On the Minimum of Magnetization Reversal Time

Abstract

A modified Landau-Lifshitz equation is solved for a single-domain sphere and an infinitely-wide thin single-domain sheet of ferromagnetic material neglecting anisotropy. The external magnetic field is switched from one direction to its opposite instantaneously at the initial time and the behavior of the magnetization vector is investigated thereafter. It is shown that there is a critical value of the damping constant corresponding to the minimum value of the (repetitive) magnetization reversal time. If the damping constant is larger than the critical value, the magnetization vector moves slower; if it is smaller, the magnetization vector moves faster but oscillates so that it takes longer time until it comes to a rest at the final position. The critical values of the Landau-Lifshitz damping constant λ are γM for the sphere and 0.013γM for the thin sheet, where γ and M are the gyromagnetic ratio and the magnetization, respectively. The computed minimum switching time for the thin sheet of 4–79 molybdenum Permalloy is of the order of 10−9 sec.

Micromagnetic simulation of magnetization reversal in rotational magnetic fields

“…These results are in agreement with previously reported switching times of ultra-thin magnetic films. Kikuchi [7] investigated the reversal time of a single domain sphere and a single domain thin film and found a minimum reversal time for a ¼ 1 and 0:1 for the sphere and the thin film, respectively. The micromagnetic simulations revealed no difference between the calculations using the finite element edge length of 2.5 and 5 nm.…”

Magnetization switching in small ferromagnetic ellipsoidal samples

“…There exists C * = C * (Ω) > 0 such that, for every λ > 0 with 14) for every m 0 ∈ H 2 (Ω, S 2 ) with ∂m 0 ∂ν ≡ 0 on ∂Ω, and Remark 5.5. The constants C * = C * (Ω) and C * * = C * * (Ω, α) will be given explicitly.…”

Switching behavior of a Stoner particle beyond the relaxation time limit

“…The switching process described by the Gilbert form of the Landau-Lifschitz equation has been studied only in special cases for a narrow range of magnetic field geometries [1][2][3]. For a static applied field, switching by homogeneous rotation of the magnetization and by nucleation and propagation of domain walls, and by combinations thereof, have been studied thoroughly [1,4].…”

“…The switching process described by the Gilbert form of the Landau-Lifschitz equation has been studied only in special cases for a narrow range of magnetic field geometries [1][2][3]. For a static applied field, switching by homogeneous rotation of the magnetization and by nucleation and propagation of domain walls, and by combinations thereof, have been studied thoroughly [1,4]. Nowadays magnetic device applications demand a deeper insight into the switching dynamics introduced by magnetic field pulses, especially on the time scale where the length of the field pulse is comparable or shorter than the typical relaxation time of the magnetization.…”