Ferromagnetic semiconductors for spintronics Theory concepts and experimental overview Tomas Jungwirth University of Nottingham Bryan Gallagher, Tom Foxon,

Ferromagnetic semiconductors for spintronics Theory concepts and experimental overview

Tomas Jungwirth

University of Nottingham Bryan Gallagher, Tom Foxon,

Richard Campion, Kevin Edmonds, Andrew Rushforth, Chris King et al.

Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine, David Williams,

Elisa de Ranieri, Byonguk Park, Sam Owen, et al.

Institute of Physics ASCR Jan Mašek, Josef Kudrnovský, František Máca,

Alexander Shick, Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, et al.

University of Texas Allan MaDonald, et al.

Texas A&MJairo Sinova, et al.

Electric field controlled spintronics

HDD, MRAMcontrolled by Magnetic field

Spintronic Transistorcontrol by

electric gates

STT MRAMspin-polarized charge current

From storage to logic

Magnetic race track memory

Current spintronics with FM metals

FM semiconductors: all features of current spintronics plus much more

Basic magnetic and magnetotransport properties of (Ga,Mn)As and related FS

Hard disk drive Hard disk drive

First hard discFirst hard disc (1956) (1956) - - classical electromagnet for read-outclassical electromagnet for read-out

From PC hard drives ('90)From PC hard drives ('90)to mto miicro-discscro-discs - - spintronispintronic read-headsc read-heads

MBMB’s’s

10’s-100’s 10’s-100’s GBGB’s’s

1 bit: 1mm x 1mm1 bit: 1mm x 1mm

1 bit: 101 bit: 10-3-3mm x 10mm x 10-3-3mmmm

Dawn of spintronicsDawn of spintronics

Anisotropic magnetoresistance (AMR) – 1850’s Anisotropic magnetoresistance (AMR) – 1850’s 1990’s 1990’s

Giant magnetoresistance (GMR) – 1988 Giant magnetoresistance (GMR) – 1988 1997 1997

Inductive read/write element

Magnetoresistive read element

Fert & Grunberg, Nobel Prize 07

MRAM – universal memoryMRAM – universal memory fast, small, low-power, durable, and non-volatile

2006- First commercial 4Mb MRAM

RAM chip that actually won't forget instant on-and-off computers

Spin-orbit couplingSpin-orbit coupling

nucleus rest frame electron rest frame

vI Q rE3

04 r

Q

3

0

4 r

rIB

EvEvB 200

1

c EvSS

2B

mc

egH B

SO

Lorentz transformation Thomas precession

2 2

ee--

Spintronics: it’s all about spin and chargeof electron communicating

quantum mechanics & special relativity Dirac equation

E=p2/2mE ih d/dtp -ih d/dr

E2/c2=p2+m2c2

(E=mc2 for p=0)

& HSO (2nd order in v/c around the non-relativistic limit)

Spin

Anisotropic Magneto-ResistanceAnisotropic Magneto-Resistance

Current sensitive to magnetization direction

~ 1% MR effect~ 1% MR effect

SO coupling from relativistic QM SO coupling from relativistic QM

FerromagnetismFerromagnetism = Pauli exclusion principle & Coulomb repulsion = Pauli exclusion principle & Coulomb repulsion

total wf antisymmetric = orbital wf antisymmetric * spin wf symmetric (aligned)

• RobustRobust (can be as strong as bonding in solids)(can be as strong as bonding in solids)

• Strong coupling to magnetic fieldStrong coupling to magnetic field (weak fields = anisotropy fields needed (weak fields = anisotropy fields needed only to reorient macroscopic moment)only to reorient macroscopic moment)

DOS

DOS

ee--

ee--

ee--

Giant Magneto-ResistanceGiant Magneto-Resistance


DOS

AP

P

>

SO-coupling not utilized

Tunneling Magneto-ResistanceTunneling Magneto-Resistance


DOS DOS

More direct link between transport and spin-split bands

Spin Transfer Torque writingSpin Transfer Torque writing

Slonczewski JMMM 96




Mn

Ga

AsMn

Dilute moment ferromagnetic semiconductors

GaAs - GaAs - standard III-V semiconductorstandard III-V semiconductor

Group-II Group-II Mn - Mn - dilute dilute magneticmagnetic moments moments & holes& holes

(Ga,Mn)As - fe(Ga,Mn)As - ferrromagneticromagnetic semiconductorsemiconductor

More tricky than just hammering an iron nail in a silicon wafer

Ohno et al. Science 98

Mn-d-like localmoments

As-p-like holes

Mn

Ga

AsMn

Strongly spin-split and spin-orbit coupled carriers in a semiconductor

LSdr

rdV

err

mc

p

mc

SeBH effSO

)(1

Strong SO due to the As p-shell (L=1) character of the top of the valence band

V

BBeffeff

pss

Beff Bex + Beff

AMR, TMR, …

Dietl et al., Abolfath et al. PRB 01

GaAs Mn

Mn

10-100x smaller Ms

One

Key problems with increasing MRAM capacity (bit density):

- Unintentional dipolar cross-links- External field addressing neighboring bits

10-100x weaker dipolar fields

10-100x smaller currents for switching

Dilute moment nature of ferromagnetic semiconductorsDilute moment nature of ferromagnetic semiconductors

Low-voltage gating (charge depletion) of ferromagnetic semiconductors

Owen, et al. arXiv:0807.0906

(Ga,Mn)As p-n junction FET

Low-voltage dependent R & MR

Switching by short low-voltage pulses

Mag

neti

zati

on

Ga

As Mn

Mn

Tc below room-temperature issue

• Low-Tc inherent feature of dilute moments but Tc 200K for 10% (Ga,Mn)As compared to Tc~300K in the 100% MnAs, i.e., Tc’s are already remarkable and the quest is still on

• New spintronics paradigms applicable to conventional ferromagnets or semiconductors

increasing Mn-doping

Wang, et al. arXiv:0808.1464Olejnik et al., PRB 08

AMRAMR TMRTMR

TAMRTAMR

) vs.( ~ IMvg

M

FM exchange int.:

Spin-orbit int.:

FM exchange int.:

)()( TDOSTDOS

)(MTDOS

Au

Discovered in GaMnAs Gould et al. PRL’04

ab intio theoryTAMR is generic to SO-coupled systems including room-Tc FMs

experiment

Bias-dependent magnitude and sign of TAMR

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

Park et al PRL '08

Consider uncommon TM combinationse.g. Mn/W voltage-dependent upto ~100% TAMR

spontaneous momentmag

netic su

sceptib

ility

spin

-orb

it cou

plin

g

Optimizing TAMR in transition-metal structures

Shick, et al PRB ‘08

GM

MGG

C

C

e

MV

MVVCQC

QQU

)(&

)]([&2

)(0

20

electric && magneticmagnetic

control of CB oscillations

Source Drain

GateVG

VDQ

Devices utilizing M-dependent electro-chemical potentials: FM SET

SO-coupling (M)

[010] M[110]

[100]

[110][010]

(Ga,Mn)As nano-constriction SET

~ 1mV in GaMnAs~ 10mV in FePt

Low-gate-voltage controlled huge magnitude and sign of MR very sensitive spintronic transistor

SO-coupling (M)

[010] M[110]

[100]

[110][010]

Wunderlich et al, PRL '06

Complexity of the relation between SO & exchange-split bands and

transport

SET

Resistor

Tunneling device

Chemical potential CBAMR

Tunneling DOS TAMR

Group velocity & lifetime AMR

Complexity of the device design

Magnitude and sensitivity to electric

fields of the MR

Datta-Das transistor

Spintronics in conventional semiconductorsSpintronics in conventional semiconductors

Datta and Das, APL ‘99

Karplus&Luttinger intrinsic AHE mechanism revived in Ga1-xMnxAs

Experiment AH 1000 (cm)-1

TheoryAH 750 (cm)-1

Anomalous Hall effect

intrinsic AHE in pure Fe:

I

_ FSO

FSO

_ __

V

Jungwirth et al. PRL ‘02,APL ’03

Yao et al. PRL ‘04

Karplus&Luttinger PR ‘54

I

_ FSO

FSO

_ __

Spin Hall effectspin-dependent deflection transverse edge spin polarization

I

_ FSO__

V

Anomalous Hall effect

M

Spin Hall effect

n

n

p

SHE mikročip, 100A supercondicting magnet, 100 A

Spin Hall effect detected optically in GaAs-based structures

Same magnetization achievedby external field generated bya superconducting magnet with 106 x larger dimensions & 106 x larger currents

Murakami et al Science 04, SInova et al. PRL 04,Wunderlich et al. PRL ‘05




(Ga,Mn)As material(Ga,Mn)As material

5 d-electrons with L=0 S=5/2 local moment

moderately shallow acceptor (110 meV) hole

- Mn local moments too dilute (near-neighbors couple AF)

- Holes do not polarize in pure GaAs

- Hole mediated Mn-Mn FM coupling

Mn

Ga

AsMn

Mn-d-like localmoments

As-p-like holes

Mn

Ga

AsMn

EF

DO

S

Energy

spin

spin

Ferromagnetic semiconductor GaAs:Mn

valence band As-p-like holes

As-p-like holes localized on Mn acceptors

<< 1% Mn ~1% Mn >2% Mn

onset of ferromagnetism near MIT

Exchange-split, SO-coupled, & itinerant holes

Mn

Ga

AsMn

Mn–hole spin-spin interaction

hybridization

Hybridization like-spin level repulsion Jpd S shole AF interaction

Mn-d

As-p

Equivalence between microscopic hybridization (weak) picture and kinetic-exchange model

Microscopic (Anderson) Hamiltonian

Schrieffer-Wolf transformation

k=0 approx.

Heff

= Jpd

<shole> || -x

Mn

As

Ga

heff

= Jpd

<S> || x

Hole Fermi surfaces

Mean-field ferromagnetic Mn-Mn coupling mediated by holes

holes

Fluctuations around the MF state

MF

= - Jpd Ss

Antiferromagnetic coupling (Jpd > 0) STOT

= S - s

GS = Jpd /2 [ (S-s)(S-s+1) - S(S+1) -s(s+1) ] = - Jpd (Ss+s)

GS

< MF

H = Jpd S . s = Jpd /2 ( S2TOT

- S2 - s2)

Magnetism in systems with coupled dilute moments and delocalized band electrons

(Ga,Mn)As

cou

pli

ng

str

eng

th /

Fer

mi

ener

gy

band-electron density / local-moment density

Jungwirth et al, RMP '06

d4

d

Weak hybrid.Delocalized holeslong-range coupl.

Strong hybrid.

More localized holesshorter-range coupl.

no holes

InSb, GaAs

GaN

GaP

d5

Nature of Mn-impurity in III-V host

Kudrnovsky et al. PRB 07

hole-Mn exchange = hybridization & splitting between Mn d-level and valence band edge

Weak hybrid.

Strong hybrid.

InSb

GaP

d5

GaAs seems close to the optimal III-V host

Mean-field butlow Tc

MF

Large TcMF but

low stiffness

Hole-mediated Mn-Mn exchange in III-V host

MIT in p-type GaAs:- shallow acc. (30meV) ~ 1018 cm-3

- Mn (110meV) ~1020 cm-3

Mobilities:- 3-10x larger in GaAs:C- similar in GaAs:Mg or InAs:Mn

> 1-2% Mn: metallic but strongly disordered

Model:SO-coupled, exch.-split Bloch VB & disorder

- conveniently simple and increasingly meaningful as metallicity increases

- no better than semi-quantitative

Random Mn disorder

Short-range ~ M . s potential

Together with central-cellshifts MIT to ~1% Mn (1020 cm-3)

(Ga,Mn)As growth

Low-T MBE to avoid precipitation & high enough T to maintain 2D growth need to optimize T & stoichiometry for each Mn-doping

high-T growth optimal-T growth

Annealing also needs to be optimized for each Mn-doping

Detrimental interstitial AF-coupled Mn-donors need to anneal out (Tc can increase by more than 100K)

Tc in (Ga,Mn)As semiquantitative theory understanding (within a factor of ~2)

No saturation seen in theory and in optimized (Ga,Mn)As samples yet

Material synthesis becomes increasingly tedious for >6% MnGa

MnGa doping

t=(Tc-T)/Tc

4.03.0

~

tM

1.5% 8%

Optimized (Ga,Mn)As materials

Wang, et al. arXiv:0808.1464Olejnik et al., PRB 08, Novak et al. PRL 08

• I-II-Mn-V ferromgantic semiconductors (so far in theory only)

III = I + II Ga = Li + Zn

• GaAs and LiZnAs are twin semiconductors

• Prediction that Mn-doped are also twin ferromagnetic semiconductors

• No limit for Mn-Zn (II-II) substitution

• Independent carrier (holes or electrons) doping by Li-Zn stoichiometry adjustment

Masek, et al. PRL 07

VB-CB

VB-IB

Mn-acceptor level (IB)

Short-range ~ M . s potential

Together with central-cellshifts MIT to ~1% Mn (1020 cm-3)

Transport in (Ga,Mn)As: MIT

GaAs VB

GaMnAs disordered VB

2.2x1020 cm-3

Jungwirth et al, PRB '07

MIT in GaAs:Mn at order of magnitude higher doping than quoted in text books

Curie point transport anomaly

Ordered magnetic semiconductors

Eu - chalcogenides

Disordered DMSs

Sharp critical contribution to resistivity at Tc ~ magnetic susceptibility

Broad peak near Tc and disappeares with annealing (higher uniformity)???

~)( dF

Eu0.95Cd0.05S

][~),(~)( 002 SSSSJTRT iipdi

Fisher&Langer, PRL‘68

singular

UdF ~)~(

vcdTdUdTd /~/

Tc

Ni, Fe

singular

Scattering off correlated spin-fluctuations

Optimized GaMnAs materials with x~4-12% and Tc~80-185K: very well behaved FMs

Annealing sequence

In GaMnAs F~d- sharp singularity at Tc in d/dT

Novak et al., PRL ‚08

T/Tc-1

• New paradigms for spintronics applicable to conventional FM and SC

• Spintronic field-effect transistors

• Well behaved ferromagnet compatible with standard SC technologies

[010] M[110]

[100]

[110][010]

Conclusions

CBAMR

(Ga,Mn)As and related FS:

Documents

Ferromagnetic semiconductors for spintronics Theory concepts and experimental overview Tomas Jungwirth University of Nottingham Bryan Gallagher, Tom Foxon,