Spin Singlet Formation in ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$: Evidence of a Helical Dimerization Pattern

The transition-metal spinel ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ undergoes a metal-insulator (M-I) transition on cooling below $T_{\mathrm{M}\mathrm{\text{−}}\mathrm{I}}=260\mathrm{K}$. A sharp reduction of the magnetic susceptibility below $T_{\mathrm{M}\mathrm{\text{−}}\mathrm{I}}$ suggests the onset of a magnetic singlet state. Using high-resolution synchrotron and neutron powder diffraction, we have solved the low-temperature crystal structure of ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$, which is found to contain dimers with short Ti-Ti distances (the locations of the spin singlets) alternating with long bonds to form helices. Band structure calculations based on hybrid exchange density functional theory show that, at low temperatures, ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ is an orbitally ordered band insulator.

Figure 1

Bottom: neutron and x-ray diffraction patterns of tetragonal ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ at 200 K. The pattern was collected using the GEM $154°$ bank. The top to bottom rows of ticks mark the positions of ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ and ${\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_3$ Bragg peaks, respectively. Right-hand side insets: portions of GEM patterns from the $63°$ and $154°$ banks showing ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ in the cubic state (top) and a refined tetragonal pattern. The down triangles mark reflections violating the body-centering condition. Left-hand side inset: the synchrotron x-ray diffraction pattern of ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ at the background level (the strongest line has an amplitude of 32 000 counts). The top to bottom rows of ticks mark the positions of ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$, ${\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_3$, and MgO Bragg peaks, respectively. The triangles mark the superlattice reflections; the circles mark an unidentified impurity. Top: The tetragonal lattice constants of ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ and Ti-Ti bond lengths as functions of temperature derived from medium-resolution (GEM) data. The solid lines are guides for the eye. The data were corrected using lattice parameters derived from the x-ray experiment.

Figure 2

The Ti-Ti bond structure in tetragonal ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ at 200 K. The red and purple bonds represent the shortest (dimerized) and the longest bonds in the ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$ structure, respectively. The dashed and solid blue bonds mark the intermediate $i_1=3.007(5)\mathrm{\AA }$ and $i_2=3.0147(3)\mathrm{\AA }$ Ti-Ti distances, respectively. A portion of the Ti tetrahedral connectivity is also shown. The inset shows a fragment of the spinel structure in the same orientation, visualized using cation-anion polyhedra. One of the “helices” is outlined in yellow.

Figure 3

Electronic DOS for the cubic (top) and the tetragonal (bottom) ${\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}}_2{\mathrm{O}}_4$. The contributions of Ti and O are indicated with different line styles (the Mg contribution to DOS is negligible in this energy range). The vertical line marks the Fermi energy.