Title:
Thermal effects on current-driven magnetization dynamics

Abstract:
One of the most interesting problems on the current-driven 
magnetization dynamics is to understand the thermal effect. The spin 
transfer torque effectively makes the originally dissipative magnetic 
system to a new system that the magnetic energy can be accumulated, 
over-damped, or dissipationless during the magnetization dynamics. Thus the 
well-established transition rate theory that is built on the near 
equilibrium Boltzmann distribution in a damped environment is no more 
applicable. Here we propose a generalized Fokker-Planck equation in the 
presence of the spin torque. In the cases where the magnetic field and the 
current density are small, we find one can recover the transition rate theory by simply replacing the
temperature by an effective one. When the magnetic field
is larger than the anisotropic field and/or the current density is
larger than a critical value, there is no energy barrier associated with
each stable solution. In these cases, the thermal fluctuation between
a stable precessional state and a stable static state involves a concept
of ``negative temperature''. We determine the thermal decaying time of
the stable precessional states by proposing a novel relaxation 
formulation.