Nonplanar ground states of frustrated antiferromagnets on an octahedral lattice

Abstract

We consider methods to identify the classical ground state for an exchange-coupled Heisenberg antiferromagnet on a non-Bravais lattice with interactions $J_{ij}$ to several neighbor distances. Here we apply this to the unusual "octahedral" lattice in which spins sit on the edge midpoints of a simple cubic lattice. Our approach is informed by the eigenvectors of $J_{ij}$ with largest eigenvalues. We discovered two families of non-coplanar states: (i) two kinds of commensurate state with cubic symmetry, each having twelve sublattices with spins pointing in (1,1,0) directions in spin space (modulo a global rotation); (ii) varieties of incommensurate conic spiral. The latter family is addressed by projecting the three-dimensional lattice to a one-dimensional chain, with a basis of two (or more) sites per unit cell.

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• Quantum effects on unconventional pinch point singularities
• Emergent Potts order in the kagomé $J_1-J_3$ Heisenberg model
• A $j_{\mathrm{eff}}=1/2$ Kitaev material on the triangular lattice: The case of NaRuO${}_2$
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
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• Fragmented spin ice and multi-$k$ ordering in rare-earth antiperovskites
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• Incommensurate Single-Angle Spiral Orderings of Classical Heisenberg Spins on Zigzag Ladder Lattices
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• Anomalous magnetic transition in a disordered quasicrystal approximant with heavy-fermion nature
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• Multi-$Q$ magnetic phases from frustration and chiral interactions
• Quantum spin models of commensurate $p$-wave magnets
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