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Over the years, the Self-Consistent Harmonic Approximation (SCHA) has beensuccessfully utilized to determine the transition temperature of many differentmagnetic models, particularly the Berezinskii-Thouless-Kosterlitz transition intwo-dimensional ferromagnets. More recently, the SCHA has found application indescribing ferromagnetic samples in spintronic experiments. In such a case, theSCHA has proven to be an efficient formalism for representing the coherentstate in the ferromagnetic resonance state. One of the main advantages of usingthe SCHA is the quadratic Hamiltonian, which incorporates thermal spinfluctuations through renormalization parameters, keeping the description simplewhile providing excellent agreement with experimental data. In this article, weinvestigate the SCHA application in easy-axis magnetic models, a subject thathas not been adequately explored to date. We obtain both semiclassical andquantum approaches of the SCHA for a general anisotropic magnetic model andemploy them to determine various quantities such as the transition temperature,spin-wave energy spectrum, magnetization, and critical exponents. To verify theaccuracy of the method, we compare the SCHA results with experimental and MonteCarlo simulation data for many distinct well-known magnetic materials.

Theoretical determination of Ising-type transition by using the Self-Consistent Harmonic Approximation