Making semiconductors magnetic:

new materials properties, devices, and future

JAIRO SINOVATexas A&M University

Institute of Physics ASCR

Hitachi CambridgeJorg Wunderlich, A. Irvine, et al

Institute of Physics ASCRTomas Jungwirth, Vít Novák, et al

Texas A&M L. Zarbo

Ohio State UniversityOct 2nd 2009

University of Nottingham Bryan Gallagher, Tom

Foxon, Richard Campion, et al.

NRISWAN

OUTLINE

• Motivation• Ferromagnetic semiconductor materials:

– (Ga,Mn)As - general picture– Growth, physical limits on Tc – Related FS materials (searching for room temperature)– Understanding critical behavior in transport

• Ferromagnetic semiconductors & spintronics– Tunneling anisotropic magnetoresistive device– Transistors (4 types)

Technologically motivated and scientifically fueled

Incorporate magnetic properties with

semiconductor tunability (MRAM, etc)

Understanding complex phenomena:•Spherical cow of ferromagnetic systems (still very complicated)•Engineered control of collective phenomena

Generates new physics:•Tunneling AMR•Coulomb blockade AMR•Nanostructure magnetic anisotropy engineering

ENGINEERING OF QUANTUM MATERIALS

More knobs than usual in semiconductors: density, strain, chemistry/pressure, SO coupling engineering

1. Create a material that marriages the tunability of semiconductors and the collective behavior of ferromagnets; once created search for room temperature systems

2. Study new effects in this new material and utilize in metal-based spintronics

3. Develop a three-terminal gated spintronic device to progress from sensors & memories to transistors & logic

Ferromagnetic semiconductor research : strategies

(Ga,Mn)As GENERAL PICTURE

Ferromagnetic semiconductors

GaAs - standard III-V semiconductor

Group-II Mn - dilute magnetic moments & holes

(Ga,Mn)As - ferromagnetic semiconductor

Need true FSs not FM inclusions in SCs

Mn

Ga

AsMn

+

Mn

Ga

As

What happens when a Mn is placed in Ga sites:Mn–hole spin-spin interaction

hybridization

Hybridization like-spin level repulsion Jpd SMn shole interaction

Mn-d

As-p

In addition to the Kinetic-exchange coupling, for a single Mn ion, the coulomb interaction gives a trapped hole (polaron) which resides just above the valence band

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

intermediate acceptor (110 meV) hole

Mn

Ga

AsMn

EF

DO

S

Energy

spin

spin

Transition to a ferromagnet when Mn concentration increasesGaAs:Mn – extrinsic p-type semiconductor

FM due to p-d hybridization (Zener local-itinerant kinetic-exchange)

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

Mn

Ga

As

Mn

Ga

AsMn

•Low-T MBE to avoid precipitation

•High enough T to maintain 2D growth

need to optimize T & stoichiometry for each Mn-doping

•Inevitable formation of interstitial Mn-double-donors compensating holes and moments need to anneal out but without loosing MnGa

high-T growth

optimal-T growth

(Ga,Mn)As GROWTH

Interstitial Mn out-diffusion limited by surface-oxide

GaMnAs

GaMnAs-oxide

Polyscrystalline20% shorter bonds

MnI++

O

Optimizing annealing-T another key factorRushforth et al, ‘08

x-ray photoemission

Olejnik et al, ‘08

10x shorther annealing with etch

(Ga,Mn)As GENERAL THEORY

HOW DOES ONE GO ABOUT UNDERSTANDING SUCH

SYSTEMS

1. One could solve the full many body S.E.: not possible AND not fun

2. Combining phenomenological models (low degrees of freedom) and approximations and comparison to other computational technieques while checking against experiments

“This is the art of condensed matter science, an intricate tangobetween theory and experiment whose conclusion can only beguessed at while the dance is in progress”

A.H.M et al., in “Electronic Structure and Magnetism in Complex Materials” (2002).

Theoretical Approaches to DMSs

• First Principles LSDA PROS: No initial assumptions, effective Heisenberg model can be extracted, good for determining chemical trends

CONS: Size limitation, difficulty dealing with long range interactions, lack of quantitative predictability, neglects SO coupling (usually)

• Microscopic TB models

•k.p Local Moment

PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), very good agreement with LDA+U calculations

CONS: neglects (usually) coulomb interaction effects, difficult to capture non-tabulated chemical trends, hard to reach large system sizes

PROS: simplicity of description, lots of computational ability, SO coupling can be incorporated, CONS: applicable only for metallic weakly hybridized systems (e.g. optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for deep impurity levels (e.g. GaMnN)

Jungwirth, Sinova, Masek, Kucera, MacDonald, Rev. of Mod. Phys. 78, 809 (2006)

Magnetism in systems with coupled dilute moments and delocalized band electrons

(Ga,Mn)As

cou

plin

g s

tren

gth

/ F

erm

i en

erg

y

band-electron density / local-moment density

Which theory is right?

KP EastwoodFast principles Jack

Impurity bandit vs Valence Joe

How well do we understand (Ga,Mn)As?

In the metallic optimally doped regime GaMnAs is well described by a disordered-valence band picture: both dc-data and ac-data are consistent with this scenario.

The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V metallic DMSs very well in the optimally annealed regime:• Ferromagnetic transition temperatures

Magneto-crystalline anisotropy and coercively Domain structure Anisotropic magneto-resistance Anomalous Hall effect MO in the visible range Non-Drude peak in longitudinal ac-conductivity • Ferromagnetic resonance • Domain wall resistance • TAMR •Transport critical behaviour •Infrared MO effects

TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

EXAMPLE: MAGNETO-OPTICAL EFFECTS IN THE INFRARED

Tc LIMITS AND STRATEGIES

Curie temperature limited to ~110K.

Only metallic for ~3% to 6% Mn

High degree of compensation

Unusual magnetization (temperature dep.)

Significant magnetization deficit

But are these intrinsic properties of GaMnAs ??

“110K could be a fundamental limit on TC”

As

GaMn

Mn Mn

Problems for GaMnAs (late 2002)

Can a dilute moment ferromagnet have a high Curie temperature ?

The questions that we need to answer are:

1. Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ?

2. Is there an extrinsic limit from the ability to create the material and its growth (prevents one to reach the optimal spot in the phase diagram)?

EXAMPLE OF THE PHYSICS TANGO

COMBINATION OF THEORY APPROACHES PREDICTS:

Tc linear in MnGa local moment concentration; falls rapidly with decreasing hole density in more than 50%

compensated samples; nearly independent of hole density for compensation < 50%.

Jungwirth, Wang, et al. Phys. Rev. B 72, 165204 (2005)

3/1pxT MnMF

c

Intrinsic properties of (Ga,Mn)As

Extrinsic effects: Interstitial Mn - a magnetism killer

Yu et al., PRB ’02:

~10-20% of total Mn concentration is incorporated as interstitials

Increased TC on annealing corresponds to removal of these defects.

Mn

As

Interstitial Mn is detrimental to magnetic order:

compensating double-donor – reduces carrier density

couples antiferromagnetically to substitutional Mn even in

low compensation samples Blinowski PRB ‘03, Mašek, Máca PRB '03

MnGa and MnI partial concentrations

Microscopic defect formation energy calculations:

No signs of saturation in the dependence of MnGa concentrationon total Mn doping

Jungwirth, Wang, et al.Phys. Rev. B 72, 165204 (2005)

As grown Materials calculation

Annealing can vary significantly increases hole densities.

Low Compensatio

n

0 2 4 6 8 100

3

6

9

12

15

18

p (

x 1

020cm

-3)

Mntotal

(%)

0 2 4 6 8 100.0

0.5

1.0

1.5

p/M

n sub

Mntotal

(%)

Obtain Mnsub assuming

change in hole density due to

Mn out diffusion

Open symbols & half closed as grown. Closed symbols annealed

High compensatio

nJungwirth, Wang, et al.Phys. Rev. B 72, 165204 (2005)

Experimental hole densities: measured by ordinary Hall effect

Theoretical linear dependence of Mnsub on total Mn confirmed experimentally

Mnsub

MnIntObtain Mnsub & MnInt assuming change in hole density due to

Mn out diffusion

Jungwirth, Wang, et al.Phys. Rev. B 72, 165204 (2005)

SIMS: measures total Mn concentration. Interstitials only compensation assumed

Experimental partial concentrations of MnGa and MnI in as grown samples

Can we have high Tc in Diluted Magnetic Semicondcutors?

Tc linear in MnGa local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples.

Define Mneff = Mnsub-MnInt

NO INTRINSIC LIMIT NO EXTRINSIC LIMIT

There is no observable limit to the amount of substitutional Mn we can put in

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

160

180

TC(K

)

Mntotal

(%)

8% Mn

Open symbols as grown. Closed symbols annealed

0 1 2 3 4 5 6 70

20

40

60

80

100

120

140

160

180

TC(K

)

Mneff

(%)

Tc as grown and annealed samples

● Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample

● Charge compensation not so important unless > 40%

● No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

160

180

TC(K

)

Mntotal

(%)

“... Ohno’s ‘98 Tc=110 K is the fundamental upper limit ..” Yu et al. ‘03

“…Tc =150-165 K independent of xMn>10% contradicting Zener kinetic exchange ...” Mack et al. ‘08

“Combinatorial” approach to growthwith fixed growth and annealing T’s

Tc limit in (Ga,Mn)As remains open

`

2008Olejnik et al

188K!!

- Effective concentration of uncompensated MnGa moments has to increase beyond 6% of the current record Tc=173K sample. A factor of 2 needed 12% Mn would still be a DMS

- Low solubility of group-II Mn in III-V-host GaAs makes growth difficult

Low-temperature MBEStrategy A: stick to (Ga,Mn)As

- alternative growth modes (i.e. with proper

substrate/interface material) allowing for larger

and still uniform incorporation of Mn in zincblende GaAs

More Mn - problem with solubility

Getting to higher Tc: Strategy A

Find DMS system as closely related to (Ga,Mn)As as possible with

• larger hole-Mn spin-spin interaction

• lower tendency to self-compensation by interstitial Mn

• larger Mn solubility

• independent control of local-moment and carrier doping (p- & n-type)

Getting to higher Tc: Strategy B

Weak hybrid.Delocalized holeslong-range coupl.

Strong hybrid.Impurity-band holesshort-range coupl.

InSb

GaP

d5

(Al,Ga,In)(As,P) good candidates, GaAs seems close to the optimal III-V host

Other (III,Mn)V’s DMSs

Mean-field butlow Tc

MF

Large TcMF but

low stiffness

Kudrnovsky et al. PRB 07

Using DEEP mathematics to find a new material

3=1+2

Steps so far in strategy B:

• larger hole-Mn spin-spin interaction : DONE BUT DANGER IN PHASE DIAGRAM

• lower tendency to self-compensation by interstitial Mn: DONE

• larger Mn solubility ?

• independent control of local-moment and carrier doping (p- & n-type)?

III = I + II Ga = Li + Zn

GaAs and LiZnAs are twin SC

Masek, et al. PRB (2006)

LDA+U says that Mn-doped are also twin DMSs

L

As p-orb.

Ga s-orb.As p-orb.

EF

It can be n and p doped!!!

No solubility limit for group-II Mn

substituting for group-II Zn !!!!

UNDERSTANDING CRITICAL

BEHAVIOUR IN TRANSPORT

Towards spintronics in (Ga,Mn)As: FM & transport

Dense-moment MSF<< d-

Eu - chalcogenides

Dilute-moment MSF~ d-

Critical contribution to resistivity at Tc

~ magnetic susceptibilityBroad peak near Tc disappeares with annealing (higher uniformity)???

~)0~~( Fkk

smalluncor Tc

EuCdSe

When density of carriers is smaller than density of local moments what matters is the long range behavior of Γ (which goes as susceptibility)

)/1~~( dkk F

vcdTddTd ~/~/

When density of carriers is similar to density of local moments what matters is the short range behavior of Γ (which goes as the energy)

Ni

Tc

Optimized materials with x=4-12.5% and Tc=80-185K

Remarkably universal both below and above Tc

Annealing sequence

d/dT singularity at Tc – consistent with kF~d-

V. Novak, et al “Singularity in temperature derivative of resistivity in (Ga,Mn)As at the Curie point”, Phys. Rev. Lett. 101, 077201 (2008).

OUTLINE

• Motivation• Ferromagnetic semiconductor materials:

– (Ga,Mn)As - general picture– Growth, physical limits on Tc – Related FS materials (searching for room temperature)– Understanding critical behavior in transport

• Ferromagnetic semiconductors & spintronics– Tunneling anisotropic magnetoresistive device– Transistors (4 types)

AMRAMR~ 1% MR effect~ 1% MR effect

TMRTMR~ 100% MR effect~ 100% MR effect

TAMRTAMR

) vs.( ~ IMvgExchange split & SO-coupled bands:

Exchange split bands:

)()(~ TDOSTDOS

)(~ MTDOS

Au

discovered in (Ga,Mn)As Gold et al. PRL’04

ab intio theory Shick, et al, PRB '06, Park, et al, PRL '08

TAMR in metal structures

experiment Park, et al, PRL '08

Also studied by Parkin et al., Weiss et al., etc.

DMS DEVICES

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0

2

4

6

8

10

0V 3V 5V 10V

carr

ier

dens

ity

[ 10

19 c

m-3

]

GaMnAs layer thickness [nm]

Gating of highly doped (Ga,Mn)As: p-n junction FET

p-n junction depletion estimates

Olejnik et al., ‘08

~25% depletion feasible at low voltages

(Ga,Mn)As/AlOx FET with large gate voltages, Chiba et al. ‘06

20 22 24 26 28 30 32 34

18.6

18.8

19.0

19.2

19.4

[10

-3c

m]

T [K]

Vg = 0V

22.5

23.0

23.5

24.0

24.5 Vg = 3V

20 22 24 26 28 30 32 34

-200

-100

0

100

d/d

T [1

0-6

T [K]

-300

-200

-100

0

AM

RIncreasing and decreasing AMR and Tc with depletion

Tc Tc

30 40 50 60 70 80 90 100

100

200

65K62K

dR/d

T

T (K)

depletion accumulation

Persistent variations of magnetic properties with ferroelectric

gates

Stolichnov et al., Nat. Mat.‘08

exy = 0.1%

exy = 0%

Electro-mechanical gating with piezo-stressors

Rushforth et al., ‘08

Strain & SO

Electrically controlled magnetic anisotropies via strain

Single-electron transistor

Two "gates": electric and magnetic

(Ga,Mn)As spintronic single-electron transistor

Huge, gatable, and hysteretic MR

Wunderlich et al. PRL ‘06

GMMGG C

C

e

MVMVVCQ

C

QQU

)(&)]([&

2

)(0

20

electric && magneticmagneticcontrol of Coulomb blockade oscillations

n-1 n n+1 n+2n-1 n n+1 n+2

EC

QQindind = = nnee

QQindind = (= (n+1/2)n+1/2)eeQ0

Q0

e2/2C

Q

D e

MQQVdQU

0

'' )()(

[010]

M[110]

[100]

[110][010]

SO-coupling (M)

Source Drain

GateVG

VDQ

Single-electron charging energy controlled by Vg and M

Theory confirms chemical potential anisotropies in (Ga,Mn)As& predicts CBAMR in SO-coupled room-Tc metal FMs

Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device

0

ONONOFFOFF

1

0

ONON OFFOFF

1

VDD

VA VB

VA

VB

Vout

0

0

0

OFFOFFONON

ONON

OFFOFF

0

0

1

1

ONONOFFOFF

A B Vout0 0 01 0 10 1 11 1 1

0

01

ONON

OFFOFF

0

0

OFFOFF

1

ONON

1

1

1

1

OFFOFF

ONON

1

1

ONON

OFFOFF

1

“OR”

Nonvolatile programmable logic

VDD

VA VB

VA

VB

Vout

Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device

0

ONONOFFOFF

1

0

ONON OFFOFF

1

A B Vout0 0 01 0 10 1 11 1 1

“OR”

Nonvolatile programmable logic

Physics of SO & exchange

SET

Resistor

Tunneling device

Chemical potential CBAMR

Tunneling DOS TAMR

Group velocity & lifetime AMR

Device design

Materials

metal FMs

FSs

FSs and metal FS with strong SO

ConclusionNo intrinsic or extrinsic limit to Tc so far: it is a materials growth issue

In the metallic optimally doped regime GaMnAs is well described by a disordered-valence band picture: both dc-data and ac-data are consistent with this scenario.

The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V metallic DMSs very well in the optimally annealed regime:

BUT it is only a peace of the theoretical mosaic with many remaining challenges!!

TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

• Ferromagnetic transition temperatures Magneto-crystalline anisotropy and coercively Domain structure Anisotropic magneto-resistance Anomalous Hall effect MO in the visible range Non-Drude peak in longitudinal ac-conductivity • Ferromagnetic resonance • Domain wall resistance • TAMR •Transport critical behaviour •Infrared MO effects

Allan MacDonald U of Texas

Tomas JungwirthInst. of Phys. ASCR

U. of Nottingham

Joerg WunderlichCambridge-Hitachi

Bryan GallagherU. Of Nottingham

Tomesz DietlInstitute of Physics, Polish Academy of

Sciences

Other collaborators: John Cerne, Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Charles Gould, Tom Fox,

Richard Campion, Laurence Eaves, Eric Yang, Andy Rushforth, Viet Novak

Hideo OhnoTohoku Univ.

Laurens MolenkampWuerzburg

Ewelina HankiewiczFordham Univesrsity

· Model Anderson Hamiltonian: (s - orbitals: conduction band; p - orbitals: valence band)

+ (Mn d - orbitals: strong on-site Hubbard int. local moment)

+ (s,p - d hybridization)

· Semi-phenomenological Kohn-Luttinger model for heavy, light, and spin-orbit split-off band holes

· Local exchange coupling: Mn: S=5/2; valence-band hole: s=1/2; J

pd > 0

k.p Local Moment - Hamiltonian

IjIjvjI

pd SsRrJ

,

ELECTRONS

Mn

ELECTRONS-Mn

Large S: treat classically

Tc LIMITS AND STRATEGIES

Can we have high Tc in Diluted Magnetic Semicondcutors?

Define Mneff = Mnsub-MnInt

(lines – theory, Masek et al 05)

NO EXTRINSIC LIMIT

Relative Mn concentrations obtained through hole density measurements and saturation moment densities measurements.

Tc linear in MnGa local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples.

NO IDENTIFICATION OF AN INTRINSIC LIMIT

Qualitative consistent picture within LDA, TB, and k.p

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

160

180

TC(K

)

Mntotal

(%)

8% Mn

Open symbols as grown. Closed symbols annealed

0 1 2 3 4 5 6 70

20

40

60

80

100

120

140

160

180

TC(K

)

Mneff

(%)

Tc as grown and annealed samples

● Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample

● Charge compensation not so important unless > 40%

● No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

III = I + II Ga = Li + Zn

GaAs and LiZnAs are twin SC

Masek, et al. PRB (2006)

LDA+U says that Mn-doped are also twin DMSs

n and p type doping through Li/Zn stoichiometry

No solubility limit for group-II Mn

substituting for group-II Zn !!!!

0 1 2 3 4 5 6 7 8 9 100

20

40

60

80

100

120

140

160

180

TC(K

)

Mntotal

(%)

Indiana & California (‘03): “ .. Ohno’s ‘98 Tc=110 K is the fundamental upper limit ..” Yu et al. ‘03

California (‘08): “…Tc =150-165 K independent of xMn>10% contradicting Zener kinetic exchange ...”

Nottingham & Prague (’08): Tc up to 185Kso far

“Combinatorial” approach to growthwith fixed growth and annealing T’s

?Mack et al. ‘08

Tc limit in (Ga,Mn)As remains open