Realization of anisotropic compass model on the diamond lattice of Cu$^{2+}$ in CuAl$_2$O$_4$

TL;DR

This paper demonstrates that CuAl$_2$O$_4$ hosts anisotropic compass interactions on a diamond lattice, leading to a stabilized spiral magnetic order, similar to phenomena observed in spin-orbit coupled iridates.

Contribution

It introduces a realistic model for CuAl$_2$O$_4$ showing how anisotropic exchange interactions emerge in cuprates with tetrahedral Cu$^{2+}$ ions, expanding the understanding of spin-orbit effects beyond iridates.

Findings

Anisotropic compass interactions are significant in CuAl$_2$O$_4$.

These interactions lift degeneracy and stabilize a single-q spiral state.

The magnetic ground state is dramatically influenced by bond-dependent exchange.

Abstract

Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ ions in CuAl$_2$O$_4$ and show that the magnetic properties of this compound are largely controlled by anisotropic compass-type exchange interactions that dramatically modify the magnetic ground state by lifting the spiral spin-liquid degeneracy and stabilizing a commensurate single-$\boldsymbol{q}$ spiral.