Sample-shape dependence of magnetic noise

Zero-field magnetic noise, characterized by the magnetic autocorrelation function Ss(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 fluctuation-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+Nχi, where N is the demagnetizing factor and χi the intrinsic susceptibility, but that only the exponential decay retains the same functional form for finite N. In frequency space, where Ss(t) Fourier transforms into the power spectrum Ss(ω), the above two factors combine to suppress the zero frequency amplitude of Ss(ω) by (1+Nχi)2, while, at high frequency, sample shape dependence becomes negligible. These results are applied to various magnetic systems and experiments, including to tests of the fluctuation-dissipation and noise measurements in spin ice, to spin glasses, to surface magnetism, and to ferromagnetic critical behavior. They may be used to imply a general result that, for any near to equilibrium magnetic system with monotonic relaxation, the internal B field will relax more slowly, and with larger amplitude, than the internal H field, both by factors of 1+χi. Published by the American Physical Society 2025