Giant phonon softening in the pseudogap phase of the quantum spin system $\mathrm{TiOCl}$

Giant anomalies are found in the temperature dependence of Raman-active phonons in the quantum magnet $\mathrm{TiOCl}$, suggesting the presence of an extended fluctuation regime. This regime coincides with a pseudogap phase identified in earlier NMR experiments. The observed large, local spin-gap is proposed to origin from coupled spin∕lattice fluctuations. Below $100\mathrm{K}$, in the long-range crystallographically distorted phase, a dimerized ground state with a smaller, global spin-gap of about $2{\Delta }_{spin}\approx 430\mathrm{K}$ exists. This transition also marks a dimensionality cross-over of the system.

Figure 1

Real part ${\sigma }_1\left(\omega \right)$ of the optical conductivity (absorption spectrum) of $\mathrm{TiOCl}$ as a function of temperature along the $b$-axis and the $a$-axis. The inset (a) shows ${\sigma }_1\left(\omega \right)$ up to the ultraviolet at $300\mathrm{K}$. The inset (b) displays the temperature dependence of the width $\left(\Gamma \right)$ of the phonon modes at 294 and $438{\mathrm{cm}}^{-1}$, respectively.

Figure 2

(Color online) Raman scattering intensity as a function of temperature in $\left(bb\right)$ polarization and with an offset for clarity. A dashed line extrapolates the scattering at high energies to lower energies $\left(T=5\mathrm{K}\right)$ to emphasize a spectral depletion for energies below $\approx 300{\mathrm{cm}}^{-1}$. The lower inset compares $\left(bb\right)$ and $\left(aa\right)$ polarization at $T=300\mathrm{K}$ with the intensity reduced by a factor $1∕3$. Four important modes are denoted by $\alpha$ to $\delta$. The upper inset shows mode energies on heating the sample. The arrows mark $T_{c1}$, $T_{c2}$, and $T^{*}$. Modes connected by dashed lines have a smaller intensity.

Figure 3

(Color online) High energy Raman scattering intensity in $\left(bb\right)$ polarization and an offset for clarity. The inset shows a ${\mathrm{Ti}}^{3+}$-displacement corresponding to the $\alpha$-phonon mode. The $d_{xy}$ orbitals with direct overlap form a chain, while dashed lines represent $d_{xz}$ and $d_{yz}$ orbitals.