Terahertz spectroscopy in the pseudo-Kagome system Cu${}_3$Bi(SeO${}_3$)${}_2$O${}_2$Br

Terahertz (THz) transmission spectra have been measured as a function of temperature and magnetic field on single crystals of Cu${}_3$Bi(SeO${}_3$)${}_2$O${}_2$Br. In time-domain THz spectra without magnetic field, two resonance absorptions are observed below the magnetic ordering temperature $T_N\sim 27.4$ K. The corresponding resonance frequencies increase with decreasing temperature and reach energies of 1.28 and 1.23 meV at 3.5 K. Multifrequency electron spin resonance transmission spectra as a function of the applied magnetic field show the field dependence of four magnetic resonance modes, which can be modeled as a ferromagnetic resonance including demagnetization and anisotropy effects.

Figure 1

(a) Electric-field transients as a function of time delay measured at 3.9 K and 295 K with ${\mathbf{E}}^{\omega }\perp c$. The 3.9 K curve is enlarged by a factor of 3 in order to distinguish from the 295 K curve. (b) Transmittance as a function of photon energy at 3.9 K and 295 K.

Figure 2

(a) Absorbance versus frequency measured at various temperatures below $T_N$ for ${\mathbf{E}}^{\omega }$ $\perp$ $c$. The downward arrow marks a resonance mode observed at 19 K. The upward arrows mark two distinct modes observed at 3.5 K, which are named as mode 1 and mode 2, respectively. The curves are shifted with respect to the 3.5 K curve by a constant value for clarity. (b) Dependence of resonance frequencies on temperature, which reach the energies of 1.23 and 1.28 meV at 3.5 K.

Figure 3

(a)–(c) Transmission electron spin resonance spectra measured at 2 K with frequencies of 325.5, 360, and 425 GHz, respectively. The external magnetic field $\mathbf{H}$ is applied along the $c$ axis and the radiation electric field ${\mathbf{E}}^{\omega }$ is perpendicular to the $c$ axis (Faraday configuration). The critical field is marked as ${\mu }_0{H}_c=0.86$ T. (d) Resonance frequencies versus resonance magnetic fields determined from various spectra. The solid line is a fit to Eq. (1) which determines a $g$ factor of 2.04(8) (see text). The two zero-field modes from time-domain spectroscopy are shown by open symbols.