Structural change and phase coexistence upon magnetic ordering in the magnetodielectric spinel Mn${}_3$O${}_4$

Cooperative Jahn-Teller ordering is well-known to drive the cubic $Fd\bar{3}m$ to tetragonal $I$4${}_1$/$amd$ structural distortion in Mn${}_3$O${}_4$ at 1170 ${}^{\circ }$C. Further structural distortion occurs in Mn${}_3$O${}_4$ upon magnetic ordering at 42 K. Employing high-resolution variable-temperature synchrotron x-ray diffraction we show that tetragonal $I$4${}_1$/$amd$ and orthorhombic $Fddd$ phases coexist, with nearly equal fractions, below the N'eel temperature of Mn${}_3$O${}_4$. Significant variation of the orthorhombic $a$ and $b$ lattice constants from the tetragonal $a$ lattice constant is observed. Structural phase coexistence in Mn${}_3$O${}_4$ is attributed to large strains due to the lattice mismatch between the tetragonal $I$4${}_1$/$amd$ and the orthorhombic $Fddd$ phases. Strain tensors determined from Rietveld refinement show a highly strained matrix of the $I{4}_1\mathrm{/}amd$ phase that accommodates the nucleated orthorhombic $Fddd$ phase in the phase coexistence regime. A comparison of the deformation observed in Mn${}_3$O${}_4$ to structural deformations of other magnetic spinels shows that phase coexistence may be a common theme when structural distortions occur below 50 K.