  We present x-ray, neutron scattering and heat capacity data that reveal a
coupled first-order magnetic and structural phase transition of the metastable
mixed-valence post-spinel compound Mn$_3$O$_4$ at 210 K. Powder neutron
diffraction measurements reveal a magnetic structure in which Mn$^{3+}$ spins
align antiferromagnetically along the edge-sharing \emph{a}-axis, with a
magnetic propagation vector k = [1/2, 0, 0]. In contrast, the Mn$^{2+}$ spins,
which are geometrically frustrated, do not order until a much lower
temperature. Although the Mn$^{2+}$ spins do not directly participate in the
magnetic phase transition at 210 K, structural refinements reveal a large
atomic shift at this phase transition, corresponding to a physical motion of
approximately 0.25 {\AA} even though the crystal symmetry remains unchanged.
This "giant" response is due to the coupled effect of built-in strain in the
metastable post-spinel structure with the orbital realignment of the Mn$^{3+}$
ion.
