Model selection of NiGa₂S₄ triangular lattice by bayesian inference

We propose a novel method for extracting effective classical spin Hamiltonians from mean-field type electronic structural calculations by means of the Bayesian inference. We apply the method for a NiS₂ triangular lattice in NiGa₂S₄, where the ground state is a spin disordered state. Starting from unrestricted Hartree-Fock calculations for the spin configurations of 16 Ni sites, we estimated that not only the strongest superexchange interaction between the third nearest neighbor-sites but also those between the nearest and the second nearest neighbor-sites should be considered for the effective classical spin Hamiltonian for NiGa₂S₄.