spin dynamics

Figure 1 (a),(e) Temperature dependences of the low frequency Raman spectra, (b),(f) temperature and (c),(d),(g),(h) magnetic field dependences of the imaginary part of the index of refraction from THz measurements for Ni₂CoTeO₆ (a-d) and NiCo₂TeO₆ (e-h). At least five spin excitations appear below T_N for both compounds, and the one at ~15 cm^-1 is simultaneously seen in the Raman spectra. The arrows in parts (a), (b), (e) and (f) indicate the temperature decrease from 300 to 5 K, whereas in (c), (d), (g) and (h), they show the increase of the external magnetic field from 0 to 7 T.

The temperature dependence of the imaginary part of the index of refraction in the THz range is shown in Figure 1(b) and (f) for Ni₂CoTeO₆ and NiCo₂TeO₆, respectively (ceramics of ∼1.9 mm thickness). The spectra were measured from 300 down to 5 K. All excitations sharpen and harden on cooling, with evident splitting for the broader ones.

At the lowest temperature of 5 K the THz spectrum of Ni₂CoTeO₆ displays five modes, whereas NiCo₂TeO₆ presents six of them. The rapid strengthening of these modes upon cooling below T_N suggests that they correspond to spin excitations. The 15 cm^-1 mode is simultaneously seen in the Raman spectra of both compounds. Ni₂CoTeO₆ and NiCo₂TeO₆ have a noncentrosymetric R3 crystal structure, so the phonons and magnons can be both IR and Raman active. Since the magnons were observed in the and Raman spectra (see Supplemental Material), they belong to the E symmetry. As the phonons near 210 - 220 cm^-1 reduce their oscillator strengths on cooling below T_N, they probably transfer their dielectric strengths to the strongest Raman-active magnons near 17 cm^-1 and therefore we assume that these excitations can be called electromagnons.