Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

Abstract

Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g. the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na 2 IrO 3 and α-RuCl 3 . We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models -Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice -or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.

Magnetic field induced competing phases in spin-orbital entangled Kitaev magnets

“…In the experimentally relevant parameter regime, K < 0 and > 0 are large while < 0 is small. In contrast to many of the previous studies [24][25][26][27][28][29][30], we investigate the classical limit of this model, that is, by treating the spins (1) as three-dimensional vectors of fixed magnitude |S i | = S for all i. We use simulated annealing to determine the ground-state spin configuration of the system.…”

“…The interaction still appears quite anisotropic at this stage, but a change of basis will bring it to a simpler and more illuminating form. and [111] respectively [25,41], the spin is given bỹ…”

“…Theoretical models for α-RuCl 3 include substantial Kitaev and symmetric anisotropic interactions, both strongly dependent on the bond directions, with additional small exchanges such as the nearest neighbor Heisenberg J, the third nearest neighbor Heisenberg J 3 , and the anisotropic [21][22][23], on the honeycomb lattice. Previous analyses are largely done on quantum models with small system sizes (typically a 24-site cluster) via exact diagonalization (ED) [24][25][26][27][28] or in quasi-one-dimensional limit via density matrix renormalization group (DMRG) [26,27,29], with varying degree of complexity. For example, a recent work [27] on the K model in an external magnetic field suggests that it allows an intermediate spin liquid phase continuously connected to the pure Kitaev model between the low-field ZZ order and high-field polarized state.…”

“…Furthermore, we calculate the thermal Hall conductivity due to magnons in some of the large unit cell orders and find that it is as large as that observed experimentally at low temperatures. While strong quantum fluctuations are present and hence it is likely for the series of competing phases to turn into spin liquids in the quantum limit, it is also evident that previous theoretical studies on quantum models with small system sizes [24][25][26][27][28][29] cannot resolve many of these large unit cell orders. Therefore, in future analyses of such quantum models, it will be important to understand the role of quantum fluctuations in the large unit cell orders unveiled in the current work.…”

Tensor network simulation of the Kitaev-Heisenberg model at finite temperature

“…break the symmetry -and introduce the bond-anisotropy at the same time -the spins can be mixed with orbital degrees of freedom, as originally argued for iridium oxides 75 . The resulting Kitaev-Heisenberg (KH) model was considered as a minimal model to study stability of the Kitaev spin liquid phase in materials like Na 2 IrO 3 , α-Li 2 IrO 3 , Li 2 RhO 3 , and α-RuCl 3 , though recent results suggest that more general extensions of the KH model are required 76,77 . In this paper we investigate the basic KH model at finite temperature as a first step towards its more realistic extensions.…”