TY - JOUR

T1 - Dissipation-relaxation dynamics of a spin- 12 particle with a Rashba-type spin-orbit coupling in an ohmic heat bath

AU - Hata, Tomohiro

AU - Nakano, Eiji

AU - Iida, Kei

AU - Tajima, Hiroyuki

AU - Takahashi, Junichi

N1 - Funding Information:
We would like to thank K. Nishimura and H. Yabu for useful discussions. This work was supported in part by Grants-in-Aid for Scientific Research from JSPS (Grants No. 17K05445, No. 18K03501, No. 18H05406, No. 18H01211, and No. 19K14619).
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - Spin-orbit coupling (SOC), which is inherent in a Dirac particle that moves under the influence of electromagnetic fields, manifests itself in a variety of physical systems, including nonrelativistic ones. For instance, it plays an essential role in spintronics developed in the past few decades, particularly by controlling spin current generation and relaxation. In the present work, by using an extended Caldeira-Leggett model, we elucidate how the interplay between spin relaxation and momentum dissipation of an open system of a single spin-12 particle with Rashba-type SOC is induced by the interactions with a spinless, three-dimensional environment. Staring from the path-integral formulation for the reduced density matrix of the system, we have derived a set of coupled nonlinear equations that consists of a quasiclassical Langevin equation for the momentum with a frictional term and a spin precession equation. The spin precesses around the effective magnetic field generated by both the SOC and the frictional term. It is found from analytical and numerical solutions to these equations that a spin torque effect included in the effective magnetic field causes a spin relaxation and that the spin and momentum orientations after a long time evolution are largely controlled by the Rashba coupling strength. Such a spin relaxation mechanism is qualitatively different from, e.g., the one encountered in semiconductors in which essentially no momentum dissipation occurs due to the Pauli blocking.

AB - Spin-orbit coupling (SOC), which is inherent in a Dirac particle that moves under the influence of electromagnetic fields, manifests itself in a variety of physical systems, including nonrelativistic ones. For instance, it plays an essential role in spintronics developed in the past few decades, particularly by controlling spin current generation and relaxation. In the present work, by using an extended Caldeira-Leggett model, we elucidate how the interplay between spin relaxation and momentum dissipation of an open system of a single spin-12 particle with Rashba-type SOC is induced by the interactions with a spinless, three-dimensional environment. Staring from the path-integral formulation for the reduced density matrix of the system, we have derived a set of coupled nonlinear equations that consists of a quasiclassical Langevin equation for the momentum with a frictional term and a spin precession equation. The spin precesses around the effective magnetic field generated by both the SOC and the frictional term. It is found from analytical and numerical solutions to these equations that a spin torque effect included in the effective magnetic field causes a spin relaxation and that the spin and momentum orientations after a long time evolution are largely controlled by the Rashba coupling strength. Such a spin relaxation mechanism is qualitatively different from, e.g., the one encountered in semiconductors in which essentially no momentum dissipation occurs due to the Pauli blocking.

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U2 - 10.1103/PhysRevB.104.144424

DO - 10.1103/PhysRevB.104.144424

M3 - Article

AN - SCOPUS:85118707190

SN - 2469-9950

VL - 104

JO - Physical Review B

JF - Physical Review B

IS - 14

M1 - 144424

ER -