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Spin-orbit coupling (SOC), which is inherent to a Dirac particle that movesunder the influence of electromagnetic fields, manifests itself in a variety ofphysical systems including non-relativistic ones. For instance, it plays anessential role in spintronics developed in the past few decades, particularlyby controlling spin current generation and relaxation. In the present work, byusing an extended Caldeira-Leggett model, we elucidate how the interplaybetween spin relaxation and momentum dissipation of an open system of a singlespin-$1/2$ particle with a Rashba type SOC is induced by the interactions witha spinless, three-dimensional environment. Staring from the path integralformulation for the reduced density matrix of the system, we have derived a setof coupled nonlinear equations that consists of a quasi-classical Langevinequation for the momentum with a frictional term and a spin precessionequation. The spin precesses around the effective magnetic field generated byboth the SOC and the frictional term. It is found from analytical and numericalsolutions to these equations that a spin torque effect included in theeffective magnetic field causes a spin relaxation and that the spin andmomentum orientations after a long time evolution are largely controlled by theRashba coupling strength. Such a spin relaxation mechanism is qualitativelydifferent from, e.g., the one encountered in semiconductors where essentiallyno momentum dissipation occurs due to the Pauli blocking.

Dissipation-relaxation dynamics of a spin-1/2 particle with a Rashba-type spin-orbit coupling in an ohmic heat bath