Frequency dependence of susceptibility in magnets with uniaxial and triaxial anisotropy

Abstract

Characterization of minerals in rocks and soils provides a window into environmental processes and improves the interpretation of paleomagnetic measurements. Mineral composition, size, and shape can be constrained using magnetic measurements. For small minerals, a promising measurement is the frequency dependence of magnetic susceptibility. The size and shape dependence of the in-phase component X’(ω) and out-of-phase component X“(ω) are derived for arbitrarily oriented superparamagnetic and single-domain magnets with uniaxial and triaxial anisotropy. In a fluctuating field, a single magnet has a thermal response parallel to the easy axis and instantaneous rotation of the moment perpendicular to it. The size and temperature variations have the same form as in earlier theories in which all the magnets are aligned with the field and can be easily adapted to the methods of Shcherbakov and Fabian (2005) and Egli (2009) for finding size distributions using multiple temperatures and frequencies. These inversions are inherently nonunique and complicated by non-SD contributions, but some robust constraints can be put on the volume distribution if the commonly used ratio χfd is 10% or greater. The anisotropy of the out-of-phase component (opAMS) has the same sense as thermoremanent magnetization (TRM) and can be used to correct the paleofield direction. Along with the anisotropy of the in-phase component (ipAMS), it can be used to gain quantitative information on the deformation of the host rock. For the line/plane, or March, deformation model, opAMS and ipAMS are calculated and it is shown how they can be used to accurately represent the strain anisotropy.