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Spintronics: How spin can act on charge carriers and - PowerPoint Presentation

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Spintronics: How spin can act on charge carriers and - PPT Presentation

vice versa Tom as Jungwirth University of Nottingham Institute of Physics Prague Mott nonrelativistic twospinchannel model of ferromagnets Dirac relativistic spinorbit coupling ID: 560658

sot spin intrinsic scattering spin sot scattering intrinsic field effect hall prl

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Slide1

Spintronics: How spin can act on charge carriers and vice versa

Tomas Jungwirth

University of Nottingham

Institute of Physics

PragueSlide2

“Mott“ non-relativistic two-spin-channel

model of ferromagnets“Dirac“ relativistic spin-orbit coupling

I

I

I

I

Mott, 1936

Dirac, 1928

Two paradigms for spintronics Slide3

SHE

& STT switchingSOT switching

-We see (anti)damping-like torque-SOT is field-like so we exclude it - non-relativistic STT in metals is dominated by the (anti)damping torque

-We also see (anti)damping-like torque-SOT is field-like but maybe there is some

(anti)damping-like SOT as well

Ralph, Buhrman,

et

al.

, Science

‘12

Miron et al., Nature ‘11Slide4

Ohmic “Dirac“ device: AMR

Magnetization-orientation-dependent scattering

Kelvin, 1857Slide5

Spin-orbit coupling

Slide6

Spin-orbit coupling

Slide7

Extraordinary magnetoresistance: AMR,

AHE, SHE, SOT.....B

V

I

_

+ + + + + + + + + + + + +

_ _ _ _ _ _ _ _ _ _

F

L

Ordinary

magnetoresistance

:

response

to

external

magnetic

field

Acting

via

classical Lorentz force

Extraordinary

magnetoresistance

:

response to

internal

quantum-relativistic

spin-orbit

field

ordinary Hall effect 1879

I

_

F

SO

_

_

V

anomalous Hall effect 1881

anisotropic

magnetoresistance

M

Lord Kelvin 1857Slide8

Linear response:

g linear in Ej

Classical Boltzmann equation Non-equilibrium distribution function Steady-state current in linear response to applied electric field Slide9

Steady-state solution for elastic (impurity) scatteringSlide10

Constant quasi-particle relaxation time solution

Steady-state solution for elastic (impurity) scattering

g(i,k)=

if Slide11

Transport relaxation time solution: back-scattering dominates

Steady-state solution for elastic (impurity) scattering

g(i,

k)=

is isotropic: depends on

|

-

|

if Slide12

No relaxation time solution

Steady-state solution for elastic (impurity) scattering

is

an

isotropic: depends on k

,

k

if Slide13

AMR in

Rashba 2D systemRashba Hamiltonian

Eigenspinors Slide14

an

isotropic

AMR

in Rashba

2D system

isotropic

QM: 1st order Born approximationSlide15

Heuristic picture from back-s

cattering matrix elements

Rashba SOI

current

Back-scattering  high resistivity

AMR

in

Rashba

2D

system

Rashba SOI

No back-scattering  low resistivitySlide16

Mott, N. F. Proc. R. Soc.

Lond. A 1929

Dyakonov and Perel 1971Spin Hall effect in PMs

Electron spin-dependent scattering off Coulomb field of heavy atoms due to spin-orbit coupling

Polarimetry of high-energy electron beams in accelerators

Electron spin-dependent scattering off Coulomb field of dopands in a semiconductor due to spin-orbit coupling

j

c

Anomalous Hall effect in FMs

1881

Polarimetry of electrons in FMs

Kato,

Awschalom

,

et al., Science‘04

Wunderlich, Kaestner, Sinova

,

T

J, PRL‘05Slide17

j

c

js

Hirsch PRL‘99

Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effectSlide18

j

c

js

Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect

Hirsch PNAS‘05

- indexSlide19

Theoretical proposal of

intrinsic spin Hall effect

FM (Ga,Mn)As

Non-magnetic GaAs

TJ,

Niu

, MacDonald

, PRL’02

Murakami, Nagaosa, & S.-C. Zhang, Science’03

Proposed detection by polarized electroluminescence

Sinova

, TJ,

MacDonald

, et al. PRL’04

Proposed detection by magneto-optical Kerr effect

Intrinsic anoumalous Hall effect in (Ga,Mn)AsSlide20

Magneto-optical Kerr microscopy

Edge polarized electro-luminescence

Extrinsic SHE Kato,

Awschalom

, et al., Science‘04

Intrinsic SHE

Wunderlich, Kaestner, Sinova

,

T

J, PRL‘05Slide21

Optically generated spin current

Optically detected charge accummulation due to iSHE

Zhao et al., PRL‘06

fs pump-and-probe: iSHE generated before first scattering in the intrinsic GaAs

 intrinsic iSHE

Werake et al., PRL‘11Slide22

AHE and SHESlide23

A

HE and SHESlide24

Skew scattering SHESlide25

Mott (skew) scattering SHE

SHE

A

MRSlide26

Skew scattering

A

HE (SHE)

: not constant, not isotropic, not even symmetric

 no relaxation time solution

Approximation:Slide27

Skew scattering

AHE (SHE)Slide28

Spin orbit torque

M

I

e

Slide29

Field-like SOTCompare with AMR or skew-scattering SHE

E=

E

x

x

^Slide30

Field-like SOT

E=

E

x

x

^

isotropic

(

r

)Slide31

Field-like SOT

isotropic

(

r

)

g(i,

k)=Slide32

Field-like SOT

E=

E

x

x

^Slide33

Intrinsic spin Hall effect in PMs

FM (Ga,Mn)As

Non-magnetic GaAs

TJ,

Niu

, MacDonald

, PRL’02

Murakami, Nagaosa, & S.-C. Zhang, Science’03

Sinova

, TJ,

MacDonald

, et al. PRL’04

Intrinsic anoumalous Hall effect in FMs

Werake et al., PRL‘11

Wunderlich, Kaestner, Sinova

,

T

J, PRL‘05Slide34

Boltzmann theory : non-equilibrium distribution function

and equilibrium states

Linear response I.Slide35

Perturbation

theory: equilibrium distribution function

and non-equilibrium states

Linear response II. Slide36

Perturbation

theory: equilibrium distribution function

and non-equilibrium states

Linear response II. Slide37

Perturbation

theory: equilibrium distribution function and non-equilibrium states

Intrinsic SHE (AHE)

Linear response II.

0

0Slide38

p

z

p

x

p

y

p

z

p

x

p

y

E=

E

x

x

^

Heuristic picture: Bloch equations Slide39

Field-like SOT

Compare with AMR or skew-scattering SHE

E=

E

x

x

^Slide40

Intrinsic antidamping SOT from linear response II.

Compare with intrinsic SHE0

000Slide41

p

z

p

x

p

y

p

z

p

x

p

y

p

z

p

x

p

y

p

z

p

x

p

y

Intrinsic SHE: transverse spin current

Intrinsic SOT: spin

polarization

H

ex

=0

H

ex

>>

H

RSlide42

p

z

p

x

p

y

p

z

Intrinsic SHE: transverse spin current

Intrinsic SOT: spin

polarization

p

x

p

ySlide43

p

z

p

x

p

y

p

x

p

y

p

z

p

x

p

y

p

x

p

y

Intrinsic SOT is antidamping-like Slide44

SHE

& STT switchingSOT switching

-We see (anti)damping-like torque-SOT is field-like so we exclude it - non-relativistic STT in metals is dominated by the (anti)damping torque-We also see (anti)damping-like torque-SOT is field-like but maybe there is some (anti)damping-like SOT as well

and maybe we found it  intrinsic SOT analogous to intrinsic SHE

Ralph, Buhrman,

et

al.

, Science

‘12

Miron et al., Nature ‘11