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 $\widehat{\mathcal{H}}\left(S\right)$ is linear in the spin operators ${\widehat{\mathit{S}}}_j$ for each lattice site $j$, the RCS Hamiltonian ${\tilde{\mathcal{H}}}_{\mathrm{cl}}$ coincides with the usual classical model ${\mathcal{H}}_{\mathrm{cl}}={lim}_{S\to \infty }\widehat{\mathcal{H}}\left(S\right)$. 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.

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• Magnetic anisotropy
• Spin dynamics
• Semiclassical methods
• Spin lattice models
• Spin wave spectroscopy