Switching time of a single spin in linearly varying field

We studied the switching time of a single spin in a field varying linearly in time using a micromagnetics simulation based on the Landau-Lifshitz-Gilbert equation. The applied field larger than the switching field or coercivity is not enough for a spin to switch but some duration of time is also necessary. We found that the value of C ₁ defined by C ₁= (H - H ₁) dt was constant when the rate of change in the field was larger than 10× γH _k ², where γ is the gyromagnetic ratio with g value = 2, H is the applied field, H ₁ is a constant, and H _k is the anisotropy field of the spin. The integration is taken from the time the spin begins switching to the switching time. The equation is a generalized form of the equation, C ₀ (H - H ₀)τsw, in a constant field H. Here, C ₀ and H ₀ are constants, and τ _sw is the switching time. We found that C ₁ in the region dH/dt >10 ×γH _K ² and C ₀ in the region H≫H K are the same, but that H ₁ does not coincide with H ₀. We found that the head field rise time has a very small effect on the switching field and time of recording media.