magneto-transport anisotropy phenomena in gamnas and beyond tomas jungwirth university of nottingham...

Magneto-transport anisotropy phenomena in GaMnAs and beyond

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, Alexander Shick. Jan Zemen, Jan Mašek, Vít Novák, Kamil

Olejník,, et al.

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

Texas A&MJairo Sinova, et al.

University of WuerzburgCharles. Gould, Laurens Molenkamp, et al.

Observations made from studies of AMR phenomena in GaMnAs (outline)

1. More than just bulk AMR in ohmic devices: TAMR, CBAMR

2. In DMSs bulk AMR has the simplest intuitive picture

3. TAMR and CBAMR are transferable to room-T metal FMs & AFMs

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 industryProblems with small magnitude and scaling

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


>1% Mn~

ferromagneticTc

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


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

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

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

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


M

M

GaMnAs

AlOx

Au

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

Gould et al. PRL ’04


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


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. PRB ‘09

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. PRB ‘09, Vyborny et al. PRB ‘09

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.


current

- -

AMR= -202-1

244-2 4+1

p [1021 cm-3]

AM

R

~ screened Coulomb potential

all scatt.backward scatt.


3/ˆ1̂~ jM eVimp

Negative and positive and crystalline AMR in R&D 2D system

Dresselhaus

Rashbacurrent

curre

nt

AMR in 2D R&D and 3D KL system from exact solution to integral Boltzmann eq.

analytical solution to the integral Boltzmann eq.

contains only cos and sin harmonics

ss sd

sdss

itinerant 4s:no exch.-split

no SO

localized 3d:exch. split

SO coupled

AMR in transition/noble metals

Model for transition metal FMs:

Banhart&Ebert EPL‘95

Miscroscopic theory: relativistic LDA & Kubo formula

theory

experiment

?

Smit 1951

FeNi

ab intio theory Wunderlich et al., PRL ’06,Shick, et al, PRB '06

TAMR and CBAMR predictions for metals

Anisotropy in DOS Anisotropy in chemical potential

ab intio theoryTAMR in SO-coupled FMs

experiment

Experimental observation of large and bias dependent TAMR

Shick et al PRB ’06, Parkin et al PRL ‘07, Park et al PRL '08

Park et al PRL '08

Experimental observation of CBAMR in metals

Bernand-Mantel et al Nat. Phys.‘09

Consider TM combinations containing Mne.g. FM Mn/W upto ~100% TAMR

spontaneous momentmag

netic su

sceptib

ility

spin

-orb

it cou

plin

g

Optimizing TAMR/CBAMR in transition-metal structures

Shick, et al PRB ‘08

But most transition/noble metals with Mn are AFMs!

AFM spintronics

Zero stray field in compensated AFMs

Ultrafast dynamics of spin excitations

spin-dn spin-up

MnMn22AuAu

Predicted strong AFM with no frustration

spin-dn spin-up

MnMnIrIr

Conventional AFM

Element specific MAE (meV)

*MAE accuracy ~0.01 meV

Magnetic moments (mB)

Local Mn-atom moment contributes only little to the MAE

Most of the MAE comes from zero moment Au, Ir atoms

Each of localized 3d(Mn)- sublattices induces the magnetic momenton 5d-site

Strong 5d-SOC produces the MAE

Summing over 3d(Mn)- sublattices

= 0 - non-zero!

complies with t-reversal symmetryof AFM

Strong 5d-SOC x 3d(Mn)-exchange filed x local susceptibility produce the MAE

TAMR and CBAMR

ADOS(ADOS([[’’’’ = = [DOS[DOS–DOS[–DOS[’’,,’]]/ DOS[’]]/ DOS[’,’,’]’]

and ATDOS = [TDOS–TDOS[’,’]]/TDOS[’,’]

ADOSADOS([001]-[110]) ~ 50 %

ATDOSATDOS([001]-[110]) ~ 20 %

Hard [001]-to-easy [110]

Sizable TAMR and CBAMR in AFMs

=Ef[001]-Ef[110]=-2.5 mV

[100]

[01

0]

1% strain

Easy [110] Easy [010] at <1% strain

ADOSADOS([110110]-[010010]) ~ 20 %

Strain-induced TAMR

Effect of in-plane strain – moment reorientations and TAMR

ATDOSATDOS([110110]-[010010]) ~ 20 %

2cos4cosMAE ||2*

||4 KK meV01.0||4 K 1%at meV07.0||2

* K

GMR/TMR and spin-torque relay on coherence & quality of interfaces in principle possible but likely very difficult to build AFM spintronics on these effects

Instead bulid AFM spintronics on a set of magnetic anisotropy phenomenaPiezo- (or other) electric control of AF moment orientation & TAMR (CBAMR)

exy = 0.1%

exy = 0%

Observations made from studies of AMR phenomena in GaMnAs (summary)

1. More than just bulk AMR in ohmic devices: TAMR, CBAMR

2. In DMSs bulk AMR has the simplest intuitive picture

3. TAMR and CBAMR are transferable to room-T metal FMs & AFMs

magneto-transport anisotropy phenomena in gamnas and beyond tomas jungwirth university of nottingham...

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