Targeting Exchange Interactions in Nanosize Molecular Magnets by Angular Momentum Technique

Abstract

In this review article we summarize the results on the application of the angular momentum technique to the evaluation of the energy pattern and magnetic properties of large metal clusters. The main emphasis is made on the irreducible tensor operator (ITO) technique which is the most powerful tool in the analysis of large spin systems. We show how the ITO technique allows the evaluation of the energy levels of high-nuclearity clusters consisting of orbitally non-degenerate ions that can be described by the Heisenberg-Dirac-Van Vleck (HDVV) model of the isotropic exchange. Then we consider a more general exchange model supplemented by the relatively small anisotropic terms in the exchange Hamiltonian, like symmetric bilinear terms, and antisymmetric exchange. We demonstrate application of ITO to the systems containing orbitally degenerate metal ions with unquenched orbital angular momentum that are first considered in the limit of isotropic exchange coupling. Orbital degeneracy creates also highly anisotropic exchange interaction that can be taken into account in the framework of orbitally dependent effective Hamiltonian. In this case application of the ITO approach allows to elaborate an efficient way for the evaluation of the energy levels with due account for all accompanying interactions such as spin-orbit coupling (SCO), low-symmetry crystal fields, etc., and to analyze the magnetic anisotropy in general terms. A separate article is devoted to the problem of mixed valency and double exchange. Finally, we mention the computer programs designed for the analysis of the exchange interactions in complex high-nuclearity magnetic clusters. It is our aim to provide the reader with the knowledge of contemporary computational approaches as applied to different kinds of spin systems which constitute the main subject of molecular magnetism expanded to its modern trends such as quantum computing and spintronics.