From Electric Current to Spin Current

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From Electric Current toSpin Current

• Dr. Shun-Qing Shen
• Department of Physics
• The University of Hong Kong
• May 24, 2005

Yantai, May 2005
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2005 The World Year of Physics

• Quantum theory 1900, Planck, 1913, Bohr, 1923,
  de Broglie, 1925/26, Schrodinger and Heisenberg,
  1926, Born,1928, Dirac.
• Theory of relativity 1905, Einstein 1915,
  Einstein,..

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Einsteins Relativity Emc2
July 16, 1945 Trinity Site National Historic
Landmark August 6, 1945 Hiroshima, Japan/Little
Boy August 9, 1945 Nagasaki, Japan/Fat Man
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From Few to Many Body Theory

• Quantum theory for atomic and molecular physics
• Quantum theory for solid metal, insulator,
  superconductivity, quantum magnetism,.
• Electronic band structure and semiconductors
  Silicon (Si), Gallium arsenide (GaAs),.

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Electronics
Computers  In February 1946, the public got its
first glimpse of the ENIAC, a machine built by
John Mauchly and J. Presper Eckert that improved
by 1,000 times on the speed of its
contemporaries.
Mechanical Calculator Electro-mechanical Computer
(1890 --) 1st GenerationVacuum Tubes ENIAC
(194446) 2nd GenerationTransistor (invented
1948) DEC (1957) 3rd GenerationIntegrated
Circuits IBM (1964) 4th GenerationVLSI Intel
(1968)
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Two obstacles in semiconductor industry

• Physical size limit atomic limit
• Quantum fluctuation the uncertainty principle

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What can we do now?
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From Basic PhysicsElectron--Charge and Spin
1891 the Irish physicist, George Stoney,
believed that electricity should have a
fundamental unit, and called this unit the
electron. 1887 J.J. Thomson discovered the
electron experimentally. 1925 The concept of
electron spin was discovered by S.A. Goudsmit and
George Uhlenbeck. 1928 Paul Dirac
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Relativistic Quantum mechanics
Paul Dirac
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Fundamentals of Spin

• In addition to their mass and electric charge,
  electrons have an intrinsic quantity of angular
  momentum called spin, almost as if they were tiny
  spinning balls.
• Associated with the spin is a magnetic field like
  that of a tiny bar magnet lined up with the spin
  axis.
• Scientists represent the spin with a vector. For
  a sphere spinning "west to east" the vector
  points "north" or "up." It points "down" for the
  opposite spin.
• In a magnetic field, electrons with "spin up" and
  "spin down" have different energies.
• In an ordinary electric circuit the spins are
  oriented at random and have no effect on current
  flow.
• Spintronic devices create spin-polarized currents
  and use the spin to control current flow.

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Spintronics?
1998, Advanced Research Projects Agency (DARPA )
This is a new technological discipline which
aims to exploit the subtle and mind-bendingly
esoteric quantum properties of the electron to
develop a new generation of electronic devices.
.The word is a blend of electronics with spin,
the quantum property it exploits. Like so many
words applied to the subatomic realm, spin has to
be taken figuratively as a convenient label for a
property that has no equivalent in gross matter.
..The adjective is spintronic.
Michael
Quinion writes for World Wide Words
spin-based electronics, where it is not the
electron charge but the electron spin that
carries information, and this offers
opportunities for a new generation of devices
combining standard microelectronics with
spin-dependent effects
Wolf
et al, Science 294, 1488 (2001)
Driving force behind spintronics Conventional
electronics has ignored the spin of electrons.
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Objective of Spintronics

• To create a revolutionary new class of
  electronics based on the spin degree of freedom
  in additional to, or in the place of, the charge
  degree of freedom

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Long-standing prerequisites

• All spintronic devices rely on spin-polarized
  carriers.
• The mobile spins need to be transferred
  efficiently across interfaces.
• Spin polarization must be preserved long enough
  for the desired operation to be carried out.

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Categories of Spintronics

• Ferromagnetic metal based devices read head
  (GMR), MRAM,
• Spin transport in semiconductors ultrafast
  switches, fully programmable all-spintronics
  microprocessors,
• Manipulation of quantum spin states of individual
  electrons, nuclear spin and magnetic clusters
  quantum logic gates,
• Devices based on spin current in semiconductor

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PRL top 10 6 over last 10 years/citation 2994
(Updated on Jan. 14, 2005)
Discovery of GMR marks the beginning of
spintronics. It results from subtle electron-spin
effects in ultra-thin 'multilayers' of magnetic
materials, which cause huge changes in their
electrical resistance when a magnetic field is
applied. GMR is 200 times stronger than ordinary
magnetoresistance. IBM soon realized that read
heads incorporating GMR materials would be able
to sense much smaller magnetic fields, allowing
the storage capacity of a hard disk to increase
from 1 to 20 gigabits. In 1997 IBM launched GMR
read heads into a market worth about a billion
dollars a year.
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Conductance
Typical Metal 10-8 Typical Semiconductor 10-4
--103
l mean free path
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Giant Magnetoresistance (GMR) Schematic
representations of transport that is parallel to
the plane of a layered magnetic metal sandwich
structure for aligned (low resistance) and
antialigned (high resistance) orientations. The
metal spacer thickness should be comparable with
the mean free path of the electrons (of order 10
nm).
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Magnetic Structure for GMR Sensor
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Datta-Das Field Effect Transistor
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Using SO spin FET
V
V/2
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Successful application of the wide range of
possible spin-dependent phenomena in
semiconductor and/or metallic systems requires
effective and efficient techniques for the
electrical injection of strongly spin-polarized
currents, as well as electrical detection of such
a current.
Spin Polarized Current electric current with
polarized spin Spin Current pure spin current
without electric current
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Way to Generate Spin Current

• Spin injection
• Spin chirality driving spin current
• Rotating magnetic field
• External electric field

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Electric current and spin current
Electric current
Spins of charge carriers are random
Two-component model for spin current
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What is the spin current?

• Electrons carry both charge and spin which
  may have two components up and down.

If the currents of electrons for different spins
are not equal,
The electric current
The spin current
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Spin Current and Vector Potential
In many body system if the vector potential for
electrons is spin dependent,
Energy eigen value
Spin-dependent current
Special Case
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Relativistic Quantum Mechanics Effect
Spin-Orbit Interaction The interaction describes
the effect of an electrons orbital motion on the
orientation of its spin.
From Dirac equation to Schrodinger equation
z
The relativistic correction factor of ½, the
Thomas precession, has been included.
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Spin-orbit coupling in 2D quantum wells

• Rashba coupling (1960) from structure inversion
  asymmetry

• Dresselhaus coupling (1955) from bulk inversion
  asymmetry.

2DEG
Spin-dependent vector potential
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Spin Hall Effect
Assumption we take the existence of the effect
in ferromagnetic metals as experimental proof
that electrons carrying a spin and associated
magnetic moment experience a transverse force
when they are moving in a longitudinal electric
field, for any of the reasons listed above or
others.
Dyakonov and Perel, 1971, Hirsch, 1999, Hu et al
2003 Murakami et al, 2003, Sinova et al, 2004,
Shen, 2004
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Extrinsic and Intrinsic SHE
Extrinsic SHE Mott spin asymmetric
scattering Dyakonov and Perel, 1971 Hirsch,
1999 Shufeng Zhang, 2000 Hu, Gao, and Shen, 2003
Intrinsic SHE caused by the spin-orbit
coupling Murakami, Nagaosa, and Zhang,
2003 Sinova et al, 2004 Shen, 2004,.
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Spinomotive Force
Ehrenfest theorem
Li, Hu, and Shen, cond-mat/0502102
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Reversible Spin Hall Effect
In GaAs, Rashba and Dresselhaus coupling are
usually of the same order of magnitudes. The
Rashba coupling is tunable by the gate voltage or
electric field perpendicular to the plain.
Nitta et al, PRL (1997) Grundler, PRL (2000)
Spin Hall conductance
Rashba
Dresselhaus
Shen, PRB (2004)
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How to measure spin current?
Relativistic effect Moving magnet induces an
electric field Moving charge induces a magnetic
field
Maxwell equations
Loss, 2003 Sun, Guo, and Wang, 2004
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Spin Hall Effect and Spin Accumulation
How to balance the spin current near the boundary?

• V

Hu, Gao, and Shen, PRB 70, 235323 (2004) Ma, Hu,
Tao, and Shen, PRB 70, 195343 (2004)
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Spin current and spin polarization
In a Rashba system,
In an energy eigenstate,
This relation provides a way to extract the spin
Current from the spin polarization in experiment.
Bao, Zhuang, Shen, and Zhang, cond-mat/0503???
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Kerr Rotation Microscopy Kato, Myers, Gossard,
and Awschalom, Science (2004)
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2D Hole System as a part of p-n junction
light-emitting diode Wunderlich, Kastner, Sinova,
and Jungwirth, PRL (2005)
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Application of spin current

• Electric current -gt electronics
• Spin current -gt spintronics

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Thank you for your attention!
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Spin Hall Conductance and Berry Phase in 2DEG
for Rashba coupling Sinova et al, PRL
(2004)
for Rashba and Dresselhaus coupling Shen,
PRB 70, 081311 (R)(2004)
Berry phase
Condition Two bands are filled. The conductance
is not a constant if only one band is filled.
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Disorder Effect

• Numerical calculations
• Sheng, Ting, and Sheng, Landauer-Buttiker
  formula/mesocopic system
• Nikolic et al
• Normura et al Kubo formula,
• Li Jian et al RD

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Resonant Spin Hall Effectin the presence of
magnetic field and Rashba spin-orbt coupling
The spin-orbit coupling competes with Zeeman
splitting to introduce additional degeneracy
between different Landau levels at certain
magnetic fields. This degeneracy, if occuring at
the Fermi level, gives rise a resonant spin Hall
conductance. The spin current as well as the
charge current is non-dissipative.
Shen, Ma, Xie, and Zhang, PRL 92, 256603 (2004)
Shen, Bao, Ma, Xie, and Zhang, cond-mat/0410169
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FIG. 1. Schematic layer structure of an inverted
In0.53Ga0.47As/In0.52Al0.48As heterostructure.
FIG. 2. Calculated conduction band diagram and
electron distribution.
Nitta et al, PRL 78, 1335 (1997)
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Rashba
Dresselhaus
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Energy spectrum
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Spin Hall current
To calculate the spin current, we study the
system in the presence of the E-field. The spin
current is evaluated in the perturbation theory.
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Average spin and spin Hall conductance
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Near the resonant point
The height of peak
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Reduced temperature
Beyond the linear response theory the truncation
approximation is introduced to reduce the problem
to a relevant two-level problem. In this way the
finite field and finite temperature effects are
investigated near the resonant peak.
The height of the peak is proportional to
1/T. The weight of the peak is proportional to
lnT.
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Resonant Spin Hall Current Density
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Boltzman Equation
the dirft velocity of carriers in the real space
the dirft velocity of carriers in the momentum
space
nonequilibrium, but steady distribution function
the collision term due to impurities scattering
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Nonequilibrium distribution function and
band-dependent potential
band-dependent potential to cause spin
inbalance to be determined self-consistently.
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Spin diffusion equation

• Van Son, Kempen, Wyder, PRL. 58, 2271 (1987)
• Valet and Fert, PRB 48, 7099 (1993)
• Zhang, PRL 85, 393 (2000)
• Hu, Gao, and Shen, PRB 70, (2004) Ma, Hu, Tao,
  Shen, PRB 70, (2004)

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Rough estimation
Hu, Gao, and Shen, PRB 70, (2004)