Polyhedral distortions and unusual magnetic order in spinel FeMn$_{2}$O$_{4}$

Spinel compounds AB$_{2}$X$_{4}$ consist of both tetrahedral (AX$_{4}$) and octahedral (BX$_{6}$) environments with the former forming a diamond lattice and the latter a geometrically frustrated pyrochlore lattice. Exploring the fascinating properties and their correlations with structural features is critical in understanding these materials. FeMn$_{2}$O$_{4}$ has been reported to exhibit one structural transition and two successive magnetic transitions. Here, we report the polyhedral distortions and their correlations to the structural and two magnetic transitions in FeMn$_{2}$O$_{4}$ by employing the high-resolution neutron powder diffraction. While a large trigonal distortion is found even in the high-temperature cubic phase, the first-order cubic-tetragonal structural transition associated with the elongation of both tetrahedra and octahedra along the $c$ axis occurs at $T_{S} \approx$ 750 K, driven by the Jahn-Teller effect of the orbital active B-site Mn$^{3+}$ cation. A strong magnetoelastic coupling is unveiled at $T_{N1}\approx 400$ K as manifested by the appearance of N\`{e}el-type collinear ferrimagnetic order, an anomaly in both tetrahedral and octahedral distortions, as well as an anomalous decrease of the lattice constant $c$ and a weak anomaly of $a$. Upon cooling below $T_{N2}\approx65$ K, it evolves to a noncollinear ferrimagnetic order with a canting of half B-site $Mn^{3+}$/$Fe^{3+}$ spins in the pyrochlore lattice, which is a unique magnetic order among spinels. Such a noncollinear order induces modifications of the O-B-O bond angles in the octahedra without affecting much the bond lengths of the tetrahedra/octahedra. Our study indicates that FeMn$_{2}$O$_{4}$ is a wonderful platform to unveil interesting magnetic order and to investigate their correlations to polyhedral distortions and lattice.