Spin-orbit coupling induced magneto-resistance effects in ferromagnetic

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Spin-orbit coupling induced magneto-resistance
effects in ferromagnetic semiconductor
structures TAMR, CBAMR, AMR
Tomas Jungwirth
University of Nottingham
Bryan Gallagher, Richard Campion, Kevin Edmonds,
Andrew Rushforth, Tom Foxon, et al.
Institute of Physics ASCR Karel Výborný, Jan
Zemen, Jan Mašek, Vít Novák, Kamil Olejník,
Ludvík Smrcka, Jan Kucera, Nataliya Goncharuk,
et al.
University Hitachi Cambridge Jorg
Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.

• Texas AM
• Jairo Sinova, et al.

University of Texas Allan MaDonald, Maxim
Trushin,et al.
Wuerzburg University Charles. Gould, Laurens
Molenkamp, et al.

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Experimental observation of (ohmic) AMR
magnetization
Lord Kelvin 1857
current
AMR sensors dawn of spintronics
Inductive read elements
Magnetoresistive read elements
1980s-1990s
Now often replaced by GMR or TMR but still
extensively used in e.g. automotive industry
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Theory of AMR current response to magnetization
via spin-orbit coupling
Model for transition metal FMs
Smit 1951
?
Miscroscopic theory relativistic LDA
Kubo formula
theory
experiment
FeNi
BanhartEbert EPL95
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Renewed research interest in AMR due to FS like
(Ga,Mn)As
Ohno. Science 98
MnGa acceptor electrical conduction similar to
conventional p-doped GaAs
metallic
0.1 Mn
insulating
ltlt0.1 Mn
Jungwirth et al. PRB 07
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Renewed research interest in AMR due to FS like
(Ga,Mn)As
(Ga,Mn)As
Mn moment Ferromagnetism reminiscent of
conventional metal band FMs (Fe, Co, Ni,..)
d?/dTcv
Ni
Tc
(Ga,Mn)As
ferromagnetic
Tc
Novak et al. PRL 08
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Renewed research interest in AMR due to FS like
(Ga,Mn)As
AMRs of order 1-10 - routine
characterization tool - semi-quantitatively
described assuming scattering of valence-band
holes
Baxter et al. PRB 02, Jungwirth et al. APL02,
03
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Simple direct link between band structure and
transport
Complexity of the device design
Magnitude, control, and tuneability of MR
SET
Chemical potential ? CBAMR
micro-structures
MTJ
Tunneling DOS ? TAMR
heterostructures
bulk
Scattering lifetimes ? ohmic AMR
Resistor
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Magnetic anisotropies in (Ga,Mn)As valence band
degenerate HH bands and LH bands in
GaAs anisotropic surface and spin-texture due
to crystal and SO coupling in As(Ga) p-orbitals
j3/2
HH
HH LH Fermi surfaces
exchange-split HH bands and LH bands in
(Ga,Mn)As anisotropic due to crystal, SO
coupling and FM exchange field
HH
HH
M
Dietl et al. PRB 01, Abolfath et al. PRB 01
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TAMR spectroscopy of tunneling DOS anisotropy
k - resolved tunneling DOS
electrode
barrier
GaMnAs
Vbias
Binpl
M
Giddings et al. PRL 04
M
Selectivity tuned by choice of barrier,
counter-electrode, or external fields
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TAMR spectroscopy of tunneling DOS anisotropy
Gould et al. PRL 04
M
M
Non-selective barrier and counter-electrode ?
only a few TAMR
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TAMR spectroscopy of tunneling DOS anisotropy
M
M
Giraud et al. APL 05, Sankowski et al. PRB07,
Ciorga et al.NJP07, Jerng JKPS 09
Very selective p-n Zener diode MTJs
Binpl
Giraud et al. Spintech 09
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TAMR spectroscopy of tunneling DOS anisotropy
M
M
Extra-momentum due to Lorentz force during
tunneling
Very selective p-n Zener diode MTJs
Binpl
Giraud et al. Spintech 09
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CBAMR M-dependent electro-chemical potentials in
a FM SET
Wunderlich et al. PRL 06
110
M
?
100
110
010
magnetic
electric
control of CB oscillations
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Huge MRs controlled by low-gate-voltage likely
the most sensitive spintronic transistors to date
Wunderlich et al. PRL 06
Schlapps et al. arXiv0904.3225
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Simple direct link between band structure and
transport
Chemical potential ? CBAMR
SET
Tunneling DOS ? TAMR
MTJ
Scattering lifetimes ? AMR
Resistor
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Simplicity of the microscopic picture of AMR in
(Ga,Mn)As
SET
CBAMR,TAMR SO FM polarized bands
M
MTJ
MnGa
MnGa
ohmic AMR main impurities FM polarized random
MnGa ? can consider bands with SO coupling only
Resistor
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Simplicity of the microscopic physical picture in
(Ga,Mn)As
current
SET
CBAMR only el.-chem potentials ? no M vs current
term
M
cryst. axis
TAMR current direction is cryst. distinct ?
inseparable M vs current term
current
M
MTJ
cryst. axis
current
M
AMR M vs current (non-crystalline) term can be
separated and dominates in (Ga,Mn)As
cryst. axis
Resistor
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Key mechanism for AMR in (Ga,Mn)As FM
impurities SO carriers in non-cryst.-like
spherical bands
KL Hamiltonian in spherical approximation
MGa
Heavy holes
current
Electro-magnetic impurity potential of MnGa
acceptor
Rushforth PRL07, Trushin et al. arXiv0904.3785,
Vyborny et al. arXiv0906.3151
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Pure magnetic MnGa impiruties positive AMR,
Backward-scattering matrix elements
current
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Electro-magnetic MnGa impiruties negative AMR,
current
Backward-scattering matrix elements
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Electro-magnetic MnGa impiruties negative AMR,
? screened Coulomb potential ?
current
all scatt.
backward scatt.
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Electro-magnetic MnGa impiruties negative AMR,
? screened Coulomb potential ?
current
all scatt.
backward scatt.
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Straightforward intuition for AMR in Rashba and
Dresselhaus 2DEGs
Trushin et al. arXiv0904.3785
exact analytical solutions to full integral
Boltzmann equation ? SO-coupled 2DEGs are ideal
testbed to study AMR
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