Charge ordering and magnetic frustration in CsFeF.

The structural, electronic and magnetic properties of a charge-ordered iron fluoride material CsFeFeF have been explored by density functional theory calculations based on the generalized gradient approximation  +  U approach, which was implemented in the VASP code. The material exhibits a 3D pyrochlore-related structure which consists of corner-shared FeF and FeF octahedra. Our results confirm that CsFeF is a Mott-Hubbard insulator, and bears a magnetically frustrated ground state in which the localized 3d electrons are antiferromagnetically coupled between the homogeneous Fe ions (Fe-Fe along the b axis, and Fe-Fe along the a axis), while interactions between the heterogeneous Fe ions (Fe-Fe along the c axis) are frustrated, consistent with Goodenough-Kanamori superexchange interactions. Although the disproportionation of the total 3d charge is extremely low, explicit evidence is provided on the charge ordering by an order parameter, which is defined as the difference in minority d orbital (in the local coordinates) occupations between the Fe and Fe cations. In addition, spin ordering and the spin-orbit coupling effect play an insignificant role in the charge ordering and the preferential occupation of the d orbital scenario in CsFeF.