MSE 7025 Magnetic Materials (and Spintronics)cfpai/MSE7025/MSE7025_Lecture13...MSE 7025 Magnetic...

MSE 7025 Magnetic Materials

(and Spintronics)

Chi-Feng Pai cfpai@ntu.edu.tw

Lecture 13: Transport measurements Episode II: Family of the magnetoresistance (MR)

Course Outline • Time Table

Week Date Lecture

1 Feb 24 Introduction

2 March 2 Magnetic units and basic E&M

3 March 9 Magnetization: From classical to quantum

4 March 16 No class (APS March Meeting, Baltimore)

5 March 23 Category of magnetism

6 March 30 From atom to atoms: Interactions I (oxides)

7 April 6 From atom to atoms: Interactions II (metals)

8 April 13 Magnetic anisotropy

9 April 20 Mid-term exam

10 April 27 Domain and domain walls

Course Outline • Time Table

Week Date Lecture

11 May 4 Magnetization process (SW or Kondorsky)

12 May 11 Characterization: VSM, MOKE

13 May 18 Characterization: FMR

14 May 25 Transport measurements in materials I: Hall effect

15 June 1 Transport measurements in materials II: MR

16 June 8 MRAM: TMR and spin transfer torque

17 June 15 Guest lecture (TBA)

18 June 22 Final exam

Transport measurement

• Out-of-plane field

– Hall voltage VH

– Hall effect

– Anomalous Hall effect (AHE)

• In-plane field

– Resistance ~ V/I

– Magnetoresistance

– Anisotropic MR (AMR)

FM layer

I

V

H

FM layer

I

V

H

x xx xJ E y yx xJ Ex xx xE J y yx xE J

• Discovered by Lord Kelvin (William Thomson) in 1856

• Originates from, again, the spin-orbit interaction

Anisotropic magnetoresistance

• AMR and planar Hall effect

FM layer

I

V

H

More scattering Higher resistance

Less scattering Lower resistance

Typical AMR ratio / 1%

(if orbitals are free to rotate)

• Discovered by Lord Kelvin (William Thomson) in 1856

• Originates from, again, the spin-orbit interaction

• Angular dependence of longitudinal resistivity

• Also affects transverse resistivity!

• Planar Hall effect (PHE)

Anisotropic magnetoresistance

• AMR and planar Hall effect

FM layer

I

V

H

2cosxx

sin cosxy

M

J

Magnetoresistance

• Family of MR

– Ordinary magnetoresistance (OMR)

– Anisotropic magnetoresistance (AMR)

• Modern family of MR

– Giant magnetoresistance (GMR)

– Tunneling magnetoresistance (TMR)

– Colossal magnetoresistance (CMR)

– Spin Hall magnetoresistance (SMR)

– Unidirectional spin Hall magnetoresistance (USMR)

– Magnetoconductance (MC)

– Ballistic magnetoresistance (BMR)

Magnetoresistance

• MR comparison

Magnetoresistance Materials Typical MR ratio Note

OMR NM Field-dependent High field

AMR FM ~1% SOI

GMR FM/NM/FM ~ 50% Spin-dependent

transmission

TMR FM/I/FM ≧100% Spin-dependent

tunneling

CMR Mn-based

perovskite oxide ~100,000%

Double-exchange and hopping

SMR NM/FMI ~0.001% SHE

USMR NM/FM ~0.001% SHE

Read-out applications

/ (0)R R

General rules of transport in magnetic materials

• For s, p, d, and f electrons…

• s and p electrons are itinerant (free electron-like)

• d electrons are localized enough to provide magnetism, and weakly delocalized to contribute transport properties

• f electrons are strongly localized (do not contribute to transport)

General rules of transport in magnetic materials

• Recall the omnipresent Drude conductivity/resistivity

2

*

1 ne

m

21

scatter FV N E

s-d scattering μ cm

(Mott, 1936)

General rules of transport in magnetic materials

• Two-current (two-channel) model

Transition metals Dilute transition metals alloys

B

B

low T

low T

(1 ) (1 )

(1 ) (1 )

B B

B B

x x x x

x x x x

General rules of transport in magnetic materials

• Two-current (two-channel) model

Transition metals Dilute transition metals alloys

B

B

low T

low T 1 B B

B B

x x

(spin-mixing)

General rules of transport in magnetic materials

• Two-current (two-channel) model

Transition metals

low T

high T low T

4

,

high T4

Spin-mixing resistivity

(Fert and Campbell, 1972) (spin is conserved)

(spin is NOT conserved)

At higher temperatures…

Ordinary magnetoresistance

• In normal metals (non-magnetic)

– Kohler’s rule

– A pictorial explanation

20

0 0c

H H HF

0H

The mean free path is reduced while a (perpendicular) magnetic field is applied

Anisotropic magnetoresistance

• In ferromagnetic materials

– Modified Kohler’s rule

2 2

0

H H Ma b

2 1cos

3

H

2 / 3ave

2cosxx

H H

2cosH

Anisotropic magnetoresistance

• Mechanism

– Internal field picture

– Spin-orbit interaction (SOI) picture

M H

Plausible but contradictory to experimental observations

0M

scatter Coulomb exchange ...SOV V V V

21

scatter FV N E

Anisotropic magnetoresistance

• Mechanism

– Spin-orbit interaction (SOI) picture

– s-d scattering

scatter Coulomb SOV V V

s

s

sd

sd

(with SOI)

(without SOI)

Anisotropic magnetoresistance

• Mechanism

– s-d scattering

s

s

sd

sd

(with SOI)

(without SOI)

Anisotropic magnetoresistance

• Mechanism – The mysterious spin-mixing through SOI

(ladder operator)

occupied empty

Compare to s-d interaction

• Using the language of second quantization

• Some notes

sd j j

j

V J r S s r R

† †

, , , ,3

† †

, , , ,

j

z

j i

sd sd

jj j

S c c c cJV V d r e

N S c c S c c

k q k k q k q R

kqk q k k q k

r r

1/ 2,absorbed into zs J

, ,

, 1 1 , 1

, 1 1 , 1

absorbed into

zS S m m S m

S S m S S m m S m

S S m S S m m S m

J

Itinerant electron

From Condensed Matter in a Nutshell By G. D. Mahan

Compare to s-d interaction

• The 1st and 2nd order perturbation terms are rather dull

• The 3rd order term is the so-called “Kondo effect” (temperature-dependent)

(1) 0sd j

j

JV V m n n

N k k

k

22

(2) 211 1

sd ii

i i g

i V g N Ec JV S S S S c J dE

E E N E E E E

k k k

3(3)

2

41 11

Fin Ec J

V S SN E E E E E E

k p

p

k p p k

Fermi-Dirac dist. (temp. dependent!)

Concentration of impurity

Compare to s-d interaction

• Resistivity (T) due to spin-flip

2 2

2

21 1 4 ln B

i

k TmT c S S N J N J

ne W

0J

(antiferromagnetic coupling)

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

Mario Baibich recalls that the study of magnetism was generally considered to be a dead end in the 1980’s. “Many a friend tried to talk me out of concentrating on this subject,” says Baibich. In fact, the field was only in a temporary lull, and the sixth most-cited Physical Review Letter that the Brazilian physicist coauthored while working as a postdoc with a group of researchers in France was just the thing to perk it up. The discovery of giant magnetoresistance (GMR) turned the study of layered magnetic structures into one of the most dynamic, and profitable, fields in physics in the last quarter century.

PRL Top Ten: #6 NUMBER SIX Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices (2455 citations)

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

GMR

AMR

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

Fe/Cr/Fe sandwich structure (Fe/Cr)n superlattices

Binasch et. al. PRB 39 4828 (1989) Baibich et. al. PRL 64 2472 (1988)

Giant magnetoresistance (GMR)

• (Perhaps) The beginning of modern magnetism or spintronics

Fe/Cr/Fe sandwich structure (Fe/Cr)n superlattices

Binasch et. al. PRB 39 4828 (1989) Baibich et. al. PRL 64 2472 (1988)

The Nobel Prize in Physics 2007 was awarded jointly to Albert Fert and Peter Grünberg "for the discovery of Giant Magnetoresistance"

Giant magnetoresistance (GMR)

• Two measurement configurations

(For fast thin-film transport properties characterization; Current distribution will be non-uniform)

(Hard to make, but provides a more uniform current dist- ribution and cleaner data)

FM

FM

NM

Giant magnetoresistance (GMR)

• Two measurement configurations

Giant magnetoresistance (GMR)

• Spin transport theory 101: Two channel model

APRPR

2

2GMR ratio AP P

AP

R RR R

R R R

PR APRDetails: Valet-Fert model (CPP configuration)

Giant magnetoresistance (GMR)

• Spin-valves

Tunneling magnetoresistance (TMR)

• S/I/F junction E1: Ferromagnetic material E2: Superconductor

http://bama.ua.edu/~pleclair/research.html

Tunneling magnetoresistance (TMR)

• S/I/F junction

S/I/N S/I/N (under H) S/I/F (under H)

Tunneling magnetoresistance (TMR)

• F/I/F junction (magnetic tunnel junction, MTJ)

1 2

1 2

2TMR ratio

1

AP P

P

R R PP

R PP

1 1

1

1 1

F F

F F

N E N EP

N E N E

Julierre’s model

Spin-polarization

Tunneling magnetoresistance (TMR)

• F/I/F junction (magnetic tunnel junction, MTJ)

1 2

1 2

2TMR ratio

1

AP P

P

R R PP

R PP

1 1

1

1 1

F F

F F

N E N EP

N E N E

Julierre’s model

Spin-polarization

Tunneling magnetoresistance (TMR)

• F/I/F junction (magnetic tunnel junction, MTJ)

– Case: Fe/Al2O3/Fe

Tunneling magnetoresistance (TMR)

• CoFeB/MgO/CoFeB MTJ

– High TMR > 100% (due to band matching)

– Standard industrial MTJ structure

– Can possess perpendicular magnetic anisotropy (p-MTJ)

S. Yuasa et al., Nature Mater. 3 868 (2004)

TMR~180%

Tunneling magnetoresistance (TMR)

• CoFeB/MgO/CoFeB MTJ

– High TMR > 100% (due to band matching)

– Standard industrial MTJ structure

– Can possess perpendicular magnetic anisotropy (p-MTJ)

S. Parkin et al., Nature Mater. 3 862 (2004)

Tunneling magnetoresistance (TMR)

• CoFeB/MgO/CoFeB MTJ

– High TMR > 100% (due to band matching)

– Standard industrial MTJ structure

– Can possess perpendicular magnetic anisotropy (p-MTJ)

S. Ikeda et al., Nature Mater. 9 721 (2010)

Tunneling magnetoresistance (TMR)

• CoFeB/MgO/CoFeB MTJ

– High TMR > 100% (due to band matching)

– Standard industrial MTJ structure

– Can possess perpendicular magnetic anisotropy (p-MTJ)

S. Ikeda et al., Nature Mater. 9 721 (2010)

Tunneling magnetoresistance (TMR)

• CoFeB/MgO/CoFeB MTJ

– Contemporary structures

Tunneling magnetoresistance (TMR)

• CoFeB/MgO/CoFeB MTJ

– Contemporary structures

Magnetic random access memory (MRAM)

• Field-control MRAM

Magnetic random access memory (MRAM)

• Field-control MRAM

– “Toggle” switch

– Standard field-control MRAM

– Circa 2000 (16 years!)

Magnetic random access memory (MRAM)

• STT-MRAM

– Current-induced spin-transfer torque (STT)

– Circa 2006 (10 years!)

H J r J

Magnetic random access memory (MRAM)

• STT-MRAM

– Current-induced spin-transfer torque (STT)

– Circa 2006 (10 years!)

Magnetic random access memory (MRAM)

• STT-MRAM

– Current-induced spin-transfer torque (STT)

– Circa 2006 (10 years!)

– Major players