Prezentacja programu PowerPoint -...
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![Page 1: Prezentacja programu PowerPoint - Magnetismmagnetism.eu/esm/2003-brasov/slides/dietl-slides-1.pdf · MAGNETIC SEMICONDUCTORSMAGNETIC SEMICONDUCTORS. Tomasz DIETL. Institute of Physics,](https://reader031.fdocuments.in/reader031/viewer/2022011823/5ed9bc6024797b75744b1612/html5/thumbnails/1.jpg)
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
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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
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Families of magnetic semiconductors
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• magnetic semiconductorsshort-range ferromagnetic super- or double exchangeEuS, ZnCr2Se4, La1-xSrxMnO3, ...
short-range antiferromagnetic superexchangeEuTe, ...
Magnetic semiconductorsMagnetic semiconductors
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now: Diluted Magnetic Semiconductors (DMS)
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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- ....
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Most of DMS: random antiferromagnetMost of DMS: random antiferromagnet
short range antiferromagnetic superexchange
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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
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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/3kB
Θ < 0 antiferro
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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.
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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
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Spin manipulations in ferromagnetic DMS
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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*, … )
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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
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d-levels of TM (3dn4s2 ) impurities in II-VI’sd-levels of TM (3dn4s2 ) impurities in II-VI’s
dn/dn+1
acceptorHHB
dn/dn-1
donorLHB
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
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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
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sp-d exchange interactions in DMS
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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
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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
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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 = <S|U-Uo|S>, W = <X|U -Uo |X> - conduction and valenceband offset integrals
α = <S|U|S>, β = <X|U|X> - s-d and p-d exchange integralsS>, X> - Bloch wave functions Energies: VNo etc.
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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)/gµB
Hspin = Js M(r)/g µ B new contribution to spin splitting
• Difference between real and VCA/MFA hamiltoniansscattering (alloy and spin-disorder scattering)
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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.
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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
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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
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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
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Origin of d-d exchange interactions in DMS
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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
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Ferromagnetic superexchange (?)Ferromagnetic superexchange (?)
Theoretical prediction: (II,Cr,V)VI J. Blinowski et al., PRB’96
K. Ando et al., PRL’03
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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
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• 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<S>
long range, ferromagnetic
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• 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 R
ij )
2 kf R
ij
− J R S Sij i j( ) .
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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
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0 5 10 15
0
1
2
3
4
5
p ≈ 5×1018 cm-3
p ≈ 1017 cm-3
px = 0.023
p -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
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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 ef
f (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
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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
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-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
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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, ....
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Strain engineering
Tensile straine.g (Ga,Mn)As/InAs
Compressive straine.g (Ga,Mn)As/GaAs
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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
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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
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Controlling quantum magnetic dotsControlling quantum magnetic dots
GATE VOLTAGE
Ferromagnetic quantum dotarray
to be demonstrated
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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.
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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 strain
spin-orbit
AMR = (ρ// - ρ⊥)/ρ//
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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
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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
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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
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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
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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)