Model for temperature-dependent magnetization of nanocrystalline materials

A magnetization model of nanocrystalline materials incorporating intragrain anisotropies, intergrain interactions, and texture effects has been extended to include the thermal fluctuations. The method relies on the stochastic Landau–Lifshitz–Gilbert theory of magnetization dynamics and permits to study the magnetic properties of nanocrystalline materials at arbitrary temperature below the Currie temperature. The model has been used to determine the intergrain exchange constant and grain boundary anisotropy constant of nanocrystalline Ni at 100 K and 298 K. It is found that the thermal fluctuations suppress the strength of the intergrain exchange coupling and also reduce the grain boundary anisotropy. In comparison with its value at 2 K, the interparticle exchange constant decreases by 16% and 42% and the grain boundary anisotropy constant decreases by 28% and 40% at 100 K and 298 K, respectively. An application of the model to study the grain size-dependent magnetization indicates that when the thermal activation energy is comparable to the free energy of grains, the decrease in the grain size leads to the decrease in the magnetic permeability and saturation magnetization. The mechanism by which the grain size influences the magnetic properties of nc–Ni is discussed