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Magnetic and electric response in multiferroic manganitesMufti, Nandang

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Magnetic and Electric Responsein Multiferroic Manganites

COVER: Magnetic field dependence of the capacitance of Tb0.98Ca0.02MnO3 for E‖c and H‖b at

temperatures close to the ferroelectric transition

The work described in this thesis was performed in the group “ Solid State Chemistry” (part of the

Zernike Institute for Advanced Materials) of the University of Groningen, The Netherlands, with

financial support provided by an Ubbo Emmius Scholarship for PhD Research.

PRINTED BY: FACILITAIR BEDRIJF RUG, GRONINGEN. November 2008.

ISBN No: 978-90-367-3673-2

Zernike Institute for Advanced Materials Ph.D. thesis series 2008-28

ISSN 1570-1530

RIJKSUNIVERSITEIT GRONINGEN

Magnetic and Electric Responsein Multiferroic Manganites

Proefschrift

ter verkrijging van het doctoraat in de

Wiskunde en Natuurwetenschappen

aan de Rijksuniversiteit Groningen

op gezag van de

Rector Magnificus, dr. F. Zwarts,

in het openbaar te verdedigen op

vrijdag 5 december 2008

om 11.00 uur

door

Nandang Mufti

geboren op 15 augustus 1972

te Garut, Indonesie

Promotor: Prof. dr. T. T. M. Palstra

Copromotor: Dr. A. A. Nugroho

Beoordelingscommissie: Prof. dr. ir. P. H. M. van Loosdrecht

Prof. dr. D. I. Khomskii

Prof. dr. J. Aarts

To my parents and my wife Rahmatun Nisa

Contents

1 Introduction 1

1.1 Multiferroics, linear magnetoelectrics and magnetodielectrics . . . . . . . . . . . . . 1

1.2 Brief overview of multiferroics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Phase diagram of RMnO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Aims of research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Bibliography 11

2 Experimental techniques 15

2.1 Single crystal preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Feed rod preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.2 Crystal growth in floating zone furnace . . . . . . . . . . . . . . . . . . . . 16

2.2 Structural characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 X-ray powder diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.2 Single crystal X-ray diffraction (SXD) . . . . . . . . . . . . . . . . . . . . 18

2.3 Measurement of physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Magnetization measurements . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 Capacitance measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.3 Pyroelectric current measurements . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Single crystal neutron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Bibliography 23

3 Relaxor ferroelectric behavior in Tb1−xCaxMnO3 25

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

VII

VIII CONTENTS

3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.1 Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.2 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.3 Dielectric properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.5 Neutron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Bibliography 39

4 Magnetic field induced relaxor ferroelectric behavior in Tb1−xCaxMnO3 41

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42



4.3.2 Dielectric properties under magnetic field . . . . . . . . . . . . . . . . . . . 45

4.3.3 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3.4 Neutron diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Bibliography 57

5 Magnetoelectric behavior of multiferroic Eu1−xHoxMnO3 59

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60


5.3.2 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3.3 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.4 Effect of applied magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

CONTENTS IX

Bibliography 73

6 Magneto(di)electric coupling in MCr2O4 (M = Mn, Co, and Ni) spinel 75

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78




6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Bibliography 87

7 Magnetoelectric coupling in MnTiO3 89

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90





7.3.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.4.1 Theoretical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Bibliography 99

Summary 101

Samenvatting 105

Acknowledgments 109

Chapter 1

Introduction

1.1. Multiferroics, linear magnetoelectrics and magnetodielectrics

Functional electronic and magnetic materials form an important part of modern technology. For

example, ferroelectrics (materials with a spontaneous electric polarization that can be switched by

an applied electric field) are widely used as tunable capacitors and form the basis of ferroelectric

random access memory (Fe-RAM) for computers. On the other hand, the materials most widely

used for recording and storing data, such as in the hard drive, are ferromagnetic (materials with

a spontaneous magnetic polarization that can be reversed by a magnetic field). Current technol-

ogy is following a trend towards device miniaturization, which has led to increased interest in the

combination of electronic and magnetic properties in a multifunctional device.Materials in which

ferroelectric and ferromagnetic properties coexist are known as “multiferroic materials”. Multifer-

roic materials are interesting not only because they exhibit ferroelectric and magnetic properties

but also due to the “magnetoelectric effect”, by which an induced electrical polarization and mag-

netization can be controlled by applying a magnetic and electric field, respectively. This effect can

potentially be exploited to allow the construction of novel spintronic devices such as tunnelling mag-

netoresistance (TMR) sensors, spin valves with functionality that is tunable by an electric field [1],

and multi-state memories in which data are written electrically and read magnetically [2]. However,

in order to be useful for applications, the magnetoelectric coupling must be both large and active at

room temperature.

The magnetoelectric effect was first postulated by Pierre Curie in the nineteenth century [3]. In

1959, Dzyaloshinskii predicted this effect in Cr2O3 based on symmetry considerations and Asrov

confirmed this prediction experimentally in 1960 [4–6]. Many investigations of this phenomenon

were carried out in the 1960s and 1970s, predominantly by the two Russian groups of Smolenskii

[7] and Venevtsev [8]. However, due to the weakness of the magnetoelectric coupling in most

1

2 Introduction

materials and the consequent difficulties of using it in applications, research activities in this subject

went into decline for about two decades [6]. The revival of interest in magnetoelectric materials

was initiated by the theoretical investigation of N. Hill in 2000 [9] and by the recent discoveries

of new mechanisms of ferroelectricity in perovskite TbMnO3, hexagonal YMnO3, RMn2O5, and

Ni2V3O8 [10–13]. It was also promoted by the recent developments in thin film growth techniques

and in experimental methods for observing magnetic and electronic domains.

The term “multiferroic” was introduced by Schmid in 1994 to define materials in which two

or three types of ferroic order (ferroelectricity, ferromagnetism and ferroelasticity) occur simulta-

neously in the same phase [14]. Today, the utilization of this term has been expanded to include

materials that exhibit any type of long-range magnetic ordering together with spontaneous polar-

ization. The term “ferroelectromagnets” was previously used to describe the same materials [7].

Another important group of materials are the “linear magnetoelectrics”, very often known as “mag-

netoelectrics”, which possess long-range magnetic ordering but no spontaneous polarization. How-

ever, electrical polarization can be induced by applying a magnetic field. Materials that allow the

linear magnetoelectric (ME) effect can be recognized from their magnetic point group symmetry. In

the Landau expression the general free energy expression describing the ME effect for non-ferroic

materials can be written as [2]:

F(E,H) = F0− 12

ε0εi jEiE j− 12

χ0χi jHiH j−αi jEiH j− 12

βi jkEiH jHk− 12

γi jkH jEiEk + ... (1.1)

Here, ε0 and χ0 are the permittivity and permeability of free space, εi j and χi j are the relative

permittivity and permeability, αi j is the linear magnetoelectric tensor, and βi jk and γi jk are higher-

order magnetoelectric coefficients. If we take the derivative of this free energy with respect to the

electric field (E) then we obtain the polarization (P). If the derivative is taken with respect to the

magnetic field (H) then the magnetization (M) is obtained:

Pi =− ∂F∂Ei

=12

ε0εi jE j +αi jH j +12

βi jkH jHk + ... (1.2)

M j =− ∂F∂H j

=12

χ0χi jHi +αi jEi +12

γi jkEiEk + ... (1.3)

All linear magnetoelectric materials contain the linear term αi jEiH j, but this does not necessarily

mean that they are multiferroic. For example, Cr2O3 is magnetoelectric but not ferroelectric. The

opposite is also true: not all multiferroics are necessarily magnetoelectric. For example, YMnO3 is a

multiferroic that is antiferromagnetic and ferroelectric, but the magnetoelectric effect is not allowed

1.2 Brief overview of multiferroics 3

by symmetry in this compound. However, multiferroics that are ferromagnetic and ferroelectric (fer-

romagnetolectric) are based on their symmetry necessarily magnetoelectric [2, 6, 15]. For example,

magnetoelectric Ni3B7O13I is ferroelectric and a canted antiferromagnet at low temperature [16].

Measurements of the dielectric constant are commonly used in the investigation of ferroelectric

materials. There is always a large anomaly in the temperature dependence of the dielectric constant

at the ferroelectric transition (Tc). Dielectric anomalies have also been observed at the magnetic

transition temperatures (TN) of various materials, such as the linear magnetoelectric Cr2O3 [17],

the multiferroics BaNiF4 [18] and BaMnF4 [19, 20], and materials that are neither linear magne-

toelectrics nor multiferroics such as MnO [21], and MnF2 [22]. The latter material is classified

as “magnetodielectric”. This term was first suggested by Lawes et al. in a study of the coupling

between the dielectric constant and magnetization of ferromagnetic SeCuO3 and antiferromagnetic

TeCuO3 [23]. Both of these compounds show a dielectric anomaly at the magnetic transition and

exhibit the “magnetodielectric effect”, that is, a change of the dielectric constant on application of a

magnetic field. A similar phenomenon has been observed in the quantum paraelectric EuTiO3 [24],

where a change in the dielectric constant of up to ∼ 7% takes place in a magnetic field of 1.5 T.

None of these compounds possess spontaneous polarization and the linear ME effect is not allowed

by symmetry. A schematic picture of the relationship between multiferroic, linear magnetoelectric

and magnetodielectric materials is shown in Figure 1.1.

Cr2O3

Sm2CuO4

TbCoO3

GdVO4

Ho2BaNiO5

BoraciteBiFeO3

TbMnO3

MnWO4

Ni3V2O8

CuOh-RMnO3

SeCuO3, TeCuO3, EuTiO3, TmFeO3, MnO, MnF2

Figure 1.1: Schematic picture of relationship between linear magnetoelectrics, multiferroics, and magnetodi-electrics [25].

1.2. Brief overview of multiferroics

It has proved difficult to discover new intrinsic multiferroic materials because the mechanisms

driving ferroelectricity and ferromagnetism are generally incompatible. Ferroelectricity is usually

generated by transition metal compounds with empty d-shells (d0). For example, in BaTiO3 the

4 Introduction

ferroelectricity is caused by cooperative shifting of the Ti4+ cation along the [111] direction; this

off-centering is stabilized by covalent bonding between the oxygen 2p orbitals and the empty d-shell

of Ti4+ [9]. On the other hand, ferromagnetism usually requires a transition metal with a partially

filled d-shell. Therefore, alternative mechanisms are required to combine these two properties.

An early approach taken by Smolenskii et al. [29] proposed the doping of paramagnetic cations

into known non-magnetic ferroelectric compounds. In the case of perovskites, this gives a B-site

that contains both a cation with an empty d-shell for ferroelectricity and a cation with a partially

filled d-shell for magnetization, for example, Pb(Mn0.5Nb0.5)O3 and Pb(Fe0.5Nb0.5)O3. The result-

ing spontaneous polarization and magnetization in these complex perovskites were similar to the

ferromagnetoelectric properties that were known in the boracites [4, 29]. However, this type of

materials tends to have rather low Curie or Neel temperatures as a result of dilution of the mag-

netic ions. Another mechanism that has been used to combine ferroelectricity and magnetism is

the stereochemical activity of Bi3+ and Pb2+ “lone-pairs” [9]. For example, in BiFeO3 and BiMnO3

ferroelectricity is induced by the 6s lone pair of Bi3+, which causes a shift away from the centrosym-

metric position of the cation with respect to the coordinating oxygen ions [9]. Materials displaying

this type mechanism are known as ”proper ferroelectrics” due to their similarity with BaTiO3, where

the main driving force of the polar state is structural instability with associated electronic pairing.

However, because the ferroelectricity and magnetism in these compounds are generated from dif-

ferent ions, the coupling between them is generally weak [9, 26]. Recent structural studies have

shown that BiMnO3 has a centrosymmetric C2/c structure rather than a non-centrosymmetric C2

structure [27, 28] at room temperature, hence BiMnO3 might be not multiferroic but rather a linear

magnetoelectric material. Another suggestions in the literatures is that this compound could be lo-

cally non-centrosymmetric and globally centrosymmetric, as also proposed for YCrO3 based on pair

distribution function analysis [31, 32].

Recently, various multiferroic materials have been discovered in which a polar state is induced

by different types of ordering; these are known as “improper ferroelectrics”. The magnitude of

polarization in this type of materials is often small, but they often display large magnetoelectric

coupling or are very sensitive to applied magnetic fields. Thus far, the known improper ferroelectrics

can be divided into three categories: geometric ferroelectrics, electronic ferroelectrics and magnetic

ferroelectrics [26].

In geometric ferroelectrics, the mechanism of ferroelectricity does not only involve cooperative

off-center shifts of transition metal cations, but rather a more complex lattice distortion. For example,

in hexagonal RMnO3 ferroelectricity is induced by simultaneous tilting of the MnO5 bipyramids and

buckling of the R-O plane [11]. Another example is BaMF4 (M = Mn, Fe, Co, and Ni), in which the

ferroelectricity originates from alternating rotations of MF6 octahedra in the bc plane accompanied


by displacement of the Ba cations along the c- axis [33].

The concept of electronic ferroelectricity is generally correlated with the concept of charge

ordering. For example, Efremov et al. have predicted that certain divalently doped perovskites

R1−xAxMnO3 that exhibit an intermediate state between site-centered and bond-centered charge or-

dering should be ferroelectric [34]. This should be the case for Pr1−xCaxMnO3 with x between 0.4

and 0.5, but the possible ferroelectricity in this system is difficult to prove due to the rather high

electrical conductivity. Ferroelectricity induced by charge ordering has been observed in LuFe2O4.

The charge ordering of Fe2+ and Fe3+, which lie on a triangular lattice in a bilayer structure, is frus-

trated. The average valence of Fe is 2.5+. Alternating triangular layers contain a mixture of Fe3+

and Fe2+ in the ratio 1:2 and 2:1, and charge transfer between the layers gives rise to the net po-

larization [26, 35]. Another mechanism in this class involves the combination of alternating charge

order and an Ising chain magnet of the ↑↑↓↓ type. Ferroelectricity is produced via exchange striction

associated with competition between nearest-neighbor (NN) ferromagnetic and next-nearest- neigh-

bor (NNN) antiferromagnetic superexchange interactions. Inversion symmetry is broken due to the

presence of shorter interatomic distances between cations with parallel spins and longer distances

between cations with anti-parallel spins, and a net polarization is induced in the chain, as shown in

Figure 1.2. This type of mechanism has recently been observed in Ca3CoMnO6 [36].

Figure 1.2: Polarization induced by the coexistence of charge order and an Ising spin chain of the ↑↑↓↓ type.The cations are shifted away from their centrosymmetric positions by exchange striction [26].

Perhaps the most interesting class of improper ferroelectrics is the magnetic ferroelectrics, in

which the ferroelectricity is induced by magnetic ordering. This category contains the best can-

didates for useful applications, because the polarization is highly tuneable by applied magnetic

fields [26]. Ferroelectricity of this type was reported a long time ago in the spin spiral compound

Cr2BeO4, which has a spontaneous polarization four to six orders of magnitude smaller than that

of normal ferroelectrics [37, 38]. This type of multiferroics became a popular field of research af-

ter the discovery of ferroelectricity in TbMnO3 in 2003 by Kimura et al., which is induced by a

spin-spiral structure on the Mn sublattice. In TbMnO3 the polarization can be rotated by 90 degrees

(a polarization flop) by an external magnetic field applied in a specific direction, which also gives

rise to a large magnetodielectric effect [10, 39]. Based on this strategy, several multiferroics with

6 Introduction

different types of structures have been found in last few years, such as Ni3V2O8 [13], CuFeO2 [40],

Ba0.5Sr1.5Zn2Fe12O22 [41], MnWO4 [42, 43], and CuO [44]. A characteristic feature common to

this type of multiferroics is the presence of competing magnetic interactions (spin frustration). For

example, in RMnO3 (R=Tb, Dy) the competition between ferromagnetic NN and antiferromagnetic

NNN superexchange interactions induces a spiral magnetic structure [39, 47].

Si

Sj

SkS

j

(c)

(b)

Si

js

(a)

Sj

d-orbitals d-orbitals

M1 M2O

eij

Si

SkS

i

Figure 1.3: (a) Microscopic mechanism of spin-induced polarization for the spin current model of Katsura et

al. [56]. Schematic pictures of the change of local electric polarization induced by spin canting in (b) counter-

clockwise and (c) clockwise (CW) spiral structures [59].

The mechanism of magnetically induced ferroelectricity in spin-spiral structures has been stud-

ied using microscopic [56] and phenomenological approaches [55]. The microscopic mechanism

considers a spin current that arises in the presence of two coupled, noncollinear spins (~Js ∝~S1×~S2).

A polarization is induced that is proportional to the vector product of the spin current and the unit

vector (e12) that connects the two magnetic ions: ~P ∝ γ( ~e12×~Js) (see figure 1.3). This effect can

also be described in terms of an inverse Dzyaloshinskii-Moriya (DM) interaction, as proposed by

Sergienko et al. [57]. In this model, two non-collinearly coupled magnetic moments displace the

oxygen atom located between them via an electron-lattice interaction [57]. In the spiral structure

the displacement of the oxygen ion is always in the same direction because the vector product of ~Sn

and ~Sn+1 has the same sign for all pairs of neighboring spins (see Figure 1.3(a)) [26, 59]. When the

exchange between two spins is reversed, the sign of the effect in the asymmetric DM interaction is


also reversed [(~Si×~S j) = -(~S j×~Si)], hence the sign of the electric polarization can be switched by a

reversal of the spin spiral (see Figure 1.3(b) and (c)).

Figure 1.4: (a) The sinusoidal spin structure does not induce polarization. (b) The spiral spin structure, in

which the polarization is orthogonal to both the spin rotation axis e3 and the wave vector Q. This figure is

reproduced from [55].

The phenomenological approach to magnetically induced ferroelectricity considers the symme-

try of electrical and magnetic dipole moments, which are different. In ferroelectrics, dipole moments

are reversed by spatial inversion (i), breaking the symmetry, but are unaffected by time reversal (t).

The opposite is true for magnetic dipoles. The coupling between the static polarization (P) and the

magnetization (M) can only be nonlinear as a result of the interplay of charge, spin, orbital and

lattice degrees of freedom [26]. The coupling described by the biquadratic term -P2M2 is always

allowed by symmetry [26, 55]. This has been demonstrated for example in YMnO3, manifested by

changes in the dielectric constant below the magnetic ordering transition [60]. If the magnetization

has gradient terms then the trilinear coupling term PM∂M is also allowed. This term induces elec-

tric polarization because it is linear in P; in the simplest case of cubic symmetry, the magnetically

induced polarization has the form [55]

P = γχe[(M ·∇)M−M(∇ ·M)] (1.4)

Here, χe is the dielectric susceptibility in the absence of magnetization. The spin-spiral structure

can be described by

M = M1e1cosQ · x+M2e2sinQ · x (1.5)

8 Introduction

Here, e1 and e2 are the unit vectors that form an orthogonal basis and Q is the wave vector of the

spiral. The spin rotation axis is e3 = e1 × e2. Using equation (1.4), the average induced polarization

is orthogonal to both e3 and Q.

~P = γχeM1M2(~e3× ~Q) (1.6)

The magnetically induced polarization depends on the values of M1 and M2. If only one of M1

or M2 is non-zero, the situation corresponds to a collinear, sinusoidal state, where the spins cannot

induce polarization. However, if both M1 and M2 are non-zero, a non-collinear spiral state is formed

that can induce polarization if the spin rotation axis is perpendicular to the wave vector [26, 55].

Another mechanism giving rise to magnetic ferroelectricity involves the so-called E-type mag-

netic ordering, found for example in orthorhombic HoMnO3. In this compound the spin configu-

ration is up-up-down-down along the [110] and [101] directions (Figure 1.5(a)) [53]. The breaking

of inversion symmetry is predicted to occur via exchange striction [54]. In this case, the NN ferro-

magnetic interactions tend to move Mn cations apart from one another while the antiferromagnetic

NNN interactions move the cations closer to each other. This movement is accompanied by the dis-

placement of oxygen in a direction approximately opposite to the shifts of the adjacent Mn-cations

(see Figure (1.5(b)). The polarization induced by this mechanism is predicted to be greater (0.5 - 6

µC/m2) than that in other improper ferroelectrics [54,58]. Polarization in orthorhombic HoMnO3 is

predicted to be found along the a and c directions [58]. However, polarization measurements have

thus far only been reported on polycrystalline samples of HoMnO3, and the magnitude was too small

(P < 2 nC/m2) to support the theoretical prediction [51].

Figure 1.5: (a) The E-type spin configuration of HoMnO3 in the ac plane. (b) The predicted displacement of

Mn (left) and oxygen (right) ions in E-type HoMnO3. This figure is taken from [58].

1.3 Phase diagram of RMnO3 9

1.3. Phase diagram of RMnO3

Rare-earth manganite perovskite oxides have attracted much attention due to various phenom-

ena such as colossal magnetoresistance (CMR), charge ordering, and the more recently discovered

ferroelectricity [10]. Materials with the chemical composition RMnO3 adopt either an orthorhom-

bic perovskite structure or a hexagonal structure; the perovskite structure with space group Pbnm is

favored for R = La-Dy and the hexagonal structure with space group P63cm is favored for R = Ho-

Lu. However, the orthorhombic perovskite structure can also be obtained for the small rare-earths

by heating the corresponding hexagonal compounds under high pressure. [46–49] The structure of

the orthorhombic manganites deviates from that of the ideal cubic perovskite structure due to two

different factors: the so-called GdFeO3 distortion which involves tilting of the MnO6 octahedra, and

Jahn-Teller (JT) distortion in which the octahedra themselves are deformed. The GdMnO3 distor-

tion is generated to compensate for cations with small ionic radius on the rare-earth-site, hence this

distortion increases with decreasing ionic radius. The degree of GdMnO3 distortion can be charac-

terized by the average Mn-O-Mn bond angle [47, 50]. The JT distortion originates from the orbital

degeneracy of the Mn3+ (d4) cation in an octahedral crystal field, where the d-orbitals are split in

energy into t2g and eg levels. The octahedra then have a tendency to distort via shifts of the oxygen

ions, thereby removing the degeneracy of the eg orbitals. The resulting structure is known as the

orbital ordered state, where on a given octahedral site one of the two eg orbitals is preferentially

occupied.

Figure 1.6: (a) Orbital ordering and (b) magnetic transitions in RMnO3 as a function of Mn-O-Mn bond angle.

(c) Magnetic structures of LaMnO3 and HoMnO3. These figures are reproduced from [47].

10 Introduction

This thesis is primarily concerned with the perovskite RMnO3 materials. A phase diagram show-

ing the orbital ordering temperatures and magnetic transitions is shown in Figure 1.6. The magnetic

structure depends on the ionic radius of the rare-earth. When the ionic radius of R is large (La-Sm),

occupied Mn dx2−r2 and dy2−r2 orbitals order in staggered fashion in the ab plane; this gives rise to

strong ferromagnetic (FM) coupling between NN Mn spins in the ab plane and weak antiferromag-

netic (AF) coupling along the c-axis, which corresponds to the so-called A-type AF structure (see

Figure 1.6c). For R cations with small ionic radius, the onset of magnetic ordering initially gives

rise to an incommensurate, sinusoidal structure. The breakdown of the A-type structure is due to an

increased degree of competition between the FM NN and AF NNN superexchange interactions in

the ab plane (see Figure 1.6c) that results from the increased degree of octahedral tilting for small

R cations. For R = Tb and Dy, the incommensurability evolves from a sinusoidal to a spiral con-

figuration with a propagation vector (0, qMn, 0) below a so-called lock-in temperature (Tlock). The

spin spiral structure is directly responsible for inducing ferroelectricity in these compounds [39,47],

as discussed above. Compounds with R = Ho-Lu and Y adopt the E-type AF structure below Tlock,

where the spin order can be described as up-up-down-down in the [110] direction; AF interactions

are retained along the c-axis [48,53]. This phase has also been predicted and recently observed to be

ferroelectric [51, 54]. We focus in this thesis on the spiral magnetic phase because the mechanism

of the ferroelectricity that it induces appears to be more prevalent than that of the E-type materials,

and is also applicable to materials other than manganites.

1.4. Aims of research

The general motivation behind the research in this thesis is to better understand the coupling

between electric and magnetic order parameters in multiferroic and magnetoelectric materials. In

magnetic ferroelectrics there are still aspects of the mechanisms that give rise to ferroelectricity that

are not fully understood. In particular, the factors that determine the strength of the magnetodi-

electric coupling and the sensitivity of the dielectric properties to applied magnetic fields are rather

unclear. Because of their promising properties, in this thesis we focus mainly on multiferroic ma-

terials with spiral magnetic structures and we try to find what parameters can be used to control

the magneto(di)electric coupling in this system. Moreover, we try to understand the mechanism of

magneto(di)electric coupling in linear magnetoelectric materials.

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Chapter 2

Experimental techniques

In this chapter, a brief description is given of the experimental methods and instruments used

in the characterization of the samples in this thesis. All the experiments were performed in our

laboratories except for neutron diffraction, which was carried out at the Hahn-Meitner-Institut (HMI)

in Berlin.

2.1. Single crystal preparation

2.1.1. Feed rod preparation

The single crystals examined in this thesis were grown from feed rods consisting of high-density

polycrystalline material. The preparation of these polycrystalline precursor materials was generally

carried out using solid state reaction. In this method, the stoichiometric raw materials were mixed

and sintered at high temperature for several hours with intermediate grinding. A controlled atmo-

sphere was required in some cases. The sintering temperature was chosen based on information

from the relevant phase diagram. It is also important to consider both the mixing process and the

grinding process, where a small, evenly distributed particle size will promote the diffusion of reac-

tants. The powder obtained after the sintering process was analyzed by X-ray diffraction to check for

impurities. Once a single-phase sample of the desired product was obtained, it was placed inside a

rubber tube (diameter∼ 7 mm, length∼ 130 mm), which was evacuated for several hours before the

powder was compressed using hydrostatic pressure at∼ 600 bar. Before compression it is important

to check that the rubber tube does not leak and that the diameter of the rod is uniform. The dense,

compressed rod is brittle and therefore care must be taken when removing the rubber from the rod.

In order to increase the density of the rod further, it was sintered at high temperature for several

hours either in a standard furnace or inside the floating zone furnace used to grow the crystals. For

15

16 Experimental techniques

sintering in the floating zone furnace, the rod was moved up or down with a translation speed of

10-20 mm/h and a rotation speed of around 5 rpm.

2.1.2. Crystal growth in floating zone furnace

Figure 2.1: (a) Layout of the four-mirror optical floating zone furnace FZ-T-10000-H-VI-VP (Crystal Systems

Corp.) and (b) The schematic of traveling solvent floating zone technique.

All of the single crystals investigated in this thesis were grown using the traveling solvent floating

zone (TSFZ) method. A commercial system supplied by Crystal Systems Corp. of the type FZ-T-

10000-H-VI-VP (see Figure 2.1) was used [1]. The furnace consists of four ellipsoidal mirrors,

equipped with a halogen lamp at the center of each mirror. The radiation from the lamps is focused

at the point where the feed rod is melted, allowing crystal growth to take place. Focusing is important

because it allows the crystal growth process to proceed in stable fashion. In this model of furnace,

lamps with a maximum power of 150, 300, 500, 1000, and 1500 W can be chosen, depending on the

melting point of the sample. Lower power lamps provide a better and sharper focus, but for flexible

crystal growth lamps with a power of 1000 W or 1500 W are commonly chosen due to the wide

range of temperatures accessible (maximum ∼ 2200◦C). High temperatures are required to grow

crystals in the rare-earth manganite and vanadate systems. The principle of the TSFZ technique is

to melt a small section of the high density, uniform feed rod by the radiation of infrared light that

has been focused on the section by means of mirrors. The resulting molten (floating) zone is then

translated along the length of the feed rod by moving the mirror upwards (see Figure 2.1). The

single crystal is grown as the end of the floating zone solidifies on a seed rod, which should be a

2.2 Structural characterization 17

material with a similar crystal structure to that of the feed rod. The growth speed (movement of the

mirror) can be varied between 0.18 and 18 mm/h. Moreover, the shaft holding the feed and seed

rods can be simultaneously or separately translated at rates of 0.18-35 mm/h. In order to stabilize

the molten zone, the feed and seed rods are rotated in opposite directions at a maximum rate of 70

rpm. The temperature and volume of the molten zone is controlled by the dc-power supply of the

lamps. A Eurotherm controller allows the power to be automatically increased or decreased to the

desired set-point at a constant rate. The crystal growth process takes place inside a sealed quartz

tube. Therefore, crystal growth can be carried out in vacuum, air, pure O2, N2, and Ar, or a mixture

of these gases. The pressure of the gases can be increased to a maximum of 10 atm. A CCD camera

is installed in order to monitor the growth process on a CRT monitor. We placed an additional camera

to record and monitor the growth process remotely via the internet.

The advantages of the TSFZ method compared to other zone-melting techniques such as the

Bridgeman and Czochralski methods are the absence of any possible contamination from a crucible,

the high controllability of the process, and the large size of the single crystals obtained. However,

there are several parameters that must be considered in order to increase the degree of success of

the single crystal growth. First, the chemical properties of the material being grown are important;

the phase diagram is important to determine the expected composition of the material, as well as the

solvent. Moreover, knowledge of the phase diagram is essential to determine whether the compound

melts congruently or incongruently. Second, the feed and seed rods should both be of good quality,

free of impurities, straight and of high density. The seed rod can be taken from part of the feed rod,

can be a single crystal or polycrystalline sample from a previous synthesis, or can be a single crystal

or polycrystalline sample of a similar compound. A single-crystal seed rod is better than a polycrys-

talline one. Third, selection of the optimal growth environment is important, such as atmosphere

and pressure. Fourth, the molten zone must be controlled, including the speed of translation, rota-

tion, and heating power. Finally, the experience and patience of the crystal grower has a significant

influence.

2.2. Structural characterization

2.2.1. X-ray powder diffraction

X-ray powder diffraction (XRPD) is a fast and reliable tool for the routine identification of solid

materials and for crystal structure refinement. In laboratory systems, X-rays are generated when

high-energy electrons collide with a metal target within a sealed tube that is under vacuum. The


source of electrons is a tungsten filament that is connected to a high voltage transformer. The wave-

length of the X-rays produced is characteristic of the metal target. The X-rays are collimated and

directed onto the sample, which has been ground to a fine powder. The diffracted beam is detected

and then processed electronically to give a count rate as a function of diffraction angle. In this

study, the XRPD measurements were carried out using Bruker D8 and Huber G670 diffractometers.

The Bruker D8 diffractometer operates using Bragg-Brentano geometry, Cu Kα radiation and an

energy-dispersive solid-state detector. This setup was used both for routine phase analysis and for

crystal structure refinement. Typical scans for phase analysis were carried out with a step-width of

0.02 degrees (2Θ) and with a counting time of 1 second per step; the data were examined using the

Powdercell software. For structural refinement typical scans were performed with a step-width of

0.02 degrees (2Θ) and a counting time of 7 seconds per step; the data were analyzed using the GSAS

software package with the EXPGUI interface [2, 3]. The Huber G670 diffractometer was used to

collect variable temperature XRPD data. This setup uses Mo Kα radiation and a G670 Guinier cam-

era comprised of a curved imaging plate as a replacement for photographic film. The linear detector

allows rapid data collection. Measurement at low temperature was performed using a closed-cycle

refrigerator system supplied by Helix Technology Corporation (8200 compressor). The diffraction

patterns cover an angular range from 0 to 100 degrees 2Θ with data at intervals of 0.005 degrees 2Θ.

An exposure time of 30 minutes was used for each measurement.

2.2.2. Single crystal X-ray diffraction (SXD)

Two single-crystal X-ray diffractometers were used: a Bruker AXS APEX and an Enraf-Nonius

CAD4. The Bruker APEX is a 3-circle diffractometer operating with Mo Kα radiation and equipped

with a CCD detector. The three circles refer to the three angles χ , φ and ω that define the relationship

between the crystal lattice plane, the incident beam and the detector. The sample is mounted on a

thin glass fiber that is attached to a brass pin and mounted on a goniometer head. Adjustment of the

goniometer head in the X, Y and Z orthogonal directions allows centering of the crystal in the X-ray

beam. The diffraction data were analyzed using the SHELXL package for least-squares refinements

and the PLATON package for checking the structural solution. The measurements and data analysis

were carried out by Auke Meetsma. The Enraf- Nonius CAD4 diffractometer was routinely used to

orient single crystals for various physical measurements. This 4-circle diffractometer operates with

Mo Kα radiation and a scintillation detector. This point detector measures just a single reflection at

a time, hence data collection for structural refinement normally takes several days with this setup,

much longer than with the Bruker APEX. However, for the orientation of a crystal 25 reflections

were sufficient, requiring a measurement time of only 2 hours.

2.3 Measurement of physical properties 19

2.3. Measurement of physical properties

2.3.1. Magnetization measurements

All of the magnetization measurements described in this thesis were performed using a Quantum

Design MPMS7 magnetometer. This system is equipped with a SQUID (superconducting quantum

interference device), which is a very sensitive device for measuring magnetic fields and is based on

superconducting loops containing Josephson junctions. The basic components of a SQUID magne-

tometer typically consist of the following: a superconducting magnet, a superconducting detection

coil (pick-up coil), a SQUID and a superconducting magnetic shield. The magnetic signal of the

sample is obtained via the superconducting pick-up coil which is connected to the SQUID device,

located away from the sample in a liquid helium bath. This device acts as a magnetic flux-to-voltage

converter. When the sample is moved up and down it produces an alternating magnetic flux in the

pick-up coil which leads to an alternating output voltage in the SQUID device. This voltage is then

amplified and read out by the magnetometer electronics. The output signal is proportional to the

magnetic moment of the sample which can be magnetized by a magnetic field produced by the su-

perconducting magnet. The MPMS7 operates at temperatures between 2 and 400K and at magnetic

fields of up to 7 T. The sensitivity of the magnetometer is 10−7 emu in reciprocating sample oscilla-

tion mode. The sample was inserted into a gelatin capsule, which has a weak diamagnetic signal. In

order to avoid movement of the sample during the measurement, the capsule was filled with cotton.

For samples with a strong magnetic moment such as TbMnO3, GE varnish was used to glue the

sample to the capsule. The capsule was then placed in a plastic straw and attached to the MPMS

sample probe using tape. It is important to check that the straw is attached properly so that it does

not break loose during the measurement. The samples were measured in a particular magnetic field

after cooling either in the absence of a magnetic field (zero-field cooled, ZFC) or in the measurement

field (field-cooled, FC).

2.3.2. Capacitance measurements

Capacitance is the ability to store electrical charge. The capacitance of a sample is the amount

of charge (Q) that can be stored divided by the applied voltage (V).

C =QV

(2.1)

The SI unit of capacitance is the farad, which corresponds to the storage of one coulomb of

charge when one volt is applied across the plates of the capacitor. The capacitance in parallel ge-

ometry is defined as C = ε0 ε(A/d), where ε0 is the permittivity of a vacuum (8.85×10−12 F/m) , ε


is the dielectric constant, A is the area of the capacitor and d is the separation distance between the

two conductive electrode plates. The dielectric constant is dimensionless. The capacitance measure-

ments were performed using a capacitance bridge (Andeen -Hagerling 2500 A) at a frequency of 1

kHz and using an Agilent LCR Meter 4284A for frequencies between 20 Hz and 1 MHz. The sample

was attached to a home-made probe which contains four triax connectors on the flange, connected to

stainless-steel coaxial wires below the flange. The inner parts of the triax connectors are connected

to the sample holder at the bottom of the probe, whereas the shields of the triax connectors are con-

nected to a copper block at the bottom of the sample holder. This probe is inserted into a Quantum

Design PPMS (Physical Properties Measurement System) model 6000. The PPMS can be operated

at temperatures between 1.8 K and 375 K and at magnetic fields between -9T and 9T. A LabView

program was developed to control the measurement and collect the data.

2.3.3. Pyroelectric current measurements

Pyroelectricity is the ability of certain materials to generate an electrical current in response to a

change in temperature. The pyroelectric effect occurs in certain classes of materials that have polar

point-group symmetry. Only 10 of the 32 point groups are polar: the triclinic group 1, the monoclinic

groups 2 and m, the orthorhombic group mm2, the trigonal groups 3 and 3m, the tetragonal groups

4 and 4mm, and the hexagonal groups 6 and 6mm [4]. In an ionic pyroelectric crystal, the positions

of the ions shift with changing temperature, giving rise to the generation of a net dipole moment and

a polarization current within the lattice. When the temperature stops changing and reaches a steady

state, the ionic shifts stop and the polarization current becomes zero. In general, a pyroelectric

material has many domains in which the spontaneous polarizations are randomly oriented. The

application of an external electric field above the Curie temperature, followed by cooling to low

temperature, can align the net dipole moments of these individual domains along a preferred polar

axis, a process known as poling. The surface of the poled material develops a polarization charge

that is temperature dependent. If electrodes are applied to the surface, this charge can be detected as

current. This current is proportional to the rate of change of temperature:

I = p(T )A∂T/∂ t (2.2)

Here, I is the current, A is the the surface area of the electrodes on the sample, ∂T/∂ t is the

rate of change of temperature with respect to time, and p(T) is defined as the pyroelectric coeffi-

cient at temperature T [5]. The pyroelectric coefficient is also defined as the rate of change of the

spontaneous polarization vector with respect to temperature:

p(T ) =∂Ps∂T

(2.3)

2.4 Single crystal neutron diffraction 21

If we combine equations 2.1 and 2.2 we obtain:

Ps =∫ I

A∂ t (2.4)

Therefore, by integrating the current density (I/A) with respect to time, the spontaneous polar-

ization (Ps) can be determined.

We used a Keithley 387 electrometer to pole the samples and a Keithley 6517 A electrometer to

measure the pyroelectric current. A LabView program was developed to control the experimental

parameters and to collect the data. The set-up and sample preparation were the same as those in the

capacitance measurements. The procedure for the pyroelectric current measurements was as follows.

First, the sample was poled from a temperature above the transition at which it becomes pyroelectric

or polar to the temperature from which the measurement was started. For magnetoelectric materials

a magnetic field was applied together with the electric field in order to obtain a single-domain state at

low temperature. The electric field was then removed and the top and bottom electrodes were shorted

in order to remove the surface charge built up during the poling process. The sample was heated

at a well-defined rate. The spontaneous polarization was obtained by integrating the pyroelectric

current with respect to time. The spontaneous polarization vanishes above the pyroelectric transition

temperature.

2.4. Single crystal neutron diffraction

Neutron diffraction is used to determine both the crystal and magnetic structures of materials.

In principle this technique is analogous to X-ray diffraction but neutrons interact with matter in a

different fashion. X-rays interact with the electron cloud surrounding each atom, hence stronger

diffraction is obtained for atoms with large atomic number (Z) than with small Z. In contrast, neu-

trons interact with the nucleus and there is no systematic dependence of the interaction on Z. The

two techniques give complementary structural information. An additional property of neutrons is

that they carry a spin, and therefore interact with magnetic moments, including those arising from

unpaired electrons in magnetic materials. Consequently, neutron diffraction can be used to deter-

mine the magnetic structure of a material. Single crystal neutron diffraction experiments were car-

ried out at the Berlin Neutron Scattering Center (BENSC) using the double-axis E4 instrument. This

instrument uses pyrolitic graphite monochromator crystals (oriented along 002) giving a neutron

wavelength of 0.244 nm. The detector is a single tube filled with 3He gas. For measurements in zero

magnetic field the sample was wrapped in aluminum foil and placed in a standard orange cryostat.

The aluminum foil gave rise to extra reflections, which sometimes overlapped with magnetic reflec-

tions from the sample. For measurements under magnetic field, a horizontal magnet cryostat (HM1,


manufactured by RMC Cryosystems) was used. This cryostat can operate in the temperature range

1.5 K to 300 K and at magnetic fields of up to 6T applied in the horizontal plane. The crystal was

oriented before mounting in the cryomagnet so that the field could be applied along the b-axis. The

main difficulty in this experiment was to find the magnetic reflections of interest; large volumes of

reciprocal space were blocked by the magnet and the tilt of the cryomagnet was limited to only a

few degrees out of the horizontal plane. Data analysis was carried out using the LAMP program [6].

Bibliography

[1] Manual of the four-mirror image furnace, Crystal Systems Corp., model FZ-T-10000-H-VI-VP.

[2] A.C. Larson and R.B. Von Dreele, “General Structure Analysis System (GSAS)”, Los Alamos

National Laboratory Report LAUR 86-748 (2000).

[3] B. H. Toby, EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst. 34, 210-213 (2001).

[4] International Tables for Crystallography, Vol. D, Physical Properties of Crystals, Edited by A.

Authier, Kluwer Academic Publishers (2003).

[5] S. Dutta, R. N. P. Choudhary and P. K. Sinha, J. Mater. Sci. 39, 3129-3135 (2004).

[6] D. Richard, M. Ferrand, and G.J. Kearley, J. Neutron Res.4, 33-39 (1996).

23

Chapter 3

Relaxor ferroelectric behavior in

Tb1−xCaxMnO3

3.1. Introduction

The rare-earth manganites RMnO3, with R = Gd, Tb and Dy, exhibit a new type of ferroelectricity

induced by a magnetic spiral structure. [1–5] They first develop incommensurate sinusoidal antifer-

romagnetic order below about 40 K. The incommensurability continuously changes upon cooling

and becomes almost constant below the “lock-in” temperature Tlock ' 28 K and ' 19 K for R =

Tb and Dy, respectively. For R = Gd a sudden drop of the incommensurability vector is observed

below Tlock ' 23 K [3, 6–8]. The transition to this long-wavelength incommensurate antiferromag-

netic phase for R = Tb and Dy is accompanied by ferroelectric ordering with a spontaneous electric

polarization P‖c. The polarization flops to P‖a when a magnetic field above a critical value is ap-

plied along the a or b direction, while it is suppressed for large fields applied along the c direction.

In contrast, for R = Gd a polarization (P‖a) is only observed for magnetic fields greater than 1 T

applied along the b-axis [3]. Recently, the polarization has been reversed in TbMnO3 by rotating the

direction of the magnetic field in the ab-plane; the 4f moment was found to play an important role in

the polarization flop [12]. The origin of the ferroelectric state in TbMnO3 is based on the existence

of a spiral magnetic structure below Tlock, which breaks both time-reversal and inversion symmetry.

It has been described theoretically by microscopic [9] and Landau phenomenological models [5].

Both approaches show that the direction of the polarization is perpendicular to the spin rotation axis

and the wave vector of the magnetic spiral. An associated lattice distortion with a doubled wave vec-

tor develops together with the Mn-spiral. A recent structural investigation of DyMnO3 has shown

that a further lattice distortion develops below the Dy-spin ordering temperature; it originates from

25

26 Relaxor ferroelectric behavior in Tb1−xCaxMnO3

coupling between the rare-earth and Mn magnetic moments, which shows that the rare-earth sub-

lattice should also be taken into account to understand the multiferroic properties [10]. The effects

of doping the rare-earth site with a divalent cation such as Ca, Sr and Ba on the spin, charge and

orbital degrees of freedom in RMnO3 have been extensively investigated. However, most studies

have focused on large doping; in particular, the consequences of introducing charge carriers for the

ferroelectric properties of R1−xAxMnO3 for x less than 10% (R = Gd, Tb, Dy) have not yet been ex-

plored. Therefore, we have synthesized single crystals of Tb1−xCaxMnO3 with nominal x = 0, 0.02,

0.05 and 0.1, and investigated their magnetic, structural and electric properties. We find that both the

ferroelectric ordering temperature and the magnitude of the spontaneous polarization are suppressed

with increasing Ca concentration. Our data indicate that Ca doping destroys the ferroelectric state

as well as the spiral magnetic structure via an intermediate state that resembles a relaxor ferroelec-

tric. We present a magnetic-electric phase diagram for Ca-doped TbMnO3 in terms of the perovskite

tolerance factor.

3.2. Experimental

Single-crystalline samples of Tb1−xCaxMnO3 with nominal values of x = 0, 0.02, 0.05 and

0.1 were grown by the floating zone method using a four-mirror furnace (Crystal Systems Corp.,

FZT-10000-H-VI-VP). To make the feed rod for crystal growth, stoichiometric amounts of Tb4O7,

CaCO3, and a 1% excess of MnO2 were mixed, ground, calcined at 1000◦C and sintered at 1200◦C

in air for 36 hours with intermediate grindings. The mixture was then compressed hydrostatically

at 600 bar in a rubber tube into a rod of diameter 7 mm and length 50 mm. This rod was heated in

air at 1400◦C for 12 hours. The crystal growth rate was between 1.5 and 5 mm/h and was carried

out in air. The seed and feed rods were counter-rotated at a speed of 15-20 rpm. The crystallinity

of the sample was checked by Laue diffraction and cut crystal pieces were oriented using an Enraf-

Nonius CAD4 single crystal diffractometer. X-ray powder diffraction (XRPD) at room temperature

was performed using a Bruker D8 diffractometer. Temperature-dependent XRPD was performed on

crushed single-crystal pieces using a Huber diffractometer equipped with a G670 Guinier camera

and a closed-cycle refrigerator. The magnetic properties were measured using a Quantum Design

MPMS-7 SQUID magnetometer. The dielectric constant was measured using an Agilent 4284A

LCR meter in combination with a Quantum Design Physical Properties Measurement System. For

polarization measurements, the samples were cooled in a poling electric field of (∼ 150 V/mm).

After poling, the polarization was determined by integrating the pyroelectric current. Changing the

sign of the poling field resulted in a change of sign of the pyroelectric current, proving the ferro-

electric nature of our samples. Single crystal neutron diffraction experiments were carried out at the

3.3 Experimental results 27

Berlin Neutron Scattering Center (BENSC) using the double-axis E4 instrument. Single crystals of

approximate size 5 × 5 mm were oriented with the bc plane in the scattering plane. Cooling was

achieved using a standard orange cryostat.

3.3. Experimental results

3.3.1. Structural properties

20 30 40 50

0

10

20

2 2

0

1 1

2

0 0

41 1

1

0 2

0

2 0

0

x= 0.05

x= 0.1

x= 0.02

Inte

nsity

(103 a

.u)

2 theta

x= 0

Tb1-xCaxMnO3

0 0

2

Figure 3.1: XRD patterns of crushed Tb1−xCaxMnO3 single crystals measured at room temperature.

The XRPD patterns of crushed Tb1−xCaxMnO3 single crystals collected at room temperature

are shown in Figure 3.1, which shows that the samples are single phase. The diffraction peaks

could be indexed in orthorhombic unit cells with spacegroup Pbnm. The unit cell parameters are

summarized in Table 3.1. The lattice parameters of TbMnO3 are in good agreement with those

previously reported [16]. All of the samples show large orthorhombic distortions, indicated by a

large ratio b/a. This distortion is due to tilting and rotation of the MnO6 octahedra caused by the size

mismatch between the Tb3+ and Mn3+ ions. The doping of Ca on the Tb site produces a decrease of

the b-parameter and almost no change in the a-parameter; as a consequence, the ratio b/a decreases.


Figure 3.2 shows the lattice parameters as function of Ca content, where the c parameter is divided

by a factor of√

2. It is clear that the lattice parameters of all the samples follow the relationship

c√

2 < a < b , which corresponds to the O’ - type orthorhombic structure [11].

Tb1−xCaxMnO3 x = 0 x = 0.02 x = 0.05 x = 0.1a (A) 5.29969(9) 5.30062(7) 5.30157(7) 5.30508(9)b (A) 5.84236(9) 5.82385(8) 5.79856(7) 5.76155(10)c (A) 7.40147(12) 7.40846(10) 7.41625(9) 7.42937(13)V (A3) 229.169(9) 228.700(7) 227.987(6) 227.082(6)Rwp 0.075 0.111 0.079 0.10Rp 0.059 0.085 0.070 0.080χ2 1.41 1.93 1.44 2.6

Table 3.1: Lattice parameters and fit parameters for the refinement of Tb1−xCaxMnO3 in the orthorhombicPbnm space group from XRPD data at room temperature

Figure 3.2: Lattice parameters of Tb1−xCaxMnO3 as a function of Ca content at room temperature.

Figure 3.3 shows the temperature dependence of the lattice parameters of Tb1−xCaxMnO3 with

x = 0, 0.02, 0.05 and 0.1 obtained from XRPD on crushed single crystals. The diffraction patterns

were consistent with space group Pbnm at all temperatures; although the lattice is known to become

incommensurate below TN [3, 4, 6], no additional satellite peaks were observed and thus the lattice

parameters are those of the average structure. The a-axis shows almost no dependence on doping

below 50 K, whereas the c-axis increases slightly with increasing Ca-content. In contrast, the b

lattice parameter rapidly decreases. TbMnO3 has a strongly distorted orthorhombic structure due

to the size mismatch between Tb3+ and Mn3+, manifested by the large differences between the

a and b lattice parameters. This type of distortion is also correlated with the magnitude of the

Jahn-Teller distortion of Mn3+ in the MnO6 octahedra [6, 16]. With increasing Ca-content, both

the orthorhombic and octahedral distortion decrease, giving rise to a rapid decrease in the b-lattice


parameter [16]. We also observe a distinct discontinuity in the lattice parameters of our x = 0 sample

at TC ∼26 K, which becomes continuous after doping. The temperature at which the discontinuity

occurs coincides with the ferroelectric transition temperature. The largest discontinuity is along the

c axis, which is the direction of the spontaneous polarization. These discontinuities are qualitatively

comparable with the anomalies in the thermal expansion at Tlock reported by Meier et al. [13] This

implies that there is strong coupling between the ferroelectricity and the lattice structure.

Figure 3.3: Temperature dependence of the lattice parameters and volume of crushed single crystals of

Tb1−xCaxMnO3. The inset shows the detailed thermal evolution of the c-axis.

3.3.2. Magnetic properties

Figure 3.4 shows the temperature dependence of the magnetic susceptibility χ(T ) between 5 and

300 K for Tb1−xCaxMnO3 single crystals measured in an applied magnetic field of H = 0.5 T for

all three crystallographic directions. Measurements were carried out under both zero-field cooled

(ZFC) and field cooled (FC) conditions. The magnetic susceptibility of the samples shows strong

anisotropy at all temperatures, decreasing in the order H‖a > H‖b > H‖c. The large magnetic

anisotropy primarily originates from the large spin-orbit coupling of the Tb3+ moment [3]. Kimura

et al. have previously reported that the magnetization and specific heat of TbMnO3 show anomalies

at 42 K, 27 K and 7 K, which correspond to Mn spin ordering, the onset of ferroelectricity, and Tb

spin ordering, respectively [2, 6]. However, it has not been reported for which directions of applied

field the anomalies exist. Our observation is that anomalies in the magnetic susceptibility only exist


for H‖c; we did not observe any anomalies for H‖a and H‖b, which might be caused by the strong

effect of the Tb moment in both directions. For x = 0.1 the ZFC and FC magnetic susceptibilities

for H‖c diverge below TN , which is typical for spin-glass-like behavior. This can be ascribed to

the existence of ferromagnetic clusters. It is well known that the mixed-valent state containing

Mn3+ and Mn4+ yields ferromagnetic interactions via the double-exchange (DE) mechanism. If the

Mn4+ concentration is low, long-range ferromagnetic order is not achieved. Similar behavior was

previously reported for Tb0.85Ca0.15MnO3 [16].

Figure 3.4: Temperature dependence of the magnetic susceptibility of Tb1−xCaxMnO3 for all three crystallo-

graphic axes: (a) x = 0, (b) x = 0.05, and (c) x = 0.1.


0 10 20 30 40 50-1.0

-0.5

0.0

0.5

x= 0.02

x= 0.05

x= 0.1

d/d

T (1

0-2)

Temperature (K)

x= 0

H//c

0 10 20 30 40 500.06

0.08

0.10

0.12

0.14

x= 0.05

x= 0.02

x= 0

(em

u/m

ol)

Temperature (K)

H//c

x= 0.1

Figure 3.5: Temperature dependence of zero-field cooled magnetic susceptibility (a) and derivative magnetic

susceptibility (b) of Tb1−xCaxMnO3 for H‖c. The down and up arrows indicate the antiferromagnetic ordering

(TN ) and ferroelectric transition (Tlock) temperatures, respectively.

In order to study the effect of increasing the Ca content on the magnetic transition, we carried

out further measurements of the low-temperature magnetic susceptibility with 0.25 K steps for a

magnetic field of 100 Oe applied parallel to the c-direction. The measured susceptibility and its

derivative are shown in Fig. 3.5. Anomalies corresponding to Mn spin ordering are apparent at TN =

41 K for x = 0 and x = 0.02 , while TN decreases slightly to ∼ 39 K for x = 0.05 and then decreases

further to ∼ 32 K for x = 0.1. The increase in the magnitude of the susceptibility in the x = 0.1

sample suggests that there is an enhancement in the ferromagnetic interactions. The dependence

of the ferroelectric transition temperature (Tlock) on Ca content is more interesting; Tlock rapidly

decreases from ∼ 26 K for x = 0 to ∼ 21 K for x = 0.02, and the transition becomes broadened at ∼15 K for x = 0.05. We will discuss these phenomena later.


3.3.3. Dielectric properties

Figure 3.6: Temperature dependence of the dielectric constant of Tb1−xCaxMnO3 for E‖a at different frequen-

cies.

The temperature dependence of the dielectric constant of Tb1−xCaxMnO3 for E‖a is shown in

Figure 3.6. The behavior of the dielectric constant of undoped TbMnO3 for E‖a is similar to that

reported by Kimura et al. [2,3], where it increases below TN and then slightly decreases below Tlock.

We observe small anomalies at Tlock ∼ 26 K for x = 0 and ∼ 21 K for x = 0.02. For x = 0.05, no

anomaly is visible. For x = 0.1 the dielectric constant decreases steadily with decreasing temperature.

In general, increasing Ca content leads to a decrease in the magnitude of the dielectric constant at all

temperatures below TN . The dielectric constant shows little dependence on frequency.

Figure 3.7 shows the temperature dependence of the dielectric constant of Tb1−xCaxMnO3 for

E‖b. Only measurements at a frequency of 1 kHz are shown, because there was again essentially no

frequency dependence. The dielectric constant for all samples decreases gradually with decreasing

temperature; small anomalies at Tlock are observed for x = 0 and x = 0.02, while no anomalies are

apparent for x = 0.05 and x = 0.01. The magnitude of the dielectric constant is smaller than for E‖a.

In contrast to the measurements of ε‖a and ε‖b, the temperature dependence of the dielectric

constant measured parallel to the c-axis shows significant frequency dependence below TN (Figure

3.8). This type of dispersion was previously observed by Goto et al., who suggested that it is cor-

related with the presence of dynamical localized charge carriers (polaron hopping mechanism) [7].


Figure 3.7: Temperature dependence of dielectric constant of Tb1−xCaxMnO3 for E‖b at 1 kHz.

Figure 3.8: Temperature dependence of the dielectric constant of Tb1−xCaxMnO3 for E‖c at different frequen-cies.


Increasing Ca content shifts this dielectric relaxation to lower temperatures and the dispersion essen-

tially vanishes at x = 0.05. Sharp peaks are observed at Tlock ∼ 26 K for x = 0 and Tlock ∼ 21 K for x

= 0.02, which correspond to the ferroelectric transition. These peaks are frequency independent. In

contrast, for x = 0.05 the peak becomes broader and is slightly shifted to higher temperature as the

frequency increases. These are general features of relaxor ferroelectric-type behavior, which will be

discussed later.

3.3.4. Polarization

0 10 20 30 40 500

200

400

600

x= 0.1

x= 0.02

x= 0.05

P c (m

C/m

2 )

P//cx= 0

Temperature (K)0 10 20 30 40 50

0

200

400

600

X= 0.1

X= 0X= 0.05

Pa (

mC

/m2 )

P//a

Temperature (K)

X= 0.02

Figure 3.9: Temperature dependence of the spontaneous polarization of Tb1−xCaxMnO3 along (a) the a-axis

and (b) the c-axis.

We carried out measurements of the electric polarization in order to prove that our Tb1−xCaxMnO3

samples were ferroelectric. The polarization was obtained by integrating the pyroelectric current, as

described in Chapter 2. It is well known that the polarization of undoped TbMnO3 is along the c-axis

and originates from the spiral magnetic structure. The direction of the polarization induced by such

a spiral structure should be perpendicular to both the magnetic easy axis and the spin propagation

vector [5, 9]. In the case of TbMnO3, the easy axis is along the a-direction (see Figure 3.4) and

the spin propagation vector is parallel to b with q = (0, 0.28, 0). Figure 3.9 shows the temperature

dependence of the polarization of Tb1−xCaxMnO3 along both the a and c directions. Spontaneous

polarization suddenly appears at TC in the x = 0 and x = 0.02 samples, typical of a ferroelectric

transition. However, for x = 0.05 the onset of polarization occurs much more gradually, pointing

to a phase transition of diffuse character. The spontaneous polarization of our undoped TbMnO3

sample is close to the value of 600 C/m2 reported by Kimura et al, and decreases dramatically with

increasing Ca content. Although we also observe a small polarization along the a-axis for x = 0 and

x = 0.02, this is probably due to a slight misorientation of the samples.


3.3.5. Neutron diffraction

0 10 20 30 40 500.02

0.03

0.04

0.05Tb

1-xCa

xMnO

3(0, 2+q,1 )

x= 0.05

x= 0.02

Peak

wid

th

Temperature (K)

0.0

0.2

0.4

0.6

0.8

x= 0.05I/I(

002)

(0,2+q,1)

x= 0.02

x 5

1.6 1.7 1.80.0

0.5

1.0

I/I(0

02)

q (r.l.u.)

2 K ( 0, 2-q, 1)

Figure 3.10: (a) Temperature dependence of normalized integrated intensity of the (0, 2+q, 1) peak. The

inset shows k-scans around (0, 2-q, 1) at 2 K. (b) Width of (0, 2+q, 1) peak. The open triangles indicate the

ferroelectric transition (Tlock) temperatures. The solid lines are guides to the eye.

In order to investigate the effect of Ca-doping on the magnetic structure, we used neutron diffrac-

tion. We studied the temperature dependence of the Mn-spin modulation of Tb1−xCaxMnO3 for x =

0.02 and x = 0.05. So-called A-type magnetic superlattice reflections, characteristic of the Mn-spin

modulation, were observed at (0, 2-q, 1) and (0, 2+q, 1) in both samples, but were much stronger for

x = 0.02 at all temperatures (see Figure 3.10(a)). Here, q is the Mn spin-spiral propagation vector

parallel to b. We normalized the integrated intensities of these superlattice reflections to the intensity

of the main 002 reflection, which contains no magnetic component. The Mn spin modulation in both

samples has the same periodicity as in undoped TbMnO3, where q ∼ 0.28. In Figure 3.10(a) the

temperature dependence of the intensity of the (0, 2+q, 1) reflection is shown; the intensities were

obtained from omega scans. The intensity increases below TC ∼ 21 K and TC ∼ 15 K for x = 0.02

and x = 0.05, respectively. No superlattice reflections were observed above the magnetic ordering


temperature of 42 K. This behavior is slightly different to that in undoped TbMnO3 [8], where the

increase in intensity of the A-type reflections in the vicinity of TC is much less pronounced. Fig-

ure 3.10(b) shows the temperature dependence of the peak width of the (0, 2+q, 1) reflection. It is

clear that the A-type peaks for x = 0.05 are broader than those for x = 0.02 below TC, indicating

that increased Ca-doping decreases the coherence length of the Mn spin-spiral structure, leading to

shorter-range order.

3.4. Discussion

Figure 3.11: Phase diagram of RMnO3 and Tb1−xCaxMnO3 showing ordering temperatures as a function of

tolerance factor. The inset shows a plot of the average Mn-O-Mn bond angle as a function of tolerance factor.

Up and down triangles correspond to magnetic ordering and ferroelectric transition of the samples doped with

x = 0%,2%,5% and 10% of Ca.

For RMnO3 perovskites an increasing ionic radius of the rare earth results in an increase of the

Mn-O-Mn bond angle. A similar effect is observed for Ca-doping on the A-site as Ca is larger then

R; doping increases the Mn-O-Mn bond angles in the ab-plane [16, 17]. However, there is a marked

difference: for Ca-doping the valence change induced on the B-site dominates the change of ionic

radius of the A-site. For example, the difference in ionic radius between Mn4+ (0.53 A) and Mn3+

(0.645A) is a greater factor in determining the structure than the difference between Ca2+(1.18 A)

and Tb3+(1.095 A). Both effects are taken into account in the perovskite tolerance factor (t), which

is defined as t = (A−O)/√

2(B−O) whereHere, (AO) and (MnO) are the average cationoxygen

interatomic distances of the A- and B-sites, respectively. The tolerance factor is linearly related to

3.4 Discussion 37

the average Mn-O-Mn bond angle (see the inset of Figure 3.11) [19–21]. The average Mn-O-Mn

bond angles in Figure 3.11 are taken from Refs. [19–21, 47]. In calculating t we have used ionic

radii from Ref. [22] and a coordination number of nine for the A-site, because these values have

been most accurately determined for small rare-earth ions. The amount of Mn4+ present on the

B-site was assumed to be the same as the Ca-content [16]. As shown in Figure 3.11, the effect

of Ca-doping in Tb1−xCaxMnO3 can be divided into two regimes. First, for x ≤ 0.05 the effect

of the tolerance factor or Mn-O-Mn bond angle dominates. Doping causes a weakening of the

relative strength of the next-nearest-neighbor superexchange interactions [6]. This results in a partial

breakdown of the spiral structure for x = 0.05 and probably to increasing preference for the A-type

antiferromagnetic structure at low temperature; this has previously been found in GdMnO3, which

has the same tolerance factor. Second, for 0.05 < x≤ 0.1, the effect of double-exchange interactions

becomes dominant, and the magnetic structure transforms to a spin-glass-like state. This behavior

can be explained by the emergence of ferromagnetic clusters [16].

Figure 3.12: Dielectric constant of Tb0.95Ca0.05MnO3 measured at different frequencies.

The onset of polarization in our x = 0.05 sample occurs in a rather diffuse fashion (see Figure

3.9(a)), suggesting that the ferroelectricity may be of the relaxor type. In order to clarify this is-

sue, we measured the temperature dependence of the dielectric constant at different frequencies (see

Figure 3.12). The broad peak shifts with increasing frequency to higher temperature. This behavior

resembles that of a relaxor ferroelectric, in which the maximum of the broad peak defines a glass-like

transition temperature, Tm, associated with a diffuse phase transition where the dipolar fluctuations

within small polar domains slow down. In relaxor ferroelectrics these domains are paraelectric at

high temperatures. Upon cooling they transform to ferroelectric clusters, each with a randomly ori-

ented dipole moment. At sufficiently low temperatures all dipolar motion freezes, and the dispersion


vanishes [15]. The existence of ferroelectric clusters in relaxor ferroelectrics is a universal feature,

although the precise mechanism of their formation is still debated [14]. In conventional relaxor

ferroelectrics, ferroelectric clusters are often generated from the disturbance of long range order by

compositional disorder, impurities, lattice vacancies or other imperfections. The correlation that fer-

roelectric clusters have with the magnetic structure is unclear because known relaxors are generally

non-magnetic. In contrast, the relaxor-like behavior of our x = 0.05 sample occurs below the mag-

netic ordering temperature. As we show in Figure 3.11, the Mn magnetic peak is broader for x =

0.05 than for x = 0.02. This implies that the relaxor-like behavior originates from a decreased co-

herence length of the Mn-spin spiral structure. No similar mechanism has previously been reported,

and therefore we propose that Tb1−xCaxMnO3 might form a new class of relaxor ferroelectrics in

which the relaxor behavior is induced by the magnetic structure. We note that further experimental

evidence, such as can be obtained by neutron diffuse scattering, is needed to prove the existence of

ferroelectric clusters in our materials.

Recently, theoretical calculations have shown that the direction of the polarization in RMnO3

depends on the helicity of the spiral mode, which is either clockwise or counter-clockwise [5, 9].

Thus, for our x = 0.05 sample, where short-range ordered spiral structures are randomly oriented,

both spiral modes are likely to exist. In this scenario, the polarization of spiral domains with opposite

handedness will cancel and the net polarization will decrease rapidly with doping. Alternatively, the

spiral ordering might simply be disrupted by doping, eventually giving way to double exchange and

leading to a decrease in the coherence length of the spiral, or to shorter range order.

3.5. Conclusion

A small degree of Ca-doping suppresses the ferroelectric state in Tb1−xCaxMnO3. This tran-

sition is governed by the appearance of Mn4+, which causes both the Mn-O-Mn bond angle and

the influence of double-exchange interactions to increase. The suppression of ferroelectricity with

doping occurs via an intermediate state at x = 0.05 with behavior resembling that of a relaxor. The

intermediate state is associated with a decreased coherence length of the Mn spin-spiral structure,

without any change in the modulation wave vector. The ferroelectric transition is signaled by lattice

discontinuities, where the largest lattice anomaly corresponds to the direction of the polarization.

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Chapter 4

Magnetic field induced relaxor

ferroelectric behavior in

Tb1−xCaxMnO3

4.1. Introduction

Much of the interest in multiferroic materials lies in the prospect of controlling charge by ap-

plying a magnetic field and controlling spin by applying a voltage. Although the polarization of

TbMnO3 is much smaller than in conventional ferroelectrics such as BaTiO3 and PZT, the ferroelec-

tricity in TbMnO3 can be controlled by an applied magnetic field [1]. For example, when a magnetic

field is applied parallel to the a or b-axis, the polarization vector rotates by 90 degrees from the

direction P‖c to P‖a. This so-called polarization flop is accompanied by a large magnetocapacitance

effect. In contrast, when a magnetic field is applied along the c-axis, the polarization is suppressed.

Similar behaviour has been observed in DyMnO3 [2,3]. A theoretical explanation of these phenom-

ena has been proposed by Mostovoy using Landau theory and a phenomenological approach [4].

For the spiral magnetic structure, which exists below Tlock in TbMnO3 and DyMnO3, the direction

of the polarization is given by P‖e3× Q, where e3 is the spin-rotation axis of the spiral and Q is the

propagation vector. In this theory, the direction of the polarization should be perpendicular to both

the spin rotation axis and the propagation vector. When a magnetic field is applied along the a-axis

or b-axis, the spin rotation axis changes from the a-axis to the c-axis in both cases. The propagation

vector remains along the b-axis. Therefore, the polarization flops from the c-axis to the a-axis. The

suppression of ferroelectricity by an applied magnetic field along the c-axis can be explained by a

disturbance of the magnetic spiral structure [4]. Although the macroscopic electrical behavior of

41

42 Magnetic field induced relaxor ferroelectric behavior in Tb1−xCaxMnO3

TbMnO3 and DyMnO3 is similar, there appear to be different mechanisms for the polarization flop.

In TbMnO3 the polarization flop is associated with a transformation from an incommensurate (IC)

to commensurate Mn spin configuration with propagation vector (0, 0.25, 0), whereas in DyMnO3

no change in the wave-vector occurs with the polarization flop. The difference does not appear to be

fundamental in nature but rather lies in the magnitude of the incommensurability. For R = Tb, the

wavevector of q = 0.28 at zero field is relatively close to the commensurate wavevector of q = 0.25 in

the high-field phase, whereas for R = Dy the zero-field wavevector of q = 0.38 is further away from

any commensurate value such as q = 1/3, so an incommensurate to commensurate transition is not

energetically favorable [5, 6].

In Section 3.1 the magnetic, dielectric and ferroelectric properties of low-doped Tb1−xCaxMnO3

with x < 0.1 were examined. It was demonstrated that on increasing the level of Ca doping, the

ferroelectricity is gradually suppressed via an intermediate state at x = 0.05 [8]. The intermediate

state exhibits the universal signature of a relaxor ferroelectric state: a broad frequency-dependent

peak in the real part of the temperature dependence of the dielectric susceptibility [7]. In undoped

RMnO3, increasing the ionic radius of the rare-earth (rR) increases the wave vector of the Mn spins.

For example, the wavevector in the ferroelectric state increases from (0, 0.280, 0) for TbMnO3 to

(0, 0.385, 0) for DyMnO3. However, although the ionic radius of Ca2+ is larger than that of Mn3+,

our neutron scattering study in Section 3.1 showed that increasing the level of Ca doping does not

change the wave-vector but rather disturbs the long-range Mn spin order via an intermediate state

that possesses short-range order. In this section, we investigate the effect of applied magnetic fields

on Tb1−xCaxMnO3 for x = 0, 0.02, 0.05 and 0.01.

4.2. Experimental

The magnetic properties were measured using a Quantum Design MPMS-7 SQUID magnetome-

ter. The dielectric constant was measured using an Agilent 4284A LCR meter and an Andeen-

Hagerling 2500A capacitance bridge in combination with a Quantum Design Physical Properties

Measurement System. Polarization measurements were performed using a Keithley 6517 electrom-

eter; the samples were cooled in a poling electric field of (∼ 150 V/mm). Single crystal neutron

diffraction experiments were carried out at the Berlin Neutron Scattering Center (BENSC) using the

double-axis E4 instrument. Single crystals of approximate size 5 × 5 mm were oriented with the

bc plane in the scattering plane. Cooling and application of external magnetic fields up to 6T were

achieved using a horizontal cryomagnet HM1. This geometry allowed magnetic fields to be applied

along either the b or c-axis of the crystal.




Figure 4.1: Magnetization as a function of magnetic field for Tb1−xCaxMnO3 with x = 0, 0.05 and 0.1 along

(a) the a-axis, (b) the b-axis, and (c) the c-axis at 5 K.

Figure 4.1 shows the magnetization of Tb1−xCaxMnO3 as a function of applied magnetic field

at 5 K. For H‖a, a metamagnetic transition at approximately 1.6 T is observed in the x = 0 sample,

which becomes less well-defined on increasing the Ca content. This is in good agreement with a

previous report by Kimura et al. on undoped TbMnO3, in which a second small metamagnetic tran-

sition was also observed at approximately 10 T for measurements at 2 K and 4 K [3]. For H‖b, we

observe an anomaly for the x = 0 sample that corresponds to a metamagnetic transition at approx-

imately 3 T; the M versus H curve becomes linear with increasing Ca content. More pronounced

metamagnetic transitions at H = 1 T and H = 4 T have been previously reported for measurements

at lower temperature [1, 3]. The first transition was associated with the Tb spin sublattice, which


underwent a transition from an incommensurate structure with a wavevector of qT b = 0.42 to a com-

mensurate structure with qT b = 1/3. The second transition was associated with the Mn spins and

involved a change in wavevector from qMn = 0.28 to qMn = 0.25, accompanied by a polarization

flop [5]. For H‖c, we observe no metamagnetic transition for any of the samples up to 5 T. However,

magnetic hysteresis is present for x = 0.1, which can be ascribed to the existence of a ferromagnetic

component, probably in a spin glass-like state.

0.0

0.5

1.0

1.5

(em

u/m

ol) x= 0.5T

x= 3Tx= 5T

x=0 and H//a

0 20 40 60 80 1000.0

0.5

1.0

1.5

(em

u/m

ol)

Temperature (K)

H= 0.5 H= 3T H= 5T

x=0.1 and H//a

0.0

0.5

1.0

1.5

(em

u/m

ol)

H=0.5T H= 3T H= 5T

x= 0.05 and H//a

0.05

0.10

0.15

x=0 and H//c

(em

u/m

ol)

H= 0.5TH= 3TH= 5T

0 20 40 60 80 1000.0

0.1

0.2

x=0.1 and H//c

(em

u/m

ol)

Temperature (K)

H = 0.1 T H = 3 T H = 5 T

0.05

0.10

0.15

x=0.05 and H//c

(em

u/m

ol) H= 0.5T

H= 3TH= 5T

Figure 4.2: Temperature dependence of magnetic susceptibility of Tb1−xCaxMnO3 for different magnetic fields

applied along the a-axis (left) and c-axis (right).

The temperature dependence of the zero-field cooled magnetic susceptibility of Tb1−xCaxMnO3

is shown in Figure 4.2. For H‖a, the low-temperature susceptibility decreases with increasing mag-

netic field for all of the samples; this is because the susceptibility is proportional to the inverse of

the magnetic field, χ= M/H, and the magnetization becomes saturated at relatively low fields (see

Figure 4.1(a)). For H‖c, we observe weak anomalies at TN and TC for x = 0, while the latter becomes


broadened for the x = 0.05 sample. The applied magnetic field has little effect on the magnetic sus-

ceptibility for the x = 0 and x = 0.05 samples, because the magnetization in this direction is only

saturated above 5 T (see Figure 4.1(c)). For the x = 0.1 sample, the maximum in susceptibility

becomes broader and shifts towards lower temperatures as the magnetic field increases. These are

typical features of spin-glass behavior.

4.3.2. Dielectric properties under magnetic field

E||a

10 20 30 40

23

24

25

26

30

34

Die

lect

ric c

onst

ant,

Temperature (K)

36

32

E||c

Figure 4.3: Temperature dependence of dielectric constant of TbMnO3 along (a) the c-axis and (b) the a-axis

in various magnetic fields, measured at 10 kHz. This figure is reproduced from Ref. [1].

The variation of the dielectric properties of undoped TbMnO3 with magnetic field has previously

been reported by Kimura et al. [1, 3]. The dielectric properties depend both on the orientation of the

sample and the magnetic field. The most interesting behavior was observed along the c-axis and

a-axis when the magnetic field was applied along the b-axis (see Figure 4.3). The main results can

be briefly summarized as follows. For E‖c sharp peaks in the dielectric constant were observed at

approximately 28 K. These correspond to the ferroelectric transition and changed little with magnetic

field. Further peaks were apparent in fields of above 5 T for both E‖c and E‖a, which correspond to

the polarization flop. These peaks shifted to higher temperature as the magnetic field was increased.


Moreover, giant magnetocapacitance of up to 10% was observed along the c-direction at the critical

field for the polarization flop at 12 K.

We performed dielectric measurements on our x = 0.02 sample in field at a frequency of 1 kHz

and with 1 K steps. The magnetic field was applied along the b-axis at 50 K, and the sample was

then cooled to 5 K in field. As displayed in Figure 4.4, at zero field we observe a sharp peak at

T ∼ 21 K for E‖c, which corresponds to the ferroelectric transition. For E‖a this peak is much

less pronounced. When a magnetic field is applied it becomes broader and shifts towards lower

temperature at fields above 5 T (TC ∼ 19 K at H = 8 T). At H = 6 T and above a second peak is

apparent, which shifts to higher temperature as the magnetic field increases. This peak corresponds

to the polarization flop. The magnetocapacitance (C(8 T)-C(0)/C(0)) reaches a value of 2.5 % for

E‖c and 11% for E‖a at 14 K.

0 10 20 30 40 5024

28

32

' a

Temperature (K)

H= 0 T H= 4 T H= 6 T H= 8 T

1 kHz x=0.02 E//a and H//b

0 10 20 30 40 5024

28

32

H= 5T H= 6T H= 7T H= 8T

' c

Temperature (K)

H= 0T H= 1T H= 2T H= 3T H= 4T

1 kHz x=0.02 E//c and H//b

Figure 4.4: Temperature dependence of the dielectric constant of Tb0.98Ca0.02MnO3 for E‖c (left panel) and

E‖a (right panel) at different magnetic fields. The magnetic field was applied along the b-axis.

0 2 4 6 8-8

-4

0

4

8

22 K 23 K 25 K

/(0

) (%

)

H (T)

19 K 20 K 20.5 K 21 K

1 kHz X= 0.02 E/c and H//b

0 2 4 6 80

1

2

3

/(0

) (%

)

H (T)

1k Hz x= 0.02 E//C and H//b

15K

10K

5K

Figure 4.5: Magnetic field dependence of the capacitance of Tb0.98Ca0.02MnO3 for E‖c and H‖b at low

temperatures (left panel) and temperatures close to TC (right panel).


In order to see the coupling between the magnetic and dielectric properties in this system, we

plot the magnetic field dependence of the capacitance for E‖c and H‖b in Figure 4.5. At 5 K, a broad

peak is apparent at approximately 2 T, which is suppressed at higher temperature. This peak might

be associated with the incommensurate-commensurate transition of the Tb wavevector, as observed

in undoped TbMnO3 [5]. Another peak observed at approximately 5 T in the 5 K data shifts to higher

field as the temperature increases, consistent with the polarization flop. For temperatures close to

TC, we observe a broad peak (at 7 T at 19 K) that shifts to lower field as the temperature increases.

Moreover, at 20.5 K the sign of the magnetocapacitance changes from positive to negative. This

behavior is due to the shifting of the ferroelectric transition temperature with field.

0 10 20 30 40 5024

25

26

' c

Temperature (K)

0 T 1 T 3 T 5 T

1 kHz x= 0.05 E//c and H//b

0 2 4 6 8 10-1.5

-1.0

-0.5

0.0

0.5

40K20K

15K

(%)

H (T)

5K

1 kHz x= 0.05 E//C and H//b

Figure 4.6: Temperature dependence of dielectric constant of Tb0.95Ca0.05MnO3 in various magnetic fields

(left panel), and magnetic field dependence of capacitance at different temperatures (right panel).

As described in Section 3.1, the dielectric constant of the x = 0.05 sample along the c-axis

exhibits behavior typical of a relaxor ferroelectric. When a magnetic field is applied along the b-axis

(H‖b), the broad peak in the dielectric constant is suppressed and shifted towards lower temperature

(see Figure 4.6). The maximum in this broad peak, at Tm, is associated with the dynamic freezing

of the polar domains. The suppression of Tm with field indicates that the relaxor state gradually

vanishes. The magnetocapacitance is negative at all temperatures, with the greatest magnitude at

∼15 K, which corresponds to Tm.


0 10 20 30 40 5023

24

25

26

' c

Temperature (K)

H= 0T H= 4T

1kHz x=0.1 E//c and H//b

0 2 4 6 8-0.2

-0.1

0.0

0.1

0.2

(0) (

%)

H (T)

x= 0.1 E//c and H//b 5K

Figure 4.7: Temperature dependence of dielectric constant of Tb0.9Ca0.1MnO3 in zero magnetic field and H =

4 T (left panel), and magnetic field dependence of capacitance at 5 K (right panel).

For the x = 0.1 sample, the temperature dependence of the dielectric constant (Figure 4.7) does

not show features typical of ferroelectric behavior. Moreover, the capacitance does not change on

applying a magnetic field. This provides more evidence that the x = 0.1 composition is no longer

ferroelectric.

4.3.3. Polarization

0 10 20 30 400

200

400

600

Temperature (K)

Pc (

C/m

2 ) 0 T 2 T 4 T 5 T 6 T 7 T 8 T

P//c and H//bx=0.02

0T2T4T5T

6T7T8T

0 10 20 30 400

100

200

300

400

Pa (

C/m

2 )

Temperature (K)

H=0 T H=4 T H=5 T H=6 T H=7 T H=8 T

x=0.02 P//a and H//b

8T

7T

6T

5T

Figure 4.8: Temperature dependence of polarization of Tb0.98Ca0.02MnO3 along the c-axis (left panel) and

a-axis (right panel) in various magnetic fields applied along the b-axis.

In order to prove that ferroelectricity is present alongside magnetoelectric coupling in this sys-

tem, we measured the spontaneous polarization. Figure 4.8(a) shows the temperature dependence of


the polarization of the x = 0.02 sample along the c-axis (Pc) in different magnetic fields applied par-

allel to the b-axis. The a-axis polarization (Pa) is shown in Figure 4.8(b). For E‖c, the spontaneous

polarization at all temperatures is strongly suppressed above 6 T and vanishes at 8 T. In contrast,

for E‖a the spontaneous polarization increases suddenly at 6 T and becomes larger with increasing

magnetic field while the onset of polarization shifts to higher temperature. This behavior is similar

to that previously observed in undoped TbMnO3, where the polarization flops from the c-axis to the

a-axis with applied magnetic field. However, the critical field required to flop the polarization in

the x = 0.02 sample is slightly higher than that required in undoped TbMnO3 (∼ 4 T) [1, 3]. The

small values of Pa measured are probably due to slight misalignment of the crystal and electrode

configuration.

0 10 20 30 400

50

100

150

200

x=0.02

Pa (

C/m

2 )

Temperature (K)

0 T 1 T 5 T 6 T 7 T

P//a and H//c

5T6T7T

Figure 4.9: Temperature dependence of polarization of Tb0.98Ca0.02MnO3 along the a-axis in various magnetic

fields applied along the c-axis.

We also measured the effect on the spontaneous polarization of applying a magnetic field along

the c-direction. As shown in Figure 4.9, the behavior of Pa is similar to that for H‖b up to H =

5 T. However, at H = 6 T, Pa drops to zero at low temperatures. This indicates that the ferroelec-

tricity is suppressed by an applied magnetic field along the c-axis, as was previously observed in

undoped TbMnO3 [3]. We note that the measured polarization along the a-axis is only due to a

slight misalignment of the crystal.

For the x = 0.05 sample, the onset of spontaneous polarization along the c-axis occurs via a

broad phase transition. When a magnetic field is applied along the b-axis, the polarization slightly

decreases (Figure 4.10). No polarization flop was observed for this composition. We suggest that

this is due to a weakening of the next-nearest-neighbor superexchange interaction; the Mn-O-Mn

bond angle in this composition is close to that of GdMnO3. The Mn spin spiral structure is most


likely disturbed by the applied field.

0 10 20 30 400

25

50

75

100

7T

P c (C

/m2 )

Temperature (K)

0T

x= 0.05 P//c and H//b

Figure 4.10: Temperature dependence of c-axis polarization of Tb0.95Ca0.05MnO3 in zero magnetic field and

in a field of 7 T applied along the b-axis.

4.3.4. Neutron diffraction

0.24 0.26 0.28 0.30

10

20

30

40x= 0.02 (0,-q,1) and H= 5.5 T

Inten

sity (

103 a.u

)

q (r.l.u)

2 K 5 K 10 K 15 K 20 K 25 K 30 K

0.24 0.26 0.28 0.30

10

20

30

40

Inten

sity (

103 a.u

)

q (r.l.u)

2 K 5 K 10 K 15 K 20 K 25 K 30 K

x= 0.02 (0,-q,1) and Hb= 4.5 T

0.24 0.26 0.28 0.30

10

20

30

40x= 0.02 (0,-q,1) and Hb= 5 T

Inten

sity (

103 a.u

)

q (r.l.u)

2 K 5 K 10 K 15 K 20 K 25 K 30 K

0.24 0.26 0.28 0.30

10

20

30

40x= 0.02 (0,-q,1) and Hb= 6 T

Inten

sity (

103 a.

u)

q (r.l.u)

2 K 5 K 10 K 15 K 20 K 25 K 30 K

Figure 4.11: Reciprocal lattice scans of the first-harmonic A-type reflection (0, -qMn, 1) of Tb0.98Ca0.02MnO3

at various temperatures and in magnetic fields of (a) H = 4.5T, (b) H = 5 T, (c) H = 5.5 T, and (d) H = 6T

applied parallel to the b-axis.

In order to understand the ferroelectric properties of the x = 0.02 sample in more detail, we

investigated the magnetic structure of the Mn sublattice in magnetic fields applied along the b and


c-axes using neutron diffraction. The crystal was mounted with the a-axis perpendicular to the

scattering plane and to the magnet, allowing measurements in the bc plane. In this geometry all

of the characteristic Mn and Tb-spin reflections are accessible: A-type (h + k = even and l = odd),

G-type (h + k = odd and l = odd), C-type (h + k = odd and l = even), and F-type (h + k = even and

l = even) [11]. In this experiment we were only able to observe A-type reflections due to the large

area of reciprocal space that was blocked by the bulky horizontal magnet. For H‖b, we followed

the position, intensity and width of the first-harmonic A-type reflection (0, -qMn, 1) in the range q

= -0.23 to -0.31, with an interval of 0.002 reciprocal lattice units. We applied magnetic fields of

between 4.5 and 6 T in steps of 0.5 T at various temperatures. The dependence of the (0, -qMn, 1)

profile on temperature and magnetic field between 4.5 T and 6 T is shown in Figure 4.11.

0.278

0.279

0.280

q (r.

l. u)

4.5 T 5 T 5.5 T 6 T

x= 0.02 (0, -q, 1) and H//b

10

15

20

25

30x= 0.02 (0, -q, 1 ) and H//b

Inte

nsity

(a.u

)

4.5 T 5 T 5.5 T 6 T

0 5 10 15 20 25 3010

12

14

16x= 0.02 (0, -q, 1 ) and H//b

FWH

M (1

0-3r.l

.u)

Temperature (K)

4.5 T 5 T 5.5 T 6 T

Figure 4.12: Temperature dependence of (a) Mn spin wavevector (qMn), (b) integrated intensity, and (c) FWHM

of the (0, -qMn, 1) reflection of Tb0.98Ca0.02MnO3 in magnetic fields applied along the b-axis.


In Figure 4.12 we plot the temperature dependence of the wave vector qMn, and the integrated

intensity and peak width of the (0, -qMn, 1) reflection at various magnetic fields, obtained by fitting

the peaks with a Gaussian function. We find that the wave vector qMn ∼ 0.28 does not change when

magnetic fields of up to 6 T are applied along the b-direction. This behavior is in contrast to undoped

TbMnO3, in which the polarization flop is accompanied by a first order transition from qMn = 0.28

to qMn = 0.25 for both H‖b and H‖a [5]. The polarization flop in our x = 0.02 sample takes place at

approximately H = 6 T, as shown in the dielectric and polarization measurements in Figures 4.4, 4.5

and 4.8. In Figure 4.12 we observe that the integrated intensity decreases at H = 6T while the peak

width increases. This behavior indicates that the coherence length of the Mn spin spiral structure

begins to decrease at 6 T, which is the maximum magnetic field obtainable with the horizontal-field

magnet.

In order to study the effect of magnetic fields applied along the c-axis, we followed the C-type

reflection (0, 1-qMn, 0). Since this reflection existed at low scattering angles and the magnetic

block was asymmetric, the observed peak was somewhat broader than the A-type reflection. The

value of qMn steadily decreases from ∼0.28 in zero field to ∼0.265 at 6 T, while the full-width at

half-maximum (FWHM) suddenly increases above 5 T (Figure 4.13), indicating that the Mn-spin

spiral structure is becoming destabilized. These results are consistent with the disappearance of

ferroelectricity above 6 T.

0 2 4 6 80.26

0.28

0.30

0.32

q (

r.l.u

)

H (T)

x= 0.02 ( 0,1-q,0) H//c at 2K

0 2 4 6 8

0.05

0.06

0.07

0.08

0.09

FW

HM

(r.

l.u)

H (T)

x= 0.02 (0, 1-q,0 ) H//c at 2K

0.69 0.72 0.75 0.7820

30

40

50

Inte

nsity

(103 a

.u.)

1-q (r. l. u)

x= 0.02 (0, 1-q, 0) H//c at 2K

0T

6T

Figure 4.13: Magnetic field dependence of Mn wavevector qMn (left panel), and FWHM (right panel) of the(0, 1-qMn, 0) reflection of Tb0.98Ca0.02MnO3 for fields applied along the c-axis. The inset shows reciprocallattice scans of the first-harmonic C-type reflection (0, 1-qMn, 0) of Tb0.98Ca0.02MnO3 in various magneticfields applied parallel to the c-axis at 2K.

4.4 Discussion 53

4.4. Discussion

0 2 4 6 8 100.7

1.4

2.1

2.8

FWH

M

H (T)

1kHz x= 0.02 E//c and H//b

Figure 4.14: FWHM of the dielectric peak at the ferroelectric transition temperature of Tb0.98Ca0.02MnO3 as

a function of magnetic field applied along the b-axis.

The ferroelectric behavior of our x = 0.02 sample is similar to that of undoped TbMnO3, where

a magnetic field applied along the b-axis induces a polarization flop from the c-axis to the a-axis.

However, the critical field required to flop the polarization is slightly higher in the x = 0.02 sample.

The polarization flop is predicted by a field-induced flop of the axis of rotation of the spin spiral

structure [4]. The critical field required to induce the spin flop depends on the magnetic exchange

interactions and the magnetic anisotropy. If we ignore the contribution from Tb3+, the higher critical

field for x = 0.02 might be correlated with a weakening of the Mn next-nearest-neighbor superex-

change interaction and decreasing magnetic anisotropy due to the existence of Mn4+. As discussed

in Section 3.4, the Mn-O-Mn bond angle increases with increasing Ca concentration.

More information on the nature of the polarization flop in the x = 0.02 sample can be obtained

by studying the behavior of the dielectric constant close to the onset of ferroelectricity at Tc. The

dielectric peak becomes broader and shifts to lower temperature as the magnetic field is increased

above 5 T, as seen in Figure 4.6. We fitted the dielectric peak using a Gaussian function and the re-

sulting FWHM is shown as a function of field in Figure 4.14. The FWHM is almost constant below

5 T and then increases with magnetic field above 5 T. This is different to the situation in undoped

TbMnO3, where the dielectric peak at the ferroelectric transition does not change in width with mag-

netic field. We suggest that a transformation from the ferroelectric state to a relaxor state occurs at

5 T in the x = 0.02 sample. In other words, a magnetic field applied along the b-axis induces a fer-

roelectric to relaxor crossover. The results of our neutron diffraction study support this hypothesis;

at 6 T the Mn-spin superlattice peak becomes broader, indicating that the coherence length of the


Mn spin spiral decreases. Ferroelectric-relaxor crossover phenomena have previously been induced

in conventional ferroelectrics, such as KTaO3 doped with 1.2% Nb and PZN (Pb(Zn1/3Nb2/3O3)

doped with 5% of PT (PbTiO3), by the application of hydrostatic pressure. In these examples pres-

sure causes a decrease in the correlation length of the dipolar interaction [7, 9]. A similar argument

can be used to explain the magnetic field induced crossover in Tb0.98Ca0.02MnO3. Doping with Ca

leads to the presence of Mn4+ on the perovskite B-site, which introduces double exchange interac-

tions with Mn3+. When the magnetic field is increased, the electron hopping rate also increases.

The electron hopping rate is proportional to cos(θ/2) , where θ is the misalignment angle between

neighboring spins [14]. The increased occurrence of double exchange at high magnetic fields then

causes a decrease in the coherence length of the spiral structure. In order to prove the existence of the

ferroelectric to relaxor crossover, we measured the frequency dependence of the dielectric constant

in zero field and at H = 8 T, as shown in Figure 4.15. In the absence of magnetic field, the dielec-

tric anomaly at the ferroelectric transition does not change much with frequency. In contrast, when a

magnetic field is applied along the b-axis, the dielectric anomaly becomes broader and shifts towards

higher temperature with increasing frequency, which resembles relaxor behavior. This phenomenon

indicates that the magnetic field induces a ferroelectric to relaxor crossover due to the decreasing

coherence length of the Mn-spin spiral structure.

10 15 20 2525

26

27

28

29

100 kHz

10 kHz

500 kHz

E//c, H//b= 0T x= 0.02

'

Temperature (K)

2 kHz

10 15 20 2526

27

28

500 kHz

300 kHz

100 kHz

10 kHz

'

Temperature (K)

Freq

2 kHzE//c, H//b= 8T x= 0.02

Figure 4.15: Temperature dependence of dielectric constant of Tb0.98Ca0.02MnO3 measured at various fre-quencies in zero field (left) and in a field of H = 8T applied along the b-axis (right).

For the x = 0.05 sample, the application of a magnetic field along the b-axis gives rise to a sup-

pression of the broad peak in εc (see Figure 4.6). As reported in Section 3.1, the x = 0.05 sample

displays behavior characteristic of a relaxor ferroelectric even in zero field. Increasing the magnetic

4.5 Conclusion 55

field will again lead to increased occurrence of electron hopping associated with double exchange,

thus decreasing the coherence length of the Mn spin spiral further and hence decreasing Tm. More-

over, this field-induced suppression of the relaxor ferroelectric state leads to a new mechanism of

magnetocapacitance; as shown in Figure 4.6, the magnitude of the large negative magnetocapaci-

tance is greatest at Tm. The polarization flop in undoped TbMnO3 is accompanied by a first-order

transition from an incommensurate spin structure with wavevector (0, 0.28, 0) to a commensurate

structure with wavevector (0, 0.25, 0) [5]. It is possible that the change of wavevector from q =

0.28 to q = 0.25 induces exchange striction, altering the Mn-O-Mn bond angles and leading to fer-

roelectricity [5, 16, 17]. In this mechanism the appearance of the c-axis electrical polarization is

not directly associated with the magnetic spiral. An alternative scenario to explain the polarization

flop is the rotation of the Mn spiral plane from the bc plane to the ab plane [4]. Figure 4.12 shows

that the incommensuration does not change (the wavevector remains at q = 0.28) as the magnetic

field is increased up to the critical field of 6 T. A similar observation has previously been made for

Eu0.6Y0.4MnO3, where the lattice modulation wavevector remains at ∼0.58 as the magnetic field

applied along the a-axis is increased through the critical value required to induce a polarization

flop [15]. Taken together, these results imply that a rotation of the spin-spiral plane plays a more

important role in the mechanism of the polarization flop than the transition from incommensurate to

commensurate spin structures.

4.5. Conclusion

We have investigated the behavior of Tb1−xCaxMnO3 with x = 0.02, 0.05 and 0.1 under mag-

netic field. For x = 0.02, the application of magnetic fields greater than 5 T along the b-axis at

temperatures close to the ferroelectric transition appears to induce a crossover from ferroelectric to

relaxor behavior. The mechanism of this crossover involves a decrease in the coherence length of the

Mn-spin spiral structure. At low temperatures, the magnetic field induces a polarization flop without

any change in the wavevector of the Mn spin spiral, which is in contrast to the incommensurate to

commensurate transition observed in undoped TbMnO3. This suggests that field-induced rotation of

the spin-spiral plane is the main factor behind the mechanism of the polarization flop reported for

various RMnO3 materials. For the x = 0.05 sample, the application of a magnetic field along the

b-axis gives rise to large negative magnetocapacitance with a novel mechanism, in which the relaxor

ferroelectric state is suppressed by field due to a decreasing coherence length of the Mn-spin spiral

structure.

Bibliography

[1] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, Nature 429, 55 (2003).

[2] T. Goto, T. Kimura, G. Lawes , A. P. Ramirez, and Y. Tokura, Phys. Rev. Lett. 92, 257201

(2004).

[3] T. Kimura, G. Lawes, T. Goto, Y. Tokura and A.P. Ramirez, Phys. Rev. B 71, 224425 (2005).


[5] N. Aliouane, D. N. Argyriou, J. Strempfer, I. Zegkinoglou, S. Landsgesell, and M. v. Zimmer-

mann, Phys. Rev. B 73, 020102 (R) (2006).

[6] J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J.

Hemberger, A. Krimmel, and M. v. Zimmermann, Phys. Rev. B 75, 212402 (2007).

[7] G. A. Samara, J. Phys.: Cond. Mat. 15, R367 (2003).

[8] N. Mufti, A. A. Nugroho, G. R. Blake, and T.T.M. Palstra, Phys. Rev. B 78, 024109 (2008).

[9] G. A. Samara, E. L. Venturini, and V. H. Schmidt, Phys. Rev. B 63, 184104 (2001).

[10] T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura,

Phys. Rev. B 68, 060403(R) (2003)

[11] R. Kajimoto, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, Phys. Rev. B 70, 012401

(2004).

[12] R. Feyerherm, E. Dudzik, N. Aliouane, and D. N. Argyriou, Phys. Rev. B 73, 180401(R)

(2006).

[13] J. Hemberger, F. Schrettle, A. Pimenov, P. Lunkenheimer, V. Y. Ivanov, A. A. Mukhin, A. M.

Balbashov, and A. Loidl, Phys. Rev. B 75, 035118 (2007).

57

58 BIBLIOGRAPHY

[14] C. Zener, Physical Review 82, 403 (1951).

[15] Y. Yamasaki, S. Miyasaka, T. Goto, H. Sagayama, T. Arima, and Y. Tokura, Phys. Rev. B 76,

184418 (2007).

[16] T. Kimura, Annual Review of Materials Research 37, 387 (2007).

[17] T. Arima, A. Tokunaga, T. Goto, et al., Phys. Rev. Lett. 96, 097202 (2006).

Chapter 5

Magnetoelectric behavior of

multiferroic Eu1−xHoxMnO3

5.1. Introduction

The search for new multiferroic materials with strong coupling between ferroelectricity and mag-

netism has attracted great interest in the last few years [1, 2]. This is largely due to the prospect

of controlling the magnetic properties using an electric field and vice versa [1–4]. Attention has

recently been focused on a new class of multiferroics that exhibit magnetic frustration; examples

include hexagonal RMnO3, CoCr2O4 spinel, the Kagome staircase compound Ni3V2O8, RMn2O5

and perovskite RMnO3 (R=Tb,Dy). In this class of materials the ferroelectricity is directly induced

by the spin structure. The perovskite RMnO3 materials exhibit a unique phenomenon in which the

direction of the spontaneous electric polarization can be rotated by 90 degrees by an applied mag-

netic field; this is accompanied by a giant magnetocapacitance effect [5, 6]. The magnetic structure

of perovskite RMnO3 depends on the ionic radius of the R cation. When the ionic radius of R is large

(La-Eu), occupied Mn dx2−r2 and dy2−r2 orbitals order in staggered fashion in the ab plane; this gives

rise to strong ferromagnetic (FM) coupling between nearest-neighbor Mn spins in the ab plane and

weak antiferromagnetic (AF) coupling along the c-axis, which corresponds to the so-called A-type

AF structure. For R cations with small ionic radius, the onset of magnetic ordering initially gives

rise to an incommensurate, sinusoidal structure. This is due to an increased degree of competition

between the nearest-neighbor (NN) and next-nearest-neighbor (NNN) superexchange interactions in

the ab plane, caused by the increased degree of octahedral tilting for small R cations. For R = Tb

and Dy, the incommensurability evolves from a sinusoidal to a spiral configuration below a so-called

59

60 Magnetoelectric behavior of multiferroic Eu1−xHoxMnO3

“lock-in” temperature (Tlock). The spin spiral structure is directly responsible for inducing ferroelec-

tricity in these compounds [5, 6]. Recent studies have shown that the rare-earth spins are strongly

coupled to the Mn spins and also make an important contribution to the electrical polarization [9].

When the R-site is non-magnetic (R = Eu, Y), the Mn spins form a spiral structure in the ab plane.

Consequently, the spontaneous polarization is parallel to the a-axis [10, 11]. It is interesting to in-

vestigate the effect of having an R-site that contains a mixture of non-magnetic (Eu3+) and magnetic

cations. We chose Ho3+ as the magnetic cation because it has the largest magnetic moment in the

rare-earth series and because the ionic radius of Ho3+ is similar to that of Y3+; Eu1−xYxMnO3 is

known to be ferroelectric for certain compositions.

5.2. Experimental

Single-crystalline samples of Eu1−xHoxMnO3 with nominal values of x = 0.2, 0.4, 0.5 and 0.75

were grown by the floating zone method. The crystal growth rate was between 1 and 2 mm/h and was

carried out in air. The seed and feed rods were counter-rotated at a speed of 18-25 rpm. The crys-

tallinity of the samples was checked by Laue diffraction and cut crystal pieces were oriented using

an Enraf-Nonius CAD4 single crystal diffractometer. The magnetic properties were measured using

a Quantum Design MPMS-7 SQUID magnetometer. The dielectric constant was measured using

an Agilent 4284A LCR meter and an Andeen-Hagerling 2500A capacitance bridge in combination

with a Quantum Design Physical Properties Measurement System. Polarization measurements were

performed using a Keithley 617 electrometer. The polarization was determined by integrating the

pyroelectric current.

5.3. Results


The temperature dependence of the magnetic susceptibility of Eu1−xHoxMnO3 is shown in Fig-

ure 5.1. At low temperature, the susceptibility is anisotropic. Although an AF transition is known

to take place at ∼45 K, no anomalies at the transition temperature are apparent in the susceptibility

data due to the large paramagnetic contribution of the Ho cation. For the x = 0.20 sample, the sus-

ceptibility along the c-axis suddenly increases at T ∼ 25 K. This is similar to previously reported

measurements of GdMnO3, where the Mn spin configuration changes from a sinusoidal AF structure

to an A-type canted AF structure at 24 K, which can be well explained by the increasing influence

of the Dzyaloshinskii-Moriya interaction compared to the single ion anisotropy [12]. The c-axis

5.3 Results 61

Figure 5.1: Magnetic susceptibility of Eu1−xHoxMnO3 for x = 0.20, 0.40, 0.50 and 0.75 as a function oftemperature. The insets show expanded views of the magnetic susceptibility along the c-axis.

susceptibility of our x = 0.2 sample then decreases at T ∼ 10 K, where a change of slope occurs in

the b-axis susceptibility. For the x = 0.4 and 0.5 samples, a change of slope in the c-axis suscepti-

bility is observed at T ∼ 26 K and T ∼ 23 K, respectively. Figure 5.2 shows the low-temperature

magnetization of Eu1−xHoxMnO3 as a function of magnetic field applied along all three crystallo-

graphic directions. Both the magnetic moment and magnetic anisotropy increase with Ho content.

The magnetic anisotropy is indicated by the increasing difference between the magnetization along

the a-axis and the other crystallographic axes. The magnetization of the x = 0.4 and 0.5 samples

shows a metamagnetic transition at H ∼1.5 T when the field is applied along the a-axis. This in-

dicates that the Ho spins are aligned in FM fashion under magnetic field. This is also observed in

TbMnO3 [6]. For magnetic fields applied along the b-axis, a metamagnetic transition is apparent at

H ∼3 T for the x = 0.4 sample whereas no anomalies are observed for the x = 0.2 and 0.75 samples.

In TbMnO3 a similar metamagnetic transition observed along the b-axis is associated with a flop of

the spiral structure from the bc plane to the ab plane, which induces a flop of the polarization from

the c-axis to the a-axis [13]. Therefore a similar polarization flop is expected for our x = 0.4 and 0.5

samples.


Figure 5.2: Magnetization of Eu1−xHoxMnO3 as a function of magnetic field applied along all three crystallo-

graphic directions.

5.3.2. Capacitance

We display in Figure 5.3 the temperature dependence of the capacitance of Eu1−xHoxMnO3 with

x = 0.2, 0.4, 0.5 and 0.75 measured along the c-direction. All of these measurements were performed

on heating. The capacitance of the x = 0.2 sample shows a broad peak between approximately 25K

and 30K. In contrast, the capacitance of the x = 0.4, 0.5 and 0.75 samples shows sharp peaks at 26K,

25K, and 20 K respectively. This observation is in good agreement with the decrease of the average

ionic radius of the R-site with doping; for the x = 0.2 sample, the average radius is the same as that

of Gd3+, whereas the ionic radius of Tb3+ corresponds to a composition between x = 0.4 and 0.5.

Thus, by analogy with TbMnO3 and DyMnO3, we expect that the sharp peaks in the x = 0.4 and x =

0.5 data are associated with the ferroelectric transition.

5.3 Results 63

Figure 5.3: Temperature dependence of c-axis capacitance of Eu1−xHoxMnO3 with x = 0.2, 0.4, 0.5 and 0.75.

5.3.3. Polarization

In order to establish whether the sharp anomaly in the capacitance measurements corresponds to

the onset of ferroelectricity, we measured the spontaneous polarization along the c-axis. For the x

= 0.2 sample no polarization is observed (see the inset of Figure 5.4), which is not surprising given

that the average ionic radius of the x = 0.2 sample is close to that of Gd3+ and that GdMnO3 is only

ferroelectric in a non-zero magnetic field. In GdMnO3 the Mn NNN superexchange interaction is

weak compared to the NN interaction, and as a result the canted A-type AF state is favored over the

spiral structure. [7]. A similar observation has been made by Yamasaki et al. for Eu0.8Y0.2MnO3

[11]. Although Hemberger et al. observed spontaneous polarization along the a-axis for the same

composition [10], the samples may have had slightly different stoichiometry. We observe electrical

polarization along the c-axis below a transition temperature Tc in our x = 0.4, 0.5 and 0.75 samples,

as shown in Figure 5.4. This result is in contrast with the Eu1−xYxMnO3 system, in which the

polarization occurs along the a-axis [10, 11]. In the Eu-Y system there is no magnetic interaction

between the Mn and rare-earth sites, because Y3+ and Eu3+ (J=0) are non-magnetic. However,

our system includes Ho3+ with a large magnetic moment (∼ 10.4µB), which might stabilize spiral

ordering in the bc plane via 4f-3d exchange interactions, resulting in polarization along the c-axis

as observed in TbMnO3 [14–16]. The highest polarization of 400 µC/m2 is obtained for x = 0.4.

It is rather surprising that we observe a decrease in both Tc and in the magnitude of the electrical


polarization with increasing Ho3+ content. The spontaneous polarization of DyMnO3 is significantly

larger (P ∼2000 µC/m2) than that of TbMnO3, and the average rare-earth ionic radius of our x =

0.75 sample is close to that of Dy3+.

0 10 20 30 40 500

200

400

x= 0.2x= 0.75

x= 0.5

0 10 20 30 400

10

20

x= 0.2

T (K)

x= 0.75

Pc (

C/m

2 )

Temperature (K)

x= 0.4

Figure 5.4: Temperature dependence of the polarization of Eu1−xHoxMnO3 along the c-axis. The inset shows

an expanded view of the x = 0.2 and x = 0.75 data.

5.4. Effect of applied magnetic field

After establishing the presence of spontaneous polarization, we investigated the behavior of the

Eu1−xHoxMnO3 system under applied magnetic field. In TbMnO3 and DyMnO3 a field applied

along the a-axis or b-axis flops the polarization, while a field applied along the c-axis suppresses

the polarization. We first studied the effect on the capacitance of applying a magnetic field applied

along b-axis. The results are shown in Figure 5.5. For the x = 0.2 sample the capacitance along the

c-direction does not change significantly up to 7 T. For the x = 0.4 sample, beside the ferroelectric

transition peak (Tc1), a second peak (Tc2) appears in the capacitance at ∼10 K for H ∼4 T and shifts

to higher temperature on increasing the magnetic field. This peak is most likely associated with a

flop of the polarization from the c-axis to the a-axis, as observed in TbMnO3. For the x = 0.5 sample

a second peak is observed at ∼7 K in fields of 4 T and 5 T, but is suppressed when the magnetic

field is increased further. In addition, a shoulder-like feature is observed below Tc1 in low fields and

is gradually suppressed as the magnetic field strength increases. For the x = 0.75 sample a second

peak appears at 6 K for H ∼5 T, and increases with increasing magnetic field. In contrast, the Tc1

peak decreases and becomes broader with increasing field.

5.4 Effect of applied magnetic field 65

0.8

1.0

1.2

Cap

acita

nce

(pF

)

0 T 3 T 4 T 5 T 6 T


0 10 20 30 40 500.8

0.9

1.0

5 T 6 T 7 T 8 T

Cap

acita

nce

(pF

)

Temperture (K)

0 T 1 T 2 T 3 T 4 T


0 10 20 30 40 500.9

1.0

1.1

1.2

1.3

4 T 5 T 6 T 7 T 8 T

Cap

acita

nce

(pF)

Temperature (K)

0 T 1 T 2 T 3 T


1.0

1.2

1.4

C

apac

itanc

e (

pF)

0 T 3 T 5 T 7 T


Figure 5.5: Temperature dependence of the c-axis capacitance of Eu1−xHoxMnO3 with x = 0.2, 0.4, 0.5 and

0.75 under various magnetic fields applied along the b-axis.

In order to investigate the low-temperature capacitance anomalies at Tc2 for the x = 0.4, 0.5 and

0.75 samples, we also measured the magnetocapacitance for magnetic fields applied along the b-axis

at different temperatures, as shown in Figure 5.6. For the x = 0.4 and 0.5 samples there are two peaks

in the 5 K magnetocapacitance. The first peak (Hc1) is consistent with the metamagnetic transition

in Figure 5.2. This peak shifts to higher magnetic fields with increasing temperature. In contrast,

the second peak (Hc2) shifts to lower fields with increasing temperature. With further increasing

temperature, a broad peak appears before the magnetocapacitance becomes negative. For the x =

0.75 sample we observe a single broad peak at 5 K for H ∼5 T that shifts to higher fields with

increasing temperature. However, the peak shifts back to lower field above 10 K.


-4

0

4

8

12

MC

( %

)

4K 5K 10K 15K 18K 20K

1 kHz X= 0.4 E//c and H//b

4K10K15K18K20K

-4

0

4

8

12

15K 20K 25K 30K

MC

(%)

5 K 7 K 10 K


0 2 4 6 8 100

2

4

6

8

10

5K 10K 15K

MC

(%)

H (T)


10K

15K

5K

Figure 5.6: Magnetocapacitance of Eu1−xHoxMnO3 with x = 0.4, 0.5 and 0.75 at various temperatures.

In order to clarify the anomalies seen in the temperature and magnetic field dependence of the

capacitance, the c-axis spontaneous polarization for magnetic fields applied along the b-axis was

measured for the x = 0.4 sample, as shown in Figure 5.7. The polarization is suppressed below

a temperature Tc2, which is ∼10 K at 5 T and shifts to higher temperatures as the magnetic field

is increased. This result confirms that the second anomaly in the capacitance (Tc2) is related to

suppression of the polarization. The polarization becomes close to zero at 7 T. In TbMnO3, the c-axis

polarization is suppressed with field due to a polarization flop. However, in our case we do not have

polarization measurements along the other crystallographic axes. Nevertheless, our magnetization

data show similar metamagnetic transitions to those observed in TbMnO3 at the critical field for the

polarization flop. No metamagnetic transition is observed for our x = 0.75 sample, suggesting the

5.4 Effect of applied magnetic field 67

absence of a polarization flop at Tc2.

0 10 20 30 40 500

100

200

300

400

Pc (

C/m

2 )

Temperature (K)

0 T 1 T 3 T 5 T 7 T

x= 0.4 E//c and H//b0T

1T3T

5T7T

x=0.4 P//c and H//b

Figure 5.7: Temperature dependence of spontaneous c-axis polarization of Eu0.6Ho0.4MnO3 under various

magnetic fields applied along the b-axis.

The response of the polarization to applied magnetic field is demonstrated for the x = 0.5 sample

in Figure 5.8. The sudden drop in polarization around 4 T for a field applied along b corresponds

to the Hc1 peak in the magnetocapacitance data, while the second peak (Hc2) corresponds to the

disappearance of polarization. It is interesting to note that the polarization changes sign at Hc1. In

order to confirm the disappearance of the polarization above 6 T, the spontaneous c-axis polarization

was also measured for magnetic fields applied along the c-axis.

-8 -4 0 4 8-80

0

80

160

240

-8 -4 0 4 8-8

-4

0

4

8

Jc (

A/m

2 )

H (T)

P c (C

/ m2 )

H (T)

5 K x= 0.5 P//c and H//b

-8 -4 0 4 80

100

200

300

400

Pc (

C/m

2 )

H (T)

5 K x= 0.5 P//c and H//c

Figure 5.8: Spontaneous c-axis polarization of Eu0.5Ho0.5MnO3 as a function of magnetic field applied along

the b-axis (left panel) and along the c-axis (right panel) at 5K. The inset shows pyroelectric current versus

magnetic field.


5.5. Discussion

Figure 5.9: Magnetic and electric phase diagram of Eu1−xHoxMnO3 in terms of Ho content. The dotted

line indicates the approximate ordering temperature of the Mn spins, which is not observed clearly in our

magnetization measurements. The label AF refers to antiferromagnetic state, FE refers to ferroelectric state and

NP refers to a non-polar state.

The magnetoelectric phase diagram of Eu1−xHoxMnO3 is shown in Figure 5.9. The ordering

temperature of the Mn spins is not clearly observed in our magnetization data, but based on the phase

diagrams of RMnO3 and Eu1−xYxMnO3, it probably lies between 40 K and 50 K. However, the fer-

roelectric transition temperature is well defined by the anomaly in the magnetic susceptibility along

the c-axis where the effect of the rare-earth magnetic moment is weak. In the case of a non-magnetic

R-site, such as Eu1−xYxMnO3, magnetic anomalies were observed in all three crystallographic di-

rections. For x ≤ 0.2, the magnetic structure develops from the AF1 configuration (presumably

sinusoidal) to a canted A-type AF configuration with decreasing temperature, and no spontaneous

polarization is observed. However, spontaneous polarization along the c-axis is observed for x≥ 0.4,

indicating that the spiral magnetic structure is developed in this regime. Although the ionic radius of

Ho3+ (1.072 A) is similar to that of Y3+ (1.075 A), the polarization in Eu1−xYxMnO3 is mainly along

the a-axis, with only a small component along the c-axis for the x = 0.5 compound at temperatures

close to the ferroelectric transition. In Eu1−xHoxMnO3 we only observe spontaneous polarization

along the c-direction, similar to TbMnO3. This suggests that the spiral structure is stabilized in the

bc plane when a large magnetic moment is present on the rare-earth site. The mechanism of this

stabilization might involve 4f-3d interactions [9].

5.5 Discussion 69

Figure 5.10: Schematic picture of the reduction in the orthogonal component of the spiral structure with in-

creasing Ho concentration.

The reason for the decrease in magnitude of the polarization upon increasing the Ho concentra-

tion is schematically described in Figure 4.10. The magnetic moment of Ho increasingly polarizes

the a-axis component of the magnetic spiral with increasing Ho concentration, while the spin com-

ponent in the bc plane decreases. Following the relationship P∼M1M2(e×q) [13], the polarization

is determined by the directions of both the spin rotation and the spiral propagation vector. Therefore,

decreasing the spin component in the bc plane gives rise to a decrease in the value of the spontaneous

polarization. This result is in contrast to the highest measured polarization value of ∼ 2000 µC/m2

for DyMnO3 [6], which has an ionic radius close to the average value of our x = 0.75 sample.

It is interesting to recall that the polarization flop in RMnO3 occurs when the spin rotation in the

bc plane changes to the ab plane under applied magnetic field. The critical fields required to induce

the polarization flop for both the x = 0.4 and x = 0.5 samples are lower than in TbMnO3 (Hb∼4.5

T). Although the average ionic radii of the rare-earth sites in the x = 0.4 (1.091 A) and x = 0.5 (1.096

A) samples are close to that of Tb3+ (1.095 A), we argue that the critical field is more strongly

influenced by the anisotropy of the rare-earth spin [13, 16]. The field dependence of magnetization

of Eu1−xHoxMnO3 is lower than TbMnO3 (see figure 4.1 and 5.2). The saturated moment at 5 K

along the a-axis is only of the order of 3 µB/f.u which is half that of TbMnO3 (∼ 6.2 µB/f.u). These

factors result in the spiral phase in Eu1−xHoxMnO3 being less stable than in TbMnO3, hence the

critical field of the polarization flop is lower. In Eu1−xHoxMnO3 we also observed a change in

sign of the polarization at the critical field (Hc1). This is an interesting phenomenon that should

be investigated further. We note that the decrease in magnitude of the polarization with increasing

field applied along b is due to the decrease in the bc-plane spin component of the magnetic spiral.

The effect of the applied magnetic field in this state results not only in a polarization flop but also

in the eventual disappearance of the polarization, resulting in a non-polar state. The disappearance

of polarization at Hc2 for fields applied along the c-axis, without any anomaly in the polarization

at Hc1, suggests that the magnetic spiral remains in the same direction with the propagation vector

along the b-axis. However, we observe that the polarization also vanishes when the magnetic field is


applied along the b-axis, as shown in Figure 5.8. This suggests that the spins become collinear with

respect to the direction of the magnetic field. This phenomenon is similar to what has previously

been observed in LiCuVO4 [17].

0

10

20

30

40

50

T

(K)

AF2, FE, P//c

AF3FE, P//a

AF4,NP

x= 0.4 H//b

AF1.NP

0

10

20

30

40

50

AF4, NP

AF3, FE. P//a

T (K

)

AF2FE. P//c

x= 0.5 H//b

AF1, NP

0 2 4 6 80

10

20

30

40

50

AF4, NPAF2, P//c

T (K

)

H (T)

AF1, NP

H//bx= 0.75

Figure 5.11: Magnetic-electric phase diagram of Eu1−xHoxMnO3 for x = 0.4, 0.5 and 0.75 in terms of magnetic

field applied along the b-axis. The label AF refers to antiferromagnetic states and NP refers to a non-polar state.

To summarize the effect of applied magnetic fields on the magnetic and electric properties, in

Figure 5.11 we construct magnetoelectric phase diagrams for the x = 0.4, 0.5 and 0.75 samples for

magnetic fields applied along the b-axis. Four phases are apparent in the phase diagram below TN .

For TFE < T < TN we assume that the magnetic structure is sinusoidal AF (AF1). The application

5.6 Conclusion 71

of a magnetic field in the b-direction seems to disturb the bc plane Mn spiral structure (AF2), which

above 15 K presumably becomes collinear (AF4), giving rise to a non-polar state. When T < 15

K, the bc plane spiral structure rotates to the ac plane (AF3) at Hc1, which is accompanied by a

polarization flop from the c-axis to the a-axis. A further transition, presumably to the collinear

AF4 structure, takes place at a higher field Hc2. The region over which the AF3 phase is stable

becomes smaller with increasing Ho3+ content, indicating that this phase is strongly influenced by

the rare-earth site spins.

5.6. Conclusion

We have investigated the effect of doping EuMnO3 with Ho3+ in order to compare the magnetic-

electric phase diagrams of RMnO3 systems with and without magnetic ordering on the rare-earth site.

In the absence of applied magnetic field, the decrease in the average ionic radius of the rare-earth

site with increasing Ho3+ content gives rise to behavior resembling that of undoped RMnO3; the

ordered Mn sublattice develops from a canted A-type configuration for x = 0.2 to a spiral structure at

higher doping. Anisotropic A-site spins might stabilize the Mn-spiral in the bc plane, giving rise to

spontaneous polarization along the c-axis. However, the polarization decreases as the Ho3+ content

increases beyond x = 0.75. When a magnetic field is applied along the b-direction, the critical field

required to induce a flop of the polarization to the a-axis for the x = 0.4 and x = 0.5 samples is

lower than that in TbMnO3, indicating that the anisotropy of the rare-earth site plays an important

role. Based on the phase diagram constructed from our measurements, the region over which the

“flopped” ab plane spiral structure is stable is also affected by the Ho3+ concentration. For x=0.75

the ferroelectric state is eventually suppressed when a magnetic field is applied along the b-axis.

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Chapter 6

Magneto(di)electric coupling in

MCr2O4 (M = Mn, Co, and Ni) spinel

6.1. Introduction

Multiferroics, materials in which ferromagnetism and ferroelectricity coexist, have attracted

much attention in recent years [1–6]. If the coupling between the magnetic and ferroelectric order

(magnetodielectric coupling) is strong enough, multiferroics potentially allow the manipulation of

electric and magnetic moments by magnetic and electric fields, respectively. However, there are still

rather few multiferroics known and the magnetodielectric coupling in many of them is weak. This is

largely due to the fact that in typical ferroelectric oxides the creation of an electric dipole moment in-

volves charge transfer between the occupied 2p orbitals of oxygen and the empty d-shell of the metal

ions. The common mechanism of ferroelectricity thus excludes transition metals with partially-filled

d-orbitals and hence the coexistence of magnetic moments and ferroelectric order [1]. Nevertheless,

in recent years an increasing number of multiferroics have been discovered in which ferroelectricity

arises from different mechanisms. For example, ferroelectricity can be directly induced by frustrated

magnetic ordering in materials such as TbMnO3, TbMn2O5, and Ni3V2O8 [2, 4, 6], which naturally

leads to strong magnetodielectric coupling. One feature common to many of the frustrated magnet

multiferroics is the existence of a spiral or helical spin structure. Here, the direction of the sponta-

neous polarization is perpendicular to both the magnetic propagation vector and to the spin plane of

the spiral. Although the microscopic mechanisms involved in the magnetodielectric coupling in this

class of multiferroics are being widely studied both experimentally and theoretically, in many cases

the mechanisms are not fully understood, especially regarding the strength of the coupling. There-

fore, it is important to investigate magnetodielectric coupling in a wide range of frustrated-magnet

75

76 Magneto(di)electric coupling in MCr2O4 (M = Mn, Co, and Ni) spinel

multiferroics. The materials MCr2O4 (M = Mn, Co and Ni) are ferrimagnetic spinels, in which the

M2+ cations occupy the tetrahedral (A) sites and the Cr3+ cations occupy the octahedral (B) sites. In

single crystal samples the onset of collinear ferrimagnetic ordering occurs at 51 K, 93 K and 74 K,

respectively. A further magnetic transition occurs at Tf ∼ 18 K, 26 K and 31 K, respectively [10,11].

In CoCr2O4 and MnCr2O4 a short-range-ordered (SRO) spiral component develops, giving a conical

magnetic structure below Ts (see Figure 6.1). A “lock-in” transition occurs at 13 K for CoCr2O4 and

at 14 K for MnCr2O4. The magnetic ground state of spinels with spiral or conical structures can be

well described by the parameter u [9]:

u =4JBBSB

3JABSA(6.1)

Here, JBB and JAB are the nearest-neighbor (NN) interactions involving spins SA and SB on the

A and B sites. In this theory the AA nearest-neighbor interaction is neglected. It is important to

note that the possible values of u range from 0 to infinity, corresponding to configurations between a

Neel ferrimagnetic structure and a state characterized by “magnetic geometric frustration” (MGF).

Below u = 8/9 the magnetic structure is described as a Neel long-range ordered configuration [9], in

the range from u = 8/9 to u = 1.298 the magnetic ground state is predicted to be a long-range ordered

spiral structure, and above u = 1.298 the magnetic structure is predicted to be locally unstable with

short-range spiral order [10]. For single crystal samples, the coherence length of the spiral reaches

the order of 10 nm at low temperatures with a propagation vector q = (0.59, 0.59, 0) for MnCr2O4

and 3.5 nm with a propagation vector q = (0.62, 0.62, 0) for CoCr2O4. The corresponding values of u

for MnCr2O4 and CoCr2O4 are 1.5 and 2.0, respectively [10]. In contrast, NiCr2O4 exhibits collinear

antiferromagnetic ordering below Ts with the propagation vector q = (0 0 1) [11]. The value of u

for NiCr2O4 is expected to be larger than that of CoCr2O4 due to the small total magnetic moment.

The rather short correlation lengths (less than 10 nm) of these spiral structures are thought to be

the result of weak geometrical frustration on the spinel B-site; the magnetic exchange interactions

between the A and B sites are weaker than those among the B-sites and are insufficient to suppress

the MGF [10]. Recently, Yamasaki et al. have reported the presence of ferroelectricity in CoCr2O4

single crystals [7], making it one of the few materials to exhibit the coexistence of ferromagnetic and

ferroelectric states. The onset of polarization occurs at Ts ∼ 26 K along the [110] direction and the

polarization can be reversed by switching the direction of the applied magnetic field. It is to be noted

that the polarization in this system is smaller than of the multiferroic RMnO3 perovskites due to the

weak spin-orbit coupling strength of Cr3+ (t32ge0g) compared to Mn3+ (t32ge1

g) [7]. The mechanism

of the induced ferroelectricity in CoCr2O4 can be explained by the spin current model for magnetic

ferroelectricity proposed by Katsura et al. [8]. These results prompted us to investigate the magnetic

and dielectric properties of the series MCr2O4 (M = Mn, Co, and Ni) in order to explore the nature of

6.2 Experiment 77

the magnetodielectric coupling in the spiral (conical) and canting magnetic structures in this system.

(d)

(c)

(b)

(a)

(a)

Figure 6.1: (a) Schematic picture of sublattices in the MCr2O4 spinel structure: tetrahedral A-site and octahe-

dral B1, B2 sites. The orientations of the spins on the A and B-sites are shown for (b) CoCr2O4, (c) MnCr2O4

and (d) NiCr2O4. This figure is taken from Refs. [10, 11].

6.2. Experiment

Polycrystalline samples of MCr2O4 (M = Mn, Co, and Ni) were prepared by solid state reaction

using a stoichiometric mixture of MnCO3, CoO, NiO and Cr2O3. The samples were first sintered

at 1000◦C for 12 h and then at 1300◦C for 24 h in flowing argon, with intermediate grinding. Two

samples of MnCr2O4 were prepared. Sample 1 was compressed hydrostatically at 600 bar in a rub-

ber tube into a rod of diameter 7 mm and length 50 mm (this sample was prepared for the purpose

of crystal growth in a floating zone furnace) before heating at 1300◦C in flowing argon. To prepare

sample 2, sample 1 was crushed and pelletized at 0.27 bar, before sintering at 1300◦C in flowing


argon for 24 h. We attempted to grow single crystals using the floating zone technique, but due

to the evaporation of Cr3+ this was not successful. We also tried to grow single crystals using the

flux technique, but this also failed due to leakage from the platinum crucible. X-ray powder diffrac-

tion at room temperature was performed using a Bruker D8 diffractometer with Cu-Kα radiation.

Magnetization measurements were performed using a Quantum Design MPMS-7 SQUID magne-

tometer. The capacitance was measured using an AH-2500A capacitance bridge and a Quantum

Design PPMS.

6.3. Results


Figure 6.2: X-ray powder diffraction patterns of MCr2O4 (M = Mn, Co, and Ni) at room temperature.

Room-temperature X-ray powder diffraction measurements showed that the MCr2O4 (M = Mn,

Co, Ni) samples were single-phase (see Figure 6.2); MnCr2O4 and CoCr2O4 adopt the cubic spinel

structure with space group Fd3m (227), with lattice parameters of 8.43727(6) A and 8.33335(9) A,

respectively. In contrast, NiCr2O4 adopts a tetragonal spinel structure with space group I41/amd

(141) and lattice parameters of a = 5.83510(12) A and c = 8.43320(14) A. The lattice parameters

of all three synthesized samples are in good agreement with those previously reported [12–14]. In

spinel MCr2O4, M2+ occupies the tetrahedral site and Cr3+ occupies the octahedral site. In NiCr2O4

the tetrahedral site containing Ni2+ (e4t42) has a Jahn-Teller distortion and is elongated along the c-

axis, giving rise to the tetragonal structure.

6.3 Results 79


Figure 6.3: Temperature dependence of magnetization of (a) MnCr2O4 (sample 1), (b) CoCr2O4, and (c)

NiCr2O4 under different applied magnetic fields. The samples were cooled in zero field (ZFC).

The magnetic susceptibility of MCr2O4 (M = Mn, Co, Ni) at different magnetic fields is shown in

Figure 6.3. The onset of ferrimagnetic ordering is observed at 43 K for MnCr2O4, 97 K for CoCr2O4,

and 75 K for NiCr2O4 in a field of 0.1 T. In all of the samples the value of Tc increases with applied

magnetic field and the transition becomes broader. Other anomalies are observed at Ts ∼ 18 K and

Tf ∼ 15 K for MnCr2O4, and Ts ∼ 27 K and Tf ∼ 15 K for CoCr2O4, which correspond to the

temperatures where the spiral component appears and to the “lock-in” transition at which the spiral

becomes fully developed, as reported by Tomiyasu et al. [10]. In MnCr2O4, both anomalies become

less well defined when the field is increased. In CoCr2O4, the anomalies are still visible up to at


least 3 T. For NiCr2O4 only one anomaly is observed at Ts ∼ 31 K, which corresponds to the onset

of the canted antiferromagnetic structure [11]. Similar to CoCr2O4, this anomaly is not affected

by increasing the magnetic field up to 3 T. Figure 6.4 shows plots of magnetization versus field at

various temperatures. The spontaneous magnetizations of MnCr2O4, CoCr2O4 and NiCr2O4 at 5 K

are estimated to be approximately 1 µB/f.u., 0.15 µB/f.u. and 0.2 µB/f.u., respectively, by linearly

extrapolating the high-field magnetization to zero field. All of these values are in good agreement

with those previously reported [10–12, 16]. These results indicate that as the magnetic moment on

the A-sites decreases, the exchange interaction between the A and B-sites leads to an increase of the

cone angle associated with the A, B1, and B2 sites. According to the theory of Lyons et al. [9], this

is also associated with an increase in the value of u. Larger values of u will result in a greater degree

of hysteresis in the magnetization versus field loops.

Figure 6.4: Field dependence of magnetization at various temperatures for (a) MnCr2O4 (sample 1), (b)

CoCr2O4, and (c) NiCr2O4.

6.3 Results 81


The temperature dependence of the dielectric constant of MCr2O4 (M = Mn, Co, Ni) is shown

in Figure 6.5. Three anomalies are apparent for MnCr2O4 and CoCr2O4, at approximately the same

temperatures as the magnetic transitions. The small differences in transition temperatures are prob-

ably due to differences in temperature between the sensor and sample during heating. For MnCr2O4

the temperature dependence of the dielectric constant was measured for both samples. In sample

1 (pelletized at 600 bar), the dielectric constant increases with decreasing temperature and reaches

a plateau at 43 K, corresponding to the ferromagnetic transition. The dielectric constant then falls

more rapidly at Ts and shows a further anomaly at Tf , which is suppressed with increasing magnetic

field. For sample 2, the dielectric constant decreases with decreasing temperature and changes slope

at Ts. Although the behavior at Ts and Tf is similar to that of sample 1, no anomaly is seen at the mag-

netic ordering temperature and the reason for the difference in slope above TN is unclear. We suggest

that this phenomenon may be due to the difference in density of the two polycrystalline samples. In

this case, extrinsic effects due to factors such as the electrodes and contacts, grain boundaries and

porosity would play a significant role.

Figure 6.5: Temperature dependence of dielectric constant at various magnetic fields for (a) MnCr2O4 (sample

1), (b) MnCr2O4 (sample 2), (c) CoCr2O4, and (d) NiCr2O4.

The dielectric constant of CoCr2O4 has previously been measured by Lawes et al. [13]; anoma-

lies were observed at T ∼ 50 K and Ts ∼ 27 K and were assigned to the onset of short-range magnetic


order and long-range magnetic order, respectively. It was argued using specific heat data that the cor-

relation length of the spiral state is different in single crystal and polycrystalline samples; in the latter

a long-range ordered (LRO) spiral develops below Ts. In contrast, we only observe anomalies at 27

K and 15 K (see Figure 6.5(b)); these agree with the onset temperature of the SRO conical structure

and the “lock-in” transition reported by Tomiyasu et al., who carried out magnetic measurements

and neutron diffraction measurements on single crystal samples [10]. The dielectric anomaly at Tf

becomes less well-defined with increasing magnetic field. In NiCr2O4, the temperature dependence

of the dielectric constant shows changes in slope at TN and Ts; the profile remains unchanged on

applying magnetic fields of up to 3 T.

Figure 6.6: Dielectric constant as a function of magnetic field (in the form of magnetodielectric response- see

text for definition) for (a) MnCr2O4, (b) CoCr2O4, and (c) NiCr2O4.

6.4 Discussion 83

Figure 6.6 shows the magnetocapacitance of the three compounds, that is, the dielectric constant

as a function of magnetic field. We define the magnetodielectric response (MD) as MD = (ε(H)-

ε(0))/ε(0), where ε(H) is the dielectric constant under field and ε(0) is the dielectric constant in

the absence of any magnetic field. For MnCr2O4, the dielectric constant suddenly drops (negative

magnetocapacitance) in very low magnetic fields. Moreover, the unusual magnetocapacitance pro-

file develops an asymmetric shape below Tf ; it is symmetric at temperatures above Ts. In contrast,

the magnetodielectric profiles of CoCr2O4 and NiCr2O4 indicate a sharp increase in the dielectric

constant in low magnetic fields, and are symmetric at all temperatures. The magnitude of the mag-

netodielectric response increases in the order MnCr2O4, CoCr2O4 and NiCr2O4.

6.4. Discussion

In order to investigate the magnetodielectric coupling in spinel MCr2O4 (M = Mn, Co, Ni), we

consider the trend of the dielectric constant below Ts. Because MCr2O4 is non-polar between Tc

and Ts [7], we have taken a linear extrapolation of the dielectric constant from this region down

to low temperature. The insets in Figure 6.7 show the residual dielectric constant after subtraction

of the linearly extrapolated values and division by the dielectric constant at 5K (-4ε/ε5K). The

residual dielectric constant, that is, the deviation from the extrapolated value, increases in the order

MnCr2O4, CoCr2O4 and NiCr2O4. The magnitude of the residual dielectric constant corresponds to

the magnetodielectric coupling strength, thus large deviation from the linearly extrapolated values

indicates large magnetodielectric coupling. In order to explain this phenomenon, we consider the

spin-orbit coupling and orbital degrees of freedom of M2+. The spin-orbit coupling is defined as

λL.S where L is the orbital angular momentum and S is the total spin. In MnCr2O4, Mn2+ (d5) has

L=0 hence no spin-orbit coupling. For CoCr2O4, Co2+ (d7) has , in tetrahedral coordination, a non-

quenched orbital orbital moment and spin orbit coupling can affect the magnetodielectric coupling.

For NiCr2O4, The Ni2+ (d8) in tetrahedral coordination is Jahn-Teller active. For this system we

observe the largest magnetodielectric coupling. We conclude that the orbital degree of freedom for

Ni2+ provides stronger coupling than the spin-orbit coupling in CoCr2O4. A similar observation

was previously made in MnT2O4 (T = Mn, V, Cr) [17], where it was proposed that the presence of

orbital degrees of freedom is a key factor in the correlation between magnetic properties, dielectric

properties and the crystal structure.


Figure 6.7: Temperature dependence of dielectric constant of MCr2O4 (M = Mn, Co, Ni). The insets show the

negative of the residual dielectric constant after subtraction of the linearly extrapolated value and division by

the dielectric constant at 5K (-4ε/ε5K).

The LRO ferrimagnetic structure and the SRO spiral structure are known to coexist below Tf in

MnCr2O4 and CoCr2O4. In MnCr2O4, there are two sets of spiral domains with propagation vectors

parallel to the [110] and -[110] directions for an easy axis parallel to [110]. In contrast, CoCr2O4

has four spiral domains with propagation vectors ±[110] and ±[110] for an easy axis along the

[001] direction [10]. Moreover, the correlation length of the spiral in single crystal MnCr2O4 (9.9

nm) is larger than that in CoCr2O4 (3.1 nm). This difference might cause the dielectric anomaly

at Tf to be more pronounced in MnCr2O4 than in CoCr2O4. For MnCr2O4, the dielectric anomaly

at Tf is suppressed by increasing the magnetic field. We believe that this phenomenon indicates an

increasing correlation length of the spiral structure. The spins will tend to align with the magnetic

6.4 Discussion 85

field, and consequently the propagation vectors in the two domains will also become aligned in the

same direction. Thus, the transition to the SRO spiral state at Tf will be suppressed, along with the

dielectric anomaly here. For CoCr2O4 the anomaly at Tf is much smaller, hence it is difficult to ob-

serve any change on the application of a magnetic field. The asymmetric magnetodielectric behavior

in MnCr2O4 is more difficult to explain. A similar phenomenon has previously been observed in

Mn3O4, for which it was argued that the asymmetry is due to the magnetic hysteresis present at low

temperatures [15]. We believe that this argument is invalid because we do not observe magnetic

hysteresis in our magnetization measurements of MnCr2O4. Moreover, in CoCr2O4 and NiCr2O4

where magnetic hysteresis is observed, the magnetodielectric behavior is symmetric. We suggest

that the increasing correlation length of the spiral structure with increasing field in MnCr2O4 might

be responsible. Further investigation of the magnetodielectric response on single crystals might give

a better understanding of this phenomenon.

Figure 6.8: Magnetodielectric response (black data points) and the square of the magnetization (colored data

points) as a function of magnetic field for (a) MnCr2O4, (b) CoCr2O4, and (c) NiCr2O4.


In Figure 6.8 we superimpose plots of the magnetodielectric response and the square of the mag-

netization for all three samples. The two types of plot overlie each other more closely for MnCr2O4

than for CoCr2O4 and NiCr2O4. Nevertheless, the magnetodielectic (-4ε/εH=0) response scales

approximately with the square of the magnetization (M2) for all three samples. This suggests that

the magnetodielectric coupling originates from the P2M2 term in the free energy expansion, which

is always allowed by symmetry in ferroelectromagnetic materials [11]. The magnitude of the mag-

netodielectric response (-4ε/εH=0)) increases in the order MnCr2O4, CoCr2O4 and NiCr2O4. This

result is consistent with the residual dielectric constant (-4ε/ε5K) at low temperatures in Figure 6.7.

Nevertheless, the magnetodielectric effect in these spinel materials is small compared to other multi-

ferroics such as TbMnO3, which has a magnetocapacitance of 10%, even though the ferroelectricity

in MnCr2O4 and CoCr2O4 is also induced by the magnetic structure. This result indicates that im-

proper ferroelectricity, such as ferroelectricity induced by the magnetic structure, is no guarantee of

obtaining a large magnetodielectric effect.

6.5. Conclusion

We have investigated the magnetic and dielectric properties of polycrystalline samples of the

spinels MCr2O4 (M = Mn, Co, and Ni). Coupling between the dielectric and magnetic properties

is observed at the onset of the magnetic spiral structure (TS) and at the “lock-in” transition (Tf ) in

MnCr2O4 and CoCr2O4, and also at the onset of the canted structure (Ts) in NiCr2O4. The strength

of the magnetodielectric coupling in this system can be explained by taking into account the spin-

orbit coupling and presence or absence of orbital degrees of freedom on the tetrahedral site. The

dielectric anomaly at Tf for MnCr2O4 is suppressed under applied magnetic fields, indicating that

the correlation length of the spiral structure increases with field. This effect might also be respon-

sible for the asymmetric behavior of the magnetodielectric response in MnCr2O4 below Tf . The

magnetodielectric response in applied magnetic fields scales with the square of the magnetization

for all three samples. Thus, the magnetodielectric coupling in this state appears to originate from

the P2M2 term in the free energy. The magnetodielectric effect in all three MCr2O4 materials is very

small, which implies that frustrated materials showing magnetically induced ferroelectricity do not

necessarily exhibit large magnetodielectric effects.

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[7] Y. Yamasaki, S. Miyasaka, Y. Kaneko, et al., Phys. Rev. Lett. 96, 207204 (2006).


[9] D. H. Lyons, K. Dwight, T. A. Kaplan, et al., Phys. Rev. 126, 540 (1962).

[10] K. Tomiyasu, J. Fukunaga, and H. Suzuki, Phys. Rev. B 70, 214434 (2004).

[11] K. Tomiyasu, I. Kagomiya, J. Phys. Soc. Japan 73, 2539 (2004).

[12] J. M. Hastings and L. M. Corliss, Physical Review 126, 556 (1962).

[13] G. Lawes, B. Melot, K. Page, C. Ederer, M. A. Hayward, Th. Proffen, and R. Seshadri, Phys.

Rev. B 74, 024413 (2006)

[14] E. Prince: J. Appl. Phys. 32, 68S (1961)

[15] R. Tackett, G. Lawes, B. C. Melot, M. Grossman, E. S. Toberer, and R. Seshadri, Phys. Rev. B

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87

88 BIBLIOGRAPHY

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Chapter 7

Magnetoelectric coupling in MnTiO3

7.1. Introduction

MnTiO3 adopts the ilmenite structure (space group R3) in which Mn2+ and Ti4+ layers alternate

along the c-axis of the lattice in the hexagonal setting [1–3]. The Mn2+ spins align in antiferromag-

netic (AF) fashion both along the c-direction and within each layer (see Figure 7.1). The magnetic

susceptibility of single crystal MnTiO3 measured by Akimitsu et al. [6] and of polycrystalline sam-

ples measured by Stickler et al. [2] revealed two-dimensional (2D) characteristics; that is, a broad

peak was observed at ∼100 K, and no anomaly was apparent at the Neel temperature (TN) of 63 K,

which was determined by ESR (electron spin resonance) measurements. This behavior is in contrast

with that of other AF ilmenite oxides such as FeTiO3, CoTiO3, and NiTiO3, in which sharp anoma-

lies appear at TN . However, a later study by Yamauchi et al. on a MnTiO3 single crystal showed both

a change in slope of the magnetic susceptibility at TN for fields applied parallel to the c-axis and a

minimum near 50 K for fields applied perpendicular to the c-axis. This anisotropy did not disappear

at TN but persisted up to 95 K [7]. Furthermore, a flop in the magnetization was observed at H ∼ 6

T for magnetic fields applied parallel to the c-axis. A neutron diffraction study by Akimitsu showed

that the Mn spins have 3D Heisenberg character below TN [4, 6], in which the sublattice magnetiza-

tion follows a power law expressed by M(T )∼ (1−T/TN)β , with β = 0.32±0.01 [5]. The ordering

develops 2D character at higher temperature due to the diminishing strength of the interlayer ex-

change interactions. The magnetic symmetry below TN was reported as R3′ [1], which allows the

linear magnetoelectric (ME) effect, with the non-zero tensor elements α11=α22, α33, and α12=α21 .

In magnetoelectric materials, electrical polarization is induced by an applied magnetic field below

the magnetic ordering temperature. Thus far, no experimental evidence of the linear ME effect has

been reported in this compound. This motivated us to study the nature of the magnetoelectric and

magnetodielectric coupling in MnTiO3.

89

90 Magnetoelectric coupling in MnTiO3

ch

ah = 5.144 Åch = 15.278 Å

Figure 7.1: Rhombohedral magnetic structure of MnTiO3 showing the five principal exchange interactions J1,J2, J3, J4 and J5. This figure is taken from Ref. [7].

7.2. Experiment

A single crystal of MnTiO3 was grown by the floating zone technique using a 4-mirror furnace

(Crystal Systems Corp. FZT-1000-H-VI-VP). The feed rod was prepared by the standard solid state

reaction of stoichiometric quantities of MnCO3 and TiO2 in air. The crystal growth rate was between

1.5 and 5 mm/h and was carried out in air. The seed and feed rods were counter-rotated at a speed of

15-20 rpm. The resulting crystals were oriented using Laue diffraction. The dielectric constant was

measured using an Andeen-Hagerling AH-2500A capacitance bridge operating at a fixed frequency

of 1 kHz. The pyroelectric current was measured using a Keithley 6517A electrometer after poling

the crystals in an electric field of ∼250 V/mm while cooling from above TN . The spontaneous

polarization was obtained by integration of the pyroelectric current. The temperature and magnetic

field were controlled through a Physical Properties Measurement System (Quantum Design), using

a home-made insert and wiring.




20 30 40 50 60

0.0

0.4

0.8

1.2

1.611

0

116

MnTiO2

Inte

nsity

(104 a

.u)

2 theta

Observed Calculated Difference

TiO2

104

Figure 7.2: X-ray powder diffraction pattern of crushed MnTiO3 single crystal at room temperature. Small

impurity peaks were observed and identified as TiO2

The crystal structure of MnTiO3 can be envisaged in either a rhombohedral or hexagonal setting;

previous studies have mostly used the latter. Figure 7.2 shows an X-ray diffraction pattern of a

crushed MnTiO3 single crystal sample. The peaks corresponding to the major phase can be fitted

using a model with the R3 space group and with lattice parameters of a = 5.138 A and c = 14.2830

A, which are in good agreement with data reported previously [7,8]. A small quantity of an impurity

phase (∼2%) was also observed and identified as TiO2.



Figure 7.3: Temperature dependence of parallel and perpendicular magnetic susceptibilities of MnTiO3. The

measurements were performed with an applied field of 0.1 T.

The temperature dependence of the magnetic susceptibility of MnTiO3 parallel (χ‖c) and per-

pendicular (χ⊥c) to the hexagonal c-axis is shown in Figure 7.3. The value of χ‖c initially increases

with temperature and shows a change of slope at TN = 64 K, as well as a broad maximum at ∼95

K. In contrast, χ⊥c is almost constant below TN before increasing suddenly at 45 K. We expect that

this anomaly is due to an Mn3O4 impurity, the magnetic structure of which is ferrimagnetic below

Tc = 45 K.


Figure 7.4: Temperature dependence of dielectric constant of MnTiO3 parallel and perpendicular to the c-axis.


The dielectric constant of MnTiO3 was measured as a function of temperature for orientations

parallel (ε‖c) and perpendicular (ε⊥c) to the hexagonal c-axis (see Figure 7.4). No anomalies were

observed at TN for either direction. However, a small anomaly is apparent at ∼43K; comparing with

the magnetization data, we suggest that this anomaly originates from the Mn3O4 impurity. When a

magnetic field is applied, we observe a sharp peak at TN for H, E‖c. This peak increases in intensity

with increasing magnetic field. For E, H⊥c, no anomaly was observed up to 8 T (see Figure 7.5).

We also measured the dielectric constant for H⊥c, E‖c and for H‖c, E⊥c (not shown in this thesis)

and again no anomalies were observed in either case. We note that for each measurement we cooled

the samples from the paramagnetic state at T ∼ 100 K while continuously applying the magnetic

field in order to obtain a single magnetic domain.

Figure 7.5: Temperature dependence of dielectric constant of MnTiO3 (a) parallel to the c-axis and (b) perpen-

dicular to the c-axis.

7.3.4. Polarization

In order to prove the presence of the linear ME effect in MnTiO3, it is important to measure

electrical polarization. Figure 7.6 shows the temperature dependence of the pyroelectric current and

polarization for E, H‖c. At zero field, no anomaly in the pyroelectric current is observed. However,

when a magnetic field is applied, an anomaly in the pyroelectric current corresponding to the onset

of polarization is apparent; the broad peak increases in intensity with magnetic field up to 6 T and

then decreases at 8 T due to the presence of a spin flop transition [7]. The maximum polarization

is 12 µC/m2. We note that in order to measure the polarization it was necessary to cool the sample

through TN with simultaneously applied electric and magnetic fields in order to obtain a single AF

domain. For E, H⊥c we did not observe any polarization.


0 20 40 60 80 1000

5

10

15

P (

C/m

2 )

Temperature (K)

0 T 2 T 4 T 6 T 8 T

5K/min E, H // c

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Pyr

oele

ctric

cur

rent

(A

/m2 )

0 T 2 T 4 T 6 T 8 T

5K/min E, H //c

Figure 7.6: Temperature dependence of (a) pyroelectric current and (b) polarization of MnTiO3 under magnetic

field.

We also measured polarization as a function of magnetic field, as shown in Figure 7.7. The

polarization has a linear response to magnetic field up to 3 T and becomes non linear at high magnetic

field. This result confirms that MnTiO3 is a linear magnetoelectric material.

-8 -4 0 4 8-8

0

8

P (

C/m

2 )

H (Tesla)

50 K E// and H//c

Figure 7.7: Magnetic field dependence of polarization of MnTiO3 at 50 K

7.4 Discussion 95

7.4. Discussion

Based on our polarization measurements, it is clear that MnTiO3 displays linear ME behavior

(see figure 7.6). That is, the polarization appears when a magnetic field is applied in a particular

direction and the polarization has a good linear response to magnetic field at when measured at

constant temperature (see figure 7.7). In MnTiO3 the polarization is induced when magnetic and

electric fields are applied along the hexagonal c-axis, which is allowed for the magnetic point group

3′.

Recently, Nenert et al. suggested that linear ME materials could exhibit stronger magnetodielec-

tric coupling than multiferroics in which symmetry does not allow the linear ME effect [9]. Linear

ME materials are characterized by linear terms in the free energy such as PM2 or LMP (P is the

polarization, M is the total magnetization, and L is the AF order parameter); the coupling in all other

multiferroics, for example YMnO3 [10], includes the biquadratic term P2M2. However, in MnTiO3

there is no dielectric anomaly at TN ; thus, we have shown that linear ME materials do not necessarily

have strong magnetodielectric coupling.

Although the dielectric constant shows an anomaly at 45 K, we believe that it originates from a

Mn3O4 impurity phase. The magnetodielectric coupling of Mn3O4 has been studied recently, and

explained by a mechanism based on spin-phonon coupling [11] and single-ion spin anisotropy [12].

The inset to Figure 7.5(a) shows the appearance of a dielectric peak at TN when a magnetic

field is applied along the hexagonal c-axis; the peak increases with increasing magnetic field. The

appearance of this anomaly coincides with the emergence of the induced polarization. The mag-

netodielectric coupling in AF linear ME materials is characterized by the free-energy term LMP,

where at non-zero magnetic fields the polarization P couples directly to the AF order parameter L.

This gives rise to a divergence in the dielectric susceptibility at TN . This dielectric behavior is similar

to that of a proper ferroelectric near the critical temperature.

7.4.1. Theoretical approach

In order to explain the behavior of the magnetic and dielectric susceptibilities in the vicinity of

TN , we expand the expression for the Landau free energy as follows:

F =a2

L2 +b4

L4 +g2

L2H2− αLEH− χ(0)m

2H2− χ(0)

e

2E2 (7.1)

Here, a = A(T −TN(0)), g is the coupling between the AF order parameter (L) and the uniform

applied magnetic field (H), α is the magnetoelectric coupling, and χ(0)m and χ(0)

e are the magnetic

and dielectric susceptibilities in the absence of ordering. If we differentiate F with respect to L, we

obtain:


∂F∂L

= (a+gH2)L+bL3− αEH = 0 (7.2)

In the absence of an electric field (E = 0),

L = (a+gH2)L+bL3 = 0 (7.3)

Because a is defined as A(T −TN(0)), we can express a + gH2 = A(T −TN(H)). We can then

extract the shift of TN with magnetic field:

TN(H) = T (0)N − gH2

A(7.4)

Using equations 7.3 and 7.4 we can obtain expressions for the order parameter L at E = 0:

L = 0 for T > TN , and L =

√A(TN(H)−T )

bfor T < TN (7.5)

Now, let us consider the magnetization (M) and polarization (P):

M =∂F∂H

= αLE +(χ(0)m −gL2)H (7.6)

P =∂F∂E

= αLH + χ(0)e E (7.7)

The magnetic susceptibility is the derivative of M with respect to H:

χm =∂M∂H

= χ(0)m −gL2 +

∂L∂H

(αE−2gLH) (7.8)

When E = H = 0, we obtain

∆χm = χm−χ(0)m =−gL2 for T < TN(H) (7.9)

Here, it is apparent that ∆χm is non-zero, hence we can expect an anomaly in the magnetic

susceptibility measurement at TN , as shown in Figure 7.3.

In order to obtain the dielectric susceptibility of MnTiO3, we must differentiate P with respect

to E:

χe =∂P∂E

= χ(0)e − α

∂L∂E

H (7.10)

If we differentiate equation 7.2 with respect to E, we obtain

(a+gH2 +3bL2)∂L∂E

− αH = 0 (7.11)

7.5 Conclusions 97

We can now combine equation 7.11 and equation 7.5 for the case of E = 0:

(∂L∂E

)

E=0=

αHA(T −TN(H))

for T > TN(H)(

∂L∂E

)

E=0=

12

αHA(TN(H)−T )

for T < TN(H)(7.12)

If we combine equations 7.10 and 7.12, we obtain:

∆χe = (χe)E=0−χ(0)e =

α2H2

A(T −TN(H))for T < TN(H)

∆χe =12

α2H2

A(TN(H)−T )for T > TN(H)

(7.13)

It is apparent that ∆χe is proportional to H2. Therefore, when H = 0, ∆χe is also zero and

hence we do not observe any dielectric anomaly at TN . However, when a magnetic field is applied,

∆χe becomes non-zero, and as a consequence a dielectric anomaly appears at TN . We suggest that

this result is general for antiferromagnetic linear magnetoelectric materials that can described by

equation 7.1

7.5. Conclusions

We have shown that MnTiO3 is a linear magnetoelectric material. At zero magnetic field, there

is no magnetodielectric coupling in this compound, which is in contrast to previous predictions for

linear magnetoelectrics. However, when a magnetic field is applied, the dielectric constant diverges

at TN due to the linear coupling between the polarization P and the AF order parameter L. We have

explained the magnetic and dielectric properties based on a Landau free energy expansion. This

provides an easy method to recognize linear magnetoelectric materials.

Bibliography

[1] G. Shirane, S. J. Pickart, and Y. Ishikawa, J. Phys. Soc. Japan 14, 1352 (1959)

[2] J. J. Stickler, S. Kern, A. Wold, et al., Phys. Rev. 164, 765 (1967).

[3] J. Akimitsu, Y. Ishikawa, and Y. Endoh, Solid State Communications 8, 87 (1970).

[4] J. Akimitsu and Y. Ishikawa, Solid State Communications 15, 1123 (1974).

[5] J. Akimitsu and H. Yamazaki, Phys. Lett. A 55, 177 (1975).

[6] J. Akimitsu and Y. Ishikawa. J. Phys. Soc. Jpn. 42 (1977), p. 462.

[7] H. Yamauchi, H. Hiroyoshi, M. Yamada, et al., Journal of Magnetism and Magnetic Materials

31-4, 1071 (1983).

[8] J. Ko and C. T. Prewitt, Phys. Chem. Miner. 15, 355 (1988)

[9] G. Nenert, and T. T. M. Palstra, Journal of Physics: Condensed Matter 19, 406213 (2007).

[10] A.A. Nugroho, N. Bellido, U. Adem, et al., Phys. Rev. B 75, 174435 (2007).

[11] R. Tackett, G. Lawes, B. C. Melot, et al., Phys. Rev. B 76, 024409 (2007).

[12] T. Suzuki and T. Katsufuji, Phys. Rev. B 77, 220402 (2008).

99

Summary

Multiferroics are materials that display spontaneous ferroelectric and magnetic ordering at the

same time. Magnetoelectrics are materials in which an electric polarization can be induced by an

applied magnetic field. The cross-coupling between the magnetism and ferroelectricity can poten-

tially be exploited in the construction of novel, multifunctional spintronic devices. However, there

are still rather few multiferroics known and the magneto(di)electric coupling in many of them is too

weak to be useful for applications. Therefore, a better understanding of the mechanisms of mag-

neto(di)electric coupling is required, as well as finding parameters by which the coupling may be

controlled.

There are several typical mechanisms by which multiferroic behaviour can be generated, includ-

ing ferroelectricity that is induced by spiral magnetic ordering. In this thesis, we mainly focus on

investigating the magnetoelectric coupling in spin-spiral systems because the polarization is often

highly tuneable using applied magnetic fields, a useful property for future applications. We choose

two systems in this class of materials; the orthorhombic rare-earth manganites RMnO3 and the chro-

mate spinels MCr2O4. In the RMnO3 system, we have investigated both the effect of substituting

the R3+ cation by divalent Ca2+, and the effect of mixing a non-magnetic rare-earth (Eu3+) with

a strongly magnetic rare-earth (Ho3+). The aim of these investigations was to find parameters that

enable systematic control of the electric and magnetic properties and the coupling between them. In

the spinel MCr2O4, the investigation was focused on understanding the mechanism of the magne-

todielectric coupling present in this system.

Another of our investigations focused on better understanding the magnetodielectric coupling

in linear magnetoelectric materials. Based on crystallographic and magnetic symmetry arguments

we identified MnTiO3 as a magnetoelectric material. We have used Landau theory to model the

experimentally measured magnetodielectric phenomena in this compound.

In Chapter 1, we introduce and explain the terms “multiferroic”, “magnetoelectric” and “mag-

netodielectric” and the relations between them. We briefly give an overview of known multiferroic

materials including the early history of multiferroics, recent discoveries that have led to a revival of

101

102 Summary

interest in this field, and a general classification of multiferroics with examples and basic theory. We

also describe the general issues and goals that have motivated our study.

Chapter 2 focuses on the experimental techniques used in our studies, which involve the prepa-

ration of single-crystal samples, structural characterization and physical measurements. Details of

standard magnetization, dielectric, and pyroelectric measurements and special techniques such as

single crystal neutron diffraction are discussed.

Chapter 3 discusses the effect of Ca-doping in single-crystal Tb1−xCaxMnO3 (x ≤ 0.1) on the

crystal and magnetic structures, magnetocapacitance, and electric polarization. We demonstrate that

the presence of Mn4+ ions on the perovskite B-site plays a significant role in causing the ferroelec-

tricity to disappear with doping. We explain this behavior in terms of the perovskite tolerance factor,

a general concept that can be used to predict the ferroelectricity in this system. We also demonstrate

the existence of an intermediate state at x = 0.05 that resembles a relaxor ferroelectric. Neutron

diffraction indicates that the coherence length of the Mn spin-spiral decreases in this composition,

without a change in the Mn-spin modulation wavevector. We claim that this forms a new class of

relaxor ferroelectrics.

In Chapter 4 we present the phenomenon of a magnetic-field induced ferroelectric to relaxor

crossover in Tb0.98Ca0.02MnO3. This effect can be explained based on a decreasing coherence length

of the Mn spin-spiral structure with increasing magnetic field. We propose that the electron hopping

rate increases with magnetic field and is responsible for the decreased spiral coherence length. We

also show that the wavevector of the Mn spin-spiral structure in Tb0.98Ca0.02MnO3 does not change

at the critical field of 6 T required to induce a polarization flop, which is in contrast to undoped

TbMnO3. These results imply that a rotation of the spin-spiral plane with magnetic field plays a more

important role in the mechanism of the polarization flop than a transition from an incommensurate

to commensurate spin structure.

In Chapter 5 we investigate the effect of doping EuMnO3 with Ho3+ in order to compare the

magnetic-electric phase diagrams of RMnO3 systems with and without magnetic ordering on the

rare-earth site. In the absence of an applied magnetic field, the decrease in the average ionic radius

of the rare-earth site with increasing Ho3+ content gives rise to behavior resembling that of undoped

RMnO3; the ordered Mn spin sublattice evolves from a canted A-type configuration for x = 0.2 to

a spiral structure at higher doping. We demonstrate that the magnetic moment of the A-site spins

might stabilize the Mn-spiral in the bc plane, giving rise to spontaneous polarization along the c-

axis. However, the polarization decreases as the Ho3+ content increases beyond x = 0.75, contrary

to expectations based on the perovskite tolerance factor. We suggest that this phenomenon is due

to a decreasing coherence length or spin component of the spin-spiral structure. When a magnetic

field is applied along the b-direction, the critical field required to induce a flop of the polarization

103

to the a-axis for the x = 0.4 and x = 0.5 samples is lower than that in TbMnO3, indicating that

the anisotropy of the rare-earth site plays an important role. Moreover, the temperature and field

region over which the “flopped” ab-plane spiral structure is stable is also affected by the Ho3+

concentration. Based on magnetic and dielectric measurements we construct a magnetic-electric

phase diagram for Eu1−xHoxMnO3.

In Chapter 6, we study the nature of the magnetodielectric coupling in polycrystalline samples

of the spinel MCr2O4 (M = Mn, Co, and Ni). We demonstrate that the residual dielectric constant,

that is, the deviation from the high-temperature extrapolated value, increases in the order MnCr2O4,

CoCr2O4 and NiCr2O4. This indicates that the spin-orbit coupling and orbital degree of freedom

on the tetrahedral site makes a significant contribution to the magnetodielectric coupling. We show

that the magnetodielectric response scales approximately with the square of the magnetization (M2),

indicating that the origin of the magnetodielectric coupling in this system is due to the term P2M2 in

the Landau free energy expansion.

Finally, in Chapter 7 we use polarization measurements to present experimental evidence for the

presence of the linear magnetoelectric effect in MnTiO3, where the electrical polarization is induced

by an applied magnetic field. We demonstrate that there is no dielectric anomaly at the onset of

magnetic ordering in the absence of magnetic field. This observation is in contrast to previous

suggestions that magnetoelectric materials always display strong magnetodielectric coupling. A

dielectric anomaly at the magnetic ordering temperature is only observed when a magnetic field is

applied. We explain this phenomenon using Landau theory. We find that the dielectric anomalies are

linearly correlated with the square of the magnetic field.

Samenvatting

Multiferroica zijn materialen die tegelijkertijd spontane ferroelektrische en magnetische orden-

ing vertonen. Magnetoelektrica zijn materialen waarin de elektrische polarisatie gegenereerd wordt

door een magnetisch veld. De kruislingse koppeling tussen ferroelektrische- en magnetische eigen-

schappen kan zich bij uitstek verdienstelijk maken in innovatieve multifunctionele spintronica. Helaas

is in de meeste materialen de koppeling te zwak om in functionele spintronica toegepast te kunnen

worden. Het is daarom van belang om de parameters te vinden die de koppeling bewerkstelligen

en daarnaast een beter inzicht te krijgen in de magneto(di)elektrische koppelingsmechanismen. Er

bestaan tal van mechanismen om multiferroisch gedrag tot stand te brengen, waaronder magnetische

spiraal ordening.

Dit proefschrift richt zich hoofdzakelijk op onderzoek naar magnetoelektrische koppeling in

spin-spiraal systemen. Het voordeel van deze systemen is dat ze een zeer gevoelige aansturing

van elektrische polarisatie toelaten door middel van aangelegde magnetische velden. Binnen deze

materiaalklasse hebben we twee systemen uitgekozen: orthorhombische zeldzame-aardmanganaten

RMnO3 en chromaat spinels MCr2O4. In het RMnO3 systeem hebben we zowel het effect van Ca2+

substitutie voor het zeldzame aardmetaal als het inmengen van het niet magnetische zeldzame aard

Eu3+ met het sterk magnetisch Ho3+ ion op de R-locatie bestudeerd. Het doel van het onderzoek

is om parameters te vinden die van belang zijn voor een goede beheersing van zowel elektrische als

magnetische eigenschappen en de koppeling daartussen mogelijk maken. In de spinel MCr2O4 stond

de opheldering van het koppelingsmechanisme centraal.

Verder hebben we een onderzoekslijn uitgezet naar magneto(di)elektrische koppeling in lineaire

magnetoelektrische materialen. Op basis van kristallografische en magnetische symmetrie argu-

menten hebben we MnTiO3 aangemerkt als magnetoelektrisch materiaal. Met behulp van Landau

theorie hebben we een model geformuleerd dat de experimenteel gemeten magnetodielektrische

fenomenen kan beschrijven.

In hoofdstuk 1 maken we kennis met de begrippen multiferroisch, magnetoelektrisch en magne-

todielektrisch en schetsen we verbanden daartussen. We geven een beknopt overzicht van bekende

105

106 Samenvatting

multiferroische materialen. Hierbij belichten we niet alleen de geschiedenis van multiferroica, maar

ook de recente ontdekkingen die eraan bijgedragen hebben dat dit onderzoeksveld wederom onder

de aandacht kwam. Verder presenteren we een algemene klassificatie van multiferroica met voor-

beelden die vergezeld worden van theorie. We formuleren de algemene vraagstukken en kerndoelen

die het onderzoek instigeerden.

Hoofdstuk 2 richt zich op de experimentele technieken die in dit onderzoek worden toegepast.

Hierbij valt te denken aan het groeien van eenkristallen en de daaropvolgende structuuropheldering

en fysische karakterisatie. We behandelen niet alleen details van standaardtechnieken als magneti-

satie, dilektrische en pyroelektrische metingen, maar ook van meer specialistische technieken zoals

eenkristal neutronen diffractie.

In hoofdstuk 3 bespreken we hoe calcium substitutie in eenkristallen van Tb1−xCaxMnO3 (x≤0.1) niet alleen zijn weerslag heeft op de kristalstructuur en de magnetische structuur, maar zich ook

manifesteert in magnetocapaciteit en elektrische polarisatie. We tonen aan dat de aanwezigheid van

Mn4+ ionen op de perovskiet B roosterpositie van doorslaggevende invloed is op het verdwijnen van

ferroelektrisch gedrag als gevolg van calcium substitutie. We verklaren dit gedrag aan de hand van

de perovskiet tolerantiefactor, een begrip dat gebruikt wordt om ferroelektrisch gedrag te kunnen

voorspellen. We staven eveneens het bestaan van een tussenliggende toestand bij een dotering van

x=0.05 die gelijkenis vertoont met een relaxor ferroelektricum. Neutronen diffractie laat zien dat de

coherentielengte van de mangaan spin spiraal afneemt in deze samenstelling, zonder dat de Mn-spin

golfvector verandert. We presenteren dit systeem als een nieuwe klasse relaxor ferroelektrica.

In hoofdstuk 4 behandelen we een door een magnetisch veld geinduceerde overgang van fer-

roelektricum naar relaxor in Tb0.98Ca0.02MnO3. Dit effect kan worden verklaard aan de hand van

een verminderende coherentielengte van de mangaan spin structuur bij toenemende magnetische

veldsterkte. We veronderstellen dat de elektron overdrachtsfrequentie toeneemt met magnetisch

veld en verantwoordelijk is voor de verminderde spiraalcoherentielengte. Eveneens laten we zien

dat de de golfvector van de mangaan spin-spiraal structuur van Tb0.98Ca0.02MnO3 niet verandert bij

een kritiek veld van 6T, benodigd om een polarisatieflop te veroorzaken. Dit gedrag is tegengesteld

aan dat van ongesubstitueerd TbMnO3. Deze experimentele observaties wijzen erop dat voor het

polarisatieflop mechanisme de rotatie van het spin-spiraal vlak met magnetische veld relevanter is

dan de overgang van een incommensurabele naar en commensurabele spin structuur.

In hoofdstuk 5 onderzoeken we het effect van Ho3+ doping op EuMnO3. We beogen daarbij een

vergelijking te maken tussen de magnetisch-elektrische fasediagrammen van RMnO3 systemen. We

zetten hierbij systemen waar sprake is van magnetische ordening op de zeldzame aard roosterpositie

af tegen systemen waar dat niet het geval is. Met toenemend Ho gehalte neemt de gemiddelde

ionstraal van de zeldzame aard roosterpositie af. In de afwezigheid van een magnetisch veld leidt

107

deze ionstraalafname tot gedrag dat gelijkenis vertoont met ongedoteerd RMnO3. Het geordend Mn

spin subrooster ontwikkelt zich van een A-type gekantelde spinordening voor x=0.2 naar en spiraal

structuur bij hogere substitutiegraad.

We laten zien dat het magnetisch moment van de A-roosterpositie spins wellicht de mangaan

spiraal in het bc vlak stabiliseert. Dit veroorzaakt een spontane polarisatie langs de c-as. Echter,

het feit dat de polarisatie afneemt als de holmium substitutie x=0.75 overschrijdt is in strijd met

het verwachtingspatroon dat op grond van de perovskiet tolerantiefactor geschetst kan worden.We

vermoeden dat dit verschijnsel optreedt door ofwel een verminderde coherentielengte ofwel een spin

component van de spin spiraal structuur. Wanneer een magnetisch veld aangelegd wordt langs de

b-as, is het kritieke veld dat nodig is om een polarisatie flop naar de a as te veroorzaken voor x=0.4

en x=0.5 monsters lager dan dat voor TbMnO3. Dit wijst erop dat de anisotropie van de zeldzame

aard roosterpositie een belangrijke rol speelt. Bovendien wordt het temperatuur- en velddomein

waarin de ”geflopte” ab- vlak spiraalstructuur stabiel blijft, beınvloed door de Ho concentratie. Op

basis van magnetische dielektrische metingen kunnen we magnetisch-elektrische fase diagrammen

construeren voor Ho1−xEuxMnO3.

In hoofdstuk 6 bestuderen we de aard van de magnetodielektrische koppeling in polykristalli-

jne monsters van het spinel MCr2O4 (M = Mn, Co, and Ni). De dilektrische restconstante is een

maat voor de afwijking van de waarde die verkregen wordt na hoge temperatuur extrapolatie. Deze

waarde neemt toe in de volgorde MnCr2O4, CoCr2O4 and NiCr2O4. Dit houdt in dat de spin-

baan koppeling en de orbitaalvrijheidsgraad op de tetrahedrale positie een grote bijdrage levert aan

de magnetodielektrische koppeling. We laten zien dat de magnetodielektrische respons ongeveer

schaalt met het kwadraat van de magnetisatie (M2). Dit duidt op magnetodielektrische koppeling

die voortkomt uit een P2M2 term in de Landau vrije energie expansie.

In hoofdstuk 7 gebruiken we tot slot polarisatie metingen als experimenteel bewijs voor het

bestaan van het lineair magnetoelektrisch effect in MnTiO3. In dit materiaal wordt de elektrische

polarisatie veroorzaakt door een aangelegd magnetisch veld. We laten zien dat er geen dielektrische

anomalie bestaat op het punt waar magnetische ordening intreedt zonder magnetisch veld. Dit inzicht

is in strijd met voorgaande suggesties dat magnetoelektrische materialen per definitie sterke magne-

todilektrische koppeling vertonen. We nemen slechts dan een dilektrische anomalie bij de magnetis-

che ordeningstemperatuur waar als een magnetisch veld wordt aangelegd. Dit verschijnsel wordt

verklaard aan de hand van Landau theorie. We stellen vast dat de dilektrische anomalien een lineair

verband tonen met het kwadraat van het magnetisch veld. Magnetocapaciteitsmetingen voorzien ons

in een toegankelijk instrument om lineair magnetoelektrische materialen te herkennen.

Acknowledgments

I would like to show my gratitude to everybody who contributed and made this book possible.

First of all I would like to thank my promotor Prof. dr. Thom Palstra for his willingness to accept me

as his PhD student and for his guidance, advice, warm encouragement, patience and frequent discus-

sions during my studies. I learned many things from you, both scientifically and non-scientifically.

You paid attention not only to my research work, but also to some problems that had nothing to do

with my work and you were also concerned with my future career. I am extraordinarily fortunate to

have a supervisor like you. Thanks for everything, Thom, I will never forget it.

I would like to express my sincere appreciation to my co-promotor Dr. Agung Nugroho, who

introduced me to my promotor and helped to arrange my PhD position. I have learned a lot from you,

for example how to grow single crystals using the floating zone furnace, measure physical properties,

and use Labview. Thank you for all you have done for me.

I gratefully thank Dr. Graeme Blake. Your brilliant input, corrections, suggestions, and your

excellent English helped me in accelerating the preparation of this thesis and to make this thesis

possible.

Prof. dr. Beatriz Noheda, I would like to thank you for nice discussions and suggestions. I have

special thanks to Jacob Baas for daily technical support. Many things would not have been possible

without you. Thanks to Dr. K. Prokes and Dr. A. Podlesnyak for their assistance and advice during

my neutron measurements at BENSC Berlin. I also would like to thank Dr. M. Mostovoy and Dr. D.

Argyriou for useful discussions. I am very grateful to the members of my reading committee, Prof.

dr. D. I. Khomskii, Prof.dr. J. Aarts, and Prof. dr. ir. P.H.M. van Loosdrecht for their constructive

comments and suggestions regarding this thesis.

Thank you Umut and Gwilherm for nice discussions and for your collaborations. Thank you

Oana and Odi for giving me the furniture to fill our house. Special thanks goes to Johan for making

the summary of this thesis into the samenvatting. To Henriet van Mil and Annette Korringa, thanks

for your kind paper-work that you did for me. Thanks to Auke Meetsma for the single crystal

diffraction work. My grateful thanks extend to all former and current members of the solid state

109

110 Acknowledgments

chemistry group for the nice atmosphere and friendship over the years; Vadim, Gwilherm, Umut,

Michael Pollet, Oana, Odi, Mylene, Diego, Claire, Christophe, Gijsbert, Ard, Prof. Rob de Groot,

Igor, Anne, Arramel, Syarif, Johan, Josee, Henk, Jacob, Alexander and our visitor Javier.

I am grateful to my former professor Tjia May On in the physics department at Insitut Teknologi

Bandung. Thanks for everything, your guidance made my dream come true. I want to thank Eko

Harjanto and family, mas Ismail and family, Indra and family, Guntur and family, Wangsa and Yeni,

mas Chalid and family, mba Ike, Puri, Insanu, pak Gani, and others for forming a big family in

Groningen and for moral support.

To all members of deGromiest (Indonesian Moslem Society in Groningen ) and PPI-G (Associa-

tion of Indonesian students in Groningen ), thanks for being together, for friendship and for sharing

an interesting life.

To all Indonesian people who live in Groningen, Bude Nanie, Wa Aisyah and family, tante Alma,

tante Harna and others, your existence makes me feel at home here.

My deep thanks are dedicated to my beloved family; to my parents, my parent in-law, my brother

and sisters for their steady support and prayers. Last but most beloved, I would like to thank my wife

Rahmatun Nisa for always understanding me and sharing life together in happiness and sadness.

Thank you for your love and everything that comes to my life with you. Being with you really

makes my life more colorful and complete.

I realize, that not all the people who have contributed either directly or indirectly to the realization

of this thesis are mentioned on this page. From the depth of my heart, I would like to thank all of

you. Terima kasih.

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