Symmetry disquisition on the $\mathrm{Ti}\mathrm{O}X$ phase diagram $(X=\mathrm{Br},\mathrm{Cl})$

The sequence of phase transitions and the symmetry of, in particular, the low temperature incommensurate and spin-Peierls phases of the quasi-one-dimensional inorganic spin-Peierls system $\mathrm{Ti}\mathrm{O}X$ ($X=\mathrm{Br}$ and Cl) have been studied using inelastic light scattering experiments. The anomalous first-order character of the transition to the spin-Peierls phase is found to be a consequence of the different symmetries of the incommensurate and spin-Peierls $(P{2}_1∕m)$ phases. The pressure dependence of the lowest transition temperature strongly suggests that magnetic interchain interactions play an important role in the formation of the spin-Peierls and the incommensurate phases. Finally, a comparison of Raman data on VOCl to the $\mathrm{Ti}\mathrm{O}X$ spectra shows that the high energy scattering previously observed has a phononic origin.

Figure 1

(Color online) Polarized Raman spectra $\left(A_g\right)$ of TiOCl and TiOBr in the high temperature phase, showing the three $A_g$ modes. Left panel: $\left(bb\right)$ polarization; right panel: $\left(aa\right)$ polarization.

Figure 2

(Color online) Polarization analysis of the Raman spectra in the three phases of TiOBr, taken at (a) 3, (b) 30, and (c) $100\mathrm{K}$. The spectra of TiOCl show the same main features and closely resemble those of TiOBr. Table reports the frequencies of the TiOCl modes. The inset shows the TiOBr spectrum in the $x(c\ast )\overline{x}$ polarization (see text).

Figure 3

(Color online) Comparison of the possible low temperature symmetries. The low temperature structures reported are discussed, considering a dimerization of the unit cell due to Ti-Ti coupling and assuming a reduction of the crystal symmetry. The red rectangle denotes the unit cell of the orthorhombic HT structure. Structure (a) is monoclinic with its unique axis parallel to the orthorhombic $c$ axis (space group $P2∕c$), (b) shows the suggested monoclinic structure for the SP phase $(P{2}_1∕m)$, and (c) depicts the alternative orthorhombic symmetry proposed for the low $T$ phase $Pmm2$.

Figure 4

(Color online) The temperature dependence of the Raman spectrum of TiOBr is depicted (an offset is added for clarity). The three modes present at all temperatures are denoted by the label $R_T$. The modes characteristic of the low temperature phase (disappearing at $T_{c1}=28\mathrm{K}$) are labeled $L_T$, and the anomalous modes observed in both the low temperature and the intermediate phase are labeled $I_T$. The right panel (b) shows the behavior of the frequency of $I_T$ modes, plotted renormalized to their frequency at $45\mathrm{K}$. It is clear that the low-frequency modes shift to higher energy while the high-frequency modes shift to lower frequency.

Figure 5

(Color online) The average crystal symmetry of the intermediate phase is proposed to be monoclinic with the unique axis parallel to the $c$ axis of the orthorhombic phase. Hence, the low temperature space group is not a subgroup of the intermediate phase, and the transition to the spin-Peierls phase is consequently of first order.

Figure 6

(Color online) (a) Magnetization as a function of temperature measured with fields of 1 and $5\mathrm{T}$ (the magnetization measured at $1\mathrm{T}$ is multiplied by a factor of 5 to evidence the linearity). The inset shows the main magnetic interactions (see text). (b) Pressure dependence of $T_{c1}$. The transition temperature for transition to the spin-Peierls phase increases with increasing pressure. The inset shows the magnetization versus the temperature after subtracting the background signal coming from the pressure cell.

Figure 7

(Color online) Raman scattering features of VOCl. (a) High energy scattering of $\mathrm{Ti}\mathrm{O}\mathrm{Cl}∕\mathrm{Br}$ and VOCl, and (b) temperature dependence of the vibrational scattering features of VOCl. No symmetry changes are observed at $T_N=80\mathrm{K}$.

Figure 8

(Color online) Sketch of the bilayer structure (b) and of the interactions introduced in the spring-model calculation (a).