Semiclassical theory for liquidlike behavior of the frustrated magnet Ca10Cr7O28

We identify the low energy effective Hamiltonian that is expected to describe the low temperature properties of the frustrated magnet ${\mathrm{Ca}}₁₀{\mathrm{Cr}}₇{\mathrm{O}}₂₈$. Motivated by the fact that this effective Hamiltonian has $S=3/2$ effective moments as its degrees of freedom, we use semiclassical spin-wave theory to study the $T=0$ physics of this effective model and argue that singular spin-wave fluctuations destabilize the spiral order favored by the exchange couplings of this effective Hamiltonian. We also use a combination of classical Monte-Carlo simulations and molecular dynamics, as well as analytical approximations, to study the physics at low, nonzero temperatures. The results of these nonzero temperature calculations capture the liquidlike structure factors observed in the temperature range accessed by recent experiments. Additionally, at still lower temperatures, they predict that a transition to nematic order in the bond energies reflects itself in the spin channel in the form of a crossover to a regime with large but finite correlation length for spiral spin correlations and a corresponding slowing down of spin dynamics.