Relation between switching time distribution and damping constant

Magnetization dynamics is strongly influenced by the damping process, which is energy dissipation of the magnetization. Especially for spin-transfer torque magnetic random-access memories (STT-MRAMs) applications, the critical current density for magnetization switching is strongly affected by the damping constant because the spin-transfer torque must overcome the damping torque for the switching. However, it is not easy to determine the damping constant of nano-scale patterned samples.
In this talk, we show the relation between the damping constant and switching time distribution in case of nano-scale patterned samples by solving Fokker-Planck equation (FPE). We derive a FPE for the probability distribution of the magnetization angle as a function of time in case of perpendicular anisotropy samples. The approximated analytic expression of FWHM of switching time distribution is obtained, and we found that the inverse of the FWHM is proportional to the applied field and the slope is related with damping constant. The analytic relation shows a good agreement with full numerical results in the limit of high energy barrier. We believe our work is helpful to estimate the damping constant of the nano-scale patterned samples.