Topological and magnetic phase transitions in the bilayer Kitaev-Ising model

Abstract

We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising interlayer interactions, deriving effective models via perturbation theory and performing Majorana mean-field theory calculations. We show that a diverse array of magnetic and topological phase transitions occur, depending on the direction of the interlayer Ising interaction and the relative sign of Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite sign of the Kitaev interaction, we observe a notable weakening of magnetic ordering tendencies and the Kitaev spin liquid survives up to a remarkably larger interlayer exchange. Our mean-field analysis suggests the emergence of an intermediate gapped ${\mathbb{Z}}_2$ spin liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated $120^{\circ }$ compass model. We furthermore use perturbation theory to study the model with the Ising axis pointing along $\hat{z}$-axis or lying in the $xy$-plane. In both cases, our analysis reveals the formation of 1D Ising chains, which remain decoupled in perturbation theory, resulting in a subextensive ground-state degeneracy. Our results highlight the interplay between topological order and magnetic ordering tendencies in bilayer quantum spin liquids.

10 pages, 5 figures

References in corpus (10)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Moiré skyrmions and chiral magnetic phases in twisted CrX${}_3$ (X $=$ I, Br, Cl) bilayers
• Evidence of Noncollinear Spin Texture in Magnetic Moiré Superlattices
• Skyrmions in twisted van der Waals magnets
• Heterobilayer moiré magnets: moiré skyrmions and the commensurate-incommensurate transition
• Kitaev spin-orbital bilayers and their moiré superlattices
• A Kitaev-type spin liquid on a quasicrystal
• Vison crystals, chiral and crystalline phases in the Yao-Lee model
• Low temperature properties in the Bilayer Kitaev model
• Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid

Cited by in corpus (4)

• Gauge Field Dynamics in Multilayer Kitaev Spin Liquids
• Magnetic order through Kondo coupling to quantum spin liquids
• Even-odd effect in multilayer Kitaev honeycomb magnets
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices