Orbital ordering in ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{F}}_4$ from first principles

First-principles calculations using the augmented plane wave plus local orbital method, as implemented in the WIEN2K code, have been used to investigate the structural, electronic, and magnetic properties of the layered perovskite ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{F}}_4$. Our calculations indicate that an orthorhombic ground state for ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{F}}_4$ is energetically favored over tetragonal. We also find that ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{F}}_4$ should be a strong two-dimensional ferromagnet, with very weak antiferromagnetic coupling between the layers, in agreement with the experiment. More importantly, an antiferrodistortive ordering of $z^2\text{−}{x}^2$ and $z^2\text{−}{y}^2$ orbitals is inferred from the density of states and from a spin density isosurface analysis.

Figure 1

(Color online) Crystal structures for ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{F}}_4$ in tetragonal (left) and orthorhombic (right) perovskite lattices. Red (big), green (middle), and yellow (small) spheres represent Cs, Ag, and F atoms, respectively.

Figure 2

(Color online) The total electronic density of states for different magnetic configurations (top: FM; middle: AFM-I; bottom: AFM-II) of tetragonal (left panel) and orthorhombic (right panel) phases.

Figure 3

(Color online) The site-decomposed electronic density of states for AFM-I-type orthorhombic ${\mathrm{Cs}}_2\mathrm{Ag}{\mathrm{F}}_4$.

Figure 4

The orbital-decomposed electronic density of states ($d$ orbitals only) of Ag1 (left) and Ag2 (right) in the AFM-I configuration.

Figure 5

(Color online) Spin density plot (isosurface at 0.1 $e∕{\AA }^3$ produced using XCRYSDEN) to illustrate staggered orbital ordering of the $z^2\text{−}{x}^2$ and $z^2\text{−}{y}^2$ orbitals (the $z^2\text{−}{x}^2$ and $z^2\text{−}{y}^2$ orbitals are obtained by rotating 45° around the $c$ axis in the coordination system) in the orthorhombic AFM-I configuration. Red and blue denote spin up and spin down, respectively. The FM configuration orbital ordering solution is similar but all Ag atoms would have the same spin (equal color).