Spin, charge, and orbital ordering inRBaMn2O5+δ(R=Y, La;0⩽δ⩽1) and their dependence on oxygen content and size of theRconstituent

Abstract

The effect of oxygen content on spin, charge, and orbital ordering in $R\mathrm{Ba}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5+\ensuremath{\delta}}$ ($R=\mathrm{Y}$, La; $0\ensuremath{\leqslant}\ensuremath{\delta}\ensuremath{\leqslant}1$) is studied by density-functional-theory-based calculations as implemented in the full-potential linearized-augmented plane-wave method. Structural optimizations using the projector augmented wave method have been performed for all the phases and the calculated structural parameters are found to be in good agreement with experimental values. Total-energy calculations have systematically been performed including force as well as stress minimization for paramagnetic, ferromagnetic, and antiferromagnetic configurations. For $\ensuremath{\delta}=0$, the ground state is found to be ferrimagnetic, whereas the variants with oxygen contents $\ensuremath{\delta}=1∕2$ and 1 give rise to an antiferromagnetic ground state, all in perfect agreement with experimental findings. The electronic-band characteristics are analyzed using total and site- and orbital-projected densities of states and the examination shows that the electronic structure undergoes a gradual change from semiconductor-to-metal behavior on going from $\ensuremath{\delta}=0$ to 1. Even the $\mathrm{GGA}+U$ approach failed to reproduce the insulating state for the phases with $\ensuremath{\delta}=1$, indicating that introduction of the experimental $CE$-type magnetic structure may be important. The charge and orbital ordering are analyzed with the help of the energy-projected-density matrices of the $d$ electrons. Very different ordering patterns have emerged for the different phases under investigation, indicating that both cation radii and oxygen stoichiometry play an important role in deciding spin, charge, and orbital ordering.