  Over the years, the Self-Consistent Harmonic Approximation (SCHA) has been
successfully utilized to determine the transition temperature of many different
magnetic models, particularly the Berezinskii-Thouless-Kosterlitz transition in
two-dimensional ferromagnets. More recently, the SCHA has found application in
describing ferromagnetic samples in spintronic experiments. In such a case, the
SCHA has proven to be an efficient formalism for representing the coherent
state in the ferromagnetic resonance state. One of the main advantages of using
the SCHA is the quadratic Hamiltonian, which incorporates thermal spin
fluctuations through renormalization parameters, keeping the description simple
while providing excellent agreement with experimental data. In this article, we
investigate the SCHA application in easy-axis magnetic models, a subject that
has not been adequately explored to date. We obtain both semiclassical and
quantum approaches of the SCHA for a general anisotropic magnetic model and
employ them to determine various quantities such as the transition temperature,
spin-wave energy spectrum, magnetization, and critical exponents. To verify the
accuracy of the method, we compare the SCHA results with experimental and Monte
Carlo simulation data for many distinct well-known magnetic materials.
