Orbital ordering in the ferromagnetic insulator Cs$_2$AgF$_4$ from first principles

TL;DR

This study uses first-principles density-functional theory to show that Cs$_2$AgF$_4$ is an insulator with specific orbital ordering that explains its ferromagnetism, contrasting with metallic phase models.

Contribution

It demonstrates the stabilization of an insulating orthorhombic phase with orbital ordering in Cs$_2$AgF$_4$ using first-principles calculations, highlighting the role of lattice distortion and electron correlation.

Findings

Cs$_2$AgF$_4$ is stabilized in an insulating orthorhombic phase.

Orbital ordering of $x^2-z^2$/$y^2-z^2$ explains ferromagnetism.

The insulating phase persists with moderate electron correlation.

Abstract

We found, using density-functional theory calculations within the generalized gradient approximation, that Cs$_2$AgF$_4$ is stabilized in the insulating orthorhombic phase rather than in the metallic tetragonal phase. The lattice distortion present in the orthorhombic phase corresponds to the $x^2-z^2$/$y^2-z^2$ hole-orbital ordering of the Ag$^{2+}$ $4d^9$ ions, and this orbital ordering leads to the observed ferromagnetism, as confirmed by the present total-energy calculations. This picture holds in the presence of moderate 4d-electron correlation. The results are compared with the picture of ferromagnetism based on the metallic tetragonal phase.