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arXiv:2311.14161

Emergence of vortex state in the $S=1$ Kitaev-Heisenberg model with single-ion anisotropy

Ayushi Singhania, Jeroen van den Brink, Satoshi Nishimoto

Published Nov 23, 2023• 0 citations
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Abstract

The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single-ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-$1$ Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a ferromagnetic state in presence of antiferromagnetic Heisenberg interactions, while a Nèel state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also propose experimental prospects for observing these novel magnetic states in material realizations.

DOI
10.48550/arxiv.2311.14161

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Emergence of vortex state in the S=1S=1S=1 Kitaev-Heisenberg model with single-ion anisotropy
The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single-ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-111 Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a ferromagnetic state in presence of antiferromagnetic Heisenberg interactions, while a Nèel state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also propose experimental prospects for observing these novel magnetic states in material realizations.
The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single-ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-1 Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a ferromagnetic state in the presence of antiferromagnetic Heisenberg interactions, whereas a Néel state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also suggest experimental prospects for observing these novel magnetic states in material realizations.
The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single-ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-1 Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a state in the presence of antiferromagnetic Heisenberg interactions, whereas a state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also suggest experimental prospects for observing these novel magnetic states in material realizations. Published by the American Physical Society 2024
We investigate the ground-state phase diagram of the spin-1 Kitaev–Heisenberg (KH) chain in the presence of uniaxial single-ion anisotropy D z using the density-matrix renormalization-group method. The relative strength of the Heisenberg and Kitaev interactions is parametrized by a coupling angle ϕ , defined by J = cos ϕ and K = sin ϕ . By combining energy-based diagnostics with finite-size extrapolations of order parameters and correlation functions, we obtain a comprehensive phase diagram as a function of ϕ and D z . The phase diagram contains ferromagnetic and Néel ordered phases, collinear states with four-site spin modulation, magnetically disordered or critical regimes, two Kitaev-dominated spin-liquid-like regions, and a topological Haldane phase near the Heisenberg limit. We find that the Kitaev-dominated disordered regions acquire finite parameter widths in the spin-1 model, whereas the Haldane phase is fragile against Kitaev-type anisotropy, especially for D z < 0 . Positive D z generally suppresses magnetic order and expands nonmagnetic regimes, while negative D z enhances Ising-like magnetic order. At D z = 0 , we also identify an exactly solvable point at tan ϕ = − 2 ( ϕ / π ≃ 1.6476 ) , which gives rise to a first-order transition between the Néel- z state and a four-site collinear state. We further contrast these findings with the spin- 1 / 2 KH chain and with the spin-1 honeycomb KH model, highlighting the distinct roles of single-ion anisotropy and dimensionality in Kitaev-type magnets.
Recently there has been considerable excitement surrounding the promising realization of high-spin Kitaev material, such as the quasi-2D compound CrI3_33​ and CrGeTe3_33​. However, the stability of quantum spin liquids (QSL) against single ion anisotropy (SIA) in these materials and the global quantum phase diagram of the extended spin-3/2 Kitaev model with finite SIA remain unclear. In this study, we perform large-scale density matrix renormalization group (DMRG) to explore the quantum phase diagram of the generalized spin-3/2 Kitaev-Heisenberg (K-H) model accompanied with SIA AcA_cAc​. In the Ac=0A_c=0Ac​=0 limit, the spin-3/2 K-H model exhibits a quantum phase diagram similar to that of a spin-1/2 system, including two QSLs around antiferromagnetic and ferromagnetic Kitaev models. For models with finite AcA_cAc​, we map out the quantum phase diagram around two Kitaev points and observe distinct types of in-plane vortex orders developed from these two QSL phases. Interestingly, series of nearly degenerate vortex configurations are discovered in each vortex phases. Using linear spin-wave theory, we demonstrate that these vortex configurations can be understood as a consequence of the quantum correction on a continuous family of degenerate classical states.
Abstract We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points ϕ=π2{\boldsymbol{\phi }}{\boldsymbol{=}}\frac{{\boldsymbol{\pi }}}{{\bf{2}}}ϕ=2π​ ϕ=π2 and φ=3π2{\boldsymbol{\varphi }}{\boldsymbol{=}}\frac{{\bf{3}}{\boldsymbol{\pi }}}{{\bf{2}}}φ=23π​ φ=3π2 are singular. Theϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.
We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points ϕ=π2 and φ=3π2 are singular. The ϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.