Thermal spin dynamics of Kitaev magnets: Scattering continua and magnetic field induced phases within a stochastic semiclassical approach

The honeycomb magnet RuCl3 is a prime candidate material for realizing the Kitaev quantum spin liquid (QSL), but it shows long-range magnetic order at low temperature. Nevertheless, its broad inelastic neutron scattering (INS) response at finite frequency has been interpreted as that of a "proximate QSL."A moderate in-plane magnetic field indeed melts the residual zigzag order, giving rise to peculiar intermediate-field phases before the high-field polarized state. In INS measurements the low-frequency spin waves disappear, leading to a broad scattering continuum in the field-induced intermediate regime, whose nature is currently under debate. Here, we study the magnetic-field-dependent spin dynamics of the K model within a stochastic semiclassical treatment, which incorporates the effect of finite-temperature fluctuations. At temperatures relevant for INS experiments, we show how the excitations of the zigzag phase broaden and that the different intermediate phases all show a similar continuum response. We discuss the implications of our results for experiments and highlight the importance of distinguishing finite-temperature fluctuations from genuine quantum fractionalization signatures in frustrated magnets.