New issues in zero dimensions: magnetic molecules

Abstract We discuss some major features of isolated magnetic molecules where intermolecular magnetic interactions are negligible and the magnetic properties are determined using a Heisenberg model of intramolecular exchange between a relatively small number of diverse paramagnetic ions. We survey some of the more challenging issues and results that have emerged to date, including the spectrum of excitations, effects of geometric frustration, and critical slowing down of the spin dynamics at low temperatures. Primary attention is given to realizable magnetic molecules.