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 a 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.

Figure 1

Strongly anisotropic magnetization vs magnetic field ($H$) for the Fe${}_{0.25}$TaS${}_2$ sample at 135 K measured with $H\parallel c$ axis (red squares) and $H\parallel ab$ plane (black circles). The magnetic moment is negligible in the $ab$ plane, indicating that the easy axis is parallel to the $c$ axis.

Figure 2

MOKE spectra at (a) 170 K, (b) 165 K, (c) 100 K, and (d) 10 K in a magnetic field of $\pm 1980$ Oe. Temperature dependence of field-cooled (e) MOKE signal at 510 nm and (f) MOKE spectra in a field of $+1980$ Oe from 300 to 10 K.

Figure 3

MOKE hysteresis loops measured at various wavelengths at a constant temperature of 135 K. The shape of the hysteresis loop changes drastically with wavelength. Solids curves are fits to the data, using Eq. (2), as discussed in detail in the text.

Figure 4

(a) Contour plot of the measured Kerr angle as a function of magnetic field and wavelength for Fe${}_{1/4}$TaS${}_2$ at 135 K. Magnetic field was swept from $+1920$ to $-1920$ Oe, and back to $+1920$ Oe, completing a full cycle. (b) Data for a reference Ga${}_{0.976}$Mn${}_{0.024}$As sample showing standard hysteresis curves with no anomalies.

Figure 5

The difference in JDOS between the spin-up and spin-down bands calculated for Fe${}_{0.25}$TaS${}_2$ (left axis), together with the experimentally measured MOKE spectrum at 140 K in an external magnetic field of 1980 Oe (right axis).

Figure 6

Spectral dependence of the fitting parameters used in Eq. (2) to fit the MOKE hysteresis loops in Fig. 3. Green circles and black triangles represent the down-sweep and up-sweep, respectively.