Fig. 6: Sublattice energetics.
From: Relativistic domain-wall dynamics in van der Waals antiferromagnet MnPS3
a Diagram of the energy versus the angle θ defined relative to the z-axis. Away from the domain wall, θ can be either 0o or 180o depending on what sublattice is considered. At the wall, θ can range within 0–180o for one sublattice, and 180–0o for the other. Bz points along of z < 0. Spins at the wall (0o < θ < 180o, which excludes fully spin-up and spin-down states) react differently than those away from the wall (i.e., θ = 0 for spin-up or theta = 180o for spin down) to an external magnetic field. Only for those at the wall, a finite Bz changes the energetic stability of the system inducing a rotation of the spins as the magnitude of θ changes to an additional energy minimum (e.g., \({\theta }_{{B}_{z} = 0}\ne {\theta }_{{B}_{z}\ne 0}\)). ΔE shows the energy gained through a rotation to the additional minimum once the field is applied. For the spins away from the wall, Bz causes a rigid shift of the energy curve while preserving its shape. This results in no change in the value of θ for the minimum energy, and thus, no rotation induced locally by the magnetic field. The energy is calculated via Eq. (8). b, c Plots of −ΔE for few atoms at different regions of the layer such as at the edges, near the edges and middle of the sheet for systems with ZZ-ZZ and ZZ-DB edges, respectively. The different sublattices (A and B) are shown individually in different colored curves. We plot −ΔE instead of ΔE to better display the variations of energy at different parts of the system. The inset in f shows a side view of the layer with the dimensions considered in the model.
