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 C1 defined by C1=∫(H−H1)dt was constant when the rate of change in the field was larger than 10 × γHk2, where γ is the gyromagnetic ratio with g value = 2, H is the applied field, H1 is a constant, and Hk 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, C0=(H−H0)τsw, in a constant field H. Here, C0 and H0 are constants, and τsw is the switching time. We found that C1 in the region dH/dt>10×γHK2 and C0 in the region H≫HK are the same, but that H1 does not coincide with H0. We found that the head field rise time has a very small effect on the switching field and time of recording media.