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Anomalous magneto-optical Kerr hysteresis loops in Fe$_{0.25}$TaS$_{2}$

We have performed magneto-optical Kerr spectroscopy measurements on intercalated transition-metal dichalcogenide Fe$_{0.25}$TaS$_{2}$ in the polar Kerr geometry as a function of temperature, magnetic field, and wavelength. The Kerr angle exhibits pronounced peaks at $\sim$775 nm (1.6 eV) and $\sim$515 nm (2.4 eV), which we attribute to spin-dependent interband optical transitions arising from states in the vicinity of the Fermi energy. Below the ferromagnetic transition temperature (165 K), we observe strongly wavelength- and magnetic-field-dependent Kerr signal. At a fixed wavelength, the magnetic-field dependence of the Kerr angle shows a clear hysteresis loop, but its shape sensitively changes with the wavelength. We propose a model that takes into account contributions from domain walls, which allowed us to derive a mathematical expression that successfully fits all the observed hysteresis loops.