Sample shape dependence of magnetic noise

Zero-field magnetic noise, characterised by the magnetic autocorrelation function $S_s(t)$, has been observed, perhaps surprisingly, to depend on sample shape $s$. The reasons for this are identified and general expressions are derived that relate the autocorrelation functions for systems of different shape to an underlying `intrinsic’ form. Assuming the flcutuatiopn-dissipation theorem, it is shown that, for any noise that relaxes monotonically, the effect of sample shape is to reduce both the noise amplitude and mean relaxation time by a factor of $1+N{\chi }_i$, where $N$ is the demagnetizing factor and ${\chi }_i$ the intrinsic susceptibility. In frequency space, where $S_s(t)$ Fourier transforms into the power spectrum $S_s(\omega )$, the above two factors combine to suppress the zero frequency amplitude of $S_s(\omega )$ by $(1+N{\chi }_i{)}^2$, while at high frequency, sample shape dependence becomes negligible. These results suggest simple and robust experimental tests of the fluctuation–dissipation theorem in magnetic systems that may be useful in distinguishing bulk from surface effects.