Nonlinear Magnetization Dynamics in Nanomagnets

Abstract

Landau–Lifshitz–Gilbert dynamics is investigated for uniformly magnetized particles subject to constant, pulsed, and circularly polarized applied fields. The Landau–Lifshitz–Gilbert equation is treated as a nonlinear dynamical system on the unit sphere. The equilibria and the phase portraits of this dynamical system, the nature of conservative (precessional) dynamics, and the nature of dissipation are discussed. Conservative Landau–Lifshitz dynamics is studied in detail and analytical expressions are derived for this dynamics in terms of elliptic functions. Then the problem of magnetization switching is studied in detail. Damping and precessional switchings of magnetization in spheroidal particles are discussed for rectangular field pulses, and expressions for critical fields and pulse durations are derived. The phenomenon of ringing, which occurs as the final stage of magnetization switching, is analytically studied using the averaging technique. The final section is devoted to the study of Landau–Lifshitz–Gilbert dynamics in uniformly magnetized particles with rotationally invariant properties, subject to a circularly polarized external field. By using geometric and topological considerations, exact uniform‐mode solutions of the full nonlinear dynamics are obtained for arbitrary values of the excitation conditions. The stability of these solutions is investigated and the conditions leading to periodic or quasiperiodic motions of the magnetization are established. Finally the problem of ferromagnetic resonance is treated using the developed analytical techniques.

Thermally Activated Transitions Between Micromagnetic States

“…In the system under investigation the energy functional is rotationally symmetric with respect to mp ; as a consequence the fields in the rotating frame are time independent, and (8) describes an autonomous dynamical system. In this frame the magnetization evolves toward the nearest energy minimum [43]. In the symmetric case when both mp and the external field are perpendicular to the plane of the thin film, the pseudoenergy, derived in Appendix A of [42], is given by…”