Spin-orbit coupling induced magneto-resistance effects in ferromagneticsemiconductor structures: TAMR, CBAMR, AMR

Tomas Jungwirth

University of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds, Andrew Rushforth, Tom Foxon, et al.

University & Hitachi 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, Ludvík Smrčka,

Jan Kučera, Nataliya Goncharuk, et al.

University of Texas Allan MaDonald, Maxim Trushin,et al.

Texas A&MJairo Sinova, et al.

Wuerzburg University Charles. Gould, Laurens Molenkamp, et al.

Experimental observation of (ohmic) AMR

Lord Kelvin 1857

Inductive read elements Magnetoresistive read elements

AMR sensors: dawn of spintronics

Now often replaced by GMR or TMR but still extensively used in e.g. automotive industry

magnetization

current

1980’s-1990’s

ss sd

sdss

itinerant 4s:no exch.-split

no SO

localized 3d:exch. split

SO coupled

Theory of AMR: current response to magnetization via spin-orbit coupling

Model for transition metal FMs:

Banhart&Ebert EPL‘95

Miscroscopic theory: relativistic LDA & Kubo formula

theory

experiment

?

Smit 1951

FeNi

x=0.07%

1%

2.5%

7%

Jungwirth et al. PRB ’07

<<0.1% Mn

~0.1% Mn

>1.5% Mn~

MnGa acceptor: electrical conduction similar to conventional p-doped GaAs

Renewed research interest in AMR due to FS like (Ga,Mn)As

metallic

insulating

Ohno. Science ’98

(Ga,Mn)As

(Ga,Mn)As

Ni

d/d

T~c

v

Tc

h+

h+

Mn moment:Ferromagnetism reminiscent of conventional metal band FMs (Fe, Co, Ni,..)

Novak et al. PRL ’08

Renewed research interest in AMR due to FS like (Ga,Mn)As

>1% Mn~

ferromagneticTc

Baxter et al. PRB ’02, Jungwirth et al. APL’02, ‘03

Renewed research interest in AMR due to FS like (Ga,Mn)As

AMR’s of order ~1-10%: - routine characterization tool- semi-quantitatively described assuming scattering of valence-band holes

SET

Resistor

Complexity of the device design

Magnitude, control, and tuneability of MR

DOS

Simple direct link between band structure and transport

Tunneling DOS TAMR

Chemical potential CBAMR

Scattering lifetimes ohmic AMR

heterostructures

bulk

micro-structures

MTJ

Magnetic anisotropies in (Ga,Mn)As valence band

Dietl et al. PRB ’01, Abolfath et al. PRB ‘01

exchange-split HH bands and LH bands in (Ga,Mn)As:

anisotropic due to crystal, SO coupling and FM exchange field

M

j=3/2

HH

HH

HH

degenerate HH bands and LH bands in GaAs:

anisotropic surface and spin-texture due to crystal and SO coupling in As(Ga) p-orbitals

HH & LH Fermi surfaces

TAMR: spectroscopy of tunneling DOS anisotropy

M

M

Selectivity tuned by choice of barrier, counter-electrode, or external fields

GaMnAs

barrier

electrode

Vbias

Binpl

Giddings et al. PRL ’04

k - resolved tunneling DOS

TAMR: spectroscopy of tunneling DOS anisotropy

M

M

GaMnAs

AlOx

Au

Non-selective barrier and counter-electrode only a few % TAMR

Gould et al. PRL ’04

TAMR: spectroscopy of tunneling DOS anisotropy

M

M

Giraud et al. APL ’05, Sankowski et al. PRB’07, Ciorga et al.NJP’07,Jerng JKPS ‘09

Giraud et al. Spintech ’09

n-GaAs:Si

p-(Ga,Mn)As

Very selective p-n Zener diode MTJs

Binpl

TAMR: spectroscopy of tunneling DOS anisotropy

M

M

Extra-momentum due to Lorentz force during tunneling

Giraud et al. Spintech ’09

Binpl

n-GaAs:Si

p-(Ga,Mn)As

Very selective p-n Zener diode MTJs

GM

MGG

C

C

e

MV

MVVCQC

QQU

)(&

)]([&2

)(0

20

electric && magneticmagnetic

control of CB oscillations

Source Drain

GateVG

VDQ

CBAMR: M-dependent electro-chemical potentials in a FM SET

Wunderlich et al. PRL ’06

[110]

[100]

[110][010]

M

Huge MRs controlled by low-gate-voltage: likely the most sensitive spintronic transistors to date

Wunderlich et al. PRL ’06

Schlapps et al. arXiv:0904.3225

SET

Resistor

Chemical potential CBAMR

Tunneling DOS TAMR

Scattering lifetimes AMR

DOS

Simple direct link between band structure and transport

MTJ

Simplicity of the microscopic picture of AMR in (Ga,Mn)As

- -MnGa MnGa

M

CBAMR,TAMR:SO & FM polarized bands

ohmic AMR: main impurities – FM polarized random MnGa can consider bands with SO coupling only

SET

MTJ

Resistor

AMR: M vs current (non-crystalline) term can be separated and dominates in (Ga,Mn)As

Simplicity of the microscopic physical picture in (Ga,Mn)As

TAMR: current direction is cryst. distinct inseparable M vs current term

CBAMR: only el.-chem potentials no M vs current term M

cryst. axis

current

M

cryst. axis

current

M

cryst. axis

current

SET

MTJ

Resistor

KL Hamiltonian in spherical approximation

Heavy holes

Electro-magnetic impurity potential of MnGa acceptor

3/ˆ1̂ˆ1̂~ js MM eeVimp

Rushforth PRL’07, Trushin et al. arXiv:0904.3785, Vyborny et al. arXiv:0906.3151

current

MGa

Key mechanism for AMR in (Ga,Mn)As:

FM impurities & SO carriers in non-cryst.-like spherical bands

Pure magnetic MnGa impiruties: positive AMR,

current

0|~|ˆ| xj0|~|ˆ| xj

0|~|ˆ| yj

0|~|ˆ| xj

jMˆ~ eVimp

- -

0|~|ˆ| yj

Backward-scattering matrix elements

)()||( IMIM

current

0||~|/ˆ1̂| jjx

0||~|/ˆ1̂| jjx

0|~|/ˆ1̂| jjy

0|~|/ˆ1̂| jjx

jeVimp /ˆ1̂~ jM

- -

Backward-scattering matrix elements

Electro-magnetic MnGa impiruties: negative AMR, )()||( IMIM

AMR= -202-1

244-2 4+1

p [1021 cm-3]

AM

R

current

- -

3/ˆ1̂~ jM eVimp

~ screened Coulomb potential

all scatt.backward scatt.

Electro-magnetic MnGa impiruties: negative AMR, )()||( IMIM

current

- -

AMR= -202-1

244-2 4+1

p [1021 cm-3]

AM

R

~ screened Coulomb potential

all scatt.backward scatt.

Electro-magnetic MnGa impiruties: negative AMR, )()||( IMIM

3/ˆ1̂~ jM eVimp

Straightforward intuition for AMR in Rashba and Dresselhaus 2DEGs

& exact analytical solutions to full integral Boltzmann equation SO-coupled 2DEGs are ideal testbed to study AMR

Trushin et al. arXiv:0904.3785