Crystal and magnetic structures of the three-dimensional spin-Peierls state of ZnCr2O4

The geometrically frustrated spinel ZnCr$_2$O$_4$ undergoes a three-dimensional spin-Peierls phase transition at T$_N$ = 12.5 K from a cubic paramagnetic state to a tetragonal Neel state. The exact nature of the lattice distortion, and the one-to-one-correspondence between the distortion and the magnetic ground state has been a long standing issue. To unveil the mystery, we have performed synchrotron X-ray diffraction measurements on a single crystal of this compound and neutron diffraction measurements on a powder sample. Our detailed analysis of the single crystal X-ray data shows that below T$_N$ the symmetry of the crystal structure is lowered from the cubic $Fd\bar3m$ to the tetragonal $I\bar4m2$ due to formation of a complex pattern of Cr-Cr clustering. The relation between the distorted crystal structure and the magnetic structure will also be discussed.