Angular dependence of nucleation by curling in a prolate spheroid

Abstract

The nucleation field is calculated for a small ferromagnetic prolate spheroid as a function of its size, its elongation, and the angle between the applied field and the spheroid axis. If there is no other switching mode except for magnetization curling and coherent rotation, these results probably represent the coercivity. The calculation is rigorous only for an isotropic particle, but a first order approximation is also given for a uniaxial or cubic anisotropy whose easy axis is parallel to the long axis of the spheroid.

Angular dependence of magnetic properties in Ni nanowire arrays

“…Here J p (z) and Y p (z) are Bessel functions of the first and second kind, respectively, and L x = 2A/µ 0 M 2 s is the exchange length. As pointed out by Aharoni [20], for a prolate spheroid with θ = 0, a jump of the magnetization at or near the curling nucleation field occurs. Therefore, the coercivity is quite close to the absolute value of the nucleation field.…”

“…However, for simplicity, expressions for the nucleation field obtained using infinite cylinders are used in all cases. The angular dependence of the curling nucleation field in a finite prolate spheroid was obtained by Aharoni [20].…”

“…However, Landeros et al [17] have shown that coherent rotation is present only in very short particles, namely, when the length of the particles is similar to the domain wall width. On the other side, Aharoni [20] calculated the angular dependence of the nucleation field in an ellipsoid when the reversal is driven by curling rotation. Escrig et al [21] extended this expression for magnetic nanotubes.…”

Energetics and switching of quasi-uniform states in small ferromagnetic particles

“…A large theoretical literature exists on rigorous results for the linear stability of this uniform state in prolate or oblate ellipsoids, and on the different instability channels, see e.g. [1,2,8,14,17]. Switching is often associated with loss of linear stability.…”

Micromagnetic simulations of cylindrical magnetic nanowires

“…This mode would correspond to homogeneous rotation of magnetization at unison along the whole length of the NW. Prior to the use of computers, the curling reversal mode was also suggested and evaluated analytically by the pioneer in the micromagnetic theory (Aharoni, 1997) based on the cylindrical symmetry property. His analytical theory for magnetization reversal is valid for homogeneous ferromagnetic prolate spheroid only.…”