Supersolid phases in a realistic three-dimensional spin model

Supersolid phases, in which a superfluid component coexists with conventional crystalline long range order, have recently attracted a great deal of attention in the context of both helium physics and quantum spin systems. Motivated by recent experiments on AgNiO$_2$~[$1$], we study the magnetic phase diagram of a realistic three-dimensional spin model with single-ion anisotropy and competing interactions on a layered triangular lattice, using classical Monte Carlo simulation techniques, complemented by spin-wave calculations and Ginzburg-Landau theory. For parameters relevant to AgNiO$_2$~[$2$], we find a cascade of different phases as a function of magnetic field, including two phases which are supersolids the sense of Liu and Fisher [$3$]. One of these phases is continuously connected with the collinear ground state of AgNiO$_2$, and is accessible at relatively low values of magnetic field. The nature of this low-field transition, and the possibility of observing this new supersolid phase in AgNiO$_2$, are discussed. \\ \\ $[$1$]$ A. Coldea {\it et al.}, arXiv:0908.4169v1.\\ $[$2$]$ E. Wheeler {\it et al.}, Phys Rev B \textbf{79}, 104421, (2009).\\ $[$3$]$ K.S. Liu and M. E. Fisher, J Low Temp Phys \textbf{10}, 655 (1973).