Interplay of magnetic field and trigonal distortion in the honeycomb $\Gamma$ model: Occurrence of a spin-flop phase

Abstract

In candidate Kitaev materials, the off-diagonal $\Gamma$ and ${\Gamma }^{\prime }$ interactions are identified to come from the spin-orbit coupling and trigonal distortion, respectively. They have generated intense research efforts because of their intimate relation to the field-induced magnetically disordered state reported in $\alpha$-RuCl${}_3$. Theoretically, while a plethora of field-induced phases has been proposed in the honeycomb lattice, a stable intermediate phase that can survive in a wide parameter region regardless of the underlying phases is still lacking. Here we focus on the interplay of an out-of-plane magnetic field and a symmetry-allowed ${\Gamma }^{\prime }$ term due to trigonal distortion in the dominant antiferromagnetic $\Gamma$ region. By using multifaceted approaches ranging from classical Monte Carlo and semiclassical spin-wave theory to density-matrix renormalization group, we identify an intriguing spin-flop phase in the presence of magnetic field and antiferromagnetic ${\Gamma }^{\prime }$ interaction, before it eventually enters into a fully polarized state. As the ${\Gamma }^{\prime }$ interaction approaches the size of $\Gamma$ one, the $\Gamma$-${\Gamma }^{\prime }$ model maps to the easy-axis XXZ antiferromagnet, where the spin-flop phase can be understood as a superfluid phase in the extended Bose-Hubbard model. Our finding thus demonstrates an exciting path from the honeycomb $\Gamma$ model towards a $U(1)$-symmetric XXZ antiferromagnet in a magnetic field.

arXiv comment15+6 pages, 11+9 figures

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• Interplay of Kitaev Interaction and Off-diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams
• Coexistence of static and dynamic local magnetic fields in an S = 3/2 honeycomb lattice antiferromagnet Co2Te3O8
• Understanding the magnetic interactions of the zig-zag honeycomb lattice: Application to $\alpha$-RuCl${}_3$