Renormalized classical theory of quantum magnets

We derive a renormalized classical spin (RCS) theory for $S>1/2$ quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced ${\mathrm{CP}}^{1}$ phase space of dipolar SU(2) coherent states. When the spin Hamiltonian $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathcal{H}}(S)$ is linear in the spin operators ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{S}}}_{j}$ for each lattice site $j$, the RCS Hamiltonian ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{H}}}_{\mathrm{cl}}$ coincides with the usual classical model ${\mathcal{H}}_{\mathrm{cl}}={lim}_{S\ensuremath{\rightarrow}\ensuremath{\infty}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathcal{H}}(S)$. In the presence of nonlinear terms, however, the RCS theory is more accurate than ${\mathcal{H}}_{\mathrm{cl}}$. For the many materials modeled by spin Hamiltonians with (nonlinear) single-ion anisotropy terms, the use of the RCS theory is essential to accurately model phase diagrams and to extract the correct Hamiltonian parameters from neutron-scattering data.