Temperature dependence of magnetization and anisotropy in uniaxial NiFe2O4 nanomagnets: Deviation from the Callen-Callen power law

Abstract

The thermal variation of magnetic anisotropy (K) and saturation magnetization (MS) for uniaxial nickel ferrite (NiFe2O4) nanomagnets are investigated. Major magnetic hysteresis loops are measured for the sample at temperatures over the range 5–280 K using a vibrating sample magnetometer. The high-field regimes of the hysteresis loops are modeled using the law of approach to saturation, based on the assumption that at sufficiently high field only direct rotation of spin-moment take place, with an additional forced magnetization term that is linear with applied field. The uniaxial anisotropy constant K is calculated from the fitting of the data to the theoretical equation. As temperature increases from 5 K to 280 K, a 49% reduction of K, accompanied by an 85% diminution of MS is observed. Remarkably, K is linearly proportional to MS2.6 in the whole temperature range violating the existing theoretical model by Callen and Callen. The unusual power-law behavior for the NiFe2O4 uniaxial nanomagnets is ascribed to the non-negligible contributions from inter-sublattice pair interactions, Neel surface anisotropy, and higher order anisotropies. A complete realization of the unusual anisotropy-magnetization scaling behavior for nanoscale two-sublattice magnetic materials require a major modification of the existing theory by considering the exact mechanism of each contributions to the effective anisotropy.