Evidence for magnon-phonon coupling in the topological magnet ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$

We perform thermodynamic and inelastic neutron scattering (INS) measurements to study the lattice dynamics (phonons) of a cubic collinear antiferromagnet ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$ which hosts topological spin excitations (magnons). While the specific heat and thermal conductivity results show that the thermal transport is dominated by phonons, the deviation of the thermal conductivity from a pure phononic model indicates that there is a strong coupling between magnons and phonons. In the INS measurements, we find a mode in the excitation spectra at 4.5 K, which exhibits a slight downward dispersion around the Brillouin zone center. This mode disappears above the Néel temperature and thus cannot be a phonon. Furthermore, the dispersion is distinct from that of a magnon. Instead, it can be explained by the magnon-polaron mode, collective excitations resulting from the hybridization between magnons and phonons. We consider the suppression of the thermal conductivity and emergence of the magnon-polaron mode to be evidence for magnon-phonon coupling in ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$.

Figure 1

(a) Temperature dependence of the specific heat for ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$. The inset is the low-temperature specific heat plotted as $C_{\mathrm{p}}/T$ vs $T^2$. The solid line is a linear fit. (b) Thermal conductivity measured along one of the three principal crystallographic axes. The inset is the measured data plotted in logarithmic scale. Curves represent different fits as described in the main text.

Figure 2

(a), (b) Constant-energy contours around (8, 0, 0) measure at 4.5 and 100 K, respectively, both with energies integrated over [6.5, 8.5] meV and another wave vector $K$ integrated over [$-0.2$, 0.2] rlu. (c), (d) Scans through (8, 0, 0) along the [100] and [001] directions, respectively, with an interval of $\pm 0.2$ rlu about the center, as indicated by the dashed rectangles in (a) and (b). Solid lines in (c) and (d) are the fits to the data with Lorentzian functions. Errors represent one standard deviation throughout the paper.

Figure 3

(a), (b) INS results for the excitation spectra of ${\mathrm{Cu}}_3{\mathrm{TeO}}_6$ measured at 4.5, 100 K, respectively. The left and right panels are the excitations propagating along the [100] and [001] directions, respectively. The integration intervals of the other two wave vectors are both chosen as $\pm 0.2$ rlu. The dashed lines are the results of the linear spin-wave calculations, based on the isotropic $J_1\text{−}{J}_9$ model described in Ref. [57]. Solid lines are guides to the eye to illustrate the slight downward dispersion of the additional mode and arrows indicate the positions of the mode. Vertical dashed lines indicate high-symmetry points in the Brillouin zone.

Figure 4

(a) and (b) Constant-$\mathit{Q}$ cuts at (8, 0, 2) at 4.5 and 100 K, respectively. The integration intervals for $H$, $K$, and $L$ are all $\pm 0.2$ rlu. Solid lines are the fits with Lorentzian functions, and the arrow indicates the position of the magnon-polaron mode.