chudnovsky symposium, mar.13&14, 2009 1 phys. rev. b 33, 251 (1986). 250+ citations

Chudnovsky Symposium, Mar.13&14, 2009

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Phys. Rev. B 33, 251 (1986). 250+ citations


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Wayne M. Saslow

Texas A&M University

Spintronics in Non-uniform Magnetic Conductors:

Dynamics with a Bend or a Twist

Spintronics in Non-uniform Magnetic Conductors:

Dynamics with a Bend or a Twist

Phys. Rev. B 76, 184434 (2007).

Bend or Twist: Domain Wall or Vortices


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What Phenomena Occur?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 ThermodynamicsWhat 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 => -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 doesn’t give coefficients.

• Onsager relations for cross-coupling coefficients.


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Time-Reversal Signature (TRS) is Crucial: Irreversibility = Dissipative Response

Reversibility = Reactive Response

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 ConductorOne-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 RateOne-Band Conductor - Heating Rate

• Rate of entropy production

• Oscillate voltage

• Phase-lock heating rate


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Two-Band ConductorTwo-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)

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 dM/dt in place of -MxH for the last term on the RHS. W.F. Brown’s Fokker-Planck theory inputs, rather than derives, Gilbert damping.

• No Onsager relations


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Uniform Conducting Magnet Uniform Conducting Magnet


• Thermodynamic forces: torque

• Structure Constant

• Output - equation of motion and fluxes

• Spin and space variables are independent.

• Onsager Relations

• Spin Seebeck implied by Stiles&Zangwill, etc.

Spin Seebeck (j by grad T)


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Experimental Spin Seebeck EffectExperimental 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 - INonuniform Conducting Magnetwith Flow of Magnetization Q - I


• Thermodynamic forces: torque

• Structure Constants

• Flux of Magnetization

• Output - equation of motion for M

Spin transfer torque (dM/dt by grad )


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Nonuniform Conducting Magnetwith Flow of Magnetization Q - IINonuniform 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 PumpingExperimental Spin Pumping

Observed via VortexCore 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 PumpingAdiabatic 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 <=> 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 AdvertisingTruth 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!Happy Birthday, Eugene!

chudnovsky symposium, mar.13&14, 2009 1 phys. rev. b 33, 251 (1986). 250+ citations

Documents

odd trs

chudnovsky symposium

intrinsic trs stokes

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timereversal signature

entropy current