The anisotropy of magnetic susceptibility of uniaxial superparamagnetic particles: Consequences for its interpretation in magnetite and maghemite bearing rocks

Abstract

A simple model that provides a quantitative description of the magnetic susceptibility of superparamagnetic to stable single‐domain uniaxial magnetic particles can be built in the framework of the theory of stochastic resonance. This model expands that of Mullins and Tile (1973) for superparamagnetic grains by considering the dependence of superparamagnetic susceptibility on the particle orientation and thus describes the anisotropy of magnetic susceptibility (AMS) of ensembles of superparamagnetic as well as single‐domain particles. The theory predicts that on the contrary of stable single domain, the maximum anisotropy of superparamagnetic particles is parallel to their easy axis and shows that the AMS of ensembles of uniaxial particle is strongly dependent on the distribution of particle grain size, coercivity, measurement temperature, and frequency. It also explains why the inverse AMS pattern expected for stable single‐domain particles is rarely observed in natural samples. We use examples of well‐characterized obsidian specimens to show that, as predicted by the theory, in the presence of significant superparamagnetic contributions, the maximum susceptibility axis of AMS is directed along the preferential direction of particles easy axis.

Frequency dependence of susceptibility in magnets with uniaxial and triaxial anisotropy

“…Equations and agree with those obtained by Lanci and Zanella [] (their equations (18) and (15) with their ϕ being equivalent to θ here); but their derivation is incorrect. Even the linear expansions of the relaxation rates (equation ) are inconsistent with their equation .…”

“…Also, the method of McNamara and Wiesenfeld [] requires a Taylor expansion for ν − ( H ) at H = 0, but as we saw above, this is undefined. Lanci and Zanella [] arrived at the correct result through a fortuitous cancelation of errors.…”

“…An essential step in the derivation of this standard result is the linear approximation for ± (H) when H is small. Lanci and Zanella [2016] claimed to extend the theory to arbitrary field directions using a result from McNamara and Wiesenfeld [1989]. However, the result relies on the assumption that the relaxation rates have the form…”

“…Lanci and Zanella [] claimed to extend the theory to arbitrary field directions using a result from McNamara and Wiesenfeld []. However, the result relies on the assumption that the relaxation rates have the form Lanci and Zanella identify f ( t ) as a multiple of an exponential (as in equation ), μ with − K u V / k B T and η 0 with − μ 0 M s H 0 V / k B T (with ).…”

“…To apply his theory of frequency‐dependent susceptibility to collections of randomly oriented magnets, Néel [] represented them by a model collection in which two thirds have easy axes perpendicular to the field, contributing nothing to the response, while the other third have axes parallel to the field. Lanci and Zanella [] claimed to have explicitly calculated the frequency dependence of susceptibility for any angle between the magnetic field and the easy axis. They used it to calculate the AMS as a function of frequency, finding that the maximum susceptibility of an SP magnet is parallel to the easy axis, in contrast to SD magnets where it is perpendicular.…”