The fundamental equations governing the evolution of the magnetization M in a ferromagnetic material are the Landau-Livshits-Gilbert equations: dM dt = −γM × Heff − γα M × (M × Heff). (1) Here, γ is the gyromagnetic constant with physical units m2V−1s−2, whereas α is dimensionless and plays the role of a phenomenological damping parameter. The parameter Ms represents the saturation magnetization and has dimension Am−1. The equations are valid in the domain Ω ⊂ R3 occupied by the ferromatgnetic material. The effective magnetic field Heff is the first variation of the Gibbs free energy E with respect to the magnetization. In the presence of an exciting magnetic field He, it read
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