Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion

Abstract

The exact solution of Kitaev's spin-$1/2$ honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and $\alpha -{\mathrm{RuCl}}_3$ are prime examples. Subsequently, it has been proposed that also spin-$1$ and spin-$3/2$ analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent $1/S$ expansion, with $S$ being the spin size. We present a comprehensive study of this model in the presence of an external magnetic field applied along two different directions, [001] and [111], for which an intricate classical phase diagram has been reported. In both settings, we employ spin-wave theory in a number of ordered phases to compute phase boundaries at the next-to-leading order in $1/S$ and show that quantum corrections substantially modify the classical phase diagram. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.

arXiv comment15+9 pages, 10+4 figures. Published version

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• Emergent Hyper-Magic Manifold in Twisted Kitaev Bilayers
• Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
• Pressure tuning of competing interactions on a honeycomb lattice
• Ferrimagnetism from quantum fluctuations in Kitaev materials
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• Bond disorder in extended Heisenberg-Kitaev models: Spin textures and in-gap states in the high-field regime
• Robust semiclassical magnetization plateau in the kagome lattice
• Stability of ordered and disordered phases in the Heisenberg-Kitaev model in a magnetic field
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions
• Strategy to Extract Kitaev Interaction using Symmetry in Honeycomb Mott Insulators
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid