Heat capacity of the quantum magnet TiOCl

Measurements of the heat capacity $C(T,H)$ of the one-dimensional quantum magnet TiOCl are presented for temperatures $2\mathrm{K}<T<300\mathrm{K}$ and magnetic fields up to 5 T. Distinct anomalies at 91 and 67 K signal two subsequent phase transitions. The lower of these transitions clearly is of first order and seems to be related to the spin degrees of freedom and the lattice. The transition at 91 K is of second order. A detailed analysis of the data reveals that the entropy change $\Delta S$ through both transitions is surprisingly small $(\sim 0.1\mathrm{R})$, pointing towards the existence of strong fluctuations well into the nonordered high-temperature phase.

Figure 1

(Color online) Heat capacity of TiOCl vs temperature. The vertical bars indicate experimental uncertainties and reveal the scatter of $C\left(T\right)$ in different measuring cycles with different temperature stimuli and using different samples. Upper inset: Magnified region of the two phase transitions. The heat capacity measured at 5 T (stars) is compared to the heat capacity in zero external field (circles), both measured on cooling: No significant difference between both curves can be detected. The temperature region around the lower transition at $T_{c1}\approx 66.7\mathrm{K}$ was remeasured (triangles) utilizing a reduced relaxation amplitude of $\delta T\approx 0.5\mathrm{K}$ on heating and subsequent cooling. For clarity these data are shifted by $50\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^2$. Lower inset: Low-temperature heat capacity plotted as $C∕T\text{vs}{T}^2$. For the results in zero magnetic field a fit using a Debye-derived phonon contribution is indicated as a solid line.

Figure 2

(Color online) Heat capacity of TiOCl plotted as $C∕T\text{vs}T$. The $S=1∕2$ contribution including a mean-field spin-Peierls transition as described in the text is indicated as a dash-dotted line. For representation purposes the calculated values have been multiplied by a factor of 3. The fit to the phonon-derived specific heat (see text) is indicated as a dashed line. The sum of both contributions is drawn as a solid line and represents the best fit to the experimental results. The inset shows the difference between calculated and measured heat capacities in a limited temperature regime.