Infrared optical properties of the spin-$\frac{1}{2}$ quantum magnet TiOCl

We report results on the electrodynamic response of TiOCl, a low-dimensional spin-$\frac{1}{2}$ quantum magnet that shows a spin gap formation for $T<\mathrm{}{T}_{c1\mathrm{}}=67\mathrm{}\mathrm{K}.$ The Fano-like shape of a few selected infrared active phonons suggests an interaction between lattice vibrations and a continuum of low-frequency (spin) excitations. The temperature dependence of the phonon mode parameters extends over a broad temperature range well above $T_{c1\mathrm{}},$ indicating the presence of an extended fluctuation regime. In the temperature interval between 200 K and $T_{c1\mathrm{}},$ there is a progressive dimensionality crossover (from two to one), as well as a spectral weight shift from low towards high frequencies. This allows us to identify a characteristic energy scale of about 430 K, ascribed to a pseudo-spin-gap.