Magnetic-stress-assisted damping of magnetization precession in multilayered metallic films

Micromagnetic dynamics of spin relaxation in multilayered metallic films of stacked microelectronic devices is modeled by a modified Landau-Lifshitz-Gilbert equation with a newly introduced form of damping torque owing its origin to coupling between precessing magnetization-vector and stress-tensor of combined intrinsic and extrinsic magnetic anisotropy. Based on the magnetization energy loss equation, the exponential relaxation time as a function of precession frequency and angle of applied rf-field is obtained, depending upon two parameters of intrinsic and extrinsic damping torques acting on precessing magnetization. It is shown that theoretically obtained from the Gabor uncertainty relation the FMR linewidth, originating from the above magnetic-stress-assisted damping of magnetization precession, provides proper account for the empirical non-linear linewidth-vs-frequency curves deduced from recent in-plane FMR measurements on multilayered ultrathin films of ferromagnetic metals.