Magnetoconductivity modulation of thin ferromagnetic films by substrate electrostriction

Signals accompanying the metallic field effect in Permalloy films that are quadratic in the applied charge density and sensitive to the direction $\theta$ and magnitude $H$ of an applied magnetic field are caused by electrostrictive strains in the substrate transmitted to the films. This magnetoconductivity modulation results from changes in magnetization direction induced by strain dependent contributions to the uniaxial anisotropy energy $K$. It shows an overall $4\theta$ dependence for an in-plane field, with a phase determined by the direction of the easy axis relative to the current, and an amplitude at given $\theta$ varying as $\frac{1}{H}$. Quantitative agreement between observed and predicted signals is good, and permits their use as a sensitive method for probing the strain dependence of $K$. Simultaneous data on very similar signals linear in the charge, also shown, bear directly on the metallic-field-effect in ferromagnetic metals.