The irregular tetrahedron of classical and quantum spins subjected to a magnetic field

Abstract

We obtain analytical expressions for the total magnetic moment and the static spin correlation functions of the classical Heisenberg model for an irregular tetrahedron array of spins that interact via two different exchange interactions and that are subject to a uniform magnetic field of arbitrary strength. This system provides a useful theoretical framework for calculating the magnetic properties of several recently synthesized molecular magnets. The tetrahedron systems, each considered for antiferromagnetic exchange, are of particular interest since they exhibit frustrated spin ordering for sufficiently low temperatures and weak magnetic fields. We compare the results with the corresponding irregular tetrahedron of quantum spins for several quantum spin values.