Anisotropic magnetoresistance and spin-injection Hall

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Anisotropic magnetoresistance and spin-injection
Hall effect in 2D spin-orbit coupled systems
Tomas Jungwirth
University of Nottingham
Bryan Gallagher, Richard Campion, Kevin Edmonds,
Andrew Rushforth, et al.
Institute of Physics ASCR Karel Výborný, Jan
Zemen, Jan Mašek, Vít Novák, Kamil Olejník, et
al.
Hitachi Cambridge, Univ. Cambridge Jorg
Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.

• Texas AM
• Jairo Sinova, et al.

University of Texas Allan MaDonald, et al.

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Extraordinary magnetoresistance AMR, AHE
Ordinary magnetoresistance response in normal
metals to external magnetic field via classical
Lorentz force
Extraordinary magnetoresistance response to
internal spin polarization in ferromagnets via
quantum-relativistic spin-orbit coupling
B
anisotropic magnetoresistance
_ _ _ _ _ _ _ _ _ _
Lord Kelvin 1857
_
FL

I
V
_
_
FSO
_
M
I
ordinary Hall effect 1879
anomalous Hall effect 1881
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Spin-orbit coupling
nucleus rest frame
electron rest frame
2
2
Lorentz transformation ? Thomas precession
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From 1950s microscopic model interpretations
often controversial
AMR Motts model of transport in metals
?ss
?s?d?
?s?d?
?ss
Smit 1951
itinerant 4s no exch.-split no SO
localized 3d exch. split SO coupled
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AHE
KarplusLuttinger 1954
(then partly forgotten till 2000s)
Berger 1970
Smit 1955
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From 1990s numerics based on relativistic ab
initio band strucrure Kubo formula
Scattering considered essential for both AMR and
AHE ? alloys like FeNi (treated in CPA)
AMR
AHE
Numerically successful but difficult to connect
with microscopic models due to complex bands in
metals
BanhartEbert EPL95
Khmelevskyi PRB 03
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AMR sensors dawn of spintronics in early 1990s
Magnetoresistive read element
Inductive read/write element
In mid 1990s replaced in HDD by GMR or TMR but
still extensively used in e.g. automotive industry
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From late 1990s AMR and AHE studied in novel
ferromagnets Ferromagnetic DMS GaMnAs with much
simpler 3D band structure than metals
Ga
Bso
As-p-like holes
As
Mn
Mn-d-like local moments
Bex Bso
Jungwirth et al. RMP06 Dietl et al. Semicond.
and Semimet. 08
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Semiquantitative numerical description of AMR and
AHE in GaMnAs
Jungwirth et al. RMP06 Dietl et al. Semicond.
and Semimet. 08
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AMR in GaMnAs DMS from full numerics to
microscopic mechanism
Anisotropic scattering rate non-crystalline and
crystalline AMR
Spherical model non-crystalline AMR only
Rushforth et al. PRL07
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AMR in GaMnAs DMS from full numerics to
microscopic mechanism
Non-crystalline AMR mechanisms
1) Polarized SO bands
2) Polarized impurities SO bands
M
MGa
current
current
Leading AMR mechanism in DMSs
Rushforth et al. PRL07
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Microscopic mechanism of AHE in GaMnAs DMS
Jungwirth et al PRL02
AHE explained by the revived intrinsic mechanism
Note Inspired to explain AHE in pure Fe,etc by
intrinsic AHE
Experiment sAH ? 1000 (W cm)-1 Theroy sAH ? 750
(W cm)-1
Yao et al PRL04
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2D SO-coupled systems ? simplest band-structures
? offer most detailed and complete understanding
of the AMR and AHE
Rashba SO-coupled 2DEG
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AMR in 2D SO-coupled systems
We will discuss a detailed theory analysis in
Rashba-Dresselhaus 2D systems
Experimentally not studied in 2D systems yet we
will comment on experiments in related 3D DMS
systems
Trushin, Vyborny et al PRB in press
(arXiv0904.3785)
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AHE in 2D SO-coupled systems
Detailed theory analysis completed
Nagaosa et al RMP to be published
(arXiv0904.4154)
We will discuss 2D AHE related experiment
Spin-injection Hall effect in a planar
photo-diode
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Heuristic link between spin-texture of 2D SO
bands, impurity potentials and AMR
Short-range magnetic impurity potential
Short-range electro-magnetic impurity potential
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Non-crystalline AMRgt0 in Rashba 2D system
Rashba Hamiltonian
Eigenspinors
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Non-crystalline AMRgt0 in Rashba 2D system
Scattering matrix elements
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Large non-crystalline AMRgt0 in Rashba 2D system
with electro-magnetic scatterrers
Scattering matrix elements of
current
current
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Negative and positive and crystalline AMR in
Dresselhaus 2D system
Dresselhaus
Rashba
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AMR in (Ga,Mn)As modeled by j3/2 Kohn-Luttinger
Hamiltonian
KL Hamiltonian
Heavy holes
Magnetic part of the impurity potential
Scattering matrix elements of
Compare with spin-1/2
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Negative AMR in (Ga,Mn)As due to electro-magnetic
MnGa impiruties
Rashba
Kohn-Luttinger
current
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AMR in 2D Rashba system from exact solution to
integral Boltzmann eq.
or
independent of
averages to 0 over Fermi cont.
quasiparticle life-time
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AMR in 2D Rashba system from exact solution to
integral Boltzmann eq.
transport life-time
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transport life-time is a good first approximation
to AMR
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AMR in 2D Rashba system from exact solution to
integral Boltzmann eq.
contains only cos? and sin? harmonics
analytical solution to the integral Boltzmann eq.
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Spintronic Hall effects in magnetic and
non-magnetic (2D) systems
Co/Pt
Wunderlich et al. IEEE 01, PRL05
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Spin-injection Hall effect Hall measurement of
spin-polarized electrical current injected into
non-magnetic system
Wunderlich et al. Nature Phys. in press,
arXives0811.3486
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Optical injection of spin-polarized charge
currents into Hall bars ? GaAs/AlGaAs planar
2DEG-2DHG photovoltaic cell
p
2DHG
i
n
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Optical injection of spin-polarized charge
currents into Hall bars ? GaAs/AlGaAs planar
2DEG-2DHG photovoltaic cell
-
p
2DHG
i
n
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Optical injection of spin-polarized charge
currents into Hall bars ? GaAs/AlGaAs planar
2DEG-2DHG photovoltaic cell
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Optical injection of spin-polarized charge
currents into Hall bars ? GaAs/AlGaAs planar
2DEG-2DHG photovoltaic cell
2DHG
2DEG
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Optical spin-generation area near the p-n junction
Simulated band-profile
p-n junction bulit-in potential (depletion length
) 100 nm ? self-focusing of the generation area
of counter-propagating e- and h
Hall probes further than 1?m from the p-n
junction ? safely outside the spin-generation
area and/or masked Hall probes
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Spin transport in a 2DEG with RashbaDresselhaus
SO
Schliemann, et al., Phys. Rev. Lett. 94, 146801
(2003) Bernevig, et al., Phys. Rev. Lett. 97,
236601 (2006) Weber, et al., Phys. Rev. Lett. 98,
076604 (2007)
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Spin dynamics in a 2DEG with Rashba Dresselhaus
SO
Steady state solution for the out of plane
spin-polarization component
Spin-diffusion along the channel of injected
spin-? electrons
SO-length 1?m
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SO-length (1?m) gtgt mean-free-path (10 nm)
Local spin-dependent transverse deflection due to
skew scattering
Spin-diffusion along the channel of injected
spin-? electrons
see also Bernevig et al., PRL06
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Skew-scattering Hall effect
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Spin injection Hall effect theoretical estimate
Local spin polarization ? calculation of the
Hall signal
Weak SO coupling regime ? extrinsic
skew-scattering term is dominant
A. Crepieux and P. Buno, PRB 01
Large Hall angles comparable to AHE in metals
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SIHE device realization
n0 averaged-SIHE / AHE
n3,n2,n1 local SIHE
Spin-generation area
2
0
1
3
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Unmasked and masked SIHE devices
5.5?m
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Vb 0V
Measured SIHE phenomenology
Vb -10V
?- ?0 ?
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SIHE spatially dependent, linear, strong
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SIHE vs AHE
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SIHE survives to high temperatures
?-
?
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Spin-detection in semiconductors

• Magneto-optical imaging
• ?non-destructive
• ? lacks nano-scale resolution
• and only an optical lab tool

Datta-Das transistor

• MR Ferromagnet
• ? electrical
• ? requires semiconductor/magnet
• hybrid design B-field to orient
• the FM

Ohno et al. Nature99, others

• spin-LED
• ? all-semiconductor
• ? requires further conversion of
• emitted light to electrical
• signal

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Spin-detection in semiconductors

• Magneto-optical imaging
• ?non-destructive
• ? lacks nano-scale resolution
• and only an optical lab tool

Crooker et al. JAP07, others

• MR Ferromagnet
• ? electrical
• ? requires semiconductor/magnet
• hybrid design B-field to orient
• the FM

Ohno et al. Nature99, others

• spin-LED
• ? all-semiconductor
• ? requires further conversion of
• emitted light to electrical
• signal

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• Spin-injection Hall effect
• ? non-destructive
• ? electrical
• ? 100-10nm resolution with current lithography
• ? in situ directly along the SC channel
• all-SC requiring no magnetic elements in
  the structure or B-field

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Application of SIHE

• Spin-photovoltaic cell polarimeter on a SC chip
  requiring no magnetic elements,
• external magnetic field, or bias form IR to
  visible light depending on the SC
• Spin-detection tool for other device concepts
  (e.g. Datta-Das transistor)
• Basic studies of quantum-relativistic
  spin-charge dynamics and AHE also in the
• intriguing strong SO regime in archetypal 2DEG
  systems

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