Phenomenological theory of permeability in films having no in-plane magnetic anisotropy: Application to spin-sprayed ferrite films

In terms of the first-order magnetocrystalline anisotropy energy constant K-1, we determined magnetic anisotropy in single-crystalline cubic films having their normal lines parallel to (hkl) axes. We found that the films have biaxial magnetic anisotropy, with which we derived permeability mu(omega)=mu(')(omega)-j mu(')(omega) (omega: angular frequency) and natural resonance angular frequency omega(0), due to magnetization rotation in single-crystalline and polycrystalline films. For films that have preferential orientation of major crystal axes (such as [100] and [110]) perpendicular to the film plane but have random orientation in the film plane (i.e., exhibiting no in-plane anisotropy), the low-frequency permeability mu(omega <omega(0)) and omega(0) follow the product rule mu(omega <omega(0))omega(2)(0)=gamma M-2(s)2/2 mu(2)(0) (M-s: spontaneous magnetization, gamma: gyromagnetic ratio, and mu(0): permeability of free space). This is similar to that which applies for films having an in-plane uniaxial magnetic anisotropy field. Our phenomenological theory gave a plausible explanation for the permeability of spin-sprayed ferrite films that have no in-plane magnetic anisotropy and yet have high mu(')(omega) of a few tens up to the gigahertz region. (C) 2006 American Institute of Physics.