Crucial role of magnetic dipole and anomalous field dependence in $\mathrm{NiP}{\mathrm{S}}_3$

Abstract

$\mathrm{NiP}{\mathrm{S}}_3$ has attracted considerable attention, yet the origin of its intriguing magnetic behaviors remains elusive due to limited insight into its low-energy anisotropy. Here, high-field torque magnetometry measurements are performed, revealing a previously unrecognized anisotropic spin response that reflects interaction terms beyond the standard XY or XXZ models. In combination with relativistic density functional theory calculations and magnetic force response theory, an effective low-energy spin Hamiltonian is constructed, elucidating not only the observed anomalous magnetic behavior but also other recent experiments. Remarkably, the magnetic dipole interaction and the associated spin-flop transition play a crucial role in driving the deviation from two-dimensional spin alignment, providing direct insight into the underlying anisotropic energy hierarchy. The generalized Hamiltonian can serve as the important fundamental ground for future study, and our approach adopted here will hopefully be relevant to many other related material systems.

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