Two-orbital degeneracy lifted local precursor to a metal-insulator transition in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>MgTi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>
Long Yang, Robert J. Koch, Hong Zheng, J. F. Mitchell, Wei‐Guo Yin, Matthew G. Tucker, Simon J. L. Billinge, Emil S. Božin
Abstract
The ${\mathrm{MgTi}}_{2}{\mathrm{O}}_{4}$ spinel exhibits a metal-insulator transition on cooling below ${T}_{s}\ensuremath{\approx}250$ K, accompanied by Ti ${t}_{2g}^{1}$ orbital ordering and spin-singlet dimerization with associated average symmetry reduction to tetragonal. By combining x-ray and neutron pair distribution function analyses to track the evolution of the local atomic structure across the transition we find that local tetragonality already exists in the metallic globally cubic phase at high temperature. Local distortions are observed up to at least 500 K, the highest temperature assessed in this study. Significantly, the high-temperature local state is not continuously connected to the orbitally ordered band insulator ground state and so the transition cannot be characterized as a trivial order-disorder type. The shortest Ti-Ti spin-singlet dimer bond lengths expand abruptly on warming across the transition, but remain shorter than those seen in the cubic average structure. These seemingly contradictory observations can be understood within the model of a local fluctuating two-orbital ${t}_{2g}$ orbital degeneracy lifted (ODL) precursor state derived from electron filling, Ti substructure topology, and point symmetry considerations. The ODL state in ${\mathrm{MgTi}}_{2}{\mathrm{O}}_{4}$ has a correlation length of about 1 nm at high temperature. We discuss that this extended character of the local distortions is consistent with the two-orbital nature of this state imposed by the charge filling and the bond charge repulsion. The ${\mathrm{MgTi}}_{2}{\mathrm{O}}_{4}$ spinel exemplifies multiorbital ODL state and presents the possibility of a widespread presence of such precursor states in scarcely studied high-temperature regimes of transition-metal-based quantum materials.