti [233, 235], and Pb [236].

Doping with poor metals, such as in Cd doped MgB2, generates MgCd3 impurities,

which serve as effective pinning centres, resulting in the enhancement of Jc values,

i.e. 5.0 × 105 A/cm2 (5 K, 0 T) with only a little drop in Tc [237]. Magnetic elements,

such as Mn [238] Co and Fe [239, 240], and Ni [208], mostly resulted in suppression

of Jc. N Novosel et al. investigated MgB2 doped with dextrin-coated magnetite

nanospheres and nanorods, and found that nanospheres can enhance Hirr and the

transport Jc at lower temperatures due to generation of magnetic pinning of vortices.

Doping MgB2 with different oxides generates different results. Doping with Al2O3

can decrease the Jc and Hirr with increasing Al2O3 level [241]. In contrast, Jc is found

to be increased with Co2O3 doping [242]. Reduction and enhancements of Jc have

also been reported for ZrO2 [243] and TiO2 doping [244], respectively. Doping with

boride compounds, such as ZrB2 and TiB2, also led to the improvement of Jc [245,

56

246]. Furthermore, doping with uranium had no significant effect on Jc in MgB2

[247].

Chemical doping can transform the nature of the pinning mechanism in MgB2. The

δTc pinning mechanism is dominant in pure MgB2 polycrystalline bulks, thin films,

and single crystals [22, 248, 249]. As one example, S R Ghorbani et al. investigated

the flux pinning mechanisms within the collective pinning model in nano-Si-doped

MgB2 and found the coexistence of both δℓ pinning and δTc pinning in their nano-Si-

doped MgB2 samples [250]. Similar results have been found for nano-carbon doped

MgB2 and succinic acid doped MgB2 [251, 252]. Doping with SiC can transform the

pinning mechanism from δTc to δℓ [253], and partial point pinning can be generated

in addition to surface pinning [254, 255]. J. L. Wang et al. investigated the pinning

mechanism in carbon doped MgB2. Doping with C and graphene oxide can transform

the pinning mechanism from δTc to δℓ, and carbon doping can also induce point

pinning in MgB2 (Figure 2-22) [256, 257].

Figure 2-22: Transformation of pinning mechanism from δTc to δℓ by graphene oxide doping [257].

57

In summary, chemical doping can improve flux pinning and hence Jc, although a

major drawback is the reduction of Tc. Therefore, we need an effective approach

which can enhance Jc and flux pinning, but without sacrificing Tc values.

2.4.4 Effects of Irradiation on SC Properties of MgB2

Irradiation is another technique that is used to enhance Jc and flux pinning in

superconductors. Soon after the discovery of superconductivity in MgB2, several

experiments were performed to enhance these parameters by artificial damage.

Although irradiation can decrease the Tc and low field Jc in a few cases, Jc in high

fields can be improved.

Initial experiments with proton irradiation showed that atomic disorder created by

proton irradiation can improve the flux pinning, thereby increasing Jc values in high

fields besides degrading Tc [258]. Similar experiments have also been performed on

single crystalline and bulk samples [259].

Figure 2-23: Reduction of Tc by irradiation in MgB2 [258]. d.p.a. is displacements per atom.

High-energy heavy ion irradiation can modify the nature of the pinning mechanism

in MgB2 thin films, resulting in enhancement of Jc, although degradation of Tc has

been a drawback [260, 261]. Considerable reduction of Tc to 7 K has been reported in

58

MgB2 thin films due to irradiation by alpha particles [262]. Similar results were also

reported for Au ion irradiation of MgB2 thin films [263]. In addition, Pb-ion

irradiation can increase the Jc in high fields [264].

Karkin et al. were the first to investigate the effects of neutron irradiation on the Tc

and the Hc2 of polycrystalline MgB2 samples. The Tc decreased significantly from 38

to 5 K as a result of irradiation, which is ascribed to a decrease in the density of

electronic states at the Fermi level. [265]. Eisterer et al. and Wang et al. also found a

reduction of Tc in MgB2 due to neutron irradiation [266, 267]. Enhancement in Jc by

neutron irradiation has been reported besides Tc suppression. For instance,

Zehetmayer et al. found enhancement of Jc in low fields, by a factor of 5 at 5 K,

along with Hc2 and Hirr [268]. Similarly, Putti et al. also found enhancement in Jc;

significantly, at high fields, Hc2 increased from 13.5 T to 20.3 T at 12 K, and Hirr

doubled at 5 K [269]. Tarantini et al. reported a significant improvement in the field

dependence of Jc, reaching a value close to 104 A/cm2 at 10 T, along with

degradation of Tc by few Kelvins [270]. Tc suppression under neutron irradiation can

be seen in Figure 2-24. Pallecchi et al. found that there was coexistence of grain

boundary and point pinning in neutron irradiated MgB2 samples [271].

Figure 2-24: Tc suppression under neutron irradiation [272].

59

Talapatra et al. also investigated the effects of 160 MeV Ne+6 ion irradiation on Jc,

Hc2, Hirr, and flux pinning in polycrystalline MgB2 [273]. MgB2 polycrystalline bulks

were also irradiated with gamma doses, resulting in enhancement of Jc values [274].

In summary, the irradiation technique can enhance Jc, especially in high fields, and

affect the pinning mechanism. Reduction in Tc and low field Jc (in some cases) are

major drawbacks of this technique, however, like chemical doping. Furthermore, this

technique is not significant for high field applications.

2.4.5 Effects of Pressure on SC Properties of MgB2

The impact of hydrostatic pressure on the nature of the pinning mechanism and Jc

has not been investigated as yet. Pressure studies in the field of superconductivity

generally emphasize the Tc dependence, and the same is the case in MgB2

investigations. Pressure studies allow us to determine the pressure dependence of Tc

and develop a framework in theoretical models to provide information on the pairing

mechanism. A large value of dTc/dP in a material shows that the crystal structure

may be tuned by applying external pressure, resulted in high values of Tc. This can

also suggest that Tc may be further improved by providing internal pressure (i.e.

chemical doping). Although a positive pressure effect on Tc has been predicted

through reduction of the interatomic B–B distance, it is well established now that

pressure can decrease the Tc of MgB2, as evidenced by various experimental studies

[275]. The pressure dependence of Tc for MgB2 was first measured in a piston-

cylinder clamp with a 3M Fluorinert FC 77 liquid pressure transmitting medium by

Lorenz et al., as can be seen in Figure 2-13 [276].

Buzea et al. has systemically studied the pressure effect on Tc [154]. Different

pressure media have been used to obtain Tc values. Negative pressure dependence

60

has been obtained, however, with different pressure coefficients [276-279]. The

observed negative pressure dependence of Tc(P) can be readily described in terms of

simple lattice stiffening within standard phonon-mediated BCS superconductivity

[280].

Figure 2-25: Pressure dependence of Tc for MgB2 [276].

The pressure dependence of Tc follows linear/quadratic behaviour, decreasing

monotonically. Buzea et al. reported that samples with higher Tc at zero pressure

have a much lower Tc(P) dependence (dTc/dp ≈ −0.2 K/GPa) than the samples with

lower Tc (dTc/dp ≈ −2K/GPa) [154]. Furthermore, samples with higher Tc have a

convex curvature of Tc(P) dependence, changing to concave for samples with lower

Tc as can be seen in Figure 2-26.

Figure 2-26: Tc as a function of pressure through different pressure media as compiled by Buzea et al.

[154] and the references therein.

61

Furthermore, the measurement of Hc2 under pressure was also carried out [281].

Moreover, the anisotropy of MgB2 is increased under pressure, as studied by

Schneider et al. [282].

2.4.6 Conclusion

MgB2 is a favourable superconducting material which might replace conventional

low Tc superconductors in practical applications, due to its relatively high Tc of 39 K,

strongly linked grains, rich multiple band structure, low fabrication cost, and

especially, its Jc values of 105-106 A/cm2 . Chemical doping and irradiation

techniques can enhance Jc either in low or high fields, but along with degradation of

Tc. Pressure studies have shown a negative effect on Tc, but only by less than 2 K in

MgB2. This is a very insignificant reduction as compared to the other existing

approaches (i.e. chemical doping and irradiation) that are mainly used for Jc

enhancement. Therefore, it is natural to investigate the effects of hydrostatic pressure

on Jc and flux pinning mechanisms in MgB2. Our detailed investigations can be

found in Chapter 7.

62

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242. Awana VPS, Isobe M, Singh KP, Takayama-Muromachi E, Kishan H.

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243. Chen SK, Glowacki BA, MacManus-Driscoll JL, Vickers ME, Majoros M.

Influence of in situ and ex situ ZrO2 addition on the properties of MgB2. Supercond. Sci. Technol. 17, 243 (2004).

244. Zhao Y, et al. Nanoparticle structure of MgB2 with ultrathin TiB2 grain

boundaries. Appl. Phys. Lett. 80, 1640-1642 (2002). 245. Ma Y, Kumakura H, Matsumoto A, Hatakeyama H, Togano K. Improvement

of critical current density in Fe-sheathed MgB2 tapes by ZrSi2, ZrB2 and WSi2 doping. Supercond. Sci. Technol. 16, 852 (2003).

246. Xu HL, et al. Effects of TiB2 doping on the critical current density of MgB2

wires. Physica C 443, 5-8 (2006). 247. Silver TM, et al. Uranium doping and thermal neutron irradiation flux

pinning effects in MgB2. Applied Superconductivity, IEEE Transactions 14, 33-39 (2004).

248. Shi ZX, et al. Flux-pinning properties of single crystalline and dense

polycrystalline MgB2. Phys. Rev. B 68, 104514 (2003). 249. Prischepa SL, et al. Critical currents of MgB2 thin films deposited in situ by

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δℓ and δTc flux pinning mechanisms in nano-Si-doped MgB2. Supercond. Sci. Technol. 23, 025019 (2010).

251. Ghorbani SR, et al. Strong competition between the δℓ and δTc flux pinning

mechanisms in MgB2 doped with carbon containing compounds. J. Appl. Phys. 107, 113921 (2010).

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pinning mechanism and enhancement of in-field Jc in succinic acid doped MgB2. Solid State Commun. 168, 1-5 (2013).

253. Ghorbani SR, Farshidnia G, Wang XL, Dou SX. Flux pinning mechanism in

SiC and nano-C doped MgB2: Evidence for transformation from δTc to δℓ pinning. Supercond. Sci. Technol. 27, 125003 (2014).

254. Shi ZX, et al. Doping effect and flux pinning mechanism of nano-SiC

additions in MgB2 strands. Supercond. Sci. Technol. 24, 065015 (2011).

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255. Martínez E, Mikheenko P, Martínez-López M, Millán A, Bevan A, Abell JS.

Flux pinning force in bulk MgB2 with variable grain size. Phys. Rev. B 75, 134515 (2007).

256. Wang JL, Zeng R, Kim JH, Lu L, Dou SX. Effects of C substitution on the

pinning mechanism of MgB2. Phys. Rev. B 77, 174501 (2008). 257. Xiang FX, Wang XL, Xun X, De Silva KSB, Wang YX, Dou SX. Evidence

for transformation from δTc to δℓ pinning in MgB2 by graphene oxide doping with improved low and high field Jc and pinning potential. Appl. Phys. Lett. 102, 152601 (2013).

258. Bugoslavsky Y, et al. Enhancement of the high-magnetic-field critical current

density of superconducting MgB2 by proton irradiation. Nature 411, 561-563 (2001).

259. Perkins GK, et al. Effects of proton irradiation and ageing on the

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260. Gupta A, et al. Study of magnetization and pinning mechanisms in MgB2 thin

film superconductors: Effect of heavy ion irradiation. Supercond. Sci. Technol. 16, 951 (2003).

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irradiated with 200 MeV Ag ions. Appl. Phys. Lett. 84, 2352-2354 (2004). 262. Gandikota R, et al. Effect of damage by 2MeV He ions on the normal and

superconducting properties of magnesium diboride. Appl. Phys. Lett. 86, 01258 (2005).

263. Narayan H, Bhatt RK, Agrawal HM, Kushwaha RPS, Kishan H. Swift heavy

ion irradiation of MgB2 thin films: A comparison between gold and silver ion irradiations. J. Phys: Condens. Matt. 19, 136209 (2007).

264. Chikumoto N, Yamamoto A, Konczykowski M, Murakami M. Magnetization

behavior of MgB2 and the effect of high energy heavy-ion irradiation. Physica C 378–381, Part 1, 466-469 (2002).

265. Kar’kin AE, et al. Superconducting properties of the atomically disordered

MgB2 compound. JETP Lett. 73, 570-572 (2001). 266. Eisterer M, et al. Neutron irradiation of MgB2 bulk superconductors.

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268. Zehetmayer M, et al. Fishtail effect in neutron-irradiated superconducting MgB2 single crystals. Phys. Rev. B 69, 054510 (2004).

269. Putti M, et al. Neutron irradiation of Mg11B2: From the enhancement to the

suppression of superconducting properties. Appl. Phys. Lett. 86, 112503 (2005).

270. Tarantini C, et al. Effects of neutron irradiation on polycrystalline Mg11B2.

Phys. Rev. B 73, 134518 (2006). 271. Pallecchi I, et al. Enhanced flux pinning in neutron irradiated MgB2. Phys.

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superconducting transition temperature of MgB2 on pressure to 20 GPa. Physica C 361, 227-233 (2001).

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3 EXPERIMENTAL

3.1 Fabrication of Samples

3.1.1 Sr4V2O6Fe2As2 Polycrystalline Bulks

For the polycrystalline Sr4V2O6Fe2As2 sample synthesis, Fe (Alfa Aesar, 99.2%) and

As (Alfa Aesar,99%) chips were sealed in an evacuated quartz tube and heat treated

for 12 hours at 700°C. Later, stoichiometric amounts of V2O5 (Aldrich, 99.6%) +

1/2×SrO2 (Aldrich) + 7/2×Sr (Alfa Aesar, 99%) + 2×FeAs were weighed, mixed,

ground thoroughly, and pelletized in rectangular form in a glove box in high purity

Ar atmosphere. The pellet was further wrapped in tantalum foil and then sealed in an

evacuated (10−5 torr) quartz tube for heat treatments at 750 and 1150°C in a single

step for 12 and 36 hours, respectively. Finally, the quartz ampoule was allowed to

cool naturally to room temperature.

3.1.2 NaFe0.7Co0.3As Single Crystals

High-quality single crystals of NaFe0.972Co0.028As were grown by use of the NaAs

flux method. NaAs was obtained by reacting a mixture of elemental Na and As in an

evacuated quartz tube at 200°C for 10 h. Then, NaAs, Fe, and Co powders were

carefully weighed according to the ratio of NaAsFeCo = 4:0.972:0.028, and

thoroughly ground. The mixture was put into an alumina crucible and then sealed in

an iron crucible under 1.5 atm of highly pure argon gas. The sealed crucibles were

heated to 950°C at a rate of 60°C/h in a tube furnace filled with the inert atmosphere

and kept at 9500C for 10 h, before being cooled slowly to 600°C at 3°C/h to grow

single crystals.

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3.1.3 Ba0.6K0.4Fe2As2 Single Crystal

A High quality 122 crystals were grown by using a flux method. The pure elements

Ba, K, Fe, As, and Sn were mixed in a mol ratio of Ba1−xKxFe2As2:Sn = 1:45–50 for

the self-flux. A crucible with a lid was used to reduce the evaporation loss of K as

well as that of As during growth. The crucible was sealed in a quartz ampoule filled

with Ar and loaded into a box furnace.

3.1.4 MgB2

The MgB2 bulk sample used in the present work was prepared by the diffusion

method. Firstly, crystalline boron powders (99.999%) with particle size of 0.2-2.4

µm were pressed into pellets. They were then put into iron tubes filled with Mg

powder (325 mesh, 99%), and the iron tubes were sealed at both ends. Allowing for

the loss of Mg during sintering, the atomic ratio between Mg and B was 1.2:2. The

sample was sintered at 800°C for 10 h in a quartz tube under flowing high purity

argon gas. Then, the sample was furnace cooled to room temperature.

3.2 Experimental Equipment

3.2.1 Vibrating Sample Magnetometer (VSM)

Magnetization measurements were carried out on a QD 14T physical properties

measurement system (PPMS) by using the Vibrating Sample Magnetometer

(VSM) option. The Quantum Design (QD) VSM for PPMS is a fast and sensitive DC

magnetometer. The VSM option includes a linear motor transport for vibrating the

sample, a coilset puck for detection, and the MultiVu software application.

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The sample is attached to the end of a sample rod, as shown in Figure 3-1. The

measurement is carried out by oscillating the sample near a detecting coil. The

magnetic measurement can be performed for 1.9 K < T < 400 K and for magnetic

field up to 14 T. For magnetic cr i t ical current densi ty (Jc) calculation, the

hysteresis loops are collected at different temperatures and magnetic fields

under different applied pressure.

Figure 3-1: Schematic drawing of VSM linear motor and its sample puck.

For a long sample with a rectangular cross-section with dimensions of l × w

perpendicular to the magnetic field direction, t h e critical current density

can be calculated using the extended Bean model:

Jc = 20∆M (l (1- l /(3w)) l < w ………..(1)

Where ∆M can be calculated by using the relation ∆𝑀 = 𝑀𝑑𝑑𝑑𝑑 − 𝑀𝑢𝑢, where

𝑀𝑢𝑢 and 𝑀𝑑𝑑𝑑𝑑 are the magnetization when sweeping fields up and down

respectively. For the zero-field-cooling (ZFC) and field-cooling (FC) measurements,

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the magnitude of applied field was 50 Oe. The transition temperature measured

from the magnetization was defined by the temperature where the

diamagnetic signal appeared. The H (field) is perpendicular to c-axis for all samples

(in a pressure cell) measurements.

3.2.2 Hydrostatic Pressure Cell

The Quantum Design High Pressure Cell with Daphne 7373 oil as a pressure

transmitting medium was used to apply hydrostatic pressure on a sample before

magnetic measurements. The pressure cell construction can be seen in Figure 3-2.

The following procedures for using the pressure cell have been taken from Quantum

Design High Pressure Cell User Manual.

Figure 3-2: Pressure cell construction.

3.2.2.1 Inserting, Pressurizing, and Removing the Sample from the Pressure Cell

A) Teflon sample tube preparation and sample insertion

1) After selecting the Teflon tube (either 2.1 or 2.6 mm OD), a Teflon tube cutting

fixture was used to cut the desired length of tube for inserting the sample. The cell kit

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includes all necessary parts to accommodate either size Teflon tube. The diameter of

the Teflon tube depends primarily on the volume of sample to be measured (Fig 3-3).

A 4.5 to 5.0 mm length of Teflon tube is recommended. Slightly longer Teflon tubes,

up to 7 mm, can be used if desired, although the maximum pressure might decrease

slightly. The ends of the Teflon tube must be cut clean and perpendicular to the length of

the tube. If not, there will be an increased chance of damage to the Teflon caps and

maximum pressure won’t be achieved. The included Teflon tube cutting fixture was used

to help get a clean cut.

Figure 3-3: Cutting the Teflon tube.

2) One end of the Teflon sample tube is sealed with a Teflon cap (Fig. 3-4). Prior to

use, the Teflon caps need to be carefully inspected to verify that they are not cracked or

otherwise damaged from previous use.

Figure 3-4: Setting the Teflon cap to one end of the Teflon tube.

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3) The Teflon sample tube/Teflon cap combination is inserted into the centre

cylinder of the pressure cell, leading with the open end of the Teflon sample tube. It

is pushed in with the appropriate diameter sample push rod until the end of the

Teflon sample tube is about even with the bevel of the centre cylinder (Figure 3-5).

The Teflon caps can be difficult to insert into the centre cylinder the first several

times they are used. For smoother insertion of the Teflon caps, the Teflon cap can be

pre-installed in the centre cylinder using the sample push rod. The teflon cap should

be worked back and forth several times until the cap moves smoothly, and it is then

removed from the centre cylinder.

Figure 3-5: Inserting Teflon tube + cap in centre cylinder.

4) The sample, manometer, and pressure transmitting medium are inserted into the

open end of the Teflon sample tube. If the included Sn or Pb wire is used for the

manometer, about 1 mm length is sufficient. Enough space should be left at the top

of the Teflon sample tube to allow the second Teflon cap to be inserted (Fig.3-6).

The teflon sample tube should be filled with as much sample as possible, with the

amount of pressure transmitting medium required to fill the teflon sample tube

minimized. If the filling factor of the manometer and sample is small (perhaps less

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than 60–70%), achieving 1 GPa will require significantly greater pressure cell

compression.

The pressure cell kit includes Daphne 7373 oil as a pressure transmitting medium.

The included syringe can be used to help apply the transmitting medium to the

Teflon sample tube.

Figure 3-6: Inserting sample and inserting 2nd Teflon cap.

5) The second end of the Teflon sample tube is sealed with a Teflon cap (Fig. 3-6).

Care should be taken to minimize any air bubbles in the Teflon sample tube

6) Using for example a Kimwipe, any excess oil or any other foreign particles should

be removed from the threads of the centre cylinder and around the Teflon caps.

7) Using the appropriate diameter sample push rod, The Teflon sample tube should

be carefully pushed so that it is roughly centred within the centre cylinder (Fig. 3-7).

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The Teflon sample tube and end caps form a very snug fit inside the centre cylinder.

Thus, a bit of force may be necessary to push the Teflon sample tube into the centre

cylinder. This is normal. Any excess grease or oil should be cleaned from around the

centre cylinder.

8) The two pistons are then inserted into the centre cylinder (Fig. 3-7).

Figure 3-7: Teflon tube is centered, setting the pistons.

9) Using a toothpick or small wire, a thin coat of Teflon powder is applied to the

threads of the centre cylinder (Fig.3-8).

Figure 3-8: Applying Teflon powder, piston backup, side cylinder, and pressurizing nut.

10) With the centre cylinder held horizontally, a piston backup is placed on each

piston (Fig. 3-8).

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11) The side cylinders are threaded finger tight to the centre cylinder. There should

be no gap between the side and centre cylinders (Fig. 3-8).

12) The threads of the two cylinder pressurization nuts are then coated with Teflon

powder (Fig. 3-8).

13) The cylinder pressurization nuts are threaded to the side cylinders finger tight

(Fig. 3-8).

14) One of the pressurization nuts is loosened byabout two turns, and the opposite

pressurization nut is tightened. The nut should tighten smoothly, indicating that the

pistons and Teflon sample tube are moving smoothly. Next, the tightened

pressurization nut is loosened by about 3 turns, and the opposite pressurization nut is

tightened. Again, the pressurization nut should tighten smoothly. The pistons and Teflon

sample tube need to be worked back and forth in this manner about 3 times. When

finished, both pressurization nuts are finger-tightened so that the sample is centred

within the centre cylinder. This is indicated by checking that the gap between the

pressurization nut and side cylinder are roughly equal on both sides (Fig. 3-9).

Figure 3-9: Final assembly before pressurizing.

The sample is now inserted in the high pressure cell and is ready for pressurization and

measurements.

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B) Pressurizing the sample

1) The length of the pressure cell will be used as a reference so the amount of

compression can later be determined (Fig. 3-10 for the recommended dimension to

measure).

2) The pressure cell is inserted into the cell clamp and cinched in place with the two

hex screws. The third hex screw is used to slightly pry the cell clamp apart in case

the cell does not easily slide into the cell clamp (Figure 3-10).

Figure 3-10: Measuring compression and inserting pressure cell into clamp.

3) The custom spanners are attached to the pressurization nuts (Fig. 3-11).

Figure 3-11: Setting the pressurization spanners.

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4) A vice or large adjustable wrench is used to hold the cell clamp stable.

5) One of the pressurization nuts is tightened by 90 degrees, then the opposite

pressurization nut by 90 degrees. To limit risk of damage to the pressurization nuts due

to over torquing, the pressurization nuts need to be slowly tightened.

6) The pressurization nuts continue to be tightened, alternating between the two

pressurization nuts in 90 degree steps, until the total cell compression is about 1 mm. For

compression greater than about 1 mm, the pressurization nuts are rotated in small steps,

30 to 45 degrees being recommended. The maximum sample compression is about 2.0

mm. 90 degrees of pressurization nut rotation represents about 0.1 mm of compression.

Note: Over pressurizing the sample region needs to be avoided. If the sample is

compressed by more than about 2.2mm, there is increased risk of damage to the pressure

cell. If the pressure is found to be below 1 GPa with 2 mm of compression, this indicates

a problem with the cell. The most probable sources of this reduced pressure are: i)too

much pressure transmitting medium / not enough sample, ii) damaged Teflon tube or

caps, resulting in a leak. For applied pressures above 1 GPa, the pistons will likely be

deformed at higher pressures, so the pistons are considered a single-use consumable. The

pistons are reusable for applied pressure under 1GPa.

C) Removing the sample

1) The cell is inserted into the cell clamp, and the two hex bolts are tightened to cinch the

cell in the cell clamp.

2) The pressurization spanners are attached to the pressurization nuts.

3) The pressurization nuts are slowly unscrewed and removed from the cell.

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4) The pressurization spanners are unthreaded to grip the side cylinders.

5) The piston backups and pistons are removed.

Note: If the applied pressure was greater than about 1 GPa, the pistons may be deformed

and wedged in the centre cylinder. To remove the pistons in this case, with the centre

cylinder cinched in one of the pressurization spanners, use some pliers to grip the

pistons. Slowly twist the pistons to remove them from the centre cylinder. If the pistons

are deformed and do not smoothly insert into the center cylinder, they should be

discarded.

6) Using the proper diameter sample push rod, push out the sample from the centre

cylinder.

3.2.2.2 Determining applied sample pressure

There are two ways to determine the applied sample pressure:

1) The transition temperature of a sample with a known pressure dependence is

measured. The pressure cell kit comes with both Pb and Sn for this purpose. Either AC

or DC magnetization can be measured to determine the applied sample pressure. AC

susceptibility measurements will typically give a sharper critical temperature (Tc)

transition and is recommended if available.

2) As the pressurization nuts are tightened, the compression of the cell can be measured.

The following Fig. 3-12 shows a typical compression vs. sample pressure for the

pressure ding along the sample Teflon tube and the filling factor of the sample.

Assuming that these are kept constant, it is possible to approximate the applied pressure.

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In the case of Fig. 3-12, the pressure was determined by measuring the Tc of a Pb

manometer. A 5 mm length of Teflon sample tube was used.

Figure 3-12: Typical sample pressure vs. cell compression.

The sample pressure is a function of temperature. This temperature dependence is

negligible for temperatures less than about 70 K (liquid N2 temperature). For room

temperature, samples that show ferromagnetic ordering can be used as a manometer. For

example, Gadolinium shows ferromagnetic ordering near 300 K and has a pressure

dependence on the Tc of 12.2 K/GPa-1. We have used this method to determine pressure.

3.2.2.3 Mounting pressure cell to VSM sample rod

The large diameter VSM coil is required to use the HMD pressure cell with the QD

VSM system.

The same adapter can be used for both the PPMS and VersaLab measurement options.

Fig. 3-13 shows the pressure cell mounted to the VSM sample rod.

95

Figure 3-13: Pressure cell threaded to VSM sample rod adapter.

96

4 HYDROSTATIC PRESSURE: A VERY EFFECTIVE APPROACH TO SIGNIFICANTLY ENHANCE Jc IN GRANULAR Sr4V2O6 Fe2As2

SUPERCONDUCTORS

4.1 Introduction

Iron based superconductors have revealed wonderful superconducting properties,

including high values of critical temperature (Tc), critical current density (Jc), upper

critical field (Hc2), and irreversibility field (Hirr). They also exhibit low anisotropy

and very strong pinning, which gives rise to high Jc (~106 A/cm2) in both single

crystals and thin films at both low and high fields [1-10]. The Jc and its field

dependence in polycrystalline bulks and tapes/wires, however, are still lower than

what is required for practical applications. Enhancement of Jc or flux pinning using

various approaches has always been a main focus of research with a view to large

current and high field applications. So far, three main methods have been used to

increase the Jc in cuprates, MgB2, and iron based superconductors: 1) texturing

processes to reduce the mismatch angle between adjacent grains and thus overcome

the weak-link problem in layer-structured superconductors; 2) introducing point

pinning centres by chemical doping and 3) high energy ion implantation or

irradiation to introduce point defect pinning centres. Jc values achieved by the

irradiation method have reached as high as 106-107 A/cm2 for both low and high

fields in single crystals and thin films [11-13]. This method is not ideal, however, for

Jc enhancement in polycrystalline pnictide superconductors.

As is well known, the weak-link issue is the predominant factor causing low Jc,

especially at high fields in pnictide polycrystalline samples, which must be

overcome. In order to improve the Jc and its field dependence in granular

superconductors, the following prerequisites should be met: i) strong grain

97

connectivity; ii) introduction of more point defects inside grains; and iii) Tc

enhancement, which can increase the effective superconducting volume as well as

Hirr and Hc2.

We have taken into account that the following facts relating to flux pinning

mechanisms must be addressed before an effective method is introduced for

polycrystalline pnictide superconductors. The coherence length is very short (ξ ≈ a

few nm), so elimination of weakly linked grain boundaries is important to achieve

high Jc [14]. The nature of the pinning mechanism plays a vital role in Jc field

dependence. It is noteworthy that a high pinning force can boost pinning strength

and, in turn, leads to higher values of Jc. The ideal size of defects for pinning should

be comparable to the coherence length [15]. Therefore, point defect pinning is more

favourable than surface pinning, as its pinning force is larger than for surface pinning

at high field, according to the Dew-Hughes model [16]. Therefore, it is very

desirable to induce more point defects in superconductors. Although chemical doping

and high energy particle irradiation can effectively induce point defects and enhance

Jc in high fields, Tc and low field Jc deteriorate greatly for various types of

superconductors. Therefore, the ideal approach should be the one which can induce

more point defects, with increased (or at least at no cost of) superconducting volume

and Tc, as well as strongly linked grain boundaries.

Hydrostatic pressure has been revealed to have a positive effect on Tc in cuprate and

pnictide superconductors. For instance, high pressure of 150 kbars can raise Tc of

Hg-1223 significantly from 135 K to a record high 153 K [17]. The Tc of hole doped

(NdCeSr)CuO4 was increased from 24 to 33 K at 3 GPa by changing the apical Cu-O

distance [18]. The enhancement of Tc for YBCO is more than 10 K at 2 GPa [19].

Excitingly, pressure also shows positive effects on Tc for various pnictide

98

superconductors. Pressure can result in improvement of Tc from 28 to 43 K at 4 GPa

for LaOFFeAs [20]. For Co doped NaFeAs, the maximum Tc can reach as high as 31

K from 16 K at 2.5 GPa [21]. Pressure can also enhance the Tc of La doped Ba-122

epitaxial films up to 30.3 K from 22.5 K, due to the reduction of electron scattering

and increased carrier density caused by lattice shrinkage [22]. A huge enhancement

of Tc from 13 to 27 K at 1.48 GPa was observed for FeSe, and it reached the high

value of 37 K at 7 GPa [23, 24].

Beside the above-mentioned significant pressure effects on Tc enhancement, pressure

can have more advantages that are relevant to the flux pinning compared to other

methods. 1) It always reduces the lattice parameters and causes the shrinkage of unit

cells, giving rise to the reduction of anisotropy. 2) Grain connectivity improvement

should also be expected, as pressure can compress both grains and grain boundaries.

3) The existence or formation of point defects can be more favourable under

pressure, since it is well known that the formation energy of point defects decreases

with increasing pressure [25-27]. 4) Pressure can cause low-angle grain boundaries

to migrate in polycrystalline bulk samples, resulting in the emergence of giant grains,

sacrificing surface pinning thereafter. Hence, a higher ratio of point pinning centres

to surface pinning centres is expected due to the formation energy and migration of

grain boundaries under pressure. 5) The significant enhancement of Tc, as above-

mentioned, means that superconducting volumes should be increased greatly below

or above the Tc without pressure. Moreover, the Hc2, Hirr, and Jc have to be enhanced

along with the Tc enhancement. These are the motivations of our present study on the

pressure effects on flux pinning and Jc enhancement in polycrystalline pnictide bulks.

We anticipated that hydrostatic pressure would increase the superconducting volume,

99

Hirr, and Hc2 due to Tc enhancement, increase the point defects, improve grain

connectivity, and reduce the anisotropy in pnictide polycrystalline bulk samples.

There is some evidence for Jc enhancement under pressure in YBa2Cu3O7−x (YBCO)

single crystal, which emphasizes the pressure effects on transport Jc for different

angle grain boundaries. A recent report also shows enhanced Jc in a pnictide single

crystal which is free of grain boundaries [28-30]. As mentioned earlier,

polycrystalline superconducting materials are commonly used in practical

applications, as they are easy to fabricate at low cost as compared to single

crystals/thin films. Their superconducting performance is hindered by grain

boundaries, however, due to granularity. Therefore, it is more important to use an

efficient approach to enhance the Jc in polycrystalline bulk samples. In this study, we

chose a polycrystalline Sr4V2O6Fe2As2 sample to demonstrate the significant effects

of the hydrostatic pressure on flux pinning and the significant enhancement of Jc and

Tc in this granular sample. It has been reported that the Tc for this compound can

range from 15 - 30 K, depending on fabrication process and carrier concentration

[31]. Generally, Tc under pressure remains nearly constant (or little increase) for

optimal doped superconductors and decreases linearly in the overdoped range. Under

doped superconductors under pressure have dome-like plots for Tc vs. pressure, so

we chose a Sr4V2O6Fe2As2 sample with the low Tc of 15 K for the proposed pressure

effect investigation to ensure a clear pressure effect on Tc [32]. Our results show that

pressure can enhance the Jc by more than 30 times at 6 K and high fields in

polycrystalline Sr4V2O6Fe2As2, along with Tc enhancement from 15 to 22 K at 1.2

GPa and Hirr enhancement by a factor of 4. Our analysis shows that pressure induced

point defects inside the grains are mainly responsible for the flux pinning

enhancement.

100

4.2 Results and Discussion

Figure 1 shows the temperature dependence of the zero-field-cooled (ZFC) and field-

cooled (FC) moments for Sr4V2O6Fe2As2 at different pressures. Pressure causes little

change to the field-cooled branch, indicating that strong pinning is retained under

pressure. The Tc without pressure is about 15 K, very similar to that of underdoped

samples reported for Sr4V2O6Fe2As2 bulks [31]. Pressure enhances Tc linearly from

15.3 K for P = 0 GPa to 22 K for P = 1.2 GPa, with the pressure coefficient, dTc/dP

= 5.34 K/GPa.

Figure 4-1: Temperature dependence of ZFC and FC moments at different pressures for Sr4V2O6Fe2As2. The inset shows the pressure dependence of Tc.

The M-H curves measured under different pressures indicate that the moment

increases with increasing pressure. The field dependence of Jc at different

temperatures obtained from the M-H curves by using Bean’s model under different

pressures is shown in a double-logarithmic plot [i.e. Figure 2]. The remarkable effect

of pressure towards the enhancement of Jc can be clearly seen. For P = 1.2 GPa, the

Jc is significantly enhanced by more than one order of magnitude at high fields at 4

and 6 K, respectively, as shown in Figure 3.

101

Figure 4-2: Field dependence of Jc under different pressures at 3, 4, 6, and 7 K.

The Jc at 6 K as a function of pressure at different fields is plotted in Figure 4. The

solid lines in Figure 4 show linear fits to the data, which give the slopes (i.e.

d(lnJc)/dP) of 1.09, 1.69, and 2.30 GPa-1 at 0, 2, and 4 T, respectively, indicating that

the effects of pressure towards the enhancement of the Jc are more significant at high

fields.

Figure 4-3: Comparison of Jc at 0 and 1.2 GPa at 4 and 6 K. The inset shows d(lnJc)/dP versus temperature, indicating enhancement of Jc at a rate of 1.08 GPa-1 at zero field.

102

Figure 4-4: Pressure dependence of Jc (logarithmic scale) at 0, 2, and 4 T at the temperature of 6 K.

We also found that the Hirr of Sr4V2O6Fe2As2 is greatly increased by pressure. The

Hirr is defined as a field where Jc reaches as low as 10 A/cm2 in Jc vs field curves for

different pressures and temperatures. As shown in Figure 5, the Hirr increases

gradually with pressure and rises to 13 T from 3.5 T at 7 K.

Figure 4-5: Hirr vs. T for different pressures.

103

The Jc vs. reduced temperature (1-T/Tc) at zero field and different pressures is plotted

in Figure 6, which shows a rough scaling behaviour as 𝐽𝑐 ∝ (1 − 𝑇 𝑇𝑐⁄ )𝛽 at different

pressures. The slope of the fitting line, β, depends on the magnetic field. The

exponent β (i.e. slope of the fitting line) is found to be 2.54, 2.73, 2.96, and 3.13 at 0,

0.25, 0.75, and 1.2 GPa, respectively. According to Ginzburg-Landau theory, the

exponent “β” is used to identify different vortex pinning mechanisms at specific

magnetic fields. It was found that β = 1 for non-interacting vortices, while β > 1.5

indicates the core pinning mechanism [33]. The different values of β (i.e. 1.7, 2, and

2.5) were also reported for YBCO films which show the functioning of different core

pinning mechanisms [34, 35]. In addition, the exponent β values that we obtained are

higher at higher pressures in our sample, indicating stronger improvement of Jc with

temperature at high pressures.

Figure 4-6: Logarithmic plot of Jc as a function of reduced temperature at different pressures and fields.

104

For polycrystalline samples, high pressure can modify the grain boundaries through

reducing the tunnelling barrier width and changing the tunnelling barrier height. The

Wentzel-Kramers-Brillouin (WKB) approximation applied to a potential barrier

gives the following simple expressions [36] :

𝐽𝑐 = 𝐽𝑐𝑐exp (−2𝑘𝑘) (1)

Where W is the barrier width, k = (2mL)1/2/ℏ is the decay constant, which depends on

the barrier height L, ℏ is the Planck constant, and Jc0 is the critical current density for

samples with no grain boundaries. The relative pressure dependence of Jc can be

obtained from Eq. (1) as:

𝑑 ln 𝐽𝑐𝑑𝑑

=𝑑 ln 𝐽𝑐0𝑑𝑑

− ��𝑑 ln𝑘𝑑𝑑

� ln �𝐽𝑐0𝐽𝑐�� −

12��𝑑 ln 𝐿𝑑𝑑

� ln �𝐽𝑐0𝐽𝑐��

= 𝑑 ln 𝐽𝑐0𝑑𝑑

+ 𝜅𝐺𝐺 ln �𝐽𝑐0𝐽𝑐� + 1

2𝜅𝐿 ln �𝐽𝑐0

𝐽𝑐� (2)

Where the compressibility in the width and height of the grain boundary are defined

by 𝜅𝐺𝐺 = −𝑑 ln𝑘/𝑑𝑑 and 𝜅𝐿 = −𝑑 ln 𝐿/𝑑𝑑 , respectively. To estimate their

contributions to the second and the third terms of Eq. (2) for Jc enhancement, we

assume to a first approximation that κGB and κL are roughly comparable to the

average linear compressibility values κa = -dlna/dP (κGB ≈ κa) and κc = -dlnc/dP (κL ≈

κc) of Sr4V2O6Fe2As2 in the FeAs plane, where a and c are the in-plane and out-of-

plane lattice parameters, respectively. We assume to a first approximation that κa = -

dlna/dP = -0.029 GPa-1, κc = -dlnc/dP = -0.065 GPa-1 [24], and the in-plane Jc0 ≅ 105

A/cm2 for a sample with no grain boundaries (single crystal) [37]. Setting Jc ≅ 2 ×

103 A/cm2 at the temperature of 6 K and ambient pressure, we find that (–

dlnW/dP)ln(Jc0/Jc) ≈ 0.11 and -0.5(dlnL/dP)ln(Jc0/Jc)] ≈ 0.13, with both values

adding up to 75% less than the above experimental value dlnJc/dP = 1.08 GPa-1. This

result suggests that the origin of the significant increase in Jc(T) under pressure does

105

not arise from the compression of the grain boundaries. Therefore, Eq. (2) suggests

that the main reason for the rapid increase of Jc with pressure is through point defects

induced under pressure, i.e., dlnJc0/dP is responsible for approximately 75% of the

total increase in the Jc with pressure.

Figure 4-7: Plots of fp vs. H/Hirr at different pressures (0, 0.75, and 1.2 GPa) for 4 (left) and 6 K (right) temperature curves. The experimental data is fitted through the Dew-Hughes model, and the

parameters are shown.

In order to further understand the Jc enhancement under pressure, the pinning force

Fp = B × Jc is calculated, and the scaling behaviour for the normalized pinning force

fp = Fp/Fp,max, is analysed for h = H/Hirr. The results are shown in Figure 7 at 4 and 6

K under 0, 0.75, and 1.2 GPa. For the scaling, we can use the Dew-Hughes formula,

i.e. 𝑓𝑑(ℎ) = 𝐴ℎ𝑝(1 − ℎ)𝑞, where p and q are parameters describing the pinning

mechanism [16]. In this model, p = 1/2 and q = 2 describes surface pinning while p =

1 and q = 2 describes point pinning, as was predicted by Kramer [38]. At ambient

pressure in the temperature range of 3-7 K, the best fits of the curves are obtained

106

with p = 0.51 ± 0.03, q = 1.86 ± 0.03, which suggests that surface pinning is the

dominant pinning mechanism in our sample. At 1.2 GPa, the best obtained values for

p and q were 0.9 ± 0.1 and 2 ± 0.1, respectively, within the studied temperature

range. This means that the dominant pinning mechanism is normal core point pinning

for high pressures. Therefore, our results show that the pressure has induced a clear

transformation from surface to point pinning.

Moreover, it is noteworthy that pressure can induce a reduction in anisotropy. The

anisotropy is defined as 𝛾 = 𝜉𝑎𝑎/𝜉𝑐 where 𝜉𝑎𝑎 is a coherence length along ab plane

and 𝜉𝑐 along c plane. At high temperatures, the pressure dependence of Tc, unit cell

volume (V), and anisotropy (𝛾) are interconnected through the following relation

[39];

−∆𝑇𝑐𝑇𝑐

= ∆𝑉(𝑇𝑐)𝑉(𝑇𝑐)

+ 𝐹(𝛾) (3)

Where 𝐹(𝛾) = [𝛾(𝑑) − 𝛾(0)/𝛾(0)]. Although, no report for bulk modulus of

Sr4V2O6Fe2As2 is yet available, we have tentatively used the bulk modulus (K= 62

GPa) of a similar superconductor i.e., SrFe2As2, to estimate ∆𝑉(𝑇c)/𝑉(𝑇𝑐), which is

found to be ∼ -0.016 at ΔP = 1 GPa, as it can be related to the bulk modulus as ΔV/V

= -ΔP/K [40] . Our experimental results yield a value of 0.486

for ∆𝑇𝑐 𝑇𝑐 = [𝑇𝑐(𝑑) − 𝑇𝑐(0)] 𝑇𝑐(0)⁄⁄ . By using these results, we can obtain 𝛾(𝑑) ≈

0.53 𝛾(0). Thus, we can conclude that the anisotropy has been reduced by almost

half at high temperature by pressure. The decrease in the unit cell parameters

suppresses its volume, leading to an increase in the Fermi vector kF = (3π2N/V)1/3,

where N is the total number of electrons in the system. The increase in the Fermi

vector promotes enhancement of the coherence length along the c-axis (𝜉𝑐 =

ℏ2𝐾𝐹 𝜋𝜋∆⁄ ) where Δ is the uniform energy gap which, in turn, leads to the

suppression of anisotropy.

107

4.3 Conclusion

In summary, hydrostatic pressure is a very effective means to significantly enhance

Tc, Jc, Hirr, and flux pinning in the granular pnictide superconductor Sr4V2O6Fe2As2.

We demonstrate that the hydrostatic pressure can significantly increase Tc from 15 to

22 K, as well as increasing Jc by up to 30 times at both low and high field and

increasing Hirr by a factor of 4 at P=1.2 GPa. Pressure introduces more point defects

inside grains, so that it is mainly responsible for Jc enhancement. In addition, we

found that the transformation from surface pinning to point pinning induced by

pressure was accompanied by a reduction of anisotropy at high temperatures. Our

findings provide an effective method to significantly enhance Tc, Jc, Hirr, and Hc2 for

other families of Fe-based superconductors in the forms of wires/tapes, films, and

single and polycrystalline bulks.

108

4.4 Experimental

For the polycrystalline Sr4V2O6Fe2As2 sample synthesis, the Fe (Alfa Aesar, 99.2%)

and As (Alfa Aesar, 99%) chips were sealed in evacuated quartz tube and heat

treated for 12 hours at 700°C. Later, the stoichiometric amounts of V2O5(Aldrich,

99.6%)+1/2×SrO2(Aldrich)+7/2×Sr (Alfa Aesar, 99%)+2×FeAs were weighed,

mixed, grounded thoroughly and palletized in rectangular form in a glove box in a

high purity Ar atmosphere. The pellet was further wrapped in tantalum foil and then

sealed in an evacuated (10−5 torr) quartz tube and put for heat treatments at 750 and

1150°C in a single step for 12 and 36 hours respectively. Finally, the quartz ampoule

was allowed to cool naturally to room temperature.

The temperature dependence of the magnetic moments and the M-H loops at

different temperatures and pressures were performed on Quantum Design Physical

Property Measurement System (QD PPMS 14T) by using Vibrating Sample

Magnetometer (VSM). We have used HMD High Pressure cell and Daphne 7373 oil

as a pressure transmitting medium to apply hydrostatic pressure on a sample. The

critical current density was calculated by using the Bean approximation.

109

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5 GIANT ENHANCEMENT IN Jc, UP TO A HUNDREDFOLD, IN SUPERCONDUCTING NaFe0.97Co0.03As SINGLE CRYSTALS UNDER

HYDROSTATIC PRESSURE

5.1 Introduction

It is already anticipated in our previous case study that the most significant approach

to enhancing Jc, particularly at high fields and temperatures, without degradation of

Tc, is the use of hydrostatic pressure [1]. Most recent research regarding Jc

enhancement and pinning mechanisms through doping and high energy ion

irradiation is mainly focused on the 1111 system (RFeAsO, where R is a rare earth

element), the 122 system (BaFe2As2, Ba0.5K0.5Fe2As2) and the iron chalcogenide 11

system. Only one report has revealed the nature of the pinning mechanism in LiFeAs

(111 type FeSCs) so far, despite its simple structure and reasonable Tc value as

compared to the 1111 and 122 types [2]. NaFeAs (Tc ≈10K) experiences three

successive phase transitions around 52, 41, and 23 K, which can be related to

structural, magnetic, and superconducting transitions, respectively [3-5]. Bulk

superconductivity in NaFeAs with Tc of ~20K can be achieved by the substitution of

Co on Fe sites, which can suppress both magnetism and structural distortion [6, 7].

The Tc of NaFe0.97Co0.03As single crystal is more sensitive to hydrostatic pressure as

compared to other 11 and 111 Fe-based superconductors, and it has a large positive

pressure coefficient [7]. In addition, Jc values for Co-doped NaFeAs compounds

have not been reported so far. Therefore, it is very interesting to see if the hydrostatic

pressure can significantly improve the flux pinning for this compounds. High-quality

NaFe0.97Co0.03As single crystals were grown by the conventional high temperature

solution growth method using the NaAs self-flux technique [7]. In this chapter, we

report that hydrostatic pressure can enhance the Jc by more than 100 times at high

113

fields at 12 K and 14K in NaFe0.97Co0.03As single crystal. This is a giant

enhancement of Jc and a record high to the best of our knowledge. The Hirr is

improved by roughly 6 times at 14K under P=1GPa.

5.2 Results and Discussion

The temperature dependence of the magnetic moment for zero-field-cooled (ZFC)

and field-cooled (FC) curves at different pressures are shown in Fig.1. The Tc

increases with pressure, from 17.95K for P = 0 GPa to 24.33K for P = 1 GPa, with a

huge pressure coefficient, i.e. dTc/dP~ 6.36K/GPa, which is nearly same to what we

have already reported for NaFe0.97Co0.03As single crystal i.e. dTc/dP=

7.06K·GPa−1[7]. Interestingly, this pressure coefficient is more than two times

greater than that of FeSe (3.2K·GPa−1) [8]. The pressure-induced enhancement of Tc

in NaFe0.97Co0.03As can be associated with the optimization of the structural

parameters of the FeAs layers, including the As–Fe–As bond angle and anion height

[7, 9].

Figure 5-1: Temperature dependence of magnetic moment at different applied pressures in both ZFC and FC runs for NaFe0.97Co0.03As.

The field dependence of Jc at different temperatures obtained from the M-H curves

by using Bean’s model, at P=0GPa, P=0.45GPa and P=1GPa are shown in Fig.2.

Remarkably, Jc is increased significantly at both low and high fields, especially with

114

enhancement of more than 10 times and up to more than 100 times for low and high

fields at both 12 and 14 K, respectively. The significant positive effect of hydrostatic

pressure on the Jc at high fields and temperatures is further reflected in Fig.3, which

shows the Jc enhancement ratio (i.e.𝐽c1𝐺𝐺𝐺 𝐽c0𝐺𝐺𝐺⁄ ) at 12 and 14K over a wide range of

fields. We have taken the Jc value at P=0GPa as a reference. The Jc ratio values at

both temperatures show significant improvements at low and high fields. Although

this result also suggests that hydrostatic pressure is more effective at high fields and

temperatures, it is worth mentioning that Jc values are well improved at zero field at

a significant rate, i.e. d(lnJc)/dP = 1.6 and 2.9 GPa-1 at 12 and 14K, respectively, as

can be seen from the inset of Fig. 3. The d(lnJc)/dP values that have been found are

more significant than for yttrium barium copper oxide(YBCO) [10].

Figure 5-2: Field dependence of Jc at different pressures (0, 0.45 and 1GPa) at different temperatures

115

Figure 5-3: Plot of 𝐽𝑐1𝐺𝐺𝐺/𝐽𝑐0𝐺𝐺𝐺 versus field at 12K and 14K. There is a giant enhancement in Jc values at P =1GPa. The inset shows the plot of d(lnJc)/dP versus temperature, which demonstrates

enhancement in lnJc at a rate of nearly 3GPa-1 at 14K.

We also found that Hirr of NaFe0.97Co0.03As is significantly increased by pressure. As

shown in Fig.4, the Hirr values improve gradually with pressure, and the Hirr value at

14K is increased from 2.6 T at P=0 GPa up to 8.67T at P=0.45GPa and roughly more

than 13 T at P=1GPa (by nearly six times).

Figure 5-4: Plot of Hirr versus temperature at different pressures. Inset shows Hirr as a function of reduced temperature.

116

In Fig.5, we show the temperature dependence of Jc at 0 and 12T under different

pressures. It follows power law [Jc∝ (1-T/Tc)β] behaviour at different pressures.

According to the Ginzburg-Landau theory, the exponent β is used to identify

different vortex pinning mechanisms at specified fields. It was found that β = 1 refers

to non-interacting vortices and β>1.5 corresponds to the core pinning mechanism

[11]. The exponent β (i.e. slope of the fitting line) is found to be 1.79 and 1.85 for

zero field, and 2.73 and 4.28 at 12T, at 0 and 1GPa, respectively, which shows strong

Jc dependence on pressure. The low values of β at P=1GPa indicate that the Jc decays

rather slowly in comparison to its values at P=0GPa. In addition, the differences

between P=0GPa and P=1GPa scaling show a real pressure effect, the factor is

roughly 2, which corresponds nicely to the low-T data in inset Fig. 3.

Figure 5-5: Logarithmic plot of critical current density as a function of reduced temperature at different pressures and magnetic fields.

For single crystals, high pressure can modify an average linear compressibility value

which is similar to those in polycrystalline and textured samples through reduction of

the tunnelling barrier width and the tunnelling barrier height of grain boundaries. The

117

Wentzel-Kramers-Brillouin (WKB) approximation applied to a potential barrier

gives the following simple expression [12-14]:

𝐽𝑐 = 𝐽𝑐𝑐exp (−2𝑘𝑘)………. (1)

Where W is the barrier width, k=(2mL)1/2/ℏ is the decay constant, which depends on

the barrier height L, ℏ is the Planck constant, and Jc0 is the critical current density at

0K and 0T, and its value is roughly 105A/cm2 in our case. The relative pressure

dependence of Jc can be obtained from Eq. (1) as[15]:

𝑑 ln 𝐽𝑐𝑑𝑑

=𝑑 ln 𝐽𝑐0𝑑𝑑

− ��𝑑 ln𝑘𝑑𝑑

� ln �𝐽𝑐0𝐽𝑐�� −

12��𝑑 ln 𝐿𝑑𝑑

� ln �𝐽𝑐0𝐽𝑐��

= 𝑑 ln 𝐽𝑐0𝑑𝐺

+ 𝜅𝐺𝐺 ln �𝐽𝑐0𝐽𝑐� + 1

2𝜅𝐿 ln �𝐽𝑐0

𝐽𝑐�……….(2)

Where the compressibility in the width and height of the grain boundary are defined

by 𝜅𝐺𝐺 = −𝑑 ln𝑘/𝑑𝑑 and 𝜅𝐿 = −𝑑 ln 𝐿/𝑑𝑑 , respectively. For single crystals, we

assume to a first approximation that κGB and κL are roughly comparable,

respectively,to the average linear compressibility values κa=-dlna/dP (κa≈-0.029 GPa-

1) and κc=-dlnc/dP (κc≈-0.065GPa-1) of NaFe0.97Co0.03As in the FeAs plane, where a

and c are the in-plane and out-of-plane lattice parameters, respectively [11].

Therefore, we can write Eq. (2) as

𝑑 ln 𝐽𝑐𝑑𝑑

~𝑑 ln 𝐽𝑐0𝑑𝑑

+ 𝜅𝐺 ln �𝐽𝑐0𝐽𝑐� +

12𝜅𝑐 ln �

𝐽𝑐0𝐽𝑐�… … … . (3)

By using Jc≅1.3 × 103 A/cm2 at 14 K, we find that (𝜅𝐺 ln(𝐽𝑐𝑐 𝐽𝑐⁄ )) ≈ 0.12GPa-1 and

(1/2𝜅𝑐 ln(𝐽𝑐𝑐 𝐽𝑐⁄ ))≈ 0.14GPa-1, so that both of them together only contribute less than

10% to the already mentioned experimental value dlnJc/dP = 2.09 GPa-1 inset of Fig.

2b). This result suggests that the origin of the significant increase in Jc(T) under

pressure does not arise from the reduction of volume but mainly due to the pressure

induced pinning centre phenomenon.

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Figure 5-6: Top panel shows normalized temperature dependence (t = T/Tc) of normalized measured Jc at 0.1T and 0T, in good agreement with δl pinning. Lower panel shows plots of Fp vs. H/Hirr at P=0GPa and P= 0.45GPa at 14K. The experimental data is fitted through D. Dew Hughes model.

To gain further insight into the pressure effect on the pinning mechanism in

NaFe0.97Co0.03As, the experimental results have been analysed by using collective

pinning theory. There are two predominant mechanisms of core pinning, i.e. 𝛿ℓ

pinning, which comes from spatial variation in the charge carrier mean free path,ℓ,

and 𝛿𝑇c pinning due to randomly distributed spatial variation in Tc. According to the

theoretical approach proposed by Griessen et al. [16], 𝐽c(𝑡)/𝐽c(o) ∝ (1 − 𝑡2)5 2� (1 +

𝑡2)−1 2� in case of 𝛿ℓ pinning, whereas 𝐽c(𝑡)/𝐽c(o) ∝ (1 − 𝑡2)7 6� (1 + 𝑡2)5 6�

corresponds to 𝛿𝑇c pinning, where 𝑡 = 𝑇𝑇c� . Fig.6 (Top Panel) shows a comparison

119

between the experimental Jc values and the theoretically expected variation within

the 𝛿ℓ and 𝛿𝑇c pinning mechanisms at 0.1T and 0 T (the so-called remanent state

shown by the solid symbols). The 𝐽c(𝑡) values have been obtained from the Jc(B)

curves at various temperatures. It is found that the experimental data at P=0 and

P=1GPa are in good agreement with theoretical 𝛿ℓ pinning. It is more likely that

pinning in NaFe0.97Co0.03As originates from spatial variation of the mean free path

“ℓ”. We observed similar results in BaFe1.9Ni0.1As2 and SiCl4 doped MgB2 at low

fields. In addition, 𝛿ℓ pinning has also been reported in FeTe0.7Se0.3 crystal [17-19].

In order to understand the nature of the pinning mechanisms in more detail, it is

useful to study the variation of the vortex pinning force density, 𝐹p = 𝐽c × B with

the field. The normalized pinning force density (𝐹p 𝐹pmax⁄ ) as a function of reduced

field (𝐻 𝐻𝑖𝑖𝑖⁄ ) at P=0GPa and P=0.45GPa at 14K is plotted in lower panel of Fig.6.

𝐻irr is estimated by using the criterion of 𝐽c ≈ 100A cm2⁄ . We can use the Dew-

Hughes formula, i.e. 𝐹p ∝ ℎ𝑚(1 − ℎ𝑛) to fit our experimental data, where m and n

are fitting parameters to describe the nature of the pinning mechanism. We found

that m=1.15 and n=2 at 0GPa, and m =1.1 and n=2.1 at 0.45GPa. According to the

Dew-Hughes model, in the case of 𝛿ℓ pinning for a system dominated just by point

pinning, the values of the fitting parameters are m=1 and n=2, with the

𝐹pnormalizedmaxima maximum occurring at ℎmax = 0.33, while ℎmax occurs at 0.20

for surface/grain boundary pinning with m=0.5 and n=2. In case of 𝛿𝑇c pinning, ℎmax

shifts to higher values, and the fitting parameters change accordingly. Further details

can be found elsewhere [20]. The values of m and n that were found in the present

study are almost the same at 0GPa and 0.45GPa, so normal core point pinning is

dominant in our material.

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Figure 5-7: Pinning force density (Fp) as a function of field at P=0GPa and P=1GPa at 12K and 14K.

The inset shows the temperature dependence of the pinning centre number density at the different pressures

Pressure can enhance the pinning force strength by a significant amount in

NaFe0.97Co0.03As single crystal. The pinning force density as a function of field at

12K and 14K is plotted in Fig.7. At high field and pressures, the Fp is found to be

over 20 and 80 times higher than at 0 GPa at 12 and 14K, respectively. Furthermore,

pressure induces more point pinning centres at 12 K and 14 K, especially at P=1GPa,

as can be seen in the inset of Fig.7. The number density of randomly distributed

effective pinning centres (Np) can be calculated from the following relation:

Σ𝐹𝑝𝜂𝑓𝑝𝑚𝑚𝑚 = 𝑁𝐺……….(4)

Where Σ𝐹𝐺 is the aggregated pinning force density, 𝑓𝑝𝑚𝐺𝑚 is the maximum

normalized elementary pinning force �𝑓𝑝�,and 𝜂 is an efficiency factor. The 𝜂 value

is 1 in the case of a plastic lattice, and the 𝜂 value is otherwise 𝑓𝑝𝑚𝐺𝑚/𝐵, where B is

the bulk modulus of the material [21]. We can assume that 𝜂 = 1, as pressure can

shrink lattice parameters. The inset of Fig.7 shows the Np versus temperature plot at

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P=0 and P=1GPa. The Np values are found to be much greater at 14 K at P=1GPa as

compared to Np at P=0GPa (nearly six times as great). It is well known that

hydrostatic pressure induces pinning centres which, in turn, leads to huge values of Jc

and increase in Np at P=1Gpa is a direct evidence of that. This is further verified in

Fig.8, which shows the plot of 𝐽𝑐 𝐽𝑐𝑚𝐺𝑚⁄ versus reduced field (i.e.ℎ = 𝐻 𝐻𝑖𝑖𝑖⁄ ) at

P=0GPa and P=1GPa for 14K and P=0GPa & P=0.45GPa for 12K. Obviously, the

hump or secondary peak effect observed at high pressures suggests that the Jc

enhancement is due to induced pinning centres.

Figure 5-8: Reduced field dependence of the normalized Jc at 14K for different pressures. The inset shows the same plot for 12K at P=0GPa and P=0.45GPa

Additionally, we found a pronounced reduction in the superconducting anisotropy at

high temperatures, by almost 63% at P=1GPa. The pressure dependence of the Tc,

volume (V) and anisotropy (𝛾) are interconnected through a relation [22]:.

−�𝑇cP−𝑇c0

𝑇c0� = �∆𝑉

𝑉� + �𝛾P −𝛾0

𝛾0�………. (5)

122

At ΔP=1GPa, ∆𝑉(𝑇c)/𝑉(𝑇c) is estimated to be -0.02, as ΔV/V=-ΔP/B, where K is the

bulk modulus. We can use the bulk modulus (B≈52.3GPa) of a similar

superconductor, i.e. Na1-xFeAs [9]. The value of 𝛾 at P=1GPa is found to be 63% less

than its value at P=0GPa.

5.3 Conclusion

Hydrostatic pressure can significantly enhance Jc by up to 102 times in

NaFe0.97Co0.03As single crystals, which is a record high enhancement. The most

significant enhancement in in-field performance of NaFe0.97Co0.03As in terms of

pinning force density (Fp) is found at P=1GPa in particular, where the Fp at high

fields is over 20 and 80 times higher at 12 and 14K, respectively, than at 0 GPa. The

hydrostatic pressure induces more effective point pinning centres and Np at 1GPa is

almost two times higher at 12K and over six times higher at 14K compared to the

value at 0GPa. Moreover, a hump or secondary peak effect is found from the plot of

the normalized Jc as a function of reduced field. Therefore, this giant enhancement in

Jc values for NaFe0.97Co0.03As exists because of more pinning centres induced by

pressure and the increase in pinning strength as well. The present study indicates that

the supercurrent carrying ability in the Fe111 can be further and significantly

increased by the proposed hydrostatic pressure technique. Our results were achieved

in single crystal sample, which means that the enhancement is intrinsic, and more

significant than other reported approaches. It gives us high expectations that the tapes

or wires made by the same compounds should carry higher supercurrents using the

hydrostatic pressure than those at ambient pressure.

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5.4 Experimental

High-quality single crystals of NaFe0.97Co0.03As have been grown by use of the NaAs

flux method. NaAs was obtained by reacting the mixture of the elemental Na and As

in anevacuated quartz tube at 2000C for 10 h. Then NaAs, Fe,and Co powders were

carefully weighed according to the ratio of NaAs:Fe:Co = 4:0.972:0.028, and

thoroughly ground. The mixtures were put into alumina crucibles and then sealed in

iron crucibles under 1.5 atm of highly pure argon gas. The sealed crucibles were

heated to 9500C at a rate of 600C/h in the tube furnace filled with the inert

atmosphere and kept at 9500C for 10 h and then cooled slowly to 6000C at 30C/h to

grow single crystals.

The temperature dependence of the magnetic moments and the M-H loops at

different temperatures and pressures were performed on Quantum Design Physical

Property Measurement System (QD PPMS 14T) by using Vibrating Sample

Magnetometer (VSM). We have used HMD High Pressure cell and Daphne 7373 oil

as a pressure transmitting medium to apply hydrostatic pressure on a sample. The

critical current density was calculated by using the Bean approximation.

124

5.5 References

1. Shabbir, B. et al. Hydrostatic pressure: A very effective approach to significantly enhance critical currentdensity in granular Sr4V2O6Fe2As2 superconductor. Sci. Rep. 5, 8213 (2015).

2. Shlyk, L., Bischoff, M., Rose, E. & Niewa, R. Flux pinning and magnetic

relaxation in Ga-doped LiFeAs single crystals. J. App. Phys. 112, 053914 (2012).

3. Chen, G. F., Hu, W. Z., Luo, J. L. & Wang, N. L. Multiple Phase Transitions

in Single-Crystalline Na1−δFeAs. Phys. Rev. Lett. 102, 227004 (2009). 4. Wang A. F. et al. Phase diagram and calorimetric properties of NaFeCoAs.

Phys. Rev. B 85, 224521 (2012). 5. Parker, D. R. et al. Control of the Competition between a Magnetic Phase and

a Superconducting Phase in Cobalt-Doped and Nickel-Doped NaFeAs using electron count. Phys. Rev. Lett. 104, 057007 (2010).

6. Wright, J. D. et al. Gradual destruction of magnetism in the superconducting

family NaFe1−xCoxAs. Phys. Rev. B 85, 054503 (2012). 7. Wang, A. F. et al. Pressure effects on the superconducting properties of

single-crystalline Co doped NaFeAs. New J. Phys. 14, 113043 (2012). 8. Medvedev, S. et al. Electronic and magnetic phase diagram of β-Fe1.01Se with

superconductivity at 36.7 K under pressure. Nat. Mater. 8, 630 (2009). 9. Liu, Q. et al. Pressure-Induced Isostructural Phase Transition and Correlation

of FeAs Coordination with the Superconducting Properties of 111-Type Na1-

xFeAs. J. Am. Chem. Soc. 133, 7892 (2011). 10. Bud’ko, S. L., Davis, M. F., Wolfe, J. C., Chu, C. W. & Hor, P. H. Pressure

and temperature dependence of the critical current density in YBa2Cu3O7-δ thin films. Phys. Rev. B 47, 2835 (1993).

11. Margadonna, S. et al. Pressure evolution of the low-temperature crystal

structure and bonding of the superconductor FeSe (Tc=37 K). Phys. Rev. B 80, 064506 (2009).

12. Halbritter, J. Pair weakening and tunnel channels at cuprate interfaces. Phys.

Rev. B 46, 14861 (1992). 13. Tomita, T., Schilling, J. S., Chen, L., Veal, B. W. & Claus, H. Pressure-

induced enhancement of the critical current density in superconducting YBa2Cu3Ox bicrystalline rings. Phys. Rev. B 74, 064517 (2006).

125

14. Browning, N. D. et al.The atomic origins of reduced critical currents at [001] tilt grain boundaries in YBa2Cu3O7−δ thin films.Physica C 294, 183 (1998).

15. Tomita, T., Schilling, J. S., Chen, L., Veal, B. W. & Claus, H. Enhancement

of the Critical Current Density of YBa2Cu3Ox Superconductors under Hydrostatic Pressure. Phys. Rev. Lett. 96, 077001 (2006).

16. Griessen, R. et al. Evidence for mean free path fluctuation induced pinning in

YBa2Cu3O7 and YBa2Cu4O8 films. Phys. Rev. Lett. 72, 1910 (1994). 17. Shahbazi, M., Wang, X. L., Choi, K. Y. & Dou, S. X. Flux pinning

mechanism in BaFe1.9Ni0.1As2 single crystals: Evidence for fluctuation in mean free path induced pinning. Appl. Phys. Lett. 103, 032605 (2013).

18. Bonura, M., Giannini, E., Viennois, R. & Senatore, C. Temperature and time

scaling of the peak-effect vortex configuration in FeTe0.7Se0.3. Phys. Rev. B 85, 134532 (2012).

19. Wang, X. L. et al. Enhancement of the in-field Jc of MgB2 via SiCl4 doping.

Phys. Rev. B 81, 224514 (2010). 20. Dew-Hughes, D. Flux pinning mechanisms in type II superconductors. Phil.

Mag. 30, 293 (1974). 21. Colliongs, E. W. Applied Superconductivity: Metallurgy, and Physics of

Titanium Alloys Vol. 2: Applications. Springer N. Y. (1986). 22. Schneider, T. & Castro, D. D. Pressure and isotope effect on the anisotropy

of MgB2. Phys. Rev. B 72, 054501 (2005).

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6 OBSERVATION OF STRONG FLUX PINNING AND POSSIBLE MECHANISM FOR CRITICAL CURRENT ENHANCEMENT

UNDER HYDROSTATIC PRESSURE IN OPTIMALLY DOPED (Ba,K)Fe2As2 SINGLE CRYSTALS

6.1 Introduction

The previous results show that Jc is enhanced significantly under hydrostatic pressure

at high fields (i.e., over one order of magnitude) in comparison to low fields, along

with enhancement of the closely related Tc by more than 5 K in iron based

superconductors [1, 2]. Until now, however, it has been unclear that the observed Jc

enhancement under pressure is correlated with improved Tc or flux pinning. While

the primary motivation for this experiment was to use an optimally doped single

crystal material (i.e., no grain boundaries), which has an unchanged Tc under

hydrostatic pressure, in order to elucidate the contributions of flux pinning to Jc

enhancement. An important secondary motivation was to investigate further the

possible contributions of Np and the pinning force strength to strong pinning.

Flux pinning has been a topic of much interest in field of superconductivity because

of its importance for applications and fundamental aspects. This interest stems from

the significance of flux pinning for high critical current density (Jc) in

superconductors, which is the defining property of a superconductor. Generally,

various types of random imperfections, such as cold-work-induced dislocations,

secondary-phase precipitates, defects induced by high energy ion irradiation, etc.,

can be used to enhance flux pinning. Unfortunately, it is difficult to discern the

maximum potential of a superconductor from these techniques, and the outcomes

hold up only to a certain level. Furthermore, the principal result of hysteresis studies

is that the critical current is only enhanced, in most of cases, either in low or high

fields, with degradation of the superconducting critical temperature (Tc) another

127

drawback. For instance, proton irradiation can only enhance flux pinning in high

fields by inducing point defects in Ba122:K. Similarly, light ion C4+ irradiation of

Ba122:Ni crystals can only enhance Jc in low fields at high temperatures [3]. High

energy particle irradiation can also decrease Tc by more than 5 K for cobalt and

nickel doped Ba-122 [4, 5].

As is well known, Jc is mostly limited by weak links (in the case of polycrystalline

bulks), and thermally activated flux creep (an intrinsic property) emerges from weak

pinning [6]. Strong pinning can be achieved either by i) inducing new effective

pinning centres, i.e., increasing the number density of pinning centres (Np), or the

vortex density, or ii) improving the pinning force.

The argument in detail is as follows: i) It is widely believed that hydrostatic pressure

can induce pinning centres, which, in turn, enhance the pinning force. The total

pinning force (Fp) and the pinning centres are correlated by Fp = Npfp where Np is the

number density of pinning centres and fp is the elementary pinning force, which is the

maximum pinning strength of an individual pinning centre, with a value that depends

on the interaction of the flux line with the defect. According to the conventional

theory, strongly interacting defects can contribute to Fp individually, provided that Fp

∝ Np, and weakly interacting defects can contribute only collectively; the collective

theory leads to Fp ∝ (Np)2 for small defect numbers [7].

ii) Secondly, an important contribution to the accumulated pinning force originates

from the pinning strengths of individual pinning centres. The ability of a pin to trap a

vortex depends on its location inside a material: a pin close to the centre traps more

vortices than the same pin near the boundary, because the pinning strength of a pin is

higher when it is near the centre [15]. Hydrostatic pressure can enhance the pinning

strength of an individual pin by pushing it towards the sample’s centre. If vortices are

128

trapped by a strong potential, however, they can merge, forming a giant vortex,

because repulsive vortex-vortex interaction usually vanishes at a very small distances

when vortex cores strongly overlap [8]. The evidence for such vortex mergers can

also be found elsewhere [9].

The discovery of iron based superconductors (FeSCs) has prompted many research

groups to investigate their fundamental properties and also assess the suitability of

these materials for applications. Generally, the Ba122:K compounds among the

FeSCs seem to be the most technologically suitable because of their isotropic nature

and high Tc, upper critical field (Hc2), and Jc values (Jc > 106 A/cm2 at 2 K and 0 T),

and because they have possible room for flux pinning enhancement [10-14]. The

depairing current density (Jd) is the maximum current density that superconducting

electrons can support before de-pairing of Cooper pairs, and is given as

𝐽𝑑 = Φ𝑜3√3𝜋𝜇𝑜𝜆2𝜉

(1)

The 𝐽𝑑 value that is found is roughly 0.3 GA/cm2 by using values of penetration

depth, λ = 105 nm and coherence length, 𝜉 = 2.7 nm [15, 16]. Our estimate indicates

that there is a significant potential to further enhance flux pinning in (Ba,K)Fe2As2.

Additionally, unchanged Tc under hydrostatic pressure has been found for optimally

doped (Ba,K)Fe2As2 [26]. Therefore, this is an ideal sample to use for investigating

flux pinning by identifying the possible contributions of Np and the pinning force.

In this chapter, we extensively investigate the flux pinning of optimally doped

(Ba,K)Fe2As2 under hydrostatic pressure. Strong pinning and therefore, critical

current can be obtained by improving the pinning force strength. As a consequence,

there are two significant implications that are beneficial to applications: i) There is

strong pinning over a wide range of field, showing weak field dependency, and ii) Jc

enhancement occurs to the same extent in low and high fields. Under pressure, a

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larger pinning force appears in (Ba,K)Fe2As2 crystal due to the increased pinning

centre number density and the emergence of giant vortexes which show high pinning

potentials. Our work is one of the very rare investigations where a nearly complete

quantitative understanding of the flux pinning contributions to Jc enhancement has

been developed.

6.2 Results and Discussion

Figure 1 shows the temperature dependence of the magnetic moments for zero-field-

cooled (ZFC) and field-cooled (FC) measurements at different pressures. Tc remains

almost unchanged at different pressures. Tc ≈ 37.95 K was found at P = 0 GPa

whereas, Tc ≈ 38.08 K at P = 1 GPa. Similar results were also reported for

Ba0.6K0.4Fe2As2 thin film [17]. Furthermore, a temperature independent magnetic

moment at low temperatures was observed, along-with a small transition width,

indicating the high quality of the crystals.

Figure 6-1: Magnetic moments versus temperature at P = 0 GPa and P = 1.2 GPa

130

The M-H loops at different pressures and temperatures (4.1, 8, 12, 16, 20, 24, 28, and

32 K) can be seen in Figure 2. Larger M-H Loops are observed at high pressure. For

instance, the larger M-H loops found at 8 K (Figure 3) for P = 0.75 and 1.2 GPa

show significant enhancement of flux pinning in both low and high fields. The field

dependence of Jc at different temperatures (4.1, 16, and 24 K) and pressures (0 and

1.2 GPa), obtained from the M-H curves by using Bean’s model, are shown in Figure

4. Nearly two-fold and five-fold Jc enhancement can be seen at 16 K and 24 K,

respectively. It is noteworthy that Jc is enhanced for Ba0.6K0.4Fe2As2 crystal under

pressure of 1.2 GPa in both low and high fields, which is not generally found with

other approaches. At 16 K and self-field, the Jc is remarkably high, approaching

nearly 1 MA/cm2, whereas Jc ≈ 2 × 105 A/cm2 was obtained at 24 K and 12 T.

Figure 6-2: M-H loops at 4.1, 8, 12, 16, 20, 24, 28, and 32 K for P = 0, 0.75, and 1.2

GPa.

131

Figure 6-3: Jc as a function of field at 0 GPa and 1.2 GPa at 4.1 K, 16 K, and 24 K.

Pressure can also improve the pinning force strength by a significant amount in

Ba0.6K0.4Fe2As2 single crystal. The pinning force (𝐹𝑝 = 𝐽c × 𝐵) as a function of field

at 8 K, 12 K, 24 K, and 28 K is plotted in Figure 5 . At high fields and pressures, the

Fp is found to be nearly 5 times higher at 8, 12, 24, and 28 K as compared to P = 0

GPa, which corresponds nicely to Jc enhancement. Figure 6 shows a comparison of

Fp obtained in our Ba0.6K0.4Fe2As2 under pressure with those of several other low and

high temperature superconducting materials [10, 18-20]. The (Ba,K)Fe2As2 shows

better in-field performance under pressure. Pressure can improve Fp values to greater

than 60 GN/m3 at H > 10 T, which are even superior to those of Nb3Sn and NbTi.

132

Figure 6-4: Fp versus field at 8 K, 12 K, 24 K, and 28 K at different pressures.

Figure 6-5: Fp for different superconductors.

With respect to the Np, pressure can also increase the number of point pinning

centres, which can suppress thermally activated flux creep, leading to Jc

enhancement [1].

133

Np can be calculated from the following relation:

Σ𝐹𝑝𝜂𝑓𝑝𝑚𝑚𝑚 = 𝑁𝑃 (1)

Where Σ𝐹𝑝 is the accumulated pinning force density, 𝑓𝑝𝑚𝑚𝑚 is the maximum

elementary pinning force �𝑓p�, which is the interaction between a flux line and a

single defect, and 𝜂 is an efficiency factor. 𝜂 = 1 corresponds to a plastic lattice, and

the 𝜂 value is otherwise 𝑓𝑝𝑚𝑚𝑚/𝐵, where B is the bulk modulus of the material. We

assume to a second order of approximation that the interaction between a flux line

and a single defect is nearly same under pressure. Therefore, we can use 𝑓𝑝𝑚𝑚𝑚 ≈ 3 ×

10-13 N for a similar superconductor (i.e., Ba122:Co) to estimate Np [21]. At 4.1 K,

Np ≈ 7.3 × 1024 m-3 at P = 0 Gpa, which increased to Np ≈ 1.2 × 1025 m-3 for P = 1.2

GPa, while at 24 K, Np ≈ 6.6 × 1023 m-3 at P = 0 Gpa, which increased to Np ≈ 3.8 ×

1024/m3 for P = 1.2 GPa.

Figure 6-6: Jc-Fp ratios at P = 1.2 GPa and P = 0 GPa. The relative change of Jc with

pressure as a function of T is given in the inset.

134

In order to investigate the possible contributions to strong flux pinning, we have

shown a preliminary result in Figure 6 which describes the field dependence of

𝐽𝑐𝑟 − 𝐹𝑝𝑟 at P = 0 GPa and P = 1.2 GPa, where 𝐽𝑐𝑟 = 𝐽𝑐1.2𝐺𝑃𝑚

𝐽𝑐0𝐺𝑃𝑚� and 𝐹𝑃𝑟 =

𝐹𝑃1.2𝐺𝑃𝑚

𝐹𝑃0𝐺𝑃𝑚� . Analysis of the 𝐽𝑐𝑟 − 𝐹𝑝𝑟 data, acquired at different temperatures,

leads to minimal values, i.e., nearly zero, which shows that that pressure can increase

the pinning force by increasing the number density and the formation of giant

vortexes, and in this way, it can increase the critical current in high and low fields.

The simplest way to show Np and Fp dependence on pressure is illustrated in Figure

7, which demonstrates that pressure can enhance flux pinning.

Figure 6-7: Fp ∝ Np holds where P < P0 (the threshold pressure value) and the size of defects, L0 ≈ ξ.

High pressure can modify grain boundaries through reduction of the tunnelling

barrier width and the tunnelling barrier height for polycrystalline bulks. The

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Wentzel-Kramers-Brillouin (WKB) approximation, which is valid for such a

potential barrier gives the following simple mathematical expression [22-24]:

𝐽𝑐 = 𝐽𝑐𝑐exp (−2𝑘𝑘) (1)

Where W is the barrier width, k = (2mL)1/2/ℏ is the decay constant, which is barrier

height (L) dependent, ℏ is the reduced Planck constant, and Jc0 is the critical current

density at 0 K and 0 T. The relative pressure dependence of Jc can be determined

from Eq. (1) as [25]:

𝑑 ln 𝐽𝑐𝑑𝑑

=𝑑 ln 𝐽𝑐0𝑑𝑑

− ��𝑑 ln𝑘𝑑𝑑

� ln �𝐽𝑐0𝐽𝑐�� −

12��𝑑 ln 𝐿𝑑𝑑

� ln �𝐽𝑐0𝐽𝑐��

= 𝑑 ln 𝐽𝑐0𝑑𝑃

+ 𝜅𝐺𝐺 ln �𝐽𝑐0𝐽𝑐� + 1

2𝜅𝐿 ln �𝐽𝑐0

𝐽𝑐� (2)

Where the compressibility in the width and height of the grain boundary are defined

by 𝜅𝐺𝐺 = −𝑑 ln𝑘/𝑑𝑑and 𝜅𝐿 = −𝑑 ln 𝐿/𝑑𝑑, respectively.

For (Ba,K)Fe2As2 single crystals, we assume to a first approximation that κGB and κL

are nearly comparable to the average linear compressibility values κa = -dlna/dP (κa

≈ 0.00318 GPa-1) and κc = -dlnc/dP (κc ≈ 0.00622 GPa-1), respectively, in the FeAs

plane, where a and c are the in-plane and out-of-plane lattice parameters [26] .

Therefore, we can write Eq. (2) correspondingly as

𝑑 ln 𝐽𝑐𝑑𝑑

≈ 𝑑 ln 𝐽𝑐0𝑑𝑑

+ 𝜅𝑚 ln �𝐽𝑐0𝐽𝑐� +

12𝜅𝑐 ln �

𝐽𝑐0𝐽𝑐� (3)

By using Jc ≈ 105 A/cm2 at 24 K and Jc0 ≈ 106 A/cm2, we find that (𝜅𝑚 ln(𝐽𝑐𝑐 𝐽𝑐⁄ )) ≈

0.0073 GPa-1 and (1/2𝜅𝑐 ln(𝐽𝑐𝑐 𝐽𝑐⁄ )) ≈ 0.0071 GPa-1, so both only contributed less

than 2% to the experimental value, i.e., dlnJc/dP = 0.92 GPa-1 from the inset of

Figure 6. This estimate indicates that the origin of the strong flux pinning under

pressure does not arise from the change in volume.

136

The Jc value as a function of reduced temperature (i.e. 1-T/Tc) at 0 and 10 T under

different pressures is shown in Figure 8. The experimental data points in different

fields and pressures follow a power law description [i.e. Jc ∝ (1-T/Tc)β], where β is a

critical exponent [27, 28]. Ginzburg-Landau theory predicts different vortex pinning

mechanisms at specified fields, with different values of exponent β. It was found that

β = 1 corresponds to non-interacting vortices and β > 1.5 refers to the core pinning

mechanism. The exponent β (i.e., slope of the fitting line) is found to be 1.74 and

1.85 for zero field, and 1.20 and 1.43 at 10 T, at 0 and 1.2 GPa, respectively, which

reveals a strong Jc dependence on pressure. The low values of β at high pressure

show that the Jc decays rather slowly in comparison to its values at low pressure.

Different values of exponent β have also been observed in MgB2 and yttrium barium

copper oxide (YBCO) [29, 30]

Figure 6-8: lnJc versus reduced temperature at different fields and pressures.

The pinning mechanisms in Ba0.6K0.4Fe2As2 have been analysed by using collective

pinning theory. Generally, core pinning comprises 1)𝛿ℓ pinning, which comes from

137

spatial variation in the charge carrier mean free path, ℓ, and 2) 𝛿𝑇c pinning due to

randomly distributed spatial variation in Tc.

Figure 6-9: Jc as a function of T/Tc. Experimental data points are in agreement with 𝜹𝜹 pinning.

Referring to the theoretical approach proposed by Griessen et al.:

𝐽c(𝑡)/𝐽c(o) ∝ (1 − 𝑡2)5 2� (1 + 𝑡2)−1 2� (2)

in the case of 𝛿ℓ pinning, while

𝐽c(𝑡)/𝐽c(0) ∝ (1 − 𝑡2)7 6� (1 + 𝑡2)5 6� (3)

applies in the case of 𝛿𝑇c pinning, where 𝑡 = 𝑇𝑇c� . Figure 8 shows almost perfect

overlapping of the experimentally obtained Jc values and the theoretically expected

variation for the 𝛿ℓ pinning mechanism at 0.1 T and 0 T (with the so-called remanent

state shown by the solid symbols). The 𝐽c(𝑡) values have been found from the Jc(B)

curves at different temperatures. The experimental data seems to be in good

agreement with the theoretical 𝛿ℓ pinning curves at P = 0 and P = 1 GPa. Therefore,

138

pinning in Ba0.6K0.4Fe2As2 emerges from spatial variation of the mean free path ℓ.

We also observed similar results in BaFe1.9Ni0.1As2 and SiCl4 doped MgB2 [31, 32].

Furthermore, 𝛿ℓ pinning has also been reported in FeTe0.7Se0.3 crystals [33].

6.3 Conclusion

We have studied the flux pinning in optimally doped Ba0.6K0.4Fe2As2 crystal under

hydrostatic pressure, analysing the critical current density determined

experimentally. We propose that strong flux pinning in a wide range of fields can be

achieved by improving the pinning force under pressure. The pressure of 1.2 GPa

improved the Fp by nearly 5 times at 8, 12, 24, and 28 K, which can increase Jc by

nearly two-fold at 4.1 K and five-fold at 16 K and 24 K in both low and high fields,

respectively. This study also demonstrates that such an optimally doped

superconductor’s performance in both low and high fields can also be further

enhanced by pressure.

139

6.4 Experimental

A High quality 122 crystals were grown by using a flux method. The pure elements

Ba, K, Fe, As, and Sn were mixed in a mol ratio of Ba1−xKxFe2As2:Sn = 1:45–50 for

the self-flux. A crucible with a lid was used to reduce the evaporation loss of K as

well as that of As during growth. The crucible was sealed in a quartz ampoule filled

with Ar and loaded into a box furnace [11]. The temperature dependence of the

magnetic moments and the M-H loops at different temperatures and pressures were

measured on a Quantum Design Physical Property Measurement System (QD PPMS

14 T) by using the Vibrating Sample Magnetometer (VSM). We used an HMD high

pressure cell and Daphne 7373 oil as a pressure transmitting medium to apply

hydrostatic pressure on the samples.

140

6.5 References

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2. Shabbir B, Wang X, Ghorbani SR, Wang AF, Dou S, Chen XH. Giant

enhancement in critical current density, up to a hundredfold, in superconducting NaFe0.97Co0.03As single crystals under hydrostatic pressure. Sci Rep 5, 10606 (2015).

3. Shahbazi M, Wang XL, Ionescu M, Ghorbani SR, Dou SX, Choi KY.

Simulation of Light C4+ Ion Irradiation and Its Enhancement to the Critical Current Density in BaFe1.9Ni0.1As2 Single Crystals. Science of Advanced Materials 6, 1650-1654 (2014).

4. Tamegai T, et al. Effects of particle irradiations on vortex states in iron-based

superconductors. Superconduct. Sci. and Technol. 25, 084008 (2012). 5. Kim H, et al. London penetration depth in BaFe1-xTx2As2 superconductors

irradiated with heavy ions. Phys. Rev. B 82, 060518 (2010). 6. Yang P, Lieber CM. Nanorod-Superconductor Composites: A Pathway to

Materials with High Critical Current Densities. Science 273, 1836-1840 (1996).

7. Kerchner HR, Christen DK, Klabunde CE, Sekula ST, Coltman RR. Low-

temperature irradiation study of flux-line pinning in type-II superconductors. Phys. Rev. B 27, 5467-5478 (1983).

8. Brandt EH. Computer simulation of vortex pinning in type II

superconductors. J Low Temp Phys 53, 41-70 (1983). 9. Grigorieva IV, et al. Pinning-Induced Formation of Vortex Clusters and

Giant Vortices in Mesoscopic Superconducting Disks. Phys. Rev. Lett 99, 147003 (2007).

10. Miura M, et al. Strongly enhanced flux pinning in one-step deposition of

BaFe2(As0.66P0.33)2 superconductor films with uniformly dispersed BaZrO3 nanoparticles. Nat Commun 4, (2013).

11. Wang X-L, et al. Very strong intrinsic flux pinning and vortex avalanches in

Ba-122 superconducting single crystals. Phys. Rev. B 82, 024525 (2010). 12. Weiss JD, et al. High intergrain critical current density in fine-grain

(Ba0.6K0.4)Fe2As2 wires and bulks. Nat Mater 11, 682-685 (2012). 13. Fang L, et al. High, magnetic field independent critical currents in

(Ba,K)Fe2As2 crystals. App. Phys. Lett 101, 012601 (2012).

141

14. Katase T, Hiramatsu H, Kamiya T, Hosono H. High Critical Current Density

4 MA/cm2 in Co-Doped BaFe2As2 Epitaxial Films Grown on (La,Sr)(Al,Ta)O3 Substrates without Buffer Layers. App. Phys. Exp. 3, 063101 (2010).

15. Ren C, Wang Z-S, Luo H-Q, Yang H, Shan L, Wen H-H. Evidence for Two

Energy Gaps in Superconducting Ba0.6K0.4Fe2As2 Single Crystals and the Breakdown of the Uemura Plot. Phys. Rev. Lett 101, 257006 (2008).

16. Shahbazi M, Wang XL, Lin ZW, Zhu JG, Dou SX, Choi KY.

Magnetoresistance, critical current density, and magnetic flux pinning mechanism in nickel doped BaFe2As2 single crystals. J. App. Phys. 109, 07E151 (2011).

17. Park E, Hoon Lee N, Nam Kang W, Park T. Pressure effects on the

superconducting thin film Ba1−xKxFe2As2. App. Phys. Lett 101, 042601 (2012).

18. Godeke A. A review of the properties of Nb3Sn and their variation with A15

composition, morphology and strain state. Superconduct. Sci. and Technol. 19, R68 (2006).

19. Cooley LD, Lee PJ, Larbalestier DC. Flux-pinning mechanism of proximity-

coupled planar defects in conventional superconductors: Evidence that magnetic pinning is the dominant pinning mechanism in niobium-titanium alloy. Phys. Rev. B 53, 6638-6652 (1996).

20. Si W, et al. High current superconductivity in FeSe0.5Te0.5-coated conductors

at 30 tesla. Nat Commun 4, 1347 (2013). 21. van der Beek CJ, et al. Vortex pinning: A probe for nanoscale disorder in

iron-based superconductors. Physica B: Condensed Matter 407, 1746-1749 (2012).

22. Halbritter J. Pair weakening and tunnel channels at cuprate interfaces. Phys.

Rev. B 46, 14861-14871 (1992). 23. Tomita T, Schilling JS, Chen L, Veal BW, Claus H. Pressure-induced

enhancement of the critical current density in superconducting YBa2Cu3Oδ bicrystalline rings. Phys. Rev. B 74, 064517 (2006).

24. Browning ND, Buban JP, Nellist PD, Norton DP, Chisholm MF, Pennycook

SJ. The atomic origins of reduced critical currents at [001] tilt grain boundaries in YBa2Cu3O7−δ thin films. Physica C: Superconductivity 294, 183-193 (1998).

25. Tomita T, Schilling JS, Chen L, Veal BW, Claus H. Enhancement of the

Critical Current Density of YBa2Cu3Oδ Superconductors under Hydrostatic Pressure. Phys. Rev. Lett 96, 077001 (2006).

142

26. Kimber SAJ, et al. Similarities between structural distortions under pressure

and chemical doping in superconducting BaFe2As2. Nat Mater 8, 471-475 (2009).

27. Cyrot M. Ginzburg-Landau theory for superconductors. Reports on Progress

in Physics 36, 103 (1973). 28. Djupmyr M, Soltan S, Habermeier HU, Albrecht J. Temperature-dependent

critical currents in superconducting YBa2Cu3O7-δ and ferromagnetic La2/3Ca1/3MnO3 hybrid structures. Phys. Rev. B 80, 184507 (2009).

29. Albrecht J, Djupmyr M, Brück S. Universal temperature scaling of flux line

pinning in high-temperature superconducting thin films. Journal of Physics: Condensed Matter 19, 216211 (2007).

30. Shabbir B, Wang XL, Ghorbani SR, Dou SX, Xiang F. Hydrostatic pressure

induced transition from δTc to δℓ pinning mechanism in MgB2. Superconduct. Sci. and Technol. 28, 055001 (2015).

31. Wang X-L, et al. Enhancement of the in-field Jc of MgB2 via SiCl4 doping.

Phys. Rev. B 81, 224514 (2010). 32. Shahbazi M, Wang XL, Choi KY, Dou SX. Flux pinning mechanism in

BaFe1.9Ni0.1As2 single crystals: Evidence for fluctuation in mean free path induced pinning. App. Phys. Lett 103, 032605 (2013).

33. Bonura M, Giannini E, Viennois R, Senatore C. Temperature and time

scaling of the peak-effect vortex configuration in FeTe0.7Se0.3. Phys. Rev. B 85, 134532 (2012).

143

7 HYDROSTATIC PRESSURE INDUCED TRANSITION FROM 𝜹𝑻𝒄 TO 𝜹𝜹 PINNING MECHANISM IN MgB2

7.1 Introduction

To generalize our hydrostatic pressure technique to other superconducting families,

we have investigated the impact of hydrostatic pressure on Jc and flux pinning

mechanisms in MgB2. Previous studies have shown that pressure of 1 GPa can

reduce Tc, but only by less than 2 K in MgB2 [1]. This is a very insignificant

reduction as compared to the other approaches (i.e. chemical doping and irradiation)

which are mainly used for Jc enhancement [2]. For instance, chemical doping can

significantly enhance Jc in MgB2, but with a considerable degradation of Tc; carbon

doping can reduce Tc from 39 K to nearly as low as 10 K, for carbon content up to

20% [3-8]. Similarly, the irradiation method can improve Jc in MgB2, but it reduces

Tc values significantly (by more than 20 K in some cases) [9-13]. Correspondingly,

the chemical doping and irradiation methods can also change the nature of the

pinning mechanism in MgB2 [10, 14-16]. The determination of Jc and the flux

pinning mechanism under hydrostatic pressure is also an important step to probe the

mechanism of superconductivity in more detail in MgB2. It is very interesting to

know whether hydrostatic pressure can increase the pinning and Jc at both low and

high fields.

Magnesium diboride (MgB2) is a promising superconducting material which can

replace conventional low critical temperature (Tc) superconductors in practical

applications, due to its relatively high Tc of 39 K, strongly linked grains, rich

multiple band structure, low fabrication cost, and especially, its high critical current

density (Jc) values of 105-106 A/cm2 [17-24]. Numerous studies have been carried out

in order to understand the vortex-pinning mechanisms in more detail, which have led

144

to real progress regarding the improvement of Jc. There are two predominant

mechanisms, 𝛿𝑇c pinning, which is associated with spatial fluctuations of the Tc, and

𝛿ℓ pinning, associated with charge carrier mean free path (ℓ) fluctuations [25-29]. In

this chapter, we report our study on pressure effects on Tc, Jc, and the flux pinning

mechanism in MgB2. Hydrostatic pressure can induce a transition from the regime

where pinning is controlled by spatial variation in the critical transition temperature

(𝛿𝑇𝑐) to the regime controlled by spatial variation in the mean free path (δℓ). In

addition, Tc and low field Jc are slightly reduced, although the Jc drops more quickly

at high fields than at ambient pressure. We found that the pressure increases the

anisotropy and reduces the coherence length, resulting in weak interaction of the

vortex cores with the pinning centres.

7.2 Results and Discussion

Figure 7-1: XRD Pattern of MgB2.

Figure 7-1 illustrates XRD patterns for the MgB2 sample. The peaks show that MgB2

sample is a single phase. The zero-field-cooling (ZFC) and field-cooling (FC) curves

at different applied pressures are plotted in figure 1. The Tc drops from 39.7 K at P =

0 GPa to 37.7 K at P = 1.2 GPa, with a pressure coefficient of -1.37 K/GPa, as can be

145

seen in the inset of figure 1. It is well known that Tc, the unit cell volume (V), and the

anisotropy (γ) under pressure can be interrelated through a mathematical relation as

in[30]

∆𝑇𝑐/(𝑃) + ∆𝑉/ + ∆𝛾/ = 0 ………..(1)

where ∆𝑇𝑐/(𝑃) = �𝑇𝑐(𝑃)−𝑇𝑐(0)

𝑇𝑐(0) �, ∆𝑉/ = �𝑉(𝑃)−𝑉(0)𝑉(0) � and ∆𝛾/ = �𝛾(𝑃)−𝛾(0)

𝛾(0)�.

The ∆𝑉/ found for MgB2 is 0.0065, as the pressure can reduce the unit cell volume

of MgB2 from 29.0391 Ǻ3 at P = 0 GPa to 28.8494 Ǻ3 at P ≈ 1.2 GPa [31]. A similar

value for ∆𝑉/ can also be obtained from ∆𝑉/ = −∆𝑃 𝐵⁄ , where B is the bulk

modulus of the material [30]. We found ∆𝑇𝑐/(𝑃) = 0.042 from figure 1. By using ∆𝑉/

and ∆𝑇𝑐/(𝑃), we can obtain from Equation (1):

∆𝛾/ = �𝛾(𝑃)−𝛾(0)𝛾(0)

� ≈ 0.036 ……….(2)

Figure 7-2: Temperature dependence of magnetic moment under different applied pressures in both

ZFC and FC runs. The inset shows the pressure dependence of the Tc for MgB2. Tc is found to decrease with a slope of dTc/dP = -1.37 K/GPa.

This indicates that the anisotropy of MgB2 is increased by applying pressure, 𝑖. 𝑒.,

𝛾(𝑃) > 𝛾(0). Therefore, the coherence length (ξ) at P = 1.2 GPa is reduced as

compared to its value at P = 0 GPa [𝑖. 𝑒. , (𝜉)𝑃 < (𝜉)0]. The density of states in

146

Bardeen-Cooper-Schrieffer (BCS)-like superconductors such as MgB2 is expressed

as

𝑁𝑠(𝐸) = 𝑁𝑛(𝐸𝐹) � 𝐸√𝐸2−∆2

�… … …. (3)

Where Nn(EF) is the density of states at the Fermi level in the normal state and Δ is

the superconductivity gap. Therefore, Ns(E) ∝ Nn(EF) and

𝑁𝑛(𝐸𝐹) ∝ 𝑉𝐸𝐹1/2 ∝ 𝑉𝑘𝐹2 … … ….(4)

where V is the total volume and kF is the Fermi wave vector [32, 33],

𝑘𝐹 = 2𝑚∆𝜉ħ

……….(5)

Combining Equations (3), (4), and (5), we obtain

𝑁𝑠(𝐸) ∝ 𝑉𝜉……….(6)

It is important to mention that pressure has no significant impact on the unit cell

volume of MgB2 up to P = 1.2 GPa. Therefore, the density of states is mainly

dependent on 𝜉. (𝜉)𝑃 < (𝜉)0 leads to a comparison regarding the density of states at

P = 1.2 GPa and P = 0 GPa

i.e. [𝑁𝑠(𝐸)]𝑃 < [𝑁𝑠(𝐸)]0 … … ….(7)

given that hydrostatic pressure can decrease the density of states in MgB2 and

therefore contributes to a reduction in Tc.

Figure 7-3: Field dependence of Jc under different pressures measured at 5 K, 8 K, 20 K, and 25 K.

147

Figure 7-4: Comparison of Jc at two pressures (0 GPa and 1.2 GPa) for 8 K and 20 K curves. The inset shows the plot of ΔJc/Jc0 versus field, illustrating the trend towards the suppression of Jc with

increasing field, nearly at a same rate of ~ -0.97 T-1 for 8 K and 20 K.

Figure 2 shows the field dependence of Jc at different temperatures (i.e. 5, 8, 20, and

25 K) and pressures (i.e. 0, 0.7, and 1.2 GPa). We found that low field Jc was

reduced slightly under pressure. The Jc drops more quickly at high fields, however,

as compared to P = 0 GPa. This is further reflected in figure 3, which shows Jc

values at 8 and 20 K under pressure. The inset shows normalized ΔJc (i.e., ΔJc =

𝐽𝑐𝑃 − 𝐽𝑐𝑜) for both 8 K and 20 K, which indicates almost a similar decay trend. We

also plotted irreversibility field (Hirr) as a function of temperature in figure 4, which

shows that Hirr decreases gradually from nearly 13 T to 11.8 T at T = 5 K for P = 1.2

GPa, which is ascribed to the observed Jc suppression.

148

Figure 7-5: Hirr as a function of temperature.

Jc as a function of reduced temperature (𝜏 = 1 − 𝑇 𝑇c⁄ , where T is the temperature

and Tc is the critical temperature) is plotted in figure 5. The temperature dependence

of Jc follows a power law description in the form of 𝐽𝑐 ∝ 𝜏𝜇 , where 𝜇 is the slope of

the fitted line and its value depends on the magnetic field [34-36]. The exponent 𝜇 in

our case is found to be nearly same at different pressures, and its values are 1.63,

2.22, and 2.65 at fields of 0, 2.5, and 5 T, respectively. Different values of exponent

𝜇 = 1, 1.7, 2, and 2.5 are also reported for standard yttrium barium copper oxide

(YBCO) films [37]. The larger exponent value at high field shows that pressure

effects are more significant at high fields as compared to low fields.

Figure 7-6: Jc as a function of reduced temperature (𝜏 = 1 − 𝑇 𝑇𝑐⁄ ) at 0, 2.5, and 5 T for pressures of

0, 0.7, and 1.2 GPa. The solid lines are fitted well to the data according to the power law in the framework of Ginzburg-Landau theory.

149

Figure 7-7: Double logarithmic plot of –log[Jc(B)/Jc(0)] as a function of field at 12 K and 20 K.

A double logarithmic plot of –log[Jc(B)/Jc(0)] as a function of field at 12 K and 20 K

for P = 0 GPa and P = 1.2 GPa is plotted in figure 6. This shows deviations at certain

fields, denoted as BSB and Bth. According to the collective theory [10], the region

below BSB is the regime where the single-vortex-pinning mechanism governs the

vortex lattice in accordance with the following expression,

𝐵𝑆𝑆 ∝ 𝐽𝑠𝑠𝐵𝑐2 ……….(8)

Where, Jsv is the critical current density in the single vortex pinning regime and Bc2 is

the upper critical field. At high fields (above the crossover field BSB), Jc(B) follows

an exponential law

𝐽𝑐(𝐵) ≈ 𝐽𝑐(0)exp {−(𝐵 𝐵0� )3 2� }………. (9)

Where, B0 represents a normalization parameter on the order of BSB. It is well known

that the deviation observed at BSB is linked to the crossover from the single-vortex-

pinning regime to the small-bundle-pinning regime, while the deviation at the

thermal crossover field (Bth) can be connected to large thermal fluctuations [24]. The

pinning behaviour can be obtained from the temperature dependence of the crossover

150

field from the single vortex regime [38]. The temperature dependence of the

crossover field can be expressed as

𝐵𝑆𝑆(𝑇) = 𝐵𝑆𝑆(0)�1 − 𝑡2

1 + 𝑡2�𝜐

… … … . (10)

Where v = 2/3 and 2 for δTc and 𝛿ℓ, respectively.

The above-mentioned Equation (10) can be found by inserting the following

expressions with t = T/Tc into Equation (8),

𝐽sv ≈ (1 − 𝑡2)7/6(1 + 𝑡2)5/6 : for δTc ……….(11)

and 𝐽sv ≈ (1 − 𝑡2)5/2(1 + 𝑡2)−1/2: for 𝛿ℓ ……….(12)

Figure 7-8: Plots of Bsb(T)/ Bsb(0) vs. T/Tc at different pressures (0, 0.7. and 1.2 GPa). The red fitted line is for δTc pinning, the black fitted line is for 𝛿ℓ pinning, and the green fitted line is for mixed

δ(𝑇c + ℓ) pinning.

151

The crossover fields (BSB) for reduced temperature (T/Tc) at P = 0 GPa, 0.7 GPa, and

1.2 GPa are plotted in figure 7. The experimental data points for BSB are scaled

through Eq. (10) for 𝛿ℓ and δTc. We found that hydrostatic pressure can induce the

transition from the δTc to the 𝛿ℓ pinning mechanism. The δTc pinning mechanism is

dominant in pure MgB2 polycrystalline bulks, thin films, and single crystals [29, 39,

40]. The coherence length is proportional to the mean free path (ℓ) of the carriers,

and therefore, pressure can enhance δℓ pinning in MgB2. It is noteworthy that Jc

drops under pressure in MgB2 due to the transition in the flux pinning mechanism.

7.3 Conclusion

In summary, the impact of hydrostatic pressure on the Jc and the nature of the

pinning mechanism in MgB2, based on the collective theory, have been investigated.

We found that the hydrostatic pressure can induce a transition from the 𝛿𝑇c to the 𝛿ℓ

pinning mechanism. Furthermore, pressure can slightly reduce low field Jc and Tc,

although pressure has a more pronounced effect on Jc at high fields. Moreover, the

pressure can also increase the anisotropy, along with causing reductions in the

coherence length and Hirr, which, in turn, leads to a weak pinning interaction.

152

7.4 Experimental

The MgB2 bulk sample used in the present work was prepared by the diffusion

method. Firstly, crystalline boron powders (99.999%) with particle size of 0.2-2.4

µm were pressed into pellets. They were then put into iron tubes filled with Mg

powder (325 mesh, 99%), and the iron tubes were sealed at both ends. Allowing for

the loss of Mg during sintering, the atomic ratio between Mg and B was 1.2:2. The

sample was sintered at 800°C for 10 h in a quartz tube under flowing high purity

argon gas. Then, the sample was furnace cooled to room temperature. The size of bar

shaped sample used for measurements is 3×2×1 mm3.The temperature dependence of

the magnetic moments and the M-H loops at different temperatures and pressures

were performed on Quantum Design Physical Property Measurement System (PPMS

14T) by using vibrating sample magnetometer (VSM). We used a Quantum Design

High Pressure Cell with Daphne 7373 oil as a pressure transmission medium to apply

hydrostatic pressure on a sample. The Jc was calculated by using the Bean

approximation.

153

7.5 References

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5. Zhuang CG, et al. Significant improvements of the high-field properties of

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CONCLUSION

Hydrostatic pressure is a very effective approach to significantly enhance Jc at

both low and high fields in FeSCs. It also enhances Tc, Hirr, Hc2, and pinning

number density by inducing more point defects, grain connectivity (in case of

polycrystalline bulks and wires/tapes) and reduce the anisotropy. We have used

this approach on polycrystalline bulks, single crystal, tape and MgB2. Details

are as follows;

A. We found that the hydrostatic pressure up to 1.2 GPa can not only

significantly increase Tc from 15 K (underdoped) to 22 K, but also significantly

enhance the irreversibility field, Hirr, by a factor of 4 at 7 K, as well as the

critical current density, Jc, by up to 30 times at both low and high fields for

Sr4V2O6Fe2As2 polycrystalline bulks. It was found that pressure can induce

more point defects, which are mainly responsible for the Jc enhancement. In

addition, pressure can also transform surface pinning to point pinning in

Sr4V2O6Fe2As2.

B. Hydrostatic pressure can significantly enhance Jc in NaFe0.972Co0.028As

single crystals by at least tenfold at low field and more than a hundredfold at

high fields. Significant enhancement in the in-field performance of

NaFe0.972Co0.028As single crystal in terms of pinning force density (Fp) is found

at high pressures. At high fields, the Fp is over 20 and 80 times higher than

under ambient pressure at12K and 14K, respectively, at P=1GPa. We have

discovered that the hydrostatic pressure induces more point pinning centres in a

157

sample, and the pinning centre number density found at 1GPa is almost twice

as high as under ambient pressure at 12K and over six times as high at 14K.

C. We have studied the flux pinning in optimally doped Ba0.6K0.4Fe2As2 crystal

under hydrostatic pressure, analysing the critical current density determined

experimentally. We propose that strong flux pinning in a wide range of fields

can be achieved by improving the pinning force under pressure. The pressure of

1.2 GPa improved the Fp by nearly 5 times at 8, 12, 24, and 28 K, which can

increase Jc by nearly two-fold at 4.1 K and five-fold at 16 K and 24 K in both

low and high fields, respectively. This study also demonstrates that such an

optimally doped superconductor’s performance in both low and high fields can

also be further enhanced by pressure.

D. The impact of hydrostatic pressure up to 1.2 GPa on the Jc and the nature of

the pinning mechanism in MgB2 have been investigated within the framework

of the collective theory. We found that the hydrostatic pressure can induce a

transition from the regime where pinning is controlled by spatial variation in

the critical transition temperature (𝛿𝑇𝑐) to the regime controlled by spatial

variation in the mean free path (δℓ). Furthermore, Tc and low field Jc are

slightly reduced, although the Jc drops more quickly at high fields than at

ambient pressure. The hydrostatic pressure can reduce the density of states

[Ns(E)], which, in turn, leads to a reduction in the critical temperature from

39.7 K at P = 0 GPa to 37.7 K at P = 1.2 GPa.

158

PUBLICATION FROM THIS WORK

1. B. Shabbir et al. Hydrostatic pressure: a very effective approach to significantly

enhance critical current density in granular iron pnictide superconductors. Sci. Rep.

5, 8213 (2015). [Nature Publishing Group IF = 5.09]

2. B. Shabbir, X. L. Wang, S. R. Ghorbani, S. X. Dou and Feixiang Xiang.

Hydrostatic pressure induced transition from 𝜹𝑻𝒄 to 𝜹𝓵 pinning mechanism

in MgB2. SUST-100905.R1 (2015). [IOP Publishing Group IF = 2.8]

3. B. Shabbir, X. L. Wang, S. R. Ghorbani, A. F. Wang, Shixue Dou and X.H.

Chen. Giant enhancement in critical current density, up to a hundredfold, in

superconducting NaFe0.97Co0.03As single crystals under hydrostatic pressure

(Accepted in Nature Scientific Reports). [Nature Publishing Group IF = 5.09]

4. B. Shabbir, X. L. Wang, Y. Ma and Shixue Dou. Observation of strong flux

pinning and possible mechanism for critical current enhancement under

hydrostatic pressure in optimally doped (Ba,K)Fe2As2 single crystals(Under

Review).