Deviation from Bloch <i>T</i> ^3/2 law in ferrite nanoparticles

Abstract

The temperature dependence of saturation magnetization of ferrite nanoparticles has been studied to investigate the applicability of Bloch spin-wave theory to the finite-size systems. T3/2 law is valid above 75 K for the smallest ferrite particles obtained in this experiment having size of 2.5 nm. The region of validity of Bloch law increases at the lower-temperature end with the increase in particle size and interparticle interactions. The anomaly from the spin-wave theory has been observed with an upturn at low temperature, which can be explained by considering the quantization of spin-wave spectrum due to the finite size of the particles.