chapter 4: spin dependent transport (lecture #5)...module: magnetism on the nanoscale, ws 2020/2021...

module: magnetism on the nanoscale, WS 2020/2021

chapter 4: spin dependent transport (lecture #5)

Dr. Sabine Wurmehl; [email protected]

Dresden, November, 23rd, 2020

mailto:[email protected]

reminder: free electron model & ….Formation of metallic Na

according to band theory

Fermi surface (model) density of states (DOS)

Fermi distribution or DOS „in reality“

DOS k2 E1/2

Landau diamagnetism

reminder: magnetic properties in metals- spin contribution

Zeemann splitting

for a metal in magnetic field • only electrons at Fermi energy contribute

• localized system: all unpaired electrons contribute

• in metals, spin of electrons leads to Pauli susceptibility cP

• cP is temperature independent

𝐻 = ½ 𝑚 (𝐩+𝑒𝐀)2 ± 𝜇𝐵𝐁

Pauli paramagnetism

with magnetic field:

k-vectors condense on tubes paralell to field

reminder: magnetic properties in metals- orbital contribution

harmonic oscillator plane wave

reminder: structure modifications and electronic correlations in the series BaT2As2 (T = Cr, Mn, Fe, Co, Ni, Cu)

S. Selter, F. Scaravaggi et al. Inorg. Chem. (2020)

Question:

What are potential reasons to not get g from all

members of the series???

from discussion (simplified):

no full information about DOS from gamma if:

• semiconducting or insulating ground state (here: BaMn2As2)

• spin density wave gap is present (afm) (here: BaFe2As2)

• superconductivity present (sc gap)

reminder: RKKY interaction

Ruderman–Kittel–Kasuya–Yosida.

https://www.researchgate.net/profile/Puspamitra_Panigrahi/publication/252771578/figure/download/fig1/AS:669380048351236@1536604048549/RKKY-interaction-the-interaction-of-magnetic-spins-mediated-by-conduction-electrons.ppm

local magnetic polarizes conduction electrons which in turn couples to another local moment at distance r

https://www.researchgate.net/profile/Puspamitra_Panigrahi/publication/252771578/figure/download/fig1/

RKKY interaction in metals

local magnetic polarizes conduction electrons which in turn couples to another local moment at distance r

indirect, itinerant exchange interaction between magnetic moments mediated by conduction electrons

• long ranged

• oscillating dependance of JRKKY on r fm or afm

• description by second-order perturbation theory

𝐽𝑅𝐾𝐾𝑌 ∝ cos(2𝑘𝐹𝑟)𝑟3

https://www.researchgate.net/profile/Heinz_Horner/publication/1940273/figure/fig1/AS:497194916474880@1495551913737/RKKY-interaction.png

https://www.researchgate.net/profile/Puspamitra_Panigrahi/publication/252771578/figure/download/fig1/AS:669380048351236@1536604048549/RKKY-interaction-the-interaction-of-magnetic-spins-mediated-by-conduction-electrons.ppm

https://www.researchgate.net/profile/Puspamitra_Panigrahi/publication/252771578/figure/download/fig1/

module: magnetism on the nanoscale, WS 2020/2021

chapter 4: spin dependent transport (lecture #5)

Dr. Sabine Wurmehl; [email protected]

Dresden, November, 23rd, 2020

mailto:[email protected]

4.0 intro „spindependent transport“

• study of spin dependent transport was fostered in ~1980s

• interesting from a fundamental point of view

• highly attractive: application in spintronics

charge + spin of electron for data processing, storage & read-out

magnetic „bit“

spintronics

spindependent transport

Is there an elegant way to monitor spin state by „easy“ way of measurement?

magnetoresistance

is there an elegant way to monitor spin state by „easy“ way of measurement?

measurement of resistance in response to magnetic field!

magnetoresistance

𝜎 = 𝑒2N(𝐸𝐹)𝑣𝐹2 𝜏/3

scales with

• DOS N(EF)

• Fermi velocity v

• scattering time t mean free path l1

𝜎= 𝜚

magnetoresistance- definition

𝑀𝑅≔Δ𝑅

𝑅= 𝑅 𝐻 −𝑅(0)

𝑅(𝐻)

known since long time: MR in metals is ~ few % (1857)

new discoveries in late 80s dramatic increase of MR ratio!

GMR ~ 50%

TMR ~1000%

CMR even larger

zoo of magnetoresistance effects

• positive magnetoresistance in non-magnetic metals

• negative magnetoresistance in ferromagnetic metals

• anisotropic magnetoresistance (AMR); MR: 3-4%

• collosal magnetoresistance (CMR); MR: 200-400% at RT, 108 % at low T

• giant magnetoresistance (GMR); MR up to 100% at RT

• tunnelling magnetoresistance (TMR); MR up to 1000%

• powder magnetoresistance (PMR)

intrinisc MR effects

extrinisc MR effects

positive MR in non-magnetic metals

(also called normal MR)

in any metal conduction electrons are scattered at impurities, phonons, defects, grain boundaries, ….

conductivity depends on „scattering events“

parametrized by mean free path l

l is the distance that an electrons travels between two scattering events

𝑙 ∝ 𝜎 𝑙 = 𝜈𝐹𝜏

mean free path

𝑙 ∝ 𝜎 𝑙 = 𝜈𝐹𝜏

mean free path is small compared to Fermi wave length

:= conductivity

l := mean free path

t:= mean time between scattering events

𝜆𝐹:= Fermi wave length

kF:= Fermi wave vector

mean free path large compared to Fermi wave length

𝑘𝐹𝑙 ≫ 1

𝑘𝐹𝑙~1

distance l is large enough

electron wave at 2nd scatterer is plane wave again

distance l is small

superposition of incoming and backscattered wave

𝜆𝐹 = 2𝜋/𝑘𝐹

https://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel2.pdf

mean free path with or without magnetic field

(a) without field (b) with field

scattering process is different with or without applied magnetic field

(c) mean free path in field


negative magnetoresistance in ferromagnets

http://www.wmi.badw.de/teaching/Lecturenotes/ME/ME_Kapitel2.pdf

resistance in ferromagnetsabove and below fm order

T. SHINJO

Spin Dependent Transport in Magnetic Nanostructures.

In: Experiments of Giant Magnetoresistance, pages 1–46.

Taylor & Francis MG Books Ltd, Bodmin (2002)

electronic transport in 3d metals

• 3d metals have both s and d electrons at Fermi level

• s electrons have much smaller effective mass broader bands

• s electrons are relevant charge carrier in 3d metals

• N.F. Mott: resistance is determined by scattering of s electrons in free d states

E

s

d

EF

σ = nse2τs

ms∗ +

nde2τd

md∗

scattering of s in d states above and below TC


high scattering rate of s electrons in d states

high resistance

• d states split, majority bands are now below EF

• no scattering of majority s electrons in majority d bands

lower resistance

negative magnetoresistance in ferromagnets

application of magnetic field increases ordering of spins viz. spin polarization

enhances effect of lower resistance in ferromagnet below TC

anisotropic magnetoresistance

MR depends on orientation between field and current

origin: spin orbit coupling affects s-d scattering differently, depending on direction of field

SOC lowers symmetry of wave functions by mixing of states

anisotropic scattering

asymmetric charge distribution due to SOC


energy of (a) and (b) is not the same

anisotropic magnetoresistance


J H

longitudinal MR

J H

transversal MR

1857 Thomson

two current model


spin flips are possible!

higher resistance!

colossal magnetoresistance (CMR)

• negative MR related to spin disorder

• observed in mixed valent manganites (Jonker and Santen 1950s)

…courtesy Laura Corredor Bohorquez…..

𝐶𝑀𝑅 ≔ −𝑅 𝐻 −𝑅(0)

𝑅(𝐻)= - Δ𝑅

𝑅

et al.

La3+substituted by Sr2+

mixed valency of Mn3+/4+

compositional range that

shows transition from

paramagnetic-semiconducing

to ferromagnetic-metallic

state

magnetic field changes spin order

spin-order and resistivity strongly linked in manganites

application of magnetic field shifts insulator-metal transition

giant magnetoresistance

• spindependent transport in multilayers

• 2 magnetic layers seperated by thin layer of non-magnetic metal

• started research hype in field of spintronics

Grünberg und Fert 1986

Nobelprice in 2007

P. Grünberg und A. Fert

S. S. P. Parkin 2002

giant magnetoresistance

M. Baibich, A. Fert et al. Phys. Rev. Letters 61, 2472 (1988)

G. Binasch, P. Grünberg et al. Phys. Rev. B 39, 4829 (1988)

Giant Magneto-ResistanceGMR:= DR/R=

𝑅𝑝−𝑅𝑎

𝑝

𝑅𝑝

„1“

„0“

http://www.spintec.fr/IMG/pdf/spin-valves.pdf

two geometries


resistor network

GMR:= DR/R=𝑅𝑝−𝑅𝑎

𝑝

𝑅𝑝

scattering rates for ,

parallel alignment

low resisitance r+

antiparallel alignment

high resistance r-


resistor network

GMR:= DR/R=𝑅𝑝−𝑅𝑎

𝑝

𝑅𝑝


scattering of s electrons

in d states

strong scattering,

high resistance

low scattering,

low resistance


GMR

RKKY in multilayersMR as fct of spacer thickness

Parkin et al. Phys. Rev. Lett. 64, 2304 (1990)

Wang et al. EPL 87 47001 (2009)

Parkin et al. Phys. Rev. B 44, 7131(R) (1991)

origin of MR dependence of spacer thickness

Parkin et al. Phys. Rev. Lett. 64, 2304 (1990)

accepted model: quantum interference

J. S. Moodera et al. Phys. Rev. Lett. 80, 2941 (1998)

Tunneling Magneto-Resistance (TMR)

early days:

• thin insulating tunnel barrier Al2O3

• two ferromagnetic layers: Simple ferromagnets as Co, Ni-Fe

Ni-Fe (permalloy)

Co

nm thin layer of Al2O3

TMR in Co-Al2O3-Permalloy

J. S. Moodera et al. Phys. Rev. Lett. 80, 2941 (1998)

Data: J. S. Moodera et al. Phys. Rev. Lett. 80, 2941 (1998)

Scheme adapted from: T. Graf et al. Prog. Sol. State. Chem. 39, 1 (2011)

Ni-Fe (permalloy)

Co

nm thin layer of Al2O3

Model: M. Julliere, Phys. Lett. A 54, 225 (1975)

tunneling Magneto-Resistance (TMR)

20% TMR ratio

Model: M. Julliere, Phys. Lett. A 54, 225 (1975)

Julliere model

∆𝑅

𝑅𝑇𝑀𝑅=𝑅𝐴−𝑅𝑃

𝑅𝐴=

2𝑃1𝑃2

1+𝑃1𝑃2with P=

𝑁↑−𝑁↓

𝑁↑+𝑁↓

tunneling depends on the density of states!

eV

barrier thickness

t

EF

barrier height f

metal 1metal 2

I12 (E) N1 (E-eV) N2 (E) T2 x f(E-eV) [1-f(E)] , T2 exp (-ctf)

I21 (E) N1 (E-eV) N2 (E) T2 x [1- f(E-eV)] f (E)

Integration and small voltages only yield:

I DOS1 DOS2 (E) x ∫ [f(E-eV)- f (E)]dE, for low T ∫ =eV

I/V DOS1 (EF) DOS2 (EF)

add-on: majority and minority states

https://www.researchgate.net/publication/293815864_Current_Driven_Magnetization_Dynamics_in_Ferromagnets_and_Antiferromagnets/figures?lo=1

Inomata et al. Appl. Phys. Lett. 86, 232503 (2005) http://www.pha.jhu.edu/~wgwang/pics/DMTJ%20TEM.jpg

deterioration by temperature dependence and interface

http://www.jst.go.jp/sicp/ws2009_sp1st/presentation/15.pdf

impact of barrier on TMR

Courtesy S. Yuasa (AIST)

Coherent tunneling – band filtering

Concept: R. de Groot et al. Phys. Rev. Lett. 50, 2024 (1983)

J. Kübler et al. Phys. Rev. B 28, 1745 (1983)

goal: material with 100% spin polarization at Fermi energy

Scheme: T. Graf et al. Prog. Sol. State. Chem. 39, 1 (2011)

optimized materials for TMR

∆𝑅

𝑅𝑇𝑀𝑅=

2𝑃1𝑃21+𝑃1𝑃2

with P=𝑁↑−𝑁↓

𝑁↑+𝑁↓Julliere model:

Good: Better:

P:= spin polarization

N:= DOS

ideal materials for spin dependent transport

Felser et al. Angew. Chem. Int. Ed. 2007, 46, 668 – 699

improvement of TMR stacks

TMR overview: T. Graf et al. Prog. Sol. State. Chem. 39, 1 (2011)

2012

Liu et al. Appl. Phys. Lett. 101, 132418 (2012)

Liu et al. Appl. Phys. Lett. 101, 132418 (2012)

TMR in Co2MnaSig Heusler films

chapter 4: spin dependent transport (lecture #5)...module: magnetism on the nanoscale, ws 2020/2021...

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