TY - JOUR

T1 - Magnetization dissipation in ferromagnets from scattering theory

AU - Brataas, Arne

AU - Tserkovnyak, Yaroslav

AU - Bauer, Gerrit E.W.

PY - 2011/8/5

Y1 - 2011/8/5

N2 - The magnetization dynamics of ferromagnets is often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parametrized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain-wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.

AB - The magnetization dynamics of ferromagnets is often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parametrized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain-wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.

UR - http://www.scopus.com/inward/record.url?scp=80052286744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052286744&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.84.054416

DO - 10.1103/PhysRevB.84.054416

M3 - Article

AN - SCOPUS:80052286744

VL - 84

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 0163-1829

IS - 5

M1 - 054416

ER -