Inverse Brillouin Function and Demonstration of Its Application

The Brillouin function arises in the quantum theory of paramagnetic materials, where it describes the dependence of the magnetization on the externally applied magnetic field and on the temperature of the system. There is no closed form exact analytical expression for the inverse Brillouin function, however, there have been several approximations proposed. In this work, we first compare relative errors and simplicity of several approximations for the inverse Brillouin function. Next, we demonstrate the application of the inverse Brillouin function by determining the Hamiltonian of the system using the simulation data of the magnetization dependence on the temperature. Then we compare the Hamiltonian that was used to set up the simulation with the Hamiltonian determined from the magnetization temperature dependence and an approximation to the inverse Brillouin function. We found that some of the approximations for the inverse Brillouin function can be used to accurately predict the Hamiltonian of the system given the magnetization dependence on temperature.