Ferromagnetic semiconductors for spintronics Theory concepts and experimental overview

Tomas Jungwirth

Institute of Physics ASCR

Jan Ma šek, Josef Kudrnovský, František Máca, Alexander Shick, Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, et al.

Hitachi Cambridge, Univ. Cambridge

Jorg Wunderlich, Andrew Irvine, David Williams, Elisa de Ranieri, Byonguk Park, Sam Owen, et al.

University of Nottingham

Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds, Andrew Rushforth, Chris King et al.

Texas A&M

Jairo Sinova, et al.

University of Texas

Allan MaDonald, et al.

Electric field controlled spintronics

From storage to logic

HDD, MRAM

controlled by Magnetic field

STT MRAM

spin-polarized charge current

Spintronic Transistor

control by electric gates 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

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

1 bit: 1mm x 1mm

MB ’s 10’s-100’s GB’s From PC hard drives ('90) to micro-discs spintronic read-heads

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

Dawn of spintronics Magnetoresistive read element Inductive read/write element Anisotropic magnetoresistance (AMR) – 1850’s



1990’s Giant magnetoresistance (GMR) – 1988



1997

Fert & Grunberg, Nobel Prize 07

MRAM – universal memory

fast, small, low-power, durable, and

non-volatile RAM chip that actually won't forget



instant on-and-off computers

2006- First commercial 4Mb MRAM

nucleus rest frame

Spin-orbit coupling

electron rest frame

I



Q

v B

  0  0

v



E

 1

c

2

v



E E



Q

4

 0

r

3

r B

  4  0

I



r

r

3

H SO



g



2



B

S

 B 

2 e mc

2

S



v



E

Lorentz transformation  Thomas precession e -

Spintronics

: it’s all about spin and charge of electron communicating

SO coupling from relativistic QM quantum mechanics & special relativity  Dirac equation

E=p 2 /2m E



ih d/dt p



-ih d/dr E 2 /c 2 =p 2 +m 2 c 2 (E=mc 2 for p=0)

Spin

Anisotropic Magneto-Resistance

& H SO (2 nd order in

v/c

around the non-relativistic limit) ~ 1% MR effect Current sensitive to magnetization direction

e e e -

Ferromagnetism

= Pauli exclusion principle & Coulomb repulsion

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

•

Robust

(can be as strong as bonding in solids) •

Strong coupling to magnetic field

(weak fields = anisotropy fields needed only to reorient macroscopic moment)

DOS

    

Giant Magneto-Resistance

SO-coupling not utilized ~ 10% MR effect

Tunneling Magneto-Resistance

More direct link between transport and spin-split bands

DOS

 

DOS

 ~ 100% MR effect

Spin Transfer Torque writing

Slonczewski JMMM 96

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

Dilute moment ferromagnetic semiconductors

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

Ohno et al. Science 98

Mn GaAs - standard III-V semiconductor Group-II Mn - dilute magnetic moments & holes (Ga,Mn)As - ferromagnetic semiconductor

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

Ga As-

p-like holes

Mn As Mn

H SO

   

B eff

Mn-

d-like local moments

   

e S



mc

     

p mc



r

 1

er dV

(

r

)

dr

   

S

  

L



V

s B eff

Strong SO due to the As

p

-shell (

L

=1) character of the top of the valence band

p Dietl et al., Abolfath et al. PRB 01 B eff B ex + B eff

AMR, TMR, …

Dilute moment nature of ferromagnetic semiconductors

Key problems with increasing MRAM capacity (bit density): - Unintentional dipolar cross-links - External field addressing neighboring bits One 10-100x weaker dipolar fields 10-100x smaller M s Ga As Mn Mn 10-100x smaller currents for switching

Low-voltage gating (charge depletion) of ferromagnetic semiconductors

Low-voltage dependent R & MR (Ga,Mn)As p-n junction FET Switching by short low-voltage pulses

Owen, et al. arXiv:0807.0906

Mn Ga As

T c below room-temperature issue

increasing Mn-doping

Mn

Wang, et al. arXiv:0808.1464

Olejnik et al., PRB 08

• Low-T c inherent feature of dilute moments but T c  200K for 10% (Ga,Mn)As compared to T c ~300K in the 100% MnAs, i.e., T c ’s are already remarkable and the quest is still on • New spintronics paradigms applicable to conventional ferromagnets or semiconductors

AMR TMR FM exchange int.: Spin-orbit int.:

 ~ 

M v g

 ( 

M

vs.

I

 )

Au TAMR

TDOS

 (

M

)

Discovered in GaMnAs

Gould et al. PRL’04

FM exchange int.:

TDOS

(  ) 

TDOS

(  )

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

TAMR is generic to SO-coupled systems including room-T c FMs ab intio theory

Park et al PRL '08

experiment

Optimizing TAMR in transition-metal structures spontaneous moment

Consider uncommon TM combinations

e.g. Mn/W



voltage-dependent upto ~100% TAMR Shick, et al PRB ‘08

Devices utilizing M-dependent electro-

chemical

potentials: FM SET

[ 110 ] [ 010 ]

M

[ 100 ] [ 110 ] [ 010 ] SO-coupling   (

M

)

Q V D

Source Drain Gate

V G U

 &

V M

(

Q



Q

0 ) 2  2

C

   ( 

M e

) &

Q

0

C



C G



C G

[

V G



V M

( 

M

)] electric & magnetic control of CB oscillations

SO-coupling   (

M

) [ 110 ] [ 010 ]

M

[ 100 ] [ 110 ] [ 010 ] ~ 1mV in GaMnAs ~ 10mV in FePt (Ga,Mn)As nano-constriction SET Low-gate-voltage controlled huge magnitude and sign of MR  very sensitive spintronic transistor

Wunderlich et al, PRL '06

Magnitude and sensitivity to electric fields of the MR Complexity of the device design Complexity of the relation between SO & exchange-split bands and transport

Chemical potential



CBAMR

SET

Tunneling DOS



TAMR

Tunneling device Resistor

Group velocity & lifetime



AMR

Spintronics in conventional semiconductors

Datta-Das transistor

Datta and Das, APL ‘99

F SO _ F SO Anomalous Hall effect

Karplus&Luttinger intrinsic AHE mechanism revived in Ga 1-x Mn x As V

Karplus&Luttinger PR ‘54 Jungwirth et al. PRL ‘02,APL ’03

I  intrinsic AHE in pure Fe:

Yao et al. PRL ‘04

Experiment



AH



1000 (

W

cm) -1



AH



Theory

750 ( W

cm) -1

Spin Hall effect

spin-dependent deflection  transverse edge spin polarization

Anomalous Hall effect Spin Hall effect

F SO

M V Spin Hall effect detected optically in GaAs-based structures I

_ F SO F SO

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

I Same magnetization achieved by external field generated by a superconducting magnet with 10 6 x larger dimensions & 10 6 x larger currents

p n n

SHE mikro čip, 100  A supercondicting magnet, 100 A

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

Mn

(Ga,Mn)As material

Ga Mn As

- Mn local moments

too dilute (near-neighbors couple AF)

-

Holes do not polarize in pure GaAs

- Hole mediated Mn-Mn FM coupling

5 

d

-electrons with L=0

S=5/2 local moment

moderately shallow acceptor (110 meV) 

hole

Ferromagnetic semiconductor GaAs:Mn

spin

 E F

Exchange-split, SO coupled, & itinerant holes

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

spin



onset of ferromagnetism near MIT

As-p-like holes localized on Mn acceptors valence band As-p-like holes

Ga As-

p-like holes

As Mn Mn Mn-

d-like local moments

Ga As Mn Mn –hole spin-spin interaction Mn As-

p

Mn-

d

hybridization Hybridization  like-spin level repulsion 

J pd

S



s hole

AF interaction

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

Microscopic (Anderson) Hamiltonian Schrieffer-Wolf transformation

k=0

approx.

Mean-field ferromagnetic Mn-Mn coupling mediated by holes

h eff =

J

pd <

S

> || x Hole Fermi surfaces

Mn As Ga

holes

H

eff =

J

pd <

s hole

> || -x

 MF

= - J pd Ss

Fluctuations around the MF state

H = J pd

S . s

= J pd

/2 (

S 2 TOT - S 2 - s 2

) Antiferromagnetic coupling (

J pd > 0) S TOT = S

-

s



GS = J pd

/2 [ (

S-s

)(

S-s+1

)

- S

(

S+1

)

-

s(s

+1

) ]

= - J pd

(

Ss+s

) 

GS <

 MF

Magnetism in systems with coupled dilute moments and delocalized band electrons band-electron density / local-moment density

Jungwirth et al, RMP '06

(Ga,Mn)As

Nature of Mn-impurity in III-V host

Weak hybrid.

Kudrnovsky et al. PRB 07

Delocalized holes long-range coupl.

InSb, GaAs GaP

Strong hybrid.

d 5

More localized holes shorter-range coupl.

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

GaN

no holes

d d 4

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

Weak hybrid.

Mean-field but low T c MF

InSb

Strong hybrid.

Large T c MF but low stiffness

GaP

GaAs seems close to the optimal III-V host

d 5

Random Mn



disorder MIT in p-type GaAs: - shallow acc. (30meV) ~ 10 18 cm -3 - Mn (110meV) ~10 20 cm -3 Short-range ~ M . s potential Together with central-cell shifts MIT to ~1% Mn (10 20 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

high-T growth

(Ga,Mn)As growth

optimal-T growth

Low-T MBE to avoid precipitation & high enough T to maintain 2D growth  need to optimize T & stoichiometry for each Mn-doping Detrimental interstitial AF-coupled Mn-donors  need to anneal out (T c can increase by more than 100K) Annealing also needs to be optimized for each Mn-doping

Optimized (Ga,Mn)As materials

1.5% Mn Ga doping 8%

Wang, et al. arXiv:0808.1464

Olejnik et al., PRB 08, Novak et al. PRL 08 M

  ~

t

 0 .

3  0 .

4 t=(Tc-T)/Tc T c 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% Mn Ga

•

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

Transport in (Ga,Mn)As: MIT

Jungwirth et al, PRB '07

GaAs VB Mn-acceptor level (IB) GaMnAs disordered VB

2.2x10

20 cm -3

VB-CB VB-IB Together with central-cell shifts MIT to ~1% Mn (10 20 cm -3 )

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

Curie point transport anomaly

Ordered magnetic semiconductors Disordered DMSs

Eu



- chalcogenides

 Sharp critical contribution to resistivity at T c ~ magnetic susceptibility

Broad

peak near T c and

disappeares

with annealing (higher uniformity)???

Scattering off correlated spin-fluctuations  (

T

) ~  ( 

R i

,

T

) ~

J

2

pd Fisher&Langer, PRL‘68

[ 

S



i

 

S

0    

S i

   

S

0  ] singular  ( 

F



d

   ) ~  singular  ( 

F d

 /

dT

~

d

   ) ~

U

~

dU

/

dT



c v

Ni, Fe Eu 0.95

Cd 0.05

S T c

In GaMnAs  F ~d    sharp singularity at T c in d  /dT

Annealing sequence

T/T c -1 Optimized GaMnAs materials with x~4-12% and Tc~80-185K: very well behaved FMs

Novak et al., PRL ‚08

Conclusions (Ga,Mn)As and related FS:

• Spintronic field-effect transistors • New paradigms for spintronics applicable to conventional FM and SC [ 110 ] [ 100 ] [ 010 ]

M

[ 110 ] [ 010 ]

CBAMR

• Well behaved ferromagnet compatible with standard SC technologies