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.