Relationship between coupling constants in Heisenberg exchange Hamiltonian and Ising model

Abstract

We show that the coupling constant involved in the Heisenberg exchange Hamiltonian is related to the coupling constant calculated in the Ising model by a simple expression of the form J(Hei)=J(Ising)/N where N is the average number of equivalent magnetic sites per cell taken for calculation. This relation is demonstrated by DFT calculations on the crystallographic geometry of MnSb alloy in different magnetic phases, and on the optimized geometries of polymers of meta-xylylene and the silicon substituted counterparts.