High pressure enhanced magnetic ordering and magnetostructural coupling in the geometrically frustrated spinel Mn3O4

${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$ represents a model system for probing geometrically frustrated magnetism, and studying the magnetic behavior of the material under high pressure could yield new insights into the magnetostructural coupling and structurally driven magnetic ordering transitions that are otherwise not observable at ambient pressure. We report here a systematic study of the crystal and magnetic structures of ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$ at high pressure up to 37 and 20 GPa using x-ray and neutron powder diffraction techniques, respectively. We find that upon compression, the crystal structure transforms from the initial tetragonal hausmannite phase of $I{4}_{1}/amd$ symmetry into the orthorhombic ${\mathrm{CaMn}}_{2}{\mathrm{O}}_{4}$-type ($Pbcm$ symmetry) phase via the intermediate orthorhombic ${\mathrm{CaTi}}_{2}{\mathrm{O}}_{4}$-type ($Bbmm$ symmetry) phase. In the tetragonal phase, the application of pressure, $P>2$ GPa, leads to the suppression of low-temperature incommensurate and commensurate antiferromagnetic (AFM) orders with a propagation vector $k=(0,\ensuremath{\sim}0.5,0)$, and the expansion of the Yafet-Kittel-type ferrimagnetic phase, becoming the only ground state. As a result, the magnetic ordering temperature ${T}_{\mathrm{N}}$ increases rapidly, from \ensuremath{\sim}43 K at $P=0\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ to \ensuremath{\sim}100 K at $P=10\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. In the orthorhombic ${\mathrm{CaMn}}_{2}{\mathrm{O}}_{4}$-type phase, the AFM ordering on the sublattice of ${\mathrm{Mn}}^{3+}$ spins with a propagation vector $k=(1/2,0,0)$ occurs below ${T}_{\mathrm{N}}=275\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for $P=20\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. This value of ${T}_{\mathrm{N}}$ is about six times greater than that obtained at ambient pressure for the tetragonal phase, indicating a strong pressure enhancement of the magnetic ordering temperature in ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$. These experimental observations have been complemented by density functional theory calculations, which shed light on the underlying mechanisms of the structurally coupled magnetic phenomena in geometrically frustrated magnetic systems under high pressure.