Spin-injection Hall effect:

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Spin-injection Hall effect  A new member of the
spintronic Hall family
JAIRO SINOVA Texas AM University Institute of
Physics ASCR
Texas AM L. Zarbo, M. Borunda, et al
Hitachi Cambridge Jorg Wunderlich, A. Irvine, et
al
Institute of Physics ASCR Tomas Jungwirth,, Vít
Novák, et al
Sanford University Shoucheng Zhang, et al
University of Maryland March 12th , 2009


Research fueled by

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Anomalous Hall transport lots to think about
AHE
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The family of spintronic Hall effects
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Towards a spin-based non-magnetic FET device
can we electrically measure the
spin-polarization?
Can we achieve direct spin polarization detection
through an electrical measurement in an all
paramagnetic semiconductor system?
Long standing paradigm Datta-Das FET

• Unfortunately it has not worked
• no reliable detection of spin-polarization in a
  diagonal transport configuration
• No long spin-coherence in a Rashba SO coupled
  system

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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
• ? destructive and requires
• semiconductor/magnet hybrid
• design B-field to orient the FM

Ohno et al. Nature99, others

• spin-LED
• ? all-semiconductor
• ? destructive and 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 SmC channel (all-SmC
requiring no magnetic elements in the structure
or B-field)
Wunderlich et al. arXives0811.3486
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Utilize technology developed to detect SHE in
2DHG and measure polarization via Hall probes
B. Kaestner, et al, JPL 02 B. Kaestner, et al
Microelec. J. 03 Xiulai Xu, et al APL 04,
Wunderlich et al PRL 05
Proposed experiment/device Coplanar photocell in
reverse bias with Hall probes along the 2DEG
channel Borunda, Wunderlich, Jungwirth, Sinova et
al PRL 07
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Device schematic - material
p
2DHG
i
n
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Device schematic - trench
-
p
2DHG
i
n
10
Device schematic n-etch
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Device schematic Hall measurement
2DHG
2DEG
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Device schematic SIHE measurement
2DHG
2DEG
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Reverse- or zero-biased Photovoltaic Cell
Transitions allowed for h?ltEg
trans. signal
s
s-
so
so
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Spin injection Hall effect experimental
observation
?-
?
n2
Local Hall voltage changes sign and magnitude
along the stripe
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Spin injection Hall effect ?? Anomalous Hall
effect
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Persistent Spin injection Hall effect
and high temperature operation
Zero bias-
?
?-
?
?-
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THEORY CONSIDERATIONS Spin transport in a 2DEG
with RashbaDresselhaus SO
The 2DEG is well described by the effective
Hamiltonian
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What is special about ?

• spin along the 110 direction is conserved
• long lived precessing spin wave for spin
  perpendicular to 110

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The long lived spin-excitation spin-helix

• Finite wave-vector spin components

• Shifting property essential

Only Sz, zero wavevector U(1) symmetry previously
known J. Schliemann, J. C. Egues, and D. Loss,
Phys. Rev. Lett. 90, 146801 (2003). K. C. Hall
et. al., Appl. Phys. Lett 83, 2937 (2003).
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Physical Picture Persistent Spin Helix

• Spin configurations do not depend on the
  particle initial momenta.
• For the same x distance traveled, the spin
  precesses by exactly the same angle.
• After a length xPh/4ma all the spins return
  exactly to the original configuration.

Thanks to SC Zhang, Stanford University
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Persistent state spin helix verified by
pump-probe experiments
Similar wafer parameters to ours
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The Spin-Charge Drift-Diffusion Transport
Equations
For arbitrary a,ß spin-charge transport equation
is obtained for diffusive regime
For propagation on 1-10, the equations decouple
in two blocks. Focus on the one coupling Sx and
Sz
For Dresselhauss 0, the equations reduce to
Burkov, Nunez and MacDonald, PRB 70, 155308
(2004)
Mishchenko, Shytov,
Halperin, PRL 93, 226602 (2004)
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Steady state spin transport in diffusive regime
Steady state solution for the spin-polarization
component if propagating along the 1-10
orientation
Spatial variation scale consistent with the one
observed in SIHE
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Understanding the Hall signal of the SIHE
Anomalous Hall effect
Spin dependent force deflects like-spin
particles
Simple electrical measurement of out of plane
magnetization
InMnAs
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Anomalous Hall effect (scaling with ?)
Strong SO coupled regime
Weak SO coupled regime
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Intrinsic deflection
STRONG SPIN-ORBIT COUPLED REGIME (?sogth/t)
Vimp(r)
Vimp(r)
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WEAK SPIN-ORBIT COUPLED REGIME (?solth/t)
Better understood than the strongly SO couple
regime
The terms/contributions dominant in the strong SO
couple regime are strongly reduced
(quasiparticles not well defined due to strong
disorder broadening). Other terms, originating
from the interaction of the quasiparticles with
the SO-coupled part of the disorder potential
dominate.
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AHE contribution

• Two types of contributions
• S.O. from band structure interacting with the
  field (external and internal)
• Bloch electrons interacting with S.O. part of the
  disorder

Type (i) contribution much smaller in the weak
SO coupled regime where the SO-coupled bands are
not resolved, dominant contribution from type (ii)
Crepieux et al PRB 01 Nozier et al J. Phys. 79
Lower bound estimate of skew scatt. contribution
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Spin injection Hall effect Theoretical
consideration
Local spin polarization ? calculation of the
Hall signal
Weak SO coupling regime ? extrinsic
skew-scattering term is dominant
Lower bound estimate
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Semiclassical Monte Carlo of SIHE
Numerical solution of Boltzmann equation
Spin-independent scattering
Spin-dependent scattering

• phonons,
• remote impurities,
• interface roughness, etc.

• side-jump, skew scattering.

AHE

• Realistic system sizes (?m).
• Less computationally intensive than other methods
  (e.g. NEGF).

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Example MC Transport Simulation in 2DEG

• Inject N particles with random momenta.
• Allow each particle to propagate from t to t? t.
• Compute particle distribution function.
• Compute observables
• Repeat for each subhistory ? t until T
  (simulation time).
• Time average results.

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Single Particle Monte Carlo

• Particle with random momentum injected from
  drain.
• Randomly generate free flight times.
• Semiclassical particle propagates freely during
  ts and spin processes due to SO interaction.
• Randomly choose scattering mechanism at the end
  of free flight.
• Randomly choose new momentum and spin after
  scattering.
• Stop at time T and collect the observable values.

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Ensemble Monte Carlo

• Obtain particle distribution
  at the end of each subhistory

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Finding Distribution in Phase Space
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Effects of B field
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The family of spintronics Hall effects
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SIHE a new tool to explore spintronics

• nondestructive electric probing tool of spin
  propagation without magnetic elements

• all electrical spin-polarimeter in the optical
  range

• Gating (tunes a/ß ratio) allows for FET type
  devices (high T operation)

• New tool to explore the AHE in the strong SO
  coupled regime

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AHE in the strong SO regime
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Why is AHE difficult theoretically in the strong
SO couple regime?

• AHE conductivity much smaller than sxx many
  usual approximations fail
• Microscopic approaches systematic but
  cumbersome what do they mean use non-gauge
  invariant quantities (final result gauge
  invariant)
• Multiband nature of band-structure (SO coupling)
  is VERY important hard to see these effects in
  semi-classical description (where other bands
  are usually ignored).
• Simple semi-classical derivations give anomalous
  terms that are gauge dependent but are given
  physical meaning (dangerous and wrong)
• Usual believes on semi-classically defined
  terms do not match the full semi-classical theory
  (in agreement with microscopic theory)
• What happens near the scattering center does not
  stay near the scattering centers (not like Las
  Vegas)
• T-matrix approximation (Kinetic energy
  conserved) no longer the case, adjustments have
  to be made to the collision integral term
• Be VERY careful counting orders of contributions,
  easy mistakes can be made.

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What do we mean by gauge dependent?
Electrons in a solid (periodic potential) have a
wave-function of the form
Gauge wand (puts an exp(ia(k)) on the Bloch
electrons)
Gauge dependent car
Gauge invariant car
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Microscopic vs. Semiclassical AHE in the strongly
SO couple regime

• Boltzmann semiclassical approach easy physical
  interpretation of different contributions (used
  to define them) but very easy to miss terms and
  make mistakes. MUST BE CONFIRMED MICROSCOPICALLY!
  How one understands but not necessarily computes
  the effect.
• Kubo approach systematic formalism but not very
  transparent.
• Keldysh approach also a systematic kinetic
  equation approach (equivalent to Kubo in the
  linear regime). In the quasi-particle limit it
  must yield Boltzmann semiclassical treatment.

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Kubo microscopic approach to transport
diagrammatic perturbation theory
Need to perform disorder average (effects of
scattering)
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intrinsic AHE approach in comparing to
experiment phenomenological proof
Berrys phase based AHE effect is reasonably
successful in many instances BUT still not a
theory that treats systematically intrinsic and
ext rinsic contribution in an equal footing
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Kubo microscopic approach to AHE
Early identifications of the contributions
Skew scattering
n, k
m, k
m, p
n, q
m, p
n, q
Side-jump scattering
matrix in band index
Vertex Corrections ? sIntrinsic ?0 or n0i
Intrinsic AHE accelerating between scatterings
Intrinsic ?s0 /eF? ?0 or n0i
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AHE in graphene linking microscopic and
semiclassical theories
EF
Armchair edge
Zigzag edge
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Kubo-Streda calculation of AHE in graphene
Single K-band with spin up
Dont be afraid of the equations, formalism can
be tedious but is systematic (slowly but steady
does it)
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Semiclassical transport of spin-orbit coupled
Bloch electrons Boltzmann Eq. and Hall current
As before we do this in two steps first
calculate steady state non-equilibrium
distribution function and then use it to compute
the current.
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Semiclassical transport of spin-orbit coupled
Bloch electrons Boltzmann Eq. and Hall current
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Comparing Boltzmann to Kubo (chiral basis)
Sinitsyn et al 2007
Kubo identifies, without a lot of effort, the
order in ni of the diagrams BUT not so much their
physical interpretation according to
semiclassical theory
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Intrinsic deflection
Popular believe t1 or 1/ni WRONG
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Next simplest example AHE in Rashba 2D system
Inversion symmetry ? no R-SO
Broken inversion symmetry ? R-SO
Bychkov and Rashba (1984)
Only when ONE both sub-band there is a
significant contribution
Nuner et al PRB08, Borunda et al PRL 07
When both subbands are occupied there is
additional vertex corrections that contribute
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Recent progress full understanding of simple
models in each approach
Up to now no 2DEGR ferromagnetis SIHE offers
this possibility
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CONCLUSIONS
Spin-injection Hall effect observed in a
conventional 2DEG - nondestructive electrical
probing tool of spin propagation - indication of
precession of spin-polarization - observations in
qualitative agreement with theoretical
expectations - optical spin-injection in a
reverse biased coplanar pn-junction large and
persistent Hall signal (applications !!!)
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EXTRA SLIDES
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A2070Kelvin Nanotechnology, University of
Glasgow
thickness composition doping function
5nm GaAs p1E19 (Be) cap
2ML GaAs un
50nm AlxGa1-xAs, x0.5 p8E18 (Be)
3nm AlxGa1-xAs, x0.3 un
90nm GaAs un channel
5nm AlxGa1-xAs, x0.3 un spacer
2ML GaAs un
n5E12 delta (Si) delta-doping
2ML GaAs un
300nm AlxGa1-xAs, x0.3 un
50 period (9ML GaAs 9ML AlGaAs, x0.3) superlattice
1000nm GaAs un
GaAs SI substrate
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The tumultuous history of AHE

• 1880-81 Hall discovers the Hall and the
  anomalous Hall effect

Hall
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The tumultuous history of AHE last three decades
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How does side-jump affect transport?
Side jump scattering
VERY STRANGE THING for spin-independent
scatterers side-jump is independent of
scatterers!!
The side-jump comes into play through an
additional current and influencing the Boltzmann
equation and through it the non-equilibrium
distribution function
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AHE in Rashba 2D system
Keldysh and Kubo match analytically in the
metallic limit
When both subbands are occupied the skew
scattering is only obtained at higher Born
approximation order AND the extrinsic
contribution is unique (a hybrid between skew and
side-jump)
Kovalev et al PRB 08
Numerical Keldysh approach (Onoda et al PRL 07,
PRB 08)