Inertial effect on minimum magnetic field for magnetization reversal in ultrafast magnetism

In the field of ultrafast magnetism, i.e., subpicosecond or femtosecond time scales, the dynamics of magnetization can be described by the inertial Landau-Lifhitz-Gilbert equation. In terms of this equation, the intrinsic characteristics are investigated in detail for the theoretical limit of the magnetization reversal field. We can find that there is a critical value for the inertia parameter tau(c), which is affected by the damping and anisotropy parameter of the system. When the inertial parameter factor tau < tau(c), the limit value of the magnetization reversal field under the ultrafast magnetic mechanism is smaller than that of the fast magnetic mechanism. When tau > tau(c), the limit value of the magnetization reversal field will be larger than the limit value under the fast magnetic mechanism. Moreover, it is important to point out that the limit value of the magnetization reversal field under the ultrafast magnetic mechanism decreases with the increasing inertial factor, as tau < tau(c)/2, which increases with inertial factor tau as tau > tau(c)/2. Finally, with the joint action of damping and anisotropy, compared with fast magnetism, we find that the limit value of the magnetization reversal field has rich variation characteristics, i.e., there is not only a linear and proportional relationship, but also an inverse relationship, which is very significant for the study of ultrafast magnetism.