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Keywords:

  • ferromagnetic resonance;
  • Fokker–Planck equation;
  • magnetization dynamics;
  • retardation effect

Abstract

The theory predicts that the spin-wave lifetime τL and the linewidth of ferromagnetic resonance ΔB can be governed by random fields and spatial memory. To that aim the effective field around which the magnetic moments perform a precession is superimposed by a stochastic time dependent magnetic field with finite correlation time. The magnetization dynamics is altered by inclusion of a spatial memory effect monitoring a non-local interaction of size ξ. The underlying Landau–Lifshitz–Gilbert equation (LLG) is modified accordingly. The stochastic LLG is equivalent to a Fokker–Planck equation which enables to calculate the mean values of the magnetization vector. Within the spin-wave approximation we present an analytical solution for the excitation energy and its damping. The lifetime and the linewidth are analyzed depending on the strength of the random field D and its correlation time τc as well as the retardation strength Γ0 and the size ξ. Whereas τL decreases with increasing D, retardation strength Γ0 and τc, the lifetime is enhanced for growing width ξ of the spatial retardation kernel. In the same manner we calculate the experimentally measurable linewidth ΔB is increased strongly when the correlation time τc ranges in the nanosecond interval.