We propose a method for inducting the Boltzmann factor to extract effective classical spin Hamiltonians from meanfield-type electronic structural calculations by means of the Bayesian inference. This method enables us to compare electronic structural calculations with experiments according to the classical model at a finite temperature. Application of this method to the unrestricted Hartree-Fock calculations for NiGa2S4 led to the estimation that the superexchange interaction between the nearest neighbor sites is ferromagnetic at low temperature, which is consistent with magnetic experiment results. This supports the theory that competition between the antiferromagnetic third neighbor interaction and ferromagnetic nearest neighbor interaction may lead to the quantum spin liquid in NiGa2S4.
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