  We analyze electronic, magnetic, and structural properties of the spinel
compound MgTi$_2$O$_4$ using the local density approximation+U method. We show
how MgTi$_2$O$_4$ 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
stabilize 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 MgTi$_2$O$_4$, and might be applicable to
frustrated materials in general.
