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Understanding the coupling between spin and phonons is critical forcontrolling the lattice thermal conductivity ($\kappa_l$) in magneticmaterials, as we demonstrate here for CrX$_3$ (X = Br and I) monolayers. Weshow that these compounds exhibit large spin-phonon coupling (SPC), dominatedby out-of-plane vibrations of Cr atoms, resulting in significantly differentphonon dispersions in ferromagnetic (FM) and paramagnetic (PM) phases. Latticethermal conductivity calculations provide additional evidence for strong SPC,where particularly large $\kappa_l$ is found for the FM phase. Most strikingly,PM and FM phases exhibit radically different behavior with tensile strain,where $\kappa_l$ increases with strain for the PM phase, and strongly decreasesfor the FM phase -- as we explain through analysis of phonon lifetimes andscattering rates. Taken all together, we uncover the very high significance ofSPC on the phonon transport in CrX$_3$ monolayers, a result extendable to other2D magnetic materials, that will be useful in further design of thermal spindevices.

Pivotal role of magnetic ordering and strain in lattice thermal conductivity of chromium-trihalide monolayers