In this work, we propose a method for calculating the free energy of anisotropic classical spin systems. We use a Hubbard-Stratonovich transformation to express the partition function of a generic bilinear superexchange Hamiltonian in terms of a functional integral over classical time-independent fields. As an example, we consider an anisotropic spin-exchange Hamiltonian on the cubic lattice as is found for compounds with strongly correlated electrons in multiorbital bands and subject to strong spin-orbit interaction. We calculate the contribution of Gaussian spin fluctuations to the free energy. While the mean-field solution of ordered states for such systems usually has full rotational symmetry, we show here that the fluctuations lead to a pinning of the spontaneous magnetization along some preferred direction of the lattice.
|Original language||English (US)|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Oct 19 2015|
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© 2015 American Physical Society. ©2015 American Physical Society.