  The transition metal spinel MgTi$_2$O$_4$ undergoes a metal-insulator
transition on cooling below $T_{M-I} = 260$ K. A sharp reduction of the
magnetic susceptibility below $T_{M-I}$ 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
MgTi$_2$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, MgTi$_2$O$_4$ is an orbitally ordered band
insulator.
