Temperature dependent first order magnetocrystalline anisotropy constant model for ferromagnetic metals

In this work, a temperature dependent first order magnetocrystalline anisotropy constant model without any fitting parameters for ferromagnetic metals is developed, based on the equivalent relation between magnetocrystalline anisotropy energy and heat energy. The model establishes the quantitative relationship between temperature dependent first order magnetocrystalline anisotropy constant, heat capacity and volume expansion coefficient, providing a new idea of studying the intrinsic relationship between magnetocrystalline anisotropy constant and temperature. The available first order magnetocrystalline anisotropy constants, including dysprosium, terbium, holmium, iron and cobalt, are predicted at different temperatures, and the predictions are all in good agreement with the reported experimental results. Compared with existing models, our model offers a more convenient and simple method for pure metals to predict the first order magnetocrystalline anisotropy constants at different temperatures. More importantly, this study helps to obtain the temperature where the first order magnetocrystalline anisotropy constant decreases to zero.