Charge ordering and magnetic frustration in CsFe 2 F 6 .

The structural, electronic and magnetic properties of a charge-ordered iron fluoride material CsFe2+ Fe3+ F6 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 Fe2+ F6 and Fe3+ F6 octahedra. Our results confirm that CsFe2 F6 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 (Fe3+ -Fe3+ along the b axis, and Fe2+ -Fe2+ along the a axis), while interactions between the heterogeneous Fe ions (Fe3+ -Fe2+ 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 yz orbital (in the local coordinates) occupations between the Fe3+ and Fe2+ 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 yz orbital scenario in CsFe2 F6 .