Prezentacja programu PowerPoint - Magnetismmagnetism.eu/esm/2003-brasov/slides/dietl-slides-1.pdf · MAGNETIC SEMICONDUCTORSMAGNETIC SEMICONDUCTORS. Tomasz DIETL. Institute of Physics,

Spintronics – material aspectsSpintronics – material aspectsWhy to do not combine complementary properties and functionalities of semiconductor and magnetic material systems?

• hybrid structures-- overlayers or inclusions of ferromagnetic metals =>source of stray fields and spin-polarized carriers

-- soft ferromagnets => local field amplifiers-- hard ferromagnets => local field generators

• ferromagnetic semiconductors

MAGNETIC SEMICONDUCTORSMAGNETIC SEMICONDUCTORS

Tomasz DIETLInstitute of Physics, Polish Academy of Sciences, Warsaw

Collaboration: Grenoble (J. Cibert et al.), Sendai (H. Ohno et al.),Austin (a. MacDonald et al.), Regensburg (D. Weiss et al.), …

1. Families of magnetic semiconductors2. Spin manipulations in ferromagnetic semiconductors3. Magnetic impurities in semiconductors4. sp-d exchange interactions5. d-d exchange interactions6. Outlook7. SummarySupport: EC: AMORE, FENIKS, ERATO (JST), A.V. Humboldt Foundation

Families of magnetic semiconductors

• magnetic semiconductorsshort-range ferromagnetic super- or double exchangeEuS, ZnCr2Se4, La1-xSrxMnO3, ...

short-range antiferromagnetic superexchangeEuTe, ...

Magnetic semiconductorsMagnetic semiconductors

now: Diluted Magnetic Semiconductors (DMS)

DMS: standard semiconductor + magnetic ions

DMS: standard semiconductor + magnetic ions

• Various magnetic ions:- mostly 3d transition metals: Sc, ..., Cu- rare earth (4f): Ce, ..., Tm- also actinides (5f), 4d TM, ...

• Various hosts:- II-VI: Cd1-xMnxTe, Hg1-xFexSe,...- IV-VI: Sn1-xMnxTe, Pb1-xEuxS- III-V: In1-xMnxSb, Ga1-xErxN, ...- IV: Ge1-xMnx, Si1-xCex- ....

Most of DMS: random antiferromagnetMost of DMS: random antiferromagnet

short range antiferromagnetic superexchange

Evidences for antiferromagnetic pairsH12 = -2JS1S2

Evidences for antiferromagnetic pairsH12 = -2JS1S2

inelastic neutron scattering

Zn0.95Mn0.05Te

T. Giebultowicz et al.H. Kepa, …, T.D., PRL’03

Evidences for antiferromagneticinteractions: magnetic susceptibility

Evidences for antiferromagneticinteractions: magnetic susceptibility

A. Lewicki et al.

Curie-Weiss law

χ = C/(T − Θ)

C = gµBS(S+1)xNo/3kBΘ < 0 antiferro

Magnetization of localized spinsMagnetization of localized spins

M(T,H) = gµBSxeffNoBS[gµBH/kB(T + TAF)

antiferromagnetic interactions

xeff < x

TAF > 0

Modified Brillouin function

Y. Shapira et al.

long-range hole-mediated ferromagnetic exchange

IV-VI: p-Pb1-x-yMnxSnyTe (Story et al.’86)III-V: In1-x-MnxAs (Ohno et al.’92)

Ga1-x-MnxAs (Ohno et al.’96) TC ≈ 100 K for x = 0.05II-VI: p-Cd1-xMnxTe/Cd1-x-yZnxMgyTe:N QW

(Haury et al.’97, Kossacki et al.’99)p-Zn1-xMnxTe:N (Ferrand et al.’99)p-Be1-xMnxTe:N (Hansen et al.’01)

Ferromagnetic DMSFerromagnetic DMS

III-V and II-VI DMS:quantum nanostructures and ferromagnetism combine

Spin manipulations in ferromagnetic DMS

Tuning magnetic ordering by electric field (ferro-FET) (In,Mn)As

Tuning magnetic ordering by electric field (ferro-FET) (In,Mn)As

H. Ohno, .., T.D., ...Nature ’00

M

IVH

Modulation-doped p-type magnetic QWsModulation-doped p-type magnetic QWs

(Cd,Mg)Te:N (Cd,Mg)Te:N(Cd,Mn)Te

J. Cibert et al. (Grenoble)

σ-σ-σ+

σ+

ENER

GY

∆E ~ M

Control offerromagnetism

by electric field in a pin

diode – ferro-LED

1700 1710

1.49 K1.651.872.052.19

2.80

3.03

4.2 K0V

PL In

tens

ity (a

.u.)

Energy (meV)

a

1700 1710

1.49 K1.651.88

2.05

2.19

2.822.97

b4.2 K

-1V

Hole liquid Depleted

V

QWp doped

n doped

undopedbarriers

Control offerromagnetism

by electric field in a pin

diode – ferro-LEDPhotoluminescence

Ec

EF

VEv

H. Boukari, …, T.D., PRL’02

V

QW

1700 1710

0 V1.5 K

Ev

Ec

EFill

umi n

ati o

n

Combined: electrostatic gate + illumination

in p-i-n diode (ferro-LED)

Combined: electrostatic gate + illumination

in p-i-n diode (ferro-LED)

1700 1710

1.49 K1.651.872.052.19

2.80

3.03

4.2 K0V

PL In

tens

ity (a

.u.)

Energy (meV)

a

1700 1710

1.49 K1.651.88

2.05

2.19

2.822.97

b4.2 K

-1V

Hole liquid Depleted

V

Ferro- diode: electric field and light tuned ferromagnetism

Optical tuning of magnetization – p-i-p diodeOptical tuning of magnetization – p-i-p diode

paramagnetic

1680 1690 1700 1710

Tp=16×1010 cm-2

(a)

4.2 K

2.7 K

2.4 K

2.1 K

1.8 K

1.2 K

Energy [ meV ]1680 1690 1700 1710

(b)

p×1010

cm-2

2.7

5.2

7.1

10

12

16

T = 1.34 K

Energy [ meV ]

ferromagnetic

Tem

pera

ture

Hol

e co

ncen

tratio

n

p = const T = const

Illum

inat

ion

CdMnTe QW8 nm

0 to 4% Mn

EFEv

Ec

pip diode: light destroys ferromagnetism

Magnetic ions in semiconductors

• position of d levels, U

• charge and spin states

• intra ion excitation energies d d*

• coupling to band states:

-- spin dependent: sp-d exchange interactions

-- spin independent: band offsets

-- crystal-field effects

Transition metals – free atomsTransition metals – free atoms

• Electronic configuration of TM atoms: 3dn4s2

1 ≤ n ≤ 10: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn

• Important role of electron correlation for open d shells- intra site correlation energy U = En+1 – En

for n =5, U ≈ 15 eV

3d5

3d6 UHB

LHB

U

Transition metals – free atomsTransition metals – free atoms

• Electronic configuration of TM atoms: 3dn4s2

1 ≤ n ≤ 10: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn

• Important role of electron correlation for open d shells- intra site correlation energy U = En+1 – En

for n =5, U ≈ 15 eV- intra-site exchange interaction: ferromagnetic

Hund’s rule: S the highest possiblefor n = 5, ES=3/2 − ES=5/2 ≈ 2 eV

3d5

3d*5

Transition metals – free atomsTransition metals – free atoms

• Electronic configuration of TM atoms: 3dn4s2

1 ≤ n ≤ 10: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn

• Important role of electron correlation for open d shells- intra site correlation energy U = En+1 – En

for n =5, U ≈ 15 eV- intra-site exchange interaction: ferromagnetic

Hund’s rule: S the highest possiblefor n = 5, ES=3/2 − ES=5/2 ≈ 2 eV

- TM atoms, 3dn4s1, e.g., Mn:ES=2 − ES=3 ≈ 1.2 eV Js-d ≈0.4 eV ferromagnetic

despite of screening and hybridization these effects survive in solids 3d5

4s1

Where d levels and carriers reside in DMS?Where d levels and carriers reside in DMS?

Possibilities:

-- manganides La1-xSrxMnO3 -- cuprates La2-xSrxCuO4Mott-Hubbard AF insulator for x 0 charge transfer AF insulator for x 0

c.b. (cation s orbitals)

d TM band

v.b. (anion p orbitals)

c.b.

v.b.

d TM band

E

DOSExperimental guide: impurity limit (EPR, d –> d*, … )

TM impurities in II-VI compoundsTM impurities in II-VI compounds

dn/dn+1

dn/dn-1

• TM atoms: 3dn4s2

• TM impurity (dn) neutral since:-- donor level dn/dn-1

resides below c.b.-- acceptor level dn/dn+1

resides above v.b.• Exceptions (charged TM)

-- Sc in CdSe

d-levels of TM (3dn4s2 ) impurities in II-VI’sd-levels of TM (3dn4s2 ) impurities in II-VI’s

dn/dn+1 acceptor

HHB

dn/dn-1donorLHB

A.Zunger, J.Baranowski, P.Vogl, J.Langer, A.Fujimori, ...

• Mn2+ (d5, S = 5/2)• AF superexchannge(random AF)

• no d levels at EF• independent control of Mn andcarrier densities (doping, light)

• strong sp-d exchange H = -IsS

TM impurities in III-V compoundsTM impurities in III-V compounds

•TM atoms: 3dn4s2

•TM impurity (dn-1) neutral if-- donor level dn-1/dn-2

resides below c.b.-- acceptor level dn-1/dn

resides above v.b.

• Mn in III-V:resonant + hydrogenic

acceptor

dn-1/dn

sp-d exchange interactions in DMS

Potential s-d exchange interaction

Spin part of Coulomb energy for s and d electrons

Esd = -Jsd(S + s)2 = -JsdS2 - Jsds2 -2JsdSs = C-2JsdSs = C- αNoSs

for Mn atom αNo = 0.4 eVinteraction of magnetic moments: Edipole-dipole ≈ 0.004 eV

in semiconductor compounds αNo reduced by • screening• admixture of s-type anion wave function

Spin dependent interaction between valence band holes and Mn spins

Spin dependent interaction between valence band holes and Mn spins

Gain of energy due tosymmetry allowed hybridization

• quantum hopping of electrons from the v.b. to the d level

• quantum hopping of electronsfrom the d level to the empty v.b states

• Hi = - βNosSi (Schriffer-Wolff)kinetic pd exchange

3d6

v.b. 3d5

Contribution to the kp hamiltonian due to the presence of a magnetic ion

Contribution to the kp hamiltonian due to the presence of a magnetic ion

• Hj = Uo (r- Rj) - sites with no magnetic ion• Hi = U(r- Ri) - J(r-Ri)sSi - sites with the magnetic ion• kp model: non-vanishing matrix elements:

V = , W = - conduction and valenceband offset integrals

α = , β = - s-d and p-d exchange integralsS>, X> - Bloch wave functions Energies: VNo etc.

Virtual crystal and molecular-field approximationsVirtual crystal and molecular-field approximations

• The translation symmetry restored by introducing anaverage potential, the same for each site:Hn = (1 - x) Uo (r - Rn) + xU(r - Rn) - xJ(r - Rn)sSn

Eg = x(VNo - WNo )

• replacing spin-operators in a volume v by a classical field:

x ΣnSn _--> M(r)/gµBHspin = Js M(r)/g µ B new contribution to spin splitting

• Difference between real and VCA/MFA hamiltoniansscattering (alloy and spin-disorder scattering)

Effects of exchange interaction and determination of exchange integralsEffects of exchange interaction and determination of exchange integrals

αNo = 0.25 eV

T. D. et al.

Determination of sp-d exchange integrals I- giant splitting of exciton states

Determination of sp-d exchange integrals I- giant splitting of exciton states

geff > 102

σ-σ-σ+

σ+

ENER

GY

v.b.

c.b.

∆E ~ M ~ BS(H)

J. Gaj et al.A. Twardowski et al.

-- p-d: Ipd ≡ βNo ≈ - 1.0 eVlarge p-d hybridization and large intra-site Hubbard U => kinetic p-d exchange (T.D. ’80, …, P. Kacman, SST’01)

-- s-d: Isd ≡ αNo ≈ 0.2 eV no s-d hybridization => potential s-d exchange

Magnetoabsorption --determination of exchange integrals

Magnetoabsorption --determination of exchange integrals

Szczytko et al.

σ−

σ+

Haury et al., Kossacki et al.Szczytko et al..

Moss-Burstein shift => positive sign of MCDFermi liquid also in insulator => positive sign of MCD

Exchange energy βNoExchange energy βNo

1

o photoemission (Fujimori et al.)o exciton splitting (Twardowski et al.)

GaAs

βNo ~ ao-3

CdTeZnTe

CdSeCdS

ZnSe

ZnS

ZnO

876540.4

4

EXC

HA

NG

E EN

ERG

Y |β

No|

[eV]

LATTICE PARAMETER ao [10-8cm]

• Antiferromagnetic(Kondo-like)

• Magnitude increases with decreasing lattice constant

Origin of d-d exchange interactions in DMS

Mechanisms of couplings between localized spins

Mechanisms of couplings between localized spins

Origin of the coupling: exchange interaction between the localized spins and band electrons, -βNoSs

• INSULATORSspin polarization of orbitals

magnetic orbitals involved:Kramers and Anderson superexchange Mn As Mn

non-magnetic orbitals involved:Bloembergen-Rowland mechanism

short-range, accounts for antiferromagneticinteractions in DMS … exceptions found

Ferromagnetic superexchange (?)Ferromagnetic superexchange (?)

Theoretical prediction: (II,Cr,V)VI J. Blinowski et al., PRB’96

K. Ando et al., PRL’03

Doped materialsDoped materials

• MIXED VALENCE MATERIALS

• Zener double exchangepossibility of hopping lowers energy

c.b. (s orbitals)

d TM band

v.b. (p orbitals)

E

DOS

Mnn Mnn+1

short range, ferromagnetic, e.g. (La,Sr)MnO3

• METALS(heavily doped

semiconductors)

c.b.

v.b.

d TM band

Zener exchange mediated by free carriersredistribution of carriers between spin subbands lowers energy

k

EFħωs = βNo

long range, ferromagnetic

• METALSRuderman-Kittel-Kasuya-Yosida interactionSpin polarization of free carriers induced by a single spin:

long range, sign of the interaction depends on kFRij

0 5 10

0

1

2

1D 2D 3D

( 2 k

f Rij )

d-1

Fd

( 2 k

f Rij )

2 kf R

ij

− J R S Sij i j( ) .

Making (II,Mn)VI DMSs ferromagnetic:Zener/RKKY MF model of doped DMS

Making (II,Mn)VI DMSs ferromagnetic:Zener/RKKY MF model of doped DMS

TC = TCW = TF – TAF superexchange

TF = S(S+1)xeffNoAFρ(s)(EF) β2/12Lcd-3

AF > 1 Stoner enhancement factor (AF= 1 if no carrier-carrier interaction)

ρ(s)(EF) = m*kFd-2 (if no spin-orbit coupling)

=> TC ~ 50 times greater for the holeslarge m*large β

T.D. et al. PRB’97,’01,‘02, Science ’00

0 5 10 15

0

1

2

3

4

5

p ≈ 5×1018 cm-3

p ≈ 1017 cm-3

px = 0.023p

-Zn

1-xMn

xTe

χ-1

[ a

.u. ]

Temperature [ K ]

TCW

Effect of dopingEffect of doping

T.D. et al. PRB’97 D.Ferrand,…,T.D. PRB’01M.Sawicki,…,T.D., pss’02

χ-1 vs. T

MIT at p ≈ 1019 cm-3

Ferromagnetic temperature in 2D p-Cd1-xMnxTe QW and 3D Zn1-xMnxTe:N

Ferromagnetic temperature in 2D p-Cd1-xMnxTe QW and 3D Zn1-xMnxTe:N

ρ(k)

3D

0.01 0.05 0.1

1

10

1

10

2D

3D

Ferr

omag

netic

Tem

p. T

F / x

eff (

K)

Fermi wave vector k (A-1)0.2

1020 cm-31018 1019

kρ(k)

ρ(k) k

k

2D

1D

H. Boukari, ..., T.D., PRL’02 D. Ferrand, ... T.D., ... PRB’01

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

TF

(q/2

k F)/

TF

(0)

q/2kF

d=1d=2d=3

Effects of confinement magnetic quantum wires - expectations

Effects of confinement magnetic quantum wires - expectations

1D: TF(q) has maximum at 2kF

spin-Peierls instability SDW

TF(q)/TF (0) for s-electrons neglecting e-e interactions and disorder

-0.03 0.00 0.030

5

10

15

0.00 0.05 0.10 0.15 0.200

2

4

6

8

10

∆Rxx

(Ω)

Magnetic field (T) Temperature (K)

∆(m

T)

50mK60mK75mK100mK125mK150mK200mK

TC = 160 mK

∆

M. Sawicki, ..., M. Kawasaki, T.D., ICPS’00

Magnetoresistance hysteresisn-Zn1-xMnxO:Al, x = 0.03

Magnetoresistance hysteresisn-Zn1-xMnxO:Al, x = 0.03

Curie temperature in p-Ga1-xMnxAstheory vs. experiment

Curie temperature in p-Ga1-xMnxAstheory vs. experiment

• Anomalous Hall effect p uncertain

• Omiya et al.:27 T, 50 mK

• Theory: TC > 300 Kfor x > 0.1and large p

• 2003: TC up to 170 K (Sendai, Notre Dame, Pen State, Nottingham, Tokyo…)

0 1 2 3 4 50

50

100

150

200

THEORY, x = 0.05

Oiwa et al.Van Esch et al.Matsukura et al.Shimizu et al.

Omiya et al.

Ga1-xMnxAs

CU

RIE

TEM

PER

ATU

RE

[K]

HOLE CONCENTRATION [1020 cm-3]

T.D. et al., PRB’01

cf. first principles studies: Shirai, Katayama-Yosida, Sanvito, Dederichs, ....

Strain engineering

Tensile straine.g (Ga,Mn)As/InAs

Compressive straine.g (Ga,Mn)As/GaAs

Effect of strain on easy axis and anisotropy field (Ga,Mn)As

Effect of strain on easy axis and anisotropy field (Ga,Mn)As

-1.0 -0.5 0.0 0.5 1.00.0

0.2

0.4

0.6

0.8

1.0tensilecompressive

B

BMs

Ms

1.5x1020 cm-3

3.5x1020 cm-3

[100] -> [001][001] -> [100]

AN

ISO

TRO

PY F

IELD

[T]

BIAXIAL STRAIN εxx [%]

(Ga,Mn)As/GaAscompressive –0.2%

B

F. Matsukura et al. film substrate

T.D. et al., PRB ‘01

T = 4.2 K

• (Ga,Mn)As/GaAs compressive strain => easy axis in plane• (Ga,Mn)As/(Ga,In)As tensile strain => easy axis out of plane

Temperature dependent anisotropy(Ga,Mn)As

Temperature dependent anisotropy(Ga,Mn)As

compressive straineasy axis flips from [001] [100]

T.D. et al., Science ’00, PRB’01

M/Ms

M. Sawicki et al., cond-mat/0212511

Controlling quantum magnetic dotsControlling quantum magnetic dots

GATE VOLTAGE

Ferromagnetic quantum dotarray

to be demonstrated

Stripe domains in (Ga,Mn)As perpendicular films

Stripe domains in (Ga,Mn)As perpendicular films

domain walls[110] [100]

9 K

65 K

T.D. et al., PRB’01

theory

Shono et al.

Transport properties: AMRTransport properties: AMR

x = 0.05compressiveε ≈ −0.002

x = 0.043tensileε ≈ 0.002

F.Matsukura, …, T.D., Physica E’03T. Jungwirth et al., APL’02

I

H strainspin-orbit

AMR = (ρ// - ρ⊥)/ρ//

Chemical trends – hole driven ferromagnetism xMn = 0.05, p = 3.5x1020 cm-3

Chemical trends – hole driven ferromagnetism xMn = 0.05, p = 3.5x1020 cm-3

Materials of light elements:

• large p-d hybridization

• small spin-orbit interaction

10 100 1000

C

ZnO

ZnTeZnSe

InAsInP

GaSb

GaPGaAs

GaNAlAs

AlPGe

Si

Curie temperature (K)

T.D. et al., Science ‘00

Chasing for functional ferromagnetic semiconductors

Chasing for functional ferromagnetic semiconductors

Ge1-xMnx Ga1-xMnxN

TC ≈ 940 KTC ≈ 940 K

Sonoda et al., J. Cryst. Growth’02Expl., LSDA, Park et al, Science ‘02

Warning: precipitates and inclusions possible

Summary III-V and II-VI ferromagnetic DMS

Summary III-V and II-VI ferromagnetic DMS

• Spin manipulations -- spin injection (cf. H. Jaffres)-- GMR, TMR-- ferro-FET, ferro-LED (electric field and light) -- dimensionality-- strain engineering

at low temperatures quantum information devices

• Theory -- Tc, M(T,H), magnetic anisotropy, domains, MCD, AHE, AMR…

• Open issue: -- interplay between Stoner and Zener magnetism near MIT

• Prospects for high TC: more materials science

Summary, spin-spin interactions in DMSSummary, spin-spin interactions in DMS

DMS with no carriers: merely antiferro superexchange

DMS with carriers: ferro Zener/RKKY• strong for holes • weak for electrons

LiteratureLiterature

DMSTD, in: Handbook on Semiconductors, vol. 3B ed. T.S. Moss (Elsevier, Amsterdam 1994) p. 1251.

ferromagnetic DMS • F. Matsukura, H. Ohno, TD, in: Handbook of

Magnetic Materials, vol. 14, Ed. K.H.J. Buschow, (Elsevier, Amsterdam 2002) p. 1

• TD, Semicond. Sci. Technol. 17, 377 (2002)

MAGNETIC SEMICONDUCTORSDMS: standard semiconductor + magnetic ionsMost of DMS: random antiferromagnetEvidences for antiferromagnetic pairs H12 = -2JS1S2Evidences for antiferromagnetic interactions: magnetic susceptibilityMagnetization of localized spinsTuning magnetic ordering by electric field (ferro-FET) (In,Mn)AsTransition metals – free atomsTransition metals – free atomsTransition metals – free atomsWhere d levels and carriers reside in DMS?TM impurities in II-VI compoundsd-levels of TM (3dn4s2 ) impurities in II-VI’sTM impurities in III-V compoundsPotential s-d exchange interactionSpin dependent interaction between valence band holes and Mn spinsContribution to the kp hamiltonian due to the presence of a magnetic ionVirtual crystal and molecular-field approximationsEffects of exchange interaction and determination of exchange integralsDetermination of sp-d exchange integrals I - giant splitting of exciton statesMagnetoabsorption --determination of exchange integralsExchange energy ?NoMechanisms of couplings between localized spinsMechanisms of couplings between localized spinsFerromagnetic superexchange (?)Making (II,Mn)VI DMSs ferromagnetic:Zener/RKKY MF model of doped DMSFerromagnetic temperature in 2D p-Cd1-xMnxTe QW and 3D Zn1-xMnxTe:NCurie temperature in p-Ga1-xMnxAstheory vs. experimentEffect of strain on easy axis and anisotropy field (Ga,Mn)AsTemperature dependent anisotropy(Ga,Mn)AsControlling quantum magnetic dotsStripe domains in (Ga,Mn)As perpendicular filmsTransport properties: AMRChemical trends – hole driven ferromagnetism xMn = 0.05, p = 3.5x1020 cm-3Chasing for functional ferromagnetic semiconductorsSummary III-V and II-VI ferromagnetic DMSSummary, spin-spin interactions in DMSLiterature