Magnetoresistive Measurements on Domain Rotation and Wall Development in Ni-Fe Alloy Films

Abstract

In low saturating magnetic field, the magnetoresistive effect in a polycrystalline ferromagnet is described by the relation ${\mathrm{\Delta \rho /\Delta \rho }}_0\mathrm{\hspace{0.17em}=\hspace{0.17em}}{\cos }^2\alpha$ where $\mathrm{\Delta \rho }$ is the resistivity change which occurs when the saturation magnetization $M_s$ is oriented first normal then at an angle $\alpha$ to the electric current $i$ . The maximum change ${\mathrm{\Delta \rho }}_0$ is characteristic of the material. The uniform rotation model of a uniaxially anisotropic film in a transverse magnetic field $H_{\perp }$ leads to a dependence of $\mathrm{\Delta \rho }$ on $H_{\perp }$ of the form ${\mathrm{\Delta \rho /\Delta \rho }}_0{\mathrm{\hspace{0.17em}=\hspace{0.17em}h}}_{\perp }^2$ when $i$ is normal to the anisotropy axis ($K$ axis) and of the form ${\mathrm{\Delta \rho /\Delta \rho }}_0{\text{\hspace{0.17em}=\hspace{0.17em}1−h}}_{\perp }^2$ when $i$ is parallel to the $K$ axis. In these expressions $h_{\perp }$ is the ratio of $H_{\perp }$ to $H_K$ , where $H_K{\text{\hspace{0.17em}=\hspace{0.17em}2K/M}}_s$ , and $K$ is the anisotropy energy constant. The present paper treats the transverse magnetization process in Ni-Fe alloy films on the basis of a simple model in which the $K$ axes in local regions of the film are dispersed in direction about an average $\mathrm{〈K〉}$ axis. For a single numerical value of the dispersion angle $\beta$ the transverse magnetoresistive behavior is described by ${\mathrm{\Delta \rho /\Delta \rho }}_0{\mathrm{\hspace{0.17em}=\hspace{0.17em}(h}}_{\perp }{\mathrm{+\beta )}}^2$ when $i$ is normal to $\mathrm{〈K〉}$ and ${\mathrm{\Delta \rho /\Delta \rho }}_0{\text{\hspace{0.17em}=\hspace{0.17em}1−(h}}_{\perp }{\mathrm{+\beta )}}^2$ when $i$ is parallel to $\mathrm{〈K〉}$ . The model also requires that the ratio of transverse remanent magnetization to $M_s$ be $\sin \beta$ . These predictions are experimentally verified for films which gave values of $\beta$ from 0.1 to 0.3 (6° to 18°), and show the applicability of the Stoner-Wohlfarth theory to domain rotation.