First-principles study on the orbital ordering of KCrF3

Abstract

The electronic, magnetic, and orbital structures of KCrF${}_{3}$ in its recently identified crystallographic phases (tetragonal and cubic) [S. Margadonna and G. Karotsis, J. Am. Chem. Soc. 128, 16436 (2006)] are studied by the first-principles method. In the tetragonal phase, both the generalized gradient approximation (GGA) and the generalized gradient approximation plus Hubbard parameter $U$ (GGA $+$ $U$) calculations show that the ground state is the $A$-type antiferromagnetic ($A$-AFM) configuration with $G$-type orbital ordering pattern. Our calculations show that the orbital structures and the magnetic configurations can be measured by the optical conductivity. In the cubic state, the GGA calculations show that the ground state is a ferromagnetic half-metal state, while the GGA $+$ $U$ (${U}_{\text{eff}}=3.0$ eV) calculations show that the $A$-AFM insulator phase is the ground state. Our calculations indicate that the electron-electron interactions rather than the electron-phonon interactions are the driving forces behind the orbital ordering.