Title: Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in semiconductors
1Spin-orbit coupling based spintronics
Extraordinary magnetoresistance studies in
semiconductors
Tomas Jungwirth
University of Nottingham
Bryan Gallagher, Tom Foxon,
Richard Campion, Kevin Edmonds, Andrew
Rushforth, Devin Giddings et al.
Institute of Physics ASCR Alexander Shick,
Jan Mašek, Josef Kudrnovský, František Máca,
Karel Výborný, Jan Zemen, Vít Novák,
Miroslav Cukr, Kamil Olejník, et al.
Hitachi Cambridge
University of Texas and
Texas AM Jorg
Wunderlich, Bernd Kaestner
Allan MacDonald, Jairo Sinova, et al.
David Williams, et a.
2Extraordinary magnetoresistance
Ordinary magnetoresistance response to external
magnetic field via classical Lorentz force
Extraordinary magnetoresistance response to
internal spin-polarization via
quantum-relativistic spin-orbit coupling
anomalous Hall effect
anisotropic magnetoresistance
e.g. ordinary (quantum) Hall effect
Discovered in the 19th century in TM
ferromagnets classical unsettled CMP field -
now accessible in semiconductors
3Conventional ferromagnetic metals
Ab initio Kubo (CPA) formula for AMR and AHE in
FeNi alloys
Motts model of transport
?ss
?s?d?
AHE
AMR
?s?d?
?ss
BanhartEbert EPL95
MottWills 36
itinerant 4s no exch.-split no SO
Khmelevskyi PRB 03
localized 3d exch. split SO coupled
difficult to match models and microscopics
4Ferromagnetic semiconductors
insulating GaMnAs
As-p-like holes
metallic GaMnAs
Mn-d-like local moments
- carriers with both strong
- SO coupling and
- exchange splitting
- - simpler band structure
- SO topology of holes dominated by As
- p-orbitals as in hosts (Mn on Ga sublattice)
favorable for exploring physical origins
5Origin of RM ? Igt RM I non-crystalline
AMR in GaMnAs
Boltzmann eq. in relax. time approximation
1st order Born approximation
4-band spherical Kohn-Luttinger model
SO-coupling spherical model
FM exchange spiitting
M
1/?k (M)
(k . s)2
Mx . sx
ky
kx
M
ky
hot spots for scattering for states moving ? M ?
RM ? Igt RM I (opposite to most metal FMs)
kx
6full 6-band Hamiltonian non-crystalline
and crystalline AMR
spherical model non-crystalline AMR only
theory
In metallic GaMnAs also magnitudes and
relative strengths of non-crystalline and
crystalline AMR terms consistent with experiment
exp.
Rushforth et al. 07
7Family of new AMR effects TAMR anisotropic TDOS
predicted and observed in metals
TAMR discovered in GaMnAs ?
Au
Shick et al.PRB'06, Bolotin et al. PRL'06, Viret
et al. EJP06, Moser et al. 06, Grigorenko et
al. 06
Gould, et al., PRL'04, Brey et al. APL04, Ruster
et al.PRL05, Giraud et al. APL05, Saito et al.
PRB05,
8Coulomb blockade AMR anisotropic chemical
potential
Q
VD
Source
Drain
Gate
VG
magnetic
electric
Predicted stronger CBAMR for metals
control of Coulomb blockade oscillations
Wunderlich et al. 06
9AHE mechanisms
KarplusLuttinger intrinsic AHE mechanism revived
in GaMnAs
KarplusLuttinger PR 54
Jungwirth et al. PRL 02,APL 03, Edmonds et al.
APL 03, Chun et al. PRL 07
Experiment sAH ? 1000 (W cm)-1 Theroy sAH ? 750
(W cm)-1
- intrinsic AHE in pure Fe ab initio Kubo eq.
Yao et al. PRL 04
Co KotzlerGil PRB 05 SrRuO3 and pyrochlore
ferromagnets Onoda and Nagaosa, J. Phys. Soc.
Jap. 01,Taguchi et al., Science 01, Fang et al
Science 03, Shindou and Nagaosa, PRL
01 Ferromagnetic spinel CuCrSeBr Lee et al.
Science 04
10- All Semiconductor systems including 2D with
model SO
Cubic (2DHG) and linear (2DEG) in k Rashba model
Kato Sci 04, Wunderlich et al PRL05, PRB06,
Sih et al. NatPhys 05
- Optical methods polarized EL
Solvable analytically
11Exploring SHE AHE fenomenologies in 2D
non-magnetic SC
-
Gate
AHE
SHE
122D model systems ideal to explore intrinsic vs.
extrinsic AHE/SHE
intrinsic
skew scattering
side jump
group velocity
semicalssical Boltzmann eq.
distribution function
quantum Kubo formula
jump
side
int.
skew
sc.
Extrinsic skew scattering term - absent in
2DEG for two-band occupation - absent in 2DHG
for any band occupation
Borunda et al. 07
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14Optical means of exploring EMR fundamentals on
systems with simple yet topologically distinct
SO-bands
15SO-coupling and electric field controlled
spintronics
1. Coulomb-blockade anisotropic
magnetoresistance 2. Spin-Hall effect
Spintronic SET in thin-film GaMnAs
Electric-field induced edge spin polarization in
GaAs 2DHG
161. Coulomb blockade AMR
Spintronic transistor - magnetoresistance
controlled by gate voltage
I
Bptp
B0
B90
Strong dependence on field angle ?hints to AMR
origin
Huge hysteretic low-field MR Sign
magnitude tunable by small gate valtages
Wunderlich, Jungwirth, Kaestner et al.,
cond-mat/0602608
17AMR nature of the effect
Coulomb blockade AMR
normal AMR
18Single electron transistor
Narrow channel SET dots due to disorder
potential fluctuations (similar to non-magnetic
narrow-channel GaAs or Si SETs)
CB oscillations low Vsd ? blocked due to SE
charging
19CB oscillation shifts by magnetication rotations
At fixed Vg peak ? valley or valley ? peak ? MR
comparable to CB negative or positive MR(Vg)
20Coulomb blockade AMR
SO-coupling ? ?(M)
magnetic
electric
control of Coulomb blockade oscillations
21Different doping expected in leads an dots in
narrow channel GaMnAs SETs
- CBAMR if change of
- ??(M) e2/2C? 10Kelvin from exp.
-
- ? consistent
-
- In room-T ferromagnet change of ??(M)100Kelvin
- CBAMR works with dot both ferro
- or paramegnetic
Calculated doping dependence of ?(M1)-?(M2)
22CBAMR SET
- Huge, hysteretic, low-field MR tunable
- by small gate voltage changes
- Combines electrical transistor action
- with permanent storage
Other FERRO SETs
- Non-hysteretic MR and large B -
- chemical potential shifts due to Zeeman effect
- Ono et al. '97, Deshmukh et al. '02
- Small MR - subtle effects of spin-coherent and
- resonant tunneling through quantum dots
- Ono et al. '97, Sahoo '05
23SPIN HALL EFFECT no ferromagnetism, spin-orbit
coupling only all-electric spintronics
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge
accumulation excludes simple electrical detection
242. Spin Hall effect
Spin-orbit only electric fields only
induced transverse spin accummulation
Detection through circularly polarized
electroluminescence
x
applied electrical current
y
z
spin (magnetization) component
Wunderlich, Kaestner, Sinova, Jungwirth, Phys.
Rev. Lett. '05 Nomura, Wunderlich, Sinova,
Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05
25Testing the co-planar spin LED only first
p-n junction current only (no SHE driving
current)
20
EL
EL peak
10
Bz0
- Can detect edge polarization
- Zero perp-to-plane component
- of polarization at Bz0 and Ip0
0
Circ. polarization
-10
-20
261.5?m channel
SHE experiments
10?m channel
- show the SHE symmetries - edge polarizations
can be separated over large distances with no
significant effect on the magnitude
27Szedge Lso jzbulk tso
Theory 8 over 10nm accum. length for the GaAs
2DHG Consistent with experimental 1-2
polarization over detection length of 100nm
Murakami et al. '03, Sinova et al.'04, Nomura et
al. '05, ...
28Other SHE experiments
Spin injection from SHE GaAs channel
Electrical measurement of SHE in Al
Valenzuela, Tinkham '06
Kato et al. '04, Sih et al. '06
100's of theory papers transport with SO-coupling
intrinsic vs.
extrinsic
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30Microscopic origin
Q
VD
Source
Drain
Gate
VG
? Coulomb blockade
Qne - discrete Q0CgVg - continuous
Q0-ne ? blocked Q0-(n1/2)e ? open
31 Sub GaAs gap spectra analysis PL vs EL
--
X bulk GaAs excitons I recombination with
impurity states B (A,C) 3D electron 2D
hole recombination
Bias dependent emission wavelength for 3D
electron 2D hole recombination A. Y. Silov et
al., APL 85, 5929 (2004)
32Circularly polarized EL
In-plane detection angle
Perp.-to plane detection angle
? NO perp.-to-plane component of polarization at
B0 ? B?0 behavior consistent with SO-split HH
subband
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341. Introduction
Non-relativistic many-body
Pauli exclusion principle Coulomb repulsion ?
Ferromagnetism
- Robust (can be as strong as bonding in solids)
- Strong coupling to magnetic field
- (weak fields anisotropy fields needed
- only to reorient macroscopic moment)
35Spin-orbit coupling (Dirac eq. in external field
?V(r) 2nd-order in v /c around
non-relativistic limit)
Beff
Bex Beff
Bex
FM without SO-coupling
GaMnAs valence band tunable FM large SO
GaAs valence band As p-orbitals ? large SO
36AMR (anisotropic magnetoresistance)
Ferromagnetism sensitivity to magnetic
field SO-coupling anisotropies in Ohmic
transport characteristics
37TMR (tunneling magnetoresistance)
Based on ferromagnetism only
spin-valve
no (few) spin-up DOS available at EF
large spin-up DOS available at EF
38Tunneling AMR anisotropic tunneling DOS due to
SO-coupling
MRAM
(Ga,Mn)As
Au
Au
- no exchange-bias needed - spin-valve with
ritcher phenomenology than TMR
Gould, Ruster, Jungwirth, et al., PRL '04, '05
39Wavevector dependent tunnelling probabilityT (ky,
kz) in GaMnAs Red high T blue low T.
thin film
Magnetization perp. to plane Magnetization
in-plane
Magnetisation in plane
constriction
Giddings, Khalid, Jungwirth, Wunderlich et al.,
PRL '05
40TAMR in metals
ab-initio calculations
Shick, Maca, Masek, Jungwirth, PRB '06
NiFe
TAMR
TMR
Bolotin,Kemmeth, Ralph, cond-mat/0602251
TMR TAMR gtgtAMR
Viret et al., cond-mat/0602298
Fe, Co break junctions TAMR gtTMR
41EXPERIMENT Spin Hall Effect
42Single Electron Transistor
Q
VD
Source
Drain
Gate
VG
? Coulomb blockade
Qne - discrete Q0CgVg - continuous
Q0-ne ? blocked Q0-(n1/2)e ? open
43Coulomb blockade anisotropic magnetoresistance
Spin-orbit coupling
Band structure (group velocities, scattering
rates, chemical potential) depend on
If lead and dot different (different carrier
concentrations in our (Ga,Mn)As SET)
magnetic
electric
control of Coulomb blockade oscillations
44Wunderlich, Jungwirth, Kaestner, Shick, et al.,
preprint
- CBAMR if change of ??(M) e2/2C?
- In our (Ga,Mn)As meV ( 10 Kelvin)
- In room-T ferromagnet change of ??(M)100K
- Room-T conventional SET
- (e2/2C? gt300K) possible
45CBAMR ? new device concepts
46Electrically generated spin polarization in
normal semiconductors SPIN HALL EFFECT
47Ordinary Hall effect
Lorentz force deflect charged-particles towards
the edge
B
_ _ _ _ _ _ _ _ _ _
_
FL
I
V
Detected by measuring transverse voltage
48Spin Hall effect
Spin-orbit coupling force deflects like-spin
particles
_
_
_
FSO
_
non-magnetic
FSO
I
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge
accumulation excludes simple electrical detection
49Microscopic theory and some interpretation
experimentally detected
spin velocity
non-conserving (ambiguous) theoretical quantity
- weak dependence on impurity scattering time -
Szedge jzbulk / vF tsoh/?so
(intrinsic) spin-precession time LsovF tso
spin-precession length Szedge Lso jzbulk tso
Nomura, Wunderlich, Sinova, Kaestner,
MacDonald, Jungwirth, Phys. Rev. B '05
50SHE experiment in GaAs/AlGaAs 2DHG
Wunderlich, Kaestner, Sinova, Jungwirth, Phys.
Rev. Lett. '05
10?m channel
- shows the basic SHE symmetries - edge
polarizations can be separated over large
distances with no significant effect on the
magnitude - 1-2 polarization over detection
length of 100nm consistent with theory
prediction (8 over 10nm accumulation length)
Nomura, Wunderlich, Sinova, Kaestner,
MacDonald, Jungwirth, Phys. Rev. B '05
51Conventionally generated spin polarization in
non-magnetic semiconductors spin injection from
ferromagnets, circular polarized light sources,
external magnetic fields
SHE small electrical currents in simple
semiconductor microchips
SHE microchip, 100?A
high-field lab. equipment, 100 A
52Spin and Anomalous Hall effects
Spin-orbit coupling force deflects like-spin
particles
InMnAs
Simple electrical measurement of magnetization
53Skew scattering off impurity potential (Extrinsic
SHE/AHE)
54SO-coupling from host atoms (Intrinsic SHE/AHE)
bands from l0 atomic orbitals ? weak
SO (electrons in GaAs) bands from lgt0 atomic
orbitals ? strong SO (holes in GaAs)
55Intrinsic AHE approach explains many experiments
- (Ga,Mn)As systems Jungwirth et al. PRL 02, APL
03 - Fe Yao, Kleinman, Macdonald, Sinova,
- Jungwirth et al PRL 04
- Co Kotzler and Gil PRB 05
- Layered 2D ferromagnets such as SrRuO3 and
pyrochlore ferromagnets Onoda and Nagaosa, J.
Phys. Soc. Jap. 01,Taguchi et al., Science 01,
Fang et al Science 03, Shindou and Nagaosa, PRL
01 - Ferromagnetic spinel CuCrSeBr Lee et al. Science
04
Experiment sAH ? 1000 (W cm)-1 Theroy sAH ? 750
(W cm)-1
56Hall effects family
- Ordinary carrier density and charge magnetic
field sensing - Quantum text-book example a strongly correlated
many-electron system with e.g. fractionally
charged quasiparticles universal, material
independent resistance - Spin and Anomalous relativistic effects in solid
state - spin and magnetization generation and
detection
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