JAIRO SINOVA

Research fueled by:

NERC

Challenges and Chemical Trends in Achieving a Room Temperature Dilute Magnetic

Semiconductor: A Spintronics Tango

2007: Frontiers in Chemical Physics WorkshopFebruary 22th 2007, Knoxville TN

Allan MacDonald U of Texas

Tomas JungwirthInst. of Phys. ASCR

U. of Nottingham

Joerg WunderlichCambridge-Hitachi

Bryan GallagherU. Of Nottingham

Ewelina HankiewiczU. of MissouriTexas A&M U.

Mario BorundaTexas A&M U.

Other collaborators: Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Laurens Molencam,

Charles Gould, Tomas Dietl, Tom Fox, Richard Campton

Xin LiuTexas A&M U.

Alexey KovalevTexas A&M U.

OUTLINEOUTLINE

Intro: Spintronics and Semiconductor Spintronics

Intro to Diluted Magnetic Semiconductors Can we have a high Tc DMS? What is the data telling us in GaMnAs:

thumbs up or down? Strategies to achieve high Tc DMSs

ELECTRONICSELECTRONICSUP TO NOW: electronics mostly based on the manipulation of the charge of the electron

Mr. Electron Two parts to hispersonality !

CHARGE

SPIN Spintronics = Controlling spin and spin flow with electric fields magnetic fields …

There is plenty of room at the bottom - Feynman,

1959

"... Up to now we have been content to dig in the ground to find minerals. ... We should consider, whether - in the great future - we can arrange atoms the way we want, the very atoms, all the way down! ... We can use not just circuits, but some system involving the quantized energy levels, or

interactions of quantized spins."

Cou

rtes

y of

Th

e A

rch

ives

, Cal

ifor

nia

In

stit

ute

of

Tec

hn

olog

y

Why semiconductors are betterWhy semiconductors are better

Bloch Wilson

allowed energyband in crystal

allowed energyband in crystal

isolated atomic levels

Pauli 1931: “One shouldn’t work with semiconductors,that is a filthy mess; who knows whether they really exist”

New New a la Feynmana la Feynman revolution in revolution in spintronics: diluted magnetic spintronics: diluted magnetic

semiconductorssemiconductors

Goal: use the storing capacity of Goal: use the storing capacity of ferromagnetism and the processing ferromagnetism and the processing capacity of semiconductors capacity of semiconductors

Does nature give us the material Does nature give us the material already? Noalready? No

Can we make it? YesCan we make it? Yes Can we understand it? Getting thereCan we understand it? Getting there Can we improve it: that is the tangoCan we improve it: that is the tango

+

Spin: used for storage

Charge: used for computation

Dilute Magnetic Semiconductors: the simple picture

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

moderately shallow acceptor (110 meV) hole

Jungwirth, Sinova, MJungwirth, Sinova, Mašek, Kučera, ašek, Kučera, MacMacDDonaldonald, , Rev. Mod. Phys. (2006)Rev. Mod. Phys. (2006), ,

http://unix12.fzu.cz/mshttp://unix12.fzu.cz/ms

- Mn local moments too dilute (near-neghbors cople AF)

- Holes do not polarize in pure GaAs

- Hole mediated Mn-Mn FM coupling

FERROMAGNETISM MEDIATED BY THE CARRIERS!!!

Ga

As

Mn

Ferromagnetic: x=1-8%

Ga1-xMnxAs

Low Temperature - MBE

courtesy of D. Basov

Inter-stitial

Anti-site

Substitutioanl Mn:acceptor +Local 5/2

moment

As anti-site deffect: Q=+2e

Interstitial Mn: double donor

BUT THINGS ARE NOT THAT SIMPLE

Tc~ 100 K, metallic

hard magnets

(III,V) DMS: man made ferromagnets (III,V) DMS: man made ferromagnets a laa la Feynman (1992-2000)Feynman (1992-2000)

anomalous Hall effectnormal: R

Hall ~ B

anomalous: RHall

~ M

•Ohno, et al PRL (1992) (InMnAs) 7.5 K•Ohno, et al APL (1996) (GaMnAs) 55 K•Ohno, Science (1998) 110 K

Curie temperature limited to ~110K.Curie temperature limited to ~110K.

Only metallic for ~3% to 6% MnOnly metallic for ~3% to 6% Mn

High degree of compensationHigh degree of compensation

Unusual magnetization (temperature dep.)Unusual magnetization (temperature dep.)

Significant magnetization deficitSignificant magnetization deficit

1996 1998 2000 20020

40

80

120

[4][3][2]

[1]

Cu

rie

tem

per

atu

re (

K)

Time

But are these intrinsic properties of GaMnAs ??

“110K could be a fundamental limit on TC” As

GaMn

Mn Mn

Problems for GaMnAs (late 2002)

OUTLINEOUTLINE

Intro: Spintronics and Semiconductor Spintronics

DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs:

thumbs up or down? Strategies to achieve high Tc DMSs

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)?

Effective magnetic couplingEffective magnetic coupling: Coulomb correlation of d-electrons & hopping AF kinetic-exchange coupling

Jpd

= + 0.6 meV nm3

Origin of coupling between localized Origin of coupling between localized moments and dilute carriersmoments and dilute carriers

MicroscopicMicroscopic: atomic orbitals & Coulomb correlation of d-electrons & hopping

Jpd

SMn

.shole

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

Theoretical Approaches to DMSsTheoretical Approaches to DMSs• First Principles Local Spin Density Approximation (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 Tight Binding models

•Phenomenological k.p Local Moment

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

CONS: neglects 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)

Which theory is right?

KP EastwoodFast principles Jack

Impurity bandit vs Valence Joe

As

GaMn

Mn Mn

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 killerExtrinsic 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 very 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 Can we have high Tc in Diluted Magnetic Semicondcutors?Semicondcutors?

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

Define MnDefine Mneffeff = Mn = Mnsubsub-Mn-MnIntInt

NO INTRINSIC LIMIT NO EXTRINSIC LIMIT

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

OUTLINEOUTLINE

Intro: Spintronics and Semiconductor Spintronics

DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs:

thumbs up or down? Strategies to achieve high Tc DMSs

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

High compensatio

n0 1 2 3 4 5 6 70

20

40

60

80

100

120

140

160

180

TC(K

)

Mneff

(%)

Linear increase of Tc with Mneff = Mnsub-MnInt

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

OUTLINEOUTLINE

Intro: Spintronics and Semiconductor Spintronics

DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs:

thumbs up or down? Strategies to achieve high Tc DMSs

- 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

conc. of wide gap component0 1

latti

ce c

onst

ant (

A)

5.4

5.7

(Al,Ga)As

Ga(As,P)

(Al,Ga)As & Ga(As,P) hosts

d5 d5

local moment - hole spin-spin coupling Jpd S . s

Mn d - As(P) p overlap Mn d level - valence band splitting

GaAs & (Al,Ga)As

(Al,Ga)As & Ga(As,P)GaAs

Ga(As,P)

MnAs

Ga

Smaller lattice const. more importantfor enhancing p-d coupling than larger gap

Mixing P in GaAs more favorable

for increasing mean-field Tc than Al

Factor of ~1.5 Tc enhancement

p-d coupling and Tc in mixed

(Al,Ga)As and Ga(As,P)

Mašek, et al. PRB (2006)Microscopic TBA/CPA or Microscopic TBA/CPA or

LDA+U/CPALDA+U/CPA

(Al,Ga)As

Ga(As,P)

Ga(As,P)

10% Mn

10% Mn

5% Mn

theory

theory

No reduction of MnI in (Al,Ga)As

Mixing P in GaAs more favorable forsuppressing Mnint formation

higher in (Al,Ga)As

and Ga(As,P)

than in GaAs

smaller interstitial space

only in Ga(As,P) theory

Mni formation in mixed (Al,Ga)As and Ga(As,P)

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)?

IIIIII = I + II = I + II Ga = Li + Zn Ga = Li + Zn

GaAs and LiZnAs are twin SC

Wei, Zunger '86;Bacewicz, Ciszek '88;Kuriyama, et al. '87,'94;Wood, Strohmayer '05

Masek, et al. PRB (2006)

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

Additional interstitial Li in

Ga tetrahedral position - donors

n-type Li(Zn,Mn)As

No solubility limit for group-II Mn

substituting for group-II Zn

theory

Electron mediated Mn-Mn coupling n-type Li(Zn,Mn)As -

similar to hole mediated coupling in p-type (Ga,Mn)As

L

As p-orb.

Ga s-orb.As p-orb.

EF

Comparable Tc's at comparable Mn and carrier doping and

Li(Mn,Zn)As lifts all the limitations of Mn solubility, correlated local-moment and carrier densities, and p-type only in (Ga,Mn)As

Li(Mn,Zn)As just one candidate of the whole I(Mn,II)V family

SUMMARYSUMMARY

No intrinsic limit to Tc: need to think in No intrinsic limit to Tc: need to think in terms of effective Mn concentrationterms of effective Mn concentration

Should use knowledge gained in (Ga,Mn)As Should use knowledge gained in (Ga,Mn)As to create new to create new a la cartea la carte materials materials

Using multiple theoretical approaches and Using multiple theoretical approaches and knowing what each is best and when IS the knowing what each is best and when IS the theory silver bullettheory silver bullet

Alloying P can help TcAlloying P can help Tc 3=2+13=2+1

BEFORE 2000

CONCLUSION:CONCLUSION:directors cutdirectors cut

BUT it takes MANY to do the spintronics tango!!

Texas A&M U., U. Texas, U. Buffalo, Nottingham, U.

Wuerzburg, U. Notre Dame, U. of Tennessee, U. of Maryland,

UCSB, Penn State, ….

It IS true that it takes two to tango

2000-2004

2006NEW DMSs ,Heterostructures

NEXT

EXTRAEXTRA

MAGNETIC ANISOTROPY

M. Abolfath, T. Jungwirth, J. Brum, A.H. MacDonald, Phys. Rev. B 63, 035305 (2001)

Condensation energy dependson magnetization orientation

<111>

<110>

<100>

compressive strain tensile strain

experiment:

Potashnik et al 2001Lopez-Sanchez and Bery 2003Hwang and Das Sarma 2005

Resistivity temperature dependence of metallic GaMnAs

theory theory

experiment

Ferromagnetic resonance: Gilbert damping

Aa,k()

I

M

Anisotropic Magnetoresistance

exp.

T. Jungwirth, M. Abolfath, J. Sinova, J. Kucera, A.H. MacDonald, Appl. Phys. Lett. 2002

GaMnAsAuAlOx Au

Tunneling anisotropic Tunneling anisotropic magnetoresistance (TAMR)magnetoresistance (TAMR)

Bistable memory device with a single magnetic layer only

Gould, Ruster, Jungwirth, et al., PRL '04

Giant magneto-resistance

(Tanaka and Higo, PRL '01)

[100]

[010]

[100]

[010]

[100]

[010]

ANOMALOUS HALL EFFECT

T. Jungwirth, Q. Niu, A.H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002)

anomalous velocity:

M0M=0

JpdNpd<S> (meV)

Berry curvature:

AHE without disorder

ANOMALOUS HALL EFFECT IN GaMnAs

Experiments

Clean limit theory

Minimal disorder theory

The valence band picture of IR absorption

F = dRe[()] = e2p / 2m

opt

mopt

independent of

(within 10%):· density· disorder· magnetic state

GaAsm

op 0.24 m

e

infrared absorption accurate density measurement

hole density: p=0.2, 0.3, ....., 0.8 nm-3

exp.

J. Sinova, et al. Phys. Rev. B 66, 041202 (2002).

x=5%

Exps: Singley et al Phys. Rev. Lett. 89, 097203 (2002)Hirakawa, et al Phys. Rev. B 65, 193312 (2002)

FINITE SIZE EXACT DIAGONALIZATION STUDIESFINITE SIZE EXACT DIAGONALIZATION STUDIES

S.-R. E. Yang, J. Sinova, T. Jungwirth, Y.P. Shim, and A.H. MacDonald, PRB 67, 045205 (03)

6-band K-L model

parabolic band model

p=0.33 nm-3, x=4.5%, compensation from anti-sites

p=0.2 nm-3, x=4.0%, compensation from anti-sites

6-band K-L model

GaAs

GaAs

f-sum rule accurate within 10 %

● Energy dependence of Jpd

● Localization effects

● Contributions due to impurity states: Flatte’s approach of starting from isolated impurities

● Systematic p and xeff study (need more than 2 meff data points)

Possible issues regarding IR absorption

Keeping Keeping ScoreScore

The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V shallow acceptor metallic DMSs very well in the regime that is valid:

• 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

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

Which theory is right?

KP EastwoodFast principles Jack

Impurity bandit vs Valence Joe

OUTLINEOUTLINE Intro: Spintronics and Semiconductor Spintronics DMS’s Intro:

III-V Semiconductors: the basic picture Perhaps Pauli was right: the messy reality Discovery and cool down of expectations

Can we have a high Tc DMS? Origin of the coupling between local moments and delocalized

carriers Basic phase diagram Theoretical approaches: no silver bullet but a good arsenal Is there an intrinsic limitation from theory Extrinsic limitations

What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs

Strategy A: focus on GaMnAs Strategy B: use what we have learned from DMSs to search for other

materials Increasing coupling strength but still sallow levels Mathematical strategy: decompose 3

d4

d

Weak hybrid.Delocalized holeslong-range coupl.

Strong hybrid.Impurity-band holesshort-range coupl.

d 5 d 4 no holes

InSb, InAs, GaAs Tc: 7 173 K

(GaN ?)

GaP Tc: 65 K

Similar hole localization tendencies

in (Al,Ga)As and Ga(As,P)

Scarpulla, et al. PRL (2005)

d5

Limits to carrier-mediated

ferromagnetism in (Mn,III)V