Magnetic permeability and zone-folded phonons in layered NiPS$_3$
Nickel phosphorus trisulfide (NiPS$_3$) stands out as a Mott insulator exhibiting XY-type antiferromagnetic order. In this work, we investigate the electrodynamic response of single-crystalline NiPS$_3$ using Terahertz Time-Domain Spectroscopy (THz-TDS) as a function of temperature. In cases where the magnetic permeability cannot be approximated to unity, conventional THz transmission analysis is often restricted to the complex refractive index, hindering the distinction between magnetic and dielectric contributions. To overcome this limitation, we demonstrate an extraction methodology capable of decoupling the magnetic permeability from the electric permittivity. Assuming that the dielectric contribution remains invariant below the N'eel temperature (TN), we used data from the paramagnetic phase to isolate the intrinsic magnetic component at 13 K. The angular and thermal dependence of the spectra revealed a magnon mode near 1 THz (for 0$^\circ$ orientation) and, distinctively, a zone-folded phonon activated by symmetry breaking (at 90$^\circ$). The isolated magnetic permeability was successfully modeled using Drude-Lorentz oscillators, enabling the extraction of fundamental spin dynamics parameters in this material.