Three-temperature atomistic spin-lattice dynamics in LAMMPS: a moment-consistent, fluctuation-dissipation-correct extension and its validation on ultrafast demagnetization and all-optical switching of GdFeCo

Abstract: Atomistic spin dynamics (ASD) codes like VAMPIRE simulate femtosecond-laser-induced ultrafast demagnetization and all-optical switching (AOS) on a rigid lattice; the SPIN package of the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) instead propagates spins and lattice together, but until now could couple its spin thermostat only to a single global temperature, precluding three-temperature (3TM) simulations. We present a validated 3TM extension with two new fixes: langevin/spin/ttm, coupling the stochastic spin bath to the local electron-temperature field of fix ttm; and moment/scale/spin, supplying the per-atom moment-dependent ($1/μ_i$) prefactor required for heterogeneous-moment systems, with deterministic terms scaling as $1/μ_i$ and, as required by the fluctuation-dissipation theorem, stochastic noise scaling as $1/\sqrt{μ_i}$. We validate the framework on single-species benchmarks-precession, the bcc-Fe Curie curve, a continuous demagnetization-remagnetization-precession trajectory, and a lattice-strain acoustic-phonon pulse unavailable to spin-only ASD codes-then on heat-induced AOS of GdFeCo with literature parameters (Radu/Ostler exchange constants, moments, and damping). The corrected integrator reproduces the experimentally reported transient ferromagnetic-like sublattice alignment, field-insensitive thermal switching, a switching probability approaching unity across a genuine 8x8 literature damping phase diagram, a non-monotonic critical-cooling-duration boundary that disappears above $T_e⁰ \approx 2000 \text{ K}$, a composition-dependent switching window centered on angular-momentum compensation, and convergence in system size with monotonic, physical damping dependence. These results establish LAMMPS as a quantitatively validated platform for three-temperature spin-lattice simulations of ultrafast magnetism.