Anisotropic magnetoresistance and spin-injection Halleffect in 2D spin-orbit coupled systems

Tomas Jungwirth

University of Nottingham Bryan Gallagher, Richard Campion, Kevin

Edmonds, Andrew Rushforth, et al.

Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri,

Byonguk Park, et al.

Institute of Physics ASCRKarel Výborný, Jan Zemen, Jan Mašek,

Vít Novák, Kamil Olejník, et al.

University of Texas Allan MaDonald, et al.

Texas A&MJairo Sinova, et al.

Extraordinary magnetoresistance: AMR, AHE

B

V

I

_

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

_ _ _ _ _ _ _ _ _ _ FL

Ordinary magnetoresistance:response in normal metals to external magnetic field via classical Lorentz force

Extraordinary magnetoresistance:response to internal spin polarization in ferromagnets via quantum-relativistic spin-orbit coupling

ordinary Hall effect 1879 I

_ FSO__

Vanomalous Hall effect 1881

anisotropic magnetoresistance

M

Lord Kelvin 1857

Spin-orbit coupling

nucleus rest frame electron rest frame

vI QrE3

04 r

Q

30

4 r

rIB

EvEvB 200

1

c EvSS

2B

mc

egH B

SO

Lorentz transformation Thomas precession

2 2

From 1950’s microscopic model interpretations – often controversial

itinerant 4s:no exch.-split

no SO

localized 3d:exch. split

SO coupled

ss sd

sdss

AMR: Mott’s model of transport in metals

Smit 1951

AHE

(then partly forgotten till 2000’s)

Karplus&Luttinger 1954

Smit 1955

Berger 1970

From 1990’s numerics based on relativistic ab initio band strucrure & Kubo formula

Numerically successful but difficult to connect with microscopic models due to complex bands in metals Banhart&Ebert EPL‘95

Khmelevskyi ‘PRB 03

AMR

AHE

Scattering considered essential for both AMR and AHE alloys like FeNi (treated in CPA)

AMR sensors: dawn of spintronics in early 1990’s

In mid 1990’s replaced in HDD by GMR or TMR but still extensively used in e.g. automotive industry

Inductive read/write element

Magnetoresistive read element

Mn-d-like localmoments

As-p-like holes

Mn

Ga

As

From late 1990’s AMR and AHE studied in novel ferromagnetsFerromagnetic DMS GaMnAs with much simpler 3D band structure than metals

Bso

Bex + Bso

Jungwirth et al. RMP’06Dietl et al. Semicond. and Semimet. ‘08

Semiquantitative numerical description of AMR and AHE in GaMnAs

Jungwirth et al. RMP’06Dietl et al. Semicond. and Semimet. ‘08

M

[110]

current))

Spherical model: non-crystalline AMR only

Anisotropic scattering rate:non-crystalline and crystalline AMR

Mcurrent

)

AMR in GaMnAs DMS: from full numerics to microscopic mechanism

Rushforth et al. PRL‘07

AMR in GaMnAs DMS: from full numerics to microscopic mechanism

M

current

Non-crystalline AMR mechanisms:

1) Polarized SO bands 2) Polarized impurities & SO bands

Leading AMR mechanism in DMSs

Rushforth et al. PRL‘07

current

MGa

Microscopic mechanism of AHE in GaMnAs DMS

AHE explained by the revived intrinsic mechanism

Jungwirth et al PRL‘02

Experiment AH 1000 (cm)-1

TheroyAH 750 (cm)-1

Note: Inspired to explain AHE in pure Fe,etc by intrinsic AHE

Yao et al PRL‘04

2D SO-coupled systems simplest band-structures offermost detailed and complete understanding of the AMR and AHE

Rashba SO-coupled 2DEG

AMR in 2D SO-coupled systems

We will discuss a detailed theory analysis in Rashba-Dresselhaus 2D systems

Experimentally not studied in 2D systems yet; we will comment on experiments in related 3D DMS systems

Trushin, Vyborny et al PRB in press (arXiv:0904.3785)

AHE in 2D SO-coupled systems

Detailed theory analysis completed

We will discuss 2D AHE related experiment: Spin-injection Hall effect in a planar photo-diode

Nagaosa et al RMP ‘to be published (arXiv:0904.4154)

Heuristic link between spin-texture of 2D SO bands, impurity potentials and AMR

Short-range magnetic impurity potential

Short-range electro-magnetic impurity potential

Non-crystalline AMR>0 in Rashba 2D system

Rashba Hamiltonian

Eigenspinors

Non-crystalline AMR>0 in Rashba 2D system

Scattering matrix elements

( )

current

Large non-crystalline AMR>0 in Rashba 2D system with electro-magnetic scatterrers

Scattering matrix elements of

( )

current

current

Negative and positive and crystalline AMR in Dresselhaus 2D system

Dresselhaus

Rashbacurrent

curre

nt

AMR in (Ga,Mn)As modeled by j=3/2 Kohn-Luttinger Hamiltonian

KL Hamiltonian

Heavy holes

Magnetic part of the impurity potential

Scattering matrix elements of

Compare with spin-1/2

Rashba Kohn-Luttinger

Negative AMR in (Ga,Mn)As due to electro-magnetic MnGa impiruties

current

AMR in 2D Rashba system from exact solution to integral Boltzmann eq.

= const. for

independent of

or

averages to 0 over Fermi cont.

quasiparticle life-time

AMR in 2D Rashba system from exact solution to integral Boltzmann eq.

transport life-time

transport life-time is a good first approximation to AMR

AMR in 2D Rashba system from exact solution to integral Boltzmann eq.

analytical solution to the integral Boltzmann eq.

contains only cos and sin harmonics

jqs

––– – –– – –– – –

+ + + + + + + + + +AHE

Ferromagnetic(polarized charge current) jq

SHE

nonmagnetic(unpolarizedcharge current)

p -AlG a As

i-G a As

n- -d o p e d AlG a As

e tc he d

2DHG2DHG

2DEG2DEG

Spintronic Hall effects in magnetic and non-magnetic (2D) systems

Wunderlich et al. IEEE 01, PRL‘05

Co/Pt

Spin-injection Hall effect: Hall measurement of spin-polarized electrical current injected into non-magnetic system

Wunderlich et al. Nature Phys. in press, arXives:0811.3486

– – – – + + + +

+ + + + – – – –

jqs

nonmagneticSpin-polarizer(e.g. ferromagnet, light)

29

i pn

2DHG

Optical injection of spin-polarized charge currents into Hall bars

GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell

-

2DHGi p

n

30

Optical injection of spin-polarized charge currents into Hall bars

GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell

i

p

n2DHG

2DEG

31

Optical injection of spin-polarized charge currents into Hall bars

GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell

2DHG

2DEG

e

h

ee

ee

e

hh

h

h h

VH

32

Optical injection of spin-polarized charge currents into Hall bars

GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell

Optical spin-generation area near the p-n junction

Simulated band-profile

p-n junction bulit-in potential (depletion length ) ~ 100 nm self-focusing of the generation area of counter-propagating e- and h+

Hall probes further than 1m from the p-n junction safely outside the spin-generation area and/or masked Hall probes

2DHG2DEG

e

h

ee

ee

e

h hh

hh

Vb

VH2

VL

2DHG2DEG

ee

hh

eeee

eeee

ee

hh hhhh

hhhh

Vb

VH2

VL

))(V(2 dis

*22

rkkkkkm

kH yyxxyxxy

2DEG

Spin transport in a 2DEG with Rashba+Dresselhaus SO

GaAs, for A 2o

3.5)(

11

3 22

2*

sogg EE

P GaAs, for AeV with 30

102 BkB z zE*

Schliemann, et al., Phys. Rev. Lett. 94, 146801 (2003)Bernevig, et al., Phys. Rev. Lett. 97, 236601 (2006)Weber, et al., Phys. Rev. Lett. 98, 076604 (2007)

weak spin orbit coupling regime:

System can be described by a set of spin-charge diff. Equation:

5meV)( ,

Spin dynamics in a 2DEG with Rashba Dresselhaus SO

2~~

4~~~

arctan,)~~~

(||,)exp(|| 21

22

41

22

21

21414

22

22

1LL

LLLLLLqiqq

]exp[)( ]011[]011[ xqxpZ

Steady state solution for the out of plane spin-polarization component

22/1 ||2

~ mL

SO-length ~1m

Spin-diffusion along the channelof injected spin- electrons

see also Bernevig et al., PRL‘06

Spin-diffusion along the channelof injected spin- electrons

Local spin-dependent transverse deflection due to skew scattering ~10nm

SO-length (~1m) >> mean-free-path (~10 nm)

))(V(2 dis

*22

rkkkkkm

kH yyxxyxxy

2DEG

GaAs, for A 2o

3.5)(

11

3 22

2*

sogg EE

P GaAs, for AeV with 30

102 BkB z zE*

Skew-scattering Hall effect

Spin injection Hall effect: theoretical estimate

Local spin polarization calculation of the Hall signal

Weak SO coupling regime extrinsic skew-scattering term is dominant

)(2)( ]011[*

]011[ xpnn

ex z

iH

A. Crepieux and P. Buno, PRB ’01

Large Hall angles – comparable to AHE in metals

0123

SIHE device realization

n3,n2,n1: local SIHE n0: averaged-SIHE / AHE

Spin-generation area

2DHG2DEG

e

h

ee

ee

e

h hh

hh

Vb

VH2

VL

2DHG2DEG

ee

hh

eeee

eeee

ee

hh hhhh

hhhh

Vb

VH2

VL

5.5m

Unmasked and masked SIHE devices

0 25 50 750

10

20R

L [k]

tm [s]

-50

-25

0

25

50

- 0 +

-50

-25

0

25

50

RH

2 [

]

Vb= 0V

Vb= -10V

2DHG2DEG

e

h

ee

ee

e

h hh

hh

Vb

VH2

VL

2DHG2DEG

ee

hh

eeee

eeee

ee

hh hhhh

hhhh

Vb

VH2

VL

Measured SIHE phenomenology

+

+

-+

+

-

Skew scattering

-

-Bso+

+

-+

+

-

Skew scattering

-

-Bso

-1.0 -0.5 0.0 0.5 1.0-2

-1

0

1

2

H [ 1

0-3 ]

H1

-1.0 -0.5 0.0 0.5 1.0

-10

-5

0

5

10

H [ 1

0-3 ]

H2

0 10 20 30 40 50-10

-5

0

5

10

H0 (x3) H2

tm [s]

H [

10-3

]

H1 (x3) H3 (x3)

- +

SIHE: spatially dependent, linear, strong

-20

-10

0

10

20

H2 H3

VH [

V]

0 20 40 60 80-4-2024

I [A

]

tm [s]

-0 - 0

Vb=-0.5V Vb=+0.5V

(a)

-20

-10

0

10

20

H2 H3

V

H [

V]

0 20 40 60 80-4-2024

tm [s]

I [A

]

-0 - 0

Vb=-5V Vb=+5V

SIHE vs AHE

0 30 60 90 120 150 180-5

0

5 100K 160K (x2) 220K (x3)

H [1

0-3]

tm [s]

SIHE survives to high temperatures

-

+

Spin-detection in semiconductors

Ohno et al. Nature’99, others

Magneto-optical imaging

non-destructive

lacks nano-scale resolution and only an optical lab tool

MR Ferromagnet

electrical

requires semiconductor/magnet hybrid design & B-field to orient the FM spin-LED

all-semiconductor

requires further conversion of emitted light to electrical signal

Datta-Das transistor

Ohno et al. Nature’99, others

Crooker et al. JAP’07, others Magneto-optical imaging

non-destructive

lacks nano-scale resolution and only an optical lab tool

MR Ferromagnet

electrical

requires semiconductor/magnet hybrid design & B-field to orient the FM spin-LED

all-semiconductor

requires further conversion of emitted light to electrical signal

Spin-detection in semiconductors

Spin-injection Hall effect

non-destructive

electrical

100-10nm resolution with current lithography

in situ directly along the SC channel & all-SC requiring no magnetic elements in the structure or B-field

Spin-photovoltaic cell: polarimeter on a SC chip requiring no magnetic elements, external magnetic field, or bias; form IR to visible light depending on the SC

Spin-detection tool for other device concepts (e.g. Datta-Das transistor)

Basic studies of quantum-relativistic spin-charge dynamics and AHE also in the intriguing strong SO regime in archetypal 2DEG systems

Application of SIHE