Electrochemical%20and%20Chemical%20Loading:%20%20How%20bulk%20flux%20and%20reactions%20adjust%20to%20the%20%20%20%20%20%20%20%20impositions%20of%20surface%20fluxes

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Phys. Rev. B 33, 251 (1986). 250 citations
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Spintronics in Non-uniform Magnetic Conductors
Dynamics with a Bend or a Twist
Bend or Twist Domain Wall or Vortices

• Wayne M. Saslow
• Texas AM University

Phys. Rev. B 76, 184434 (2007).
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What Phenomena Occur?

• Spin Seebeck Effect A temperature gradient
  causes spin-polarized currents. "Observation of
  the spin Seebeck effect", K. Uchida, S.
  Takahashi, K. Harii, J. Ieda, W. Koshibae, K.
  Ando, S. Maekawa and E. Saitoh, Nature 455,
  778-781 (9 October 2008).
• Spin Transfer Torque (bulk) A spin-polarized
  current transfers angular momentum and torque to
  the magnetization. Now well-known.
• Spin Pumping (bulk) Dynamics of the
  magnetization causes spin-polarized current flow.
  "Universal Electromotive Force Induced by Domain
  Wall Motion", S. A. Yang, G. S. D. Beach, C.
  Knutson, D. Xiao, Q. Niu, M. Tsoi, and J. L.
  Erskine, Phys. Rev. Lett. 103, 067201 (2009).

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What Theoretical Approach?Irreversible
Thermodynamics

• Local thermodynamics holds initially.
• Equations of motion taken to ensure that local
  thermodynamics holds at all future times.
• Non-negative heating rate R (even under t gt -t).
• R is a sum of products of thermodynamic fluxes j
  with corresponding thermodynamic forces
  R-jsidT/dxi
• Thermodynamic fluxes are proportional to
  thermodynamic forces. Irreversible
  thermodynamics doesnt give coefficients.
• Onsager relations for cross-coupling
  coefficients.

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Time-Reversal Signature (TRS) is Crucial
Irreversibility Dissipative Response
Reversibility Reactive Response

• Thermodynamic densities and thermodynamic forces
  (affinities) have well-defined signatures under
  time-reversal.
• Time-derivatives (e.g. dM/dt) and fluxes (e.g. j)
  have intrinsic time-reversal signature (TRS).
• Each part of the time-derivatives and fluxes
  allowed by irreversible thermodynamics has a
  definite TRS same TRS as intrinsic makes them
  reactive opposite TRS from intrinsic makes them
  dissipative.
• Examples
• (1) Mass moving through a fluid force has even
  intrinsic TRS Stokes damping force has odd TRS.
  These are opposite, so Stokes damping is
  dissipative.
• (2) Insulating solid (NaCl) Entropy current has
  odd intrinsic TRS temperature gradient has even
  TRS. These are opposite, so thermal conduction
  is dissipative.

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One-Band Conductor

• Thermodynamic variables (densities) entropy s
  and number n, with even TRS.
• Thermodynamic forces gradients of temperature
  and electrochemical potential, with even TRS.
  Real-space vector index i.
• For this system, all thermodynamic fluxes have
  odd intrinsic TRS. entropy flux
• number flux
• current flux
• Thermodynamic forces have even TRS all these
  fluxes are dissipative.
• Subject to Onsager Relation (ensures equal
  dissipation rates for the two cross-terms)

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One-Band Conductor - Heating Rate

• Rate of entropy production
• Oscillate voltage
• Phase-lock heating rate

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Two-Band Conductor

• Thermodynamic variables (densities)
• entropy s and number n1 and n2, with even TRS.
• Thermodynamic forces gradients of temperature
  and electrochemical potentials, with even TRS.
  Real-space vector index i.
• Thermodynamic fluxes with odd intrinsic TRS
• All these fluxes are dissipative.
• Subject to Onsager Relations

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Uniform Insulating Magnet (No Diffusion)

• Thermodynamic variables (densities)
  magnetization M has odd intrinsic TRS.
• Thermodynamic forces torque MxH has even
  intrinsic TRS.
• New Element - Structure Constant has odd
  intrinsic TRS.
• Equation of motion (vectors indicate spin-space)
• First (Larmor) term has even TRS, which matches
  the intrinsic TRS of dM/dt, so no damping.
• Second (Landau-Lifshitz) term has odd TRS, so
  damping. Many other authors also get LL damping
  with their versions of irreversible
  thermodynamics (Baryakhtar, Iwata, Barta).
• Irreversible thermodynamics does not give the
  put-in-by-hand, self-referential Gilbert damping,
  with adM/dt in place of -lMxH for the last term
  on the RHS. W.F. Browns Fokker-Planck theory
  inputs, rather than derives, Gilbert damping.
• No Onsager relations

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Uniform Conducting Magnet

• Thermodynamic variables (densities)
• Thermodynamic forces torque
• Structure Constant
• Output - equation of motion and fluxes
• Spin and space variables are independent.
• Onsager Relations
• Spin Seebeck implied by StilesZangwill, etc.

Spin Seebeck (j by grad T)
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Experimental Spin Seebeck Effect
Oct. 2008 Nature observation by Japanese group
K. Uchida, S. Takahashi, K. Harii, J. Ieda, W.
Koshibae, K. Ando, S. Maekawa E. Saitoh
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Nonuniform Conducting Magnetwith Flow of
Magnetization Q - I

• Thermodynamic variables (densities)
• Thermodynamic forces torque
• Structure Constants
• Flux of Magnetization
• Output - equation of motion for M

Spin transfer torque (dM/dt by grad m)
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Nonuniform Conducting Magnetwith Flow of
Magnetization Q - II

• Flux of Magnetization
• Output - fluxes
• Many Onsager Relations
• New, Non-Dissipative Onsager Relations

Spin pumping (j by MxH)
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Experimental Spin Pumping
Observed via Vortex Core motion (Yang et al)
Proposed Observation via Domain Wall
Motion (Barnes Maekawa, Duine, Saslow)
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Adiabatic vs Non-Adiabatic Spin Transfer Torque
and Spin Pumping

• L terms are dissipative (odd TRS, opposite even
  TRS of dM/dt). Associated with
  misleadingly-named Adiabatic Spin Transfer Torque
  and Adiabatic Spin Pumping. Think of adiabatic
  as adiabatic-in-space, not adiabatic-in-time.
• L terms are non-dissipative (even TRS, same as
  even TRS of dM/dt). Associated with
  misleadingly-named Non-adiabatic Spin Transfer
  Torque and Non-adiabatic Spin Pumping.
• Spin Transfer Torque, Spin Pumping, Spin Seebeck
  effects have all been observed, the Spin Pumping
  effect only recently.
• What about other theories of Spin Transfer
  Torque and Spin Pumping? They all use a form of
  the Spin-Berry phase (up and down spins have
  different phases). Space-derivative of
  Spin-Berry phase gives Spin Transfer Torque
  current is proportional to gradient of a phase,
  as for a superfluid. Time-derivative of
  Spin-Berry phase gives Spin Pumping (relative
  change of up and down phases rotates
  magnetization).
• These theories are appropriate to a
  superconducting magnet, not an ordinary
  conducting magnet. These theories give opposite
  TRS for thermodynamic forces than for ordinary
  conducting magnets. They have the Onsager
  symmetries reversed (L ltgt L), and they call the
  adiabatic spin transfer torque and adiabatic spin
  pumping terms non-dissipative whereas they are
  in fact dissipative.

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Truth In Advertising

• Early theories by Berger and Slonczewski. Very
  heuristic, physically motivated, but not
  easily-understood. Likely had no influence on
  recent theories of bulk spin pumping. But
  definitely predicted surface spin pumping and
  surface spin transfer torque.
• First recent theory of bulk spin pumping S. E.
  Barnes and S. Maekawa, Phys. Rev. Lett. 98,
  246601 (2007). Called it spin motive force.
• Additional theory by R. Duine, Phys. Rev. B 77,
  014409 (2008). Called it spin pumping.
• Further theory by U Texas group of Niu, one of
  whom (Yang) is lead author on the paper from the
  Erskine-Tsoi group, reporting the observation of
  bulk spin pumping. Universal emf induced by
  domain wall motion.

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Happy Birthday, Eugene!