Spin exchange interactions of a spin dimer: Analysis of broken-symmetry spin states in terms of the eigenstates of Heisenberg and Ising spin Hamiltonians

Abstract

We examined the eigenstates of the Heisenberg spin Hamiltonian Ĥ=−JŜ1⋅Ŝ2 and the Ising spin Hamiltonian ĤIsing=−JŜ1zŜ2z for a general spin dimer consisting of M unpaired spins at one spin site and N unpaired spins at the other spin site, and then analyzed how the broken-symmetry spin state of a spin dimer is related to the eigenstates of Ĥ and ĤIsing. Our work shows that the description of the highest-spin and broken-symmetry spin states of a spin dimer by Ĥ is the same as that by ĤIsing. For the analysis of spin exchange interactions of a magnetic solid on the basis of density functional theory, the use of the Heisenberg spin Hamiltonian in the “cluster” approach is consistent with that of the Ising spin Hamiltonian in the “noncluster” approach.