Abstract: Single-molecule magnets (SMMs) have attracted considerable attention as promising candidates for next-generation spintronic devices. Their magnetic bi-stability, however, is limited by spinlattice relaxation, a process in which molecular spins dissipate energy to lattice phonons. Since the relaxation dynamics are dictated by the spin’s chemical environment, establishing a direct theoretical connection between molecular structure and relaxation behavior is essential for rational molecular design, despite the inherent complexity of the underlying mechanisms. Here, we explore the mechanism of the Orbach process by reducing the master equation with uniformization method, revealing how the static effective Hamiltonian governs the relaxation energy barrier. To alleviate the heavy cost of calculating thousands of non-equilibrium structures, we propose a new approach that introduces a spin-phonon coupling parameters drawn from a Lorentz distribution. The validity of this simplified protocol is confirmed using seven representative lanthanide SMMs. This work not only deepens the fundamental understanding of Orbach relaxation but also provides an efficient framework for quickly simulating the relaxation behavior of SMMs, thereby facilitating faster targeted molecular design.

Key words: Single-molecule magnets, Spin-phonon coupling, Relaxation time, Master equation, Ab initio calculation