Large-angle analytical solution of magnetization precession in ferromagnetic resonance

Abstract

Dynamics of magnetization M driven by microwave are derived analytically from the nonlinear Landau–Lifshitz–Gilbert equation. Analytical M and susceptibility are obtained self-consistently under a positive circularly polarized microwave field, h = ( h cos ⁡ ω t , h sin ⁡ ω t , 0 ) , with frequency ω , which is perpendicular to a static field, H = ( 0 , 0 , H ) . It is found that the orbital of M is always a cone along H. However, with increasing h the polar angle θ of M initially increases, then keeps 90° when h ⩾ h 0 = α ω / γ in ferromagnetic resonance (FMR) mode, where α is Gilbert damping constant and γ is gyromagnetic ratio. These effects result in a nonlinear variation of FMR signal as h increases to h ⩾ h 0 , where the maximum of resonance peak decreases from a steady value, linewidth increases from a decreasing trend. These analytical solutions provide a complete picture of the dynamics of M with different h and H.