Optical evidence for a magnetically driven structural transition in the spin web Cu$_3$TeO$_6$

Cu$_3$TeO$_6$ is a modest frustrated $S=1/2$ spin system, which undergoes an anti-ferromagnetic transition at $T_N\sim61$ $K$. The anti-ferromagnetic spin alignment in Cu$_3$TeO$_6$ below $T_N$ is supposed to induce a magneto-elastic strain of the lattice. The complete absorption spectrum of Cu$_3$TeO$_6$ is obtained through Kramers-Kronig transformation of the optical reflectivity, measured from the far-infrared up to the ultraviolet spectral range as a function of temperature ($T$). Below $T^*\sim 50$ $K$, we find a new mode at 208 $cm^{-1}$. The spectral weight associated to this additional mode increases as $\propto (T^*- T)^{1/2}$ with decreasing $T$ below $T^*$. The implication of the optical findings will be discussed in relation to the magnetic phase transition at $T_N$.