Much interest has emerged in the realization of materials with quantum spin liquid ground states, which would provide fertile ground for realizing exotic excitations. Three ``Kitaev'' spin liquid candidate materials have been proposed -- Na
2IrO
3, $\ensuremath{\alpha}$-RuCl
3, and $\ensuremath{\alpha}$-Li
2IrO
3 -- and there has been many diverging proposals for the most relevant interactions. Here, the authors re-evaluate carefully the magnetic interactions in these materials, using nonperturbative exact diagonalization methods. The results clarify misconceptions in the literature and help estimate the potential for realizing the spin liquid state in real materials.
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li) 2 IrO 3 iridates and RuCl 3 . In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
We develop a gauge-invariant renormalized mean-field theory (RMFT) to reliably find the quantum spin liquid (QSL) states and their field response for realistic Kitaev materials under strong magnetic fields and described by the generalized Kitaev J-K-Γ-
Γ′ model. Remarkably, while our RMFT reproduces previous results based on using more complicated numerical methods, it also predicts several new stable QSL states. In particular, since Kitaev spin liquid (KSL) is no longer a saddle point solution, a new exotic 2-cone state distinct from the KSL is found to describe experimental observations well, and hence should be the candidate state realized in the Kitaev material, α-RuCl3. We further explore the mechanism for the suppression of the observed thermal Hall conductivity at low temperatures within the fermionic framework, and show that the polar-angle dependence of the fermionic gap can distinguish the found 2-cone state from the KSL state in further experiments.
The authors report on a proximate Kitaev spin liquid regime in two different honeycomb iridates in a broad temperature and energy range. The common phenomenology with $\ensuremath{\alpha}$-RuCl
3 defines what constitutes a ``Kitaev material'' beyond the existence of a dominant bond-directional exchange.
The quantum spin liquid (QSL) state has been searched intensively in Kitaev-like materials, such as the Iridium oxides
A2IrO
3 and
α-RuCl
3. The half-filled Kitaev-Hubbard model with bond dependent hopping terms is used to describe the Kitaev-like materials, which is calculated using the state-of-the-art fermionic projected entangled pair states (fPEPS) method. We find a QSL phase near the Mott insulator transition, which has a strong first-order transition to the semi-metal phase with the decrease of Hubbard
U. We suggest that a promising routine to find the QSL is to find the Iridium oxides that are near the Mott insulator transitions.
Contrary to the original expectation,
Na2IrO3 is not a Kitaev's quantum spin liquid (QSL) but shows a zigzag-type antiferromagnetic order in experiments. Here, we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka et al., Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for
Na2IrO3 proposed by Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and N\'eel temperatures. (1) Two peaks in the temperature dependence of specific heat at ${T}_{\ensuremath{\ell}}$ and
Th caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, a prominent plateau or shoulder pinned at
2Rln2 in the temperature dependence of entropy, where
R is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio ${T}_{\ensuremath{\ell}}/{T}_{h}$ close to or less than 0.03. According to the proposed criteria,
Na2IrO3 is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of
Na2IrO3 on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to ${({\mathrm{Na}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x})}_{2}{\mathrm{IrO}}_{3}$ and other related materials are also discussed.