Magnetic neuroevolution potential puts spins into the energy surface, running two-million-atom spin-lattice dynamics on one consumer GPU

The new framework makes potential energy depend on atomic positions and magnetic moments together, so different magnetic orders at the same atomic arrangement no longer share one energy surface. A standard neuroevolution potential uses only atomic species and coordinates as inputs and cannot distinguish magnetic configurations of a given atomic structure, although those configurations differ in energy, atomic forces and virials. On CrN, Fe and FeGe, both models were trained on the same dataset for the same number of iterations; the standard model gives energy root-mean-square errors of 27.7, 47.0 and 10.3 meV/atom, which fall to 2.6, 6.3 and 2.0 meV/atom once magnetic descriptors are added.

Magnetic information enters the network input as five descriptor blocks, concatenated with structural descriptors and passed to species-dependent single-hidden-layer feedforward networks whose atomic energies are summed. The five channels are isotropic exchange, bond-dependent anisotropic exchange, chiral exchange, single-ion anisotropy and on-site moment magnitude, and the neighbor-dependent channels reuse the radial functions of the angular structural descriptors. Training uses spin-constrained density functional theory data, with a separable natural evolution strategy updating radial expansion coefficients and network parameters together; atomic forces, virials and magnetic energy gradients are all obtained analytically from the same energy function.

One model computes lattice vibrations, magnetic excitations and magnetic transitions within a single spin-lattice dynamics scheme. Conventional linear spin-wave theory works on a fixed lattice near a prescribed equilibrium magnetic configuration and does not produce finite-temperature line broadening. The magnetic spectral energy density peaks of Fe at 50 K broadly follow the linear spin-wave dispersion, broadening becomes pronounced at 300 K, and the dispersion branches of FeGe are less clearly resolved at 200 K.

The demonstrated scope is CrN, Fe and FeGe, covering collinear and noncollinear magnetic configurations; performance benchmarks run on a single consumer-grade GPU with a 0.2 fs time step, from systems of 8 atoms up to more than two million atoms. Subsequent FeGe calculations are performed in the ferromagnetic state, although structural optimization in the helical state also gives a folded lattice constant in agreement with experiment.

Discrepancies remain between the calculated FeGe phonon spectrum and the experimental reference, which consists of characteristic Raman peaks used for phase identification rather than a complete dispersion along high-symmetry paths, and the measurement temperature and corresponding magnetic state are not explicitly specified. The effect of spin-lattice coupling on the magnetic transition temperature is system dependent: in Fe the coupling brings the transition temperature closer to experiment and improves convergence with system size, whereas the two schemes differ little for FeGe. In the magnetic spectral analysis, a larger intrinsic linewidth corresponds to a shorter magnon lifetime only after numerical resolution and other broadening mechanisms are excluded.