Transformation between spin-Peierls and incommensurate fluctuating phases of Sc-doped TiOCl

Single crystals of ${\mathrm{Sc}}_x$${\mathrm{Ti}}_{1-x}\text{OCl}(x=0.005)$ have been grown by the vapor phase transport technique. Specific heat measurements prove the absence of phase transitions for 4–200 K. Instead, an excess entropy is observed over a range of temperatures that encompasses the incommensurate phase transition at 90 K and the spin-Peierls transition at 67 K of pure TiOCl. Temperature-dependent x-ray diffraction on ${\mathrm{Sc}}_x$${\mathrm{Ti}}_{1-x}$OCl gives broadened diffraction maxima at incommensurate positions between $T_{c1}=61.5\left(3\right)$ and $\sim 90$ K, and at commensurate positions below 61.5 K. These results are interpreted as due to the presence of an incommensurate phase without long-range order at intermediate temperatures, and of a highly disturbed commensurate phase without long-range order at low temperatures. The commensurate phase is attributed to a fluctuating spin-Peierls state on an orthorhombic lattice. The monoclinic symmetry and local structure of the fluctuations are equal to the symmetry and structure of the ordered spin-Peierls state of TiOCl. A novel feature of ${\mathrm{Sc}}_x$${\mathrm{Ti}}_{1-x}\text{OCl}(x=0.005)$ is a transformation from one fluctuating phase (the incommensurate phase at intermediate temperatures) to another fluctuating phase (the spin-Peierls-like phase). This transformation is not a phase transition occurring at a critical temperature, but it proceeds gradually over a temperature range of $\sim 10$ K wide. The destruction of long-range order requires much lower levels of doping in TiOCl than in other low-dimensional electronic crystals, like the canonical spin-Peierls compound ${\mathrm{CuGeO}}_3$. An explanation for the higher sensitivity to doping has not been found, but it is noticed that it may be the result of an increased two-dimensional character of the doped magnetic system. The observed fluctuating states with long correlation lengths are reminiscent of Kosterlitz–Thouless-type phases in two-dimensional systems.

Figure 1

Temperature dependence of the heat capacity $C_p$ plotted as $C_p/T$ of ${\mathrm{Sc}}_x$${\mathrm{Ti}}_{1-x}\text{OCl}(x=0.005)$ (red squares) and of TiOCl (black circles). The latter data are in agreement with Ref. [18].

Figure 2

Diffracted intensity as a function of the scattering angle $2\theta$ and the crystal orientation $\omega$ for several Bragg reflections at temperatures of 8 and 80 K. $\Delta 2\theta$ and $\Delta \omega$ indicate the deviation from the center of scan in units of $0.01$ deg.

Figure 3

Diffracted intensity versus the scattering angle $2\theta$ at $T=80$ K. Data points have been obtained by integration along $\omega$ in the $\omega$–$2\theta$ maps (see Fig. 2). The solid curves represent fits by pseudo-Voigt functions.

Figure 4

$q$ Scans along ${\mathbf{a}}^{*}$ centered at $\left(0-2.5-3\right)$ at selected temperatures as indicated. Solid curves represent pseudo-Voigt functions fitted to the data.

Figure 5

Temperature dependence of the incommensurate component $q_1$ of the modulation wave vector $\mathbf{q}$ = $(q_1,1/2,0)$, as determined from $q$ scans. The solid line represents a fit of Eq. (1) to the data, resulting in $q_1^0=0.026\left(2\right),T_{c1}=61.5\left(3\right)$ K, and $2\beta =0.32\left(3\right)$.

Figure 6

Temperature dependence of the full width at half maximum (FWHM) of the commensurate superlattice reflections and the main reflection $\left(1-1-8\right)$, as they have been derived from fits of Lorentzians to the $\omega$ scans centered at the indicated positions. Error bars are given. $\omega$ Scans of $\pm 0.5$ deg wide correspond to directions in reciprocal space of $\pm \left(0.0020-0.03350.0120\right)$ $\sim$ $\left(0-31\right)$ for reflection $\left(1-0.5-9\right)$; $\pm (-0.0275-0.00060.0034)$ $\sim$ $\left(-801\right)$ for $\left(0-1.5-1\right)$; and $\pm (-0.0154-0.00020.0018)$ $\sim$ $\left(-801\right)$ for $\left(0-2.5-3\right)$. The vertical dashed line indicates the critical temperature $T_{c1}=61.5$ K (see Fig. 5).

Figure 7

(a) Crystal structure of ${\mathrm{Sc}}_x$${\mathrm{Ti}}_{1-x}$OCl, and (b) modulation of one ribbon along $\mathbf{b}$. Arrows indicate displacements out of the basic structure with magnitudes 20$\times$ their true values.