AC Magnetic Susceptibility of a Permalloy Thin Film

Abstract

Measurements of noise in magnetic thin films have variously reported $1/f$ noise, white noise, and random telegraph noise. The $1/f$ noise experiments claim magnetic noise by relating the magnetic noise to the susceptibility with use of the fluctuation-dissipation theorem. However, neither the linearity of the susceptibility necessary for application of fluctuation-dissipation nor the frequency dependence of susceptibility was explored. To investigate more fully the frequency dependence and linearity of the magnetic susceptibility of a magnetic film, we measured the AC susceptibility of a 100 nm thick film of permalloy as a function of the magnitude $H_{AC}$ and frequency $f$ of an applied AC magnetic field over the full hysteresis loop of the films, i.e., the measurements were performed while slowly varying an applied DC magnetic field, $H_{DC}$. The AC frequency range was from 20 Hz to 5 kHz while the AC field range was between 0.2 G and 1 G. At $H_{DC} = 0$ the response of the system was measured as a function of $H_{AC}$ at 200 Hz. It was found to be nonlinear but became reasonably close to linear for $H_{AC} < 1 G$ - the coercive field was approximately 15 G. The in-phase and out-of-phase components approximately follow power laws with frequency, with exponents 0.69 and -0.2. The behavior of the out-of-phase component is roughly consistent with previously measured white magnetic noise and a simple harmonic oscillator model, but the in-phase component does not follow the prediction of this model.