Precessional Motion Observation in Permalloy Film Using Fs-Time-Resolved Magneto-Optical Kerr Microscope

Abstract

We report a femtosecond pump-probe magneto-optical Kerr effect (MOKE) microscopic system enabling the study of vectorial spin dynamics with submicron spatial resolution using an 11-fs pulsed laser source. We applied the system to investigate the spin precessional motion of a patterned disk of Permalloy placed in an in-plane biasing magnetic field. The vector components of the spins perpendicular to the field`s direction showed a phase difference of about $\pi/2$, which represents an elliptic motion in the magnetic phase trajectory. A numerical calculation utilizing the Stoner model of the Landau-Lifshitz-Gilbert equation yielded a damping parameter of $\alpha$ = 0.016. A theoretical simulation with the shape of the magnetic field pulse, considering surface recombination of the photoconductive switch and multiple reflections of the waveguide, accurately predict the experimental observation of vectorial precessional motion. We devised the phenomenological method to exactly quantify the phase difference between precessional components and derived the analytic relation of the phase difference via the linearlized LLG equation with the assumption of low value of a scalar uniform damping constant, which well predicts the simulation result. We apply this method to the experimental data and calculate the phase lag angle of $\sim$ 2$^{\circ}$. This implies that an origin of the phase-lag angle is a non-zero damping constant. We report spatially non-uniform relaxation of spin precessional motion in a confined Permalloy microdisk. Non-uniform relaxation is examined with the relaxation time distributions of spin-wave modes using the wavelet transform technique. The spatial relaxation variation is found to be caused mainly by the mode conversion and the superposition of the fundamental mode and magnetostatic backward volume wave mode. The experimental data are in good agreement with micromagnetic simulations.