Orbital-spin order and the origin of structural distortion in MgTi₂O₄

We analyze electronic, magnetic, and structural properties of the spinel compound MgTi₂O₄ using the local-density approximation+U method. We show how MgTi₂O₄ undergoes to a canted orbital-spin ordered state, where charge, spin, and orbital degrees of freedom are frozen in a geometrically frustrated network by electron interactions. In our picture orbital order stabilizes the magnetic ground state and controls the degree of structural distortions. The latter is dynamically derived from the cubic structure in the correlated LDA+U potential. Our ground-state theory provides a consistent picture for the dimerized phase of MgTi₂O₄, and might be applicable to frustrated materials in general.