Fourth-order quantum master equations reveal that spin-phonon decoherence undercuts long magnetization relaxation times in single-molecule magnets

Abstract: Spin-phonon interaction is known to drive magnetic relaxation in solid-state systems, but little evidence is available on how it affects coherence time. Here we extend fourth-order quantum master equations to account for coherence terms and describe the full effect of up to two-phonon processes on spin dynamics. We numerically implement this method fully ab initio for a single-molecule magnet with large magnetization blocking temperature and show that while strong axial magnetic anisotropy ensures slow magnetic relaxation approaching seconds at 77 K, the superposition of Kramers doublets is coherent for less than 10 ns due to a novel two-phonon pure dephasing mechanism.