Series expansions for the magnetisation of a solid superparamagnetic system of non-interacting particles with anisotropy

The calculation of the magnetisation curve of an assembly of non-interactin g fine superparamagnetic particles, with uniaxial anisotropy and easy axes fixed in a solid non-magnetic matrix is considered. The presence of anisotr opy complicates the calculation which otherwise would result in the Langevi n function. The calculation for particles with anisotropy and easy axes fix ed at arbitrary angles to the external field, requires the calculation of t he partition function, which has previously been expressed exactly as a dou ble integral or as a sum of single integrals. We have recently shown how th e partition function can be reduced to a single integral and here we show h ow this can be expressed as a double infinite series containing known funct ions. Special cases are considered, some existing analytic formulae are reo btained, and some new analytic formulae are presented. For identical partic les the deviation from the Langevin function is known to be considerable. T he formulae presented should facilitate the incorporation of the effects of anisotropy. (C) 1999 Elsevier Science B.V. All rights reserved.