Model for the FC and ZFC Ferrimagnetic Spinel

TL;DR

This paper presents a theoretical model for ferrimagnetic spinel materials that explains differences in magnetic properties observed in field-cooled and zero-field cooled preparations, matching experimental magnetization and specific heat data.

Contribution

The study introduces a two-sublattice spin system model that accounts for the effects of external magnetic fields during preparation, providing insights into the magnetic behavior of ferrimagnetic spinels.

Findings

Model accurately reproduces magnetization-temperature curves for FC and ZFC spinels.

Explains the anomalous temperature dependence of specific heat in these materials.

Shows the effective reduction of sublattice B spin due to applied magnetic field during preparation.

Abstract

There are two methods of preparation of ferrimagnetic spinel. If, during the preparation, an external magnetic field as high as 300 O\"{e} is applied upon cooling the material is named field-cooled (FC). If the applied field is about 1O\"{e} the material is zero-field cooled (ZFC). To explore the magnetic and thermodynamic properties of these materials we consider two-sublattice spin system, defined on the bcc lattice, with spin-$s^A$ operators $\bf{S_{i}^A}$ at the sublattice $A$ site and spin-$s^B$ operators $\bf{S_{i}^B}$ at the sublattice $B$ site, where $s^A>s^B$. The subtle point is the exchange between sublattice A and B spins, which is antiferromanetic. Applying magnetic field along the sublattice A magnetization, during preparation of the material, one compensates the Zeeman splitting, due to the exchange, of sublattice B electrons. This effectively leads to a decrease of the $s^B$ spin. We consider a model with $s^B$ varying parameter which accounts for the applied, during the preparation, magnetic field. It is shown that the model agrees well with the observed magnetization-temperature curves of zero field cooled (ZFC) and non-zero field cooled (FC) spinel ferrimagnetic spinel and explains the anomalous temperature dependence of the specific heat.