Heisenberg models forCaV4O9: Expansions about high-temperature, plaquette, Ising, and dimer limits

Abstract

We study antiferromagnetic, S=1/2 Heisenberg models with nearest- and second-neighbor interactions on the one-fifth-depleted square lattice which describes the spin degrees of freedom in the spin-gap system ${\mathrm{CaV}}_{4}$${\mathrm{O}}_{9}$. High-temperature expansions are used to calculate the temperature-dependent susceptibility, and Ising expansions are used to study phase boundaries and properties of the N\'eel-ordered phase, while plaquette and dimer expansions are used to calculate the ground-state properties and excitation spectra of magnetically disordered phases. The temperature dependences of the susceptibility and the spin gap are compared with experimental data on ${\mathrm{CaV}}_{4}$${\mathrm{O}}_{9}$. Within the parameter space we have considered, the data are best accounted for by a Hamiltonian in which the second-neighbor interactions are equal to (or perhaps somewhat less than) half the nearest-neighbor exchange, but the fits are not entirely satisfactory. The low-temperature triplet and singlet excitation spectra have many striking features which should be observable in neutron and Raman scattering experiments and would allow for more confident estimation of model parameters.