Singular Point Detection of Nanostructured Magnets

Abstract

The singular point detection (SPD) is a technique for the measurement of magnetic anisotropy fields and critical fields of magnetic phase transitions, by the use polycrystalline samples. It is based on the principle that the analytic singularity characterising the transition can be revealed in the polycrystalline aggregate by observing the differential susceptibility tensor χij and its covariant derivatives. Examples are the ordinary reversible parallel susceptibility (RPS), χp=dM/dH and the reversible transverse susceptibility (RTS), χt. In both cases the observation direction is parallel to the perturbing field ΔH and the derivatives with respect to H are in fact the directional derivatives along the bias field H0. These are particular cases of a more general quantity formed by the inner product of χij/l, the covariant derivative of χij, with three unit vectors in arbitrary directions. The process of successive derivatives then leads to a generalised susceptibility of order n which is specified by the observation direction and the set of n unit-vectors of the exciting fields. A variety of experimental configurations can be obtained by modulating fields at different frequencies. The SPD theory predicts peculiar singularities in the behaviour of high order susceptibilities.