Distribution of Non-uniform Demagnetization Fields in Paramagnetic Bulk Solids

A general calculation for the distribution of non-uniform demagnetization fields in paramagnetic bulk solids is described and the fields for various sample geometries are calculated. Cones, ellipsoids, paraboloids and hyperboloids with similar sample aspect ratios are considered. Significant differences in their demagnetization fields are observed. The calculation shows that the demagnetization field magnitudes decrease along the axis of symmetry (along $z$) where an externally applied magnetic field is aligned, and increase in the vicinity of the lateral surfaces with the largest field values found in the cone and the narrowest field distributions found in the hyperboloid. Application is made to the theoretical modeling of the $^{1}$H-NMR spectra of a single crystal of field-induced superconductor $λ$-(BETS)$_{2}$FeCl$_{4}$ with a rectangular sample geometry, providing a good fit to the measured NMR spectra. This calculation is also applicable to diamagnetic or ferromagnetic materials in general.