Interpreting Stone's model of Berry Phases

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We show that a simple quantum-mechanical model, put forward by Stone sometime ago, affords description of site magnetoelectricity, a phenomenon which takes place in crystals (and molecular systems) when space inversion is locally broken and coexistence of electric and magnetic moments is permitted by the site point group. We demonstrate this by identifying a local order parameter, which is odd under both space inversion and time reversal. This order parameter (a magnetic quadrupole) characterises Stone's ground state. Our results indicate that the model, extended to a lattice of sites, could be relevant to the study of electronic properties of transition-metal oxides. A generalisation of Stone's hamiltonian to cover cases of different symmetry is also discussed.