Monte Carlo Simulation for Ising Spins on the Corner-Sharing Tetrahedron Lattices

Abstract

We have studied magnetic ordering of frustrated classical Ising spins on the antiferromagnetic corner-sharing tetrahedron lattices in one, two and three dimensions together with one dimensional triangle lattice by means of Monte Carlo simulation. If the interaction is confined to the nearest neighbors, the corner-sharing tetrahedron systems in all dimensions exhibit no long range order and spins in each tetrahedron plaquette are in the six-fold degenerate antiferomagnetic ground state at low temperatures as governed by the “ice rule”. The residual entropy per spin of the two and three dimensional arrays of tetrahedra, 0.202 k B , indicates thease systems to be less frustrated than the triangular and the Kagome lattices. The fact that no appericiable difference is observed between the two and the three dimensional lattices indicates that the ordering in each plaquette plays the most important role in the ordering process in these lattices. As temperature is raised, spins of each plaquette fluctuate predomi...