Deviation from Bloch T3/2 law in ferrite nanoparticles

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. T-3/2 law is valid above similar to 75K for the smallest ferrite particles obtained in this experiment having size of similar to 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.