Competing Magnetic Ground States in Copper-Doped Pb$_{10}$P$_{6}$O$_{25}$

TL;DR

This study uses advanced computational methods to explore the magnetic behavior of copper impurities in a lead phosphate compound, revealing localized magnetism without long-range magnetic order.

Contribution

It provides a detailed theoretical analysis of the electronic and magnetic properties of copper-doped Pb$_{10}$(PO$_4$)$_6$O, highlighting the localized nature of magnetism and the absence of long-range order.

Findings

Incommensurate antiferromagnetic instability identified

Heisenberg exchange coupling estimated at ~1 meV

Magnetism is localized on copper impurities

Abstract

We investigate the electronic and magnetic properties of copper-doped Pb$_{10}$(PO$_4$)$_6$O using a combination of density functional theory and many-body perturbation theory. The flat half-filled electronic band at the Fermi level is found to give way to an incommensurate antiferromagnetic instability with wave vector $(0.28\pi ,\pm 0.47\pi ,\pi )$ within the random phase approximation arising predominantly from Cu-$d_{yz}$ and Cu-$d_{xz}$ orbitals. Moreover, the Heisenberg exchange coupling between neighboring copper atoms is estimated to be $\sim 1$ meV. Our results suggest that magnetism in copper-doped Pb$_{10}$(PO$_4$)$_6$O is localized on the impurity copper site, with no long-range ordering. These findings support the picture that copper behaves as a magnetic impurity within the Pb-apatite matrix.