  We present temperature-dependent x-ray diffraction and temperature- and
field-dependent Raman scattering studies of single crystal Mn3O4, which reveal
the novel magnetostructural phases that evolve in the spinels due to the
interplay between strong spin-orbital coupling, geometric frustration, and
applied magnetic field. We observe a structural transition from tetragonal to
monoclinic structures at the commensurate magnetic transition at T2=33K, show
that the onset and nature of this structural transition can be controlled with
an applied magnetic field, and find evidence for a field-tuned quantum phase
transition to a tetragonal incommensurate or spin glass phase.
