Angular and Magnitude Dispersion of the Anisotropy in Magnetic Films

Abstract

A physical model for the angular and magnitude dispersion of the anisotropy of magnetic films has been investigated. It is based on the effect of anisotropic strain on a microscopic scale acting on magnetostrictive material. If the strain-induced anisotropy component Hks is less than the intrinsic unstrained value Hko the following results are obtained: (1) Regions with highest and lowest local Hk values are unskewed. Regions with maximum skew have approximately average Hk. (2) Although local skew α and the resultant anisotropy Hk are not uniquely related since each depends on both direction and magnitude of applied stress, their maximum values for a composite film having isotropic strain on a macroscopic scale are related by; αmax=(1/2) arcsin (Hk max−Hko)/Hko. The following measurements have been taken which tend to support the theory. (1) The angular distribution function has been found to be Gaussian using a measurement technique for which the angle can be read with ±0.1°. (2) The broadening of the Stoner-Wohlfarth switching threshold depends on both angular and magnitude variations. A machine calculation was performed to give this broadening as a function of ασ and Hkσ, the standard deviation of the angular and magnitude distributions, respectively. Using a measured ασ=1.0° the best fit gave Hkσ=0.1 H̄k, which agrees with theory within a factor of three. The data showed that the Hk distribution is not completely symmetric but has approximately 10% of the film with Hk>2Hko. Measurements of angular dispersion as a function of applied stress for films of known chemical inhomogeneity yield results an order of magnitude below those calculated, using the model described. This is thought to represent the ``stiffening'' effect of magnetostatic and exchange interactions.