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

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-$\mathbf{q}$ spiral.

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• Generic Spiral Spin Liquids
• Interplay of the Jahn--Teller Effect and Spin-Orbit Coupling: The Case of Trigonal Vibronic Modes
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• Fingerprints of spin-current physics on magnetoelectric response in the spin-$1/2$ magnet Ba${}_2$CuGe${}_2$O${}_7$
• IrF4: From Tetrahedral Compass Model to Topological Semimetal
• Pressure-induced transition from Jeff=1/2 to S=1/2 states in CuAl2O4
• Structural stability of CuAl${}_2$O${}_4$ under pressure
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Disorder-induced spin excitation continuum and spin-glass ground state in the inverse spinel CuGa${}_2$O${}_4$
• Electron-Nuclear Hyperfine Coupling in Quantum Kagome Antiferromagnets from First-Principles Calculation and a Reflection of the Defect Effect