We study the magnetic interactions in Mott-Hubbard systems with partially filled $t_{2g}$-levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr$_2$IrO$_4$.
We calculate the dynamical spin structure factor of the generalized spin-$1/2$ compass spin chain using the density matrix renormalization group. The model, also known as the twisted Kitaev spin chain, was recently proposed to be relevant for the description of the spin chain compound CoNb$_2$O$_6$. It features bond-dependent interactions and interpolates between an Ising chain and a one-dimensional variant of Kitaev's honeycomb spin model. The structure factor, in turn, is found to interpolate from gapped and non-dispersive in the Ising limit to gapless with non-trivial continua in the Kitaev…
The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in $5d^2$ Mott insulators, we provide a microscopic route to uncover the Kitaev multipolar liquid, featuring fractionalized excitations out of non-Kramers doublets carrying multipole moments. The key ingredient is the magnetic field that allows for bond-anisotropic quadrupole-octupole interactions via mixing with the excited triplet …
Ground State Properties of the Doped Kitaev-Heisenberg Chain: Topological Superconducting and Mott Insulating Phases Driven by Magnetic Frustration
University of Warsaw（华沙大学）；TU Wien（维也纳工业大学）；Technical University Dresden（德累斯顿工业大学）；Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿联邦材料研究所理论固态物理研究所）
The Kitaev spin liquid, a ground state of the bond-dependent Kitaev model in a honeycomb lattice has been a centre of attraction, since a microscopic theory to realize such an interaction in solid-state materials was discovered. A challenge in real materials though is the presence of the Heisenberg and another bond-dependent Gamma interactions detrimental to the Kitaev spin liquid, and there have been many debates on their relative strengths. Here we offer a strategy to extract the Kitaev interaction out of a full microscopic model by utilizing the symmetries of the Hamiltonian. Two tilted mag…
We propose an exactly solvable quantum spin-1/2 model with time reversal invariance on a two dimensional brick-wall lattice, where each unit cell consists of three sites. We find that the ground states are algebraic quantum spin liquid states. The spinon excitations are gapless and the energy dispersion is linear around two Dirac points. The ground states are of three-fold topological degeneracy on a torus. Breaking the time reversal symmetry opens a bulk energy gap and the $Z_2$ vortices obey non-Abelian statistics.
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find clos…
Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. Compass-type interactions appear in diverse physical systems including Mott insulators with orbital degrees of freedom (where interactions sensitively depend on the spatial orientation of the orbitals involved), the low energy effective theories of frustrated quantum magnets, systems with strong spin-orbit couplings (such as the iridates), vacancy centers, and cold atomic gases. Kitaev's models, in particular the …
A bond-directional anisotropic exchange interaction, called the Kitaev interaction, is a promising route to realize quantum spin liquids. The Kitaev interactions were found in Mott insulators with the strong spin-orbit coupling, in the presence of quantum interference between indirect electron transfers. Here we theoretically propose a different scenario by introducing a polar structural asymmetry that unbalances the quantum interference. We show that the imbalance activates additional exchange processes and gives rise to a dominant antiferromagnetic Kitaev interaction, in stark contrast to th…
In the search for quantum spin liquids, candidate materials for the Kitaev model and its extensions have been intensively explored during the past decade, as the models realize the exact quantum spin liquids in the ground state. Thus far, insulating magnets in the low-spin $d^5$ electron configuration under the strong spin-orbit coupling have been studied for realizing the Kitaev-type bond-dependent anisotropic interactions between the spin-orbital entangled Kramers doublets. To extend the candidates, here we investigate the systems in a high-spin $d^7$ electron configuration, whose ground sta…
Honeycomb iridates are thought to have strongly spin-anisotropic exchange interactions that could lead to an extraordinary state of matter known as the Kitaev quantum spin liquid. The realization of this state requires almost perfectly frustrated interactions between the magnetic Ir$^{4+}$ ions, but small imbalances in energy make other ordered states more favorable. Indeed, the closeness in energy of these ordered states is itself a signature of the intrinsic frustration in the system. In this work, we illustrate that small magnetic fields can be employed to drive the frustrated quantum magne…
The quantum spin liquid (QSL) state has been searched intensively in Kitaev-like materials, such as the Iridium oxides $A_2$IrO$_3$ 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 Irid…
Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid ground states and anyonic excitations. Another example is the geometrically frustrated quantum $120^\circ$ model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed "the tripod model", which contains a contin…
$α$-RuCl$_3$ has been hinted as a spin-orbital-assisted Mott insulator in proximity to a Kitaev spin liquid state. Here we present ARPES measurements on single crystal $α$-RuCl$_3$ in both the pristine and electron-doped states, and combine them with LDA+SOC+U calculations performed for the several low-energy competing magnetically ordered states as well as the paramagnetic state. A large Mott gap is found in the measured band structure of the pristine compound that persists to more than 20 times beyond the magnetic ordering temperature, though the paramagnetic calculation shows almost no gap.…
We study the effects of doping a Mott insulator on the honeycomb lattice where spins interact via direction dependent Kitaev couplings J_K, and weak antiferromagnetic Heisenberg couplings J. This model is known to have a spin liquid ground state and may potentially be realized in correlated insulators with strong spin orbit coupling. The effect of hole doping is studied within a t-J-J_K model, treated using the SU(2) slave boson formulation, which correctly captures the parent spin liquid. We find superconductor ground states with spin triplet pairing that spontaneously break time reversal sym…
We review the consequences of intrinsic frustration of the orbital superexchange and of spin-orbital entanglement. While Heisenberg perturbing interactions remove frustration in the compass model, the lowest columnar excitations are robust in the nanoscopic compass clusters and might be used for quantum computations. Entangled spin-orbital states determine the ground states in some cases, while in others concern excited states and lead to measurable consequences, as in the $R$VO$_3$ perovskites. On-site entanglement for strong spin-orbit coupling generates the frustrated Kitaev-Heisenberg mode…
Motivated by the recent experimental observation of a Mott insulating state for the layered Iridate Na2IrO3, we discuss possible ordering states of the effective Iridium moments in the presence of strong spin-orbit coupling and a magnetic field. For a field pointing in the [111] direction - perpendicular to the hexagonal lattice formed by the Iridium moments - we find that a combination of Heisenberg and Kitaev exchange interactions gives rise to a rich phase diagram with both symmetry breaking magnetically ordered phases as well as a topologically ordered phase that is stable over a small ran…
The Heisenberg-Kitaev (HK) model on the triangular lattice is conceptually interesting for its interplay of geometric and exchange frustration. HK models are also thought to capture the essential physics of the spin-orbital entanglement in effective $j=1/2$ Mott insulators studied in the context of various 5d transition metal oxides. Here we argue that the recently synthesized Ba$_3$IrTi$_2$O$_9$ is a prime candidate for a microscopic realization of the triangular HK model. We establish that an infinitesimal Kitaev exchange destabilizes the 120$^\circ$ order of the quantum Heisenberg model and…
We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that Kitaev materials with bond-anisotropic interactions are generally expected to show both one- and two-magnon responses. It is further shown that, in order to obtain the correct leading contributions to the Raman vertex operator $\mc{R}$, one must take into account the precise, photon-assisted microscopic hopping processes of the electrons and that, in systems with multiple hopping paths, $\mc{R}$ contains terms beyond those appearing in the …
In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in the orbital space and in the real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.
We study the effect of a magnetic field on the low energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realisation of the Kitaev model and its extensions. We explicitly calculate the variation of the excha…
The fate of exotic spin liquid states with fractionalized excitations at finite temperature ($T$) is of great interest, since signatures of fractionalization manifest in finite-temperature ($T$) dynamics in real systems, above the tiny magnetic ordering scales. Here, we study a Jordan-Wigner fermionized Kitaev spin liquid at finite $T$ employing combined Exact diagonalization and Monte Carlo simulation methods. We uncover $(i)$ checkerboard or stripy-ordered flux crystals depending on density of flux, and $(ii)$ establish, surprisingly, that: $(a)$ the finite-$T$ version of the $T=0$ transitio…
The current efforts to find the materials hosting Kitaev model physics have been focused on Mott insulators of d^5 pseudospin-1/2 ions Ir^{4+} and Ru^{3+} with t_{2g}^5(S=1/2, L=1) electronic configuration. Here we propose that the Kitaev model can be realized in materials based on d^7 ions with t_{2g}^5e_g^2(S=3/2, L=1) configuration such as Co^{2+}, which also host the pseudospin-1/2 magnetism. Considering possible exchange processes, we have derived the d^7 pseudospin-1/2 interactions in 90^{\circ} bonding geometry. The obtained Hamiltonian comprises the bond-directional Kitaev K and isotro…
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 Na2IrO3 and alpha-RuCl3. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary sp…
We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^\circ$ magnetic order, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a…
Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ …
A Kitaev-Heisenberg-J2-J3 model is proposed to describe the Mott-insulating layered iridates A2IrO3 (A=Na,Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest neighbor couplings J1, J2 and J3. A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the J1-J2-J3 one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate…
We introduce a novel mean-field theory (MFT) around the exactly soluble two-leg ladder limit for the planar quantum compass model (QCM). In contrast to usual MFT, our construction respects the stringent constraints imposed by emergent, lower (here $d=1$) dimensional symmetries of the QCM. Specializing our construction to the QCM on a periodic four-leg ladder, we find that a first-order transition separates two mutually dual Ising nematic phases, in good accord with state-of-the-art numerics for the planar QCM. One pseudo-spin-flip excitation in the ordered phase turns out to be two (Jordan-Wig…
We study the spectrum of a bilayer of Kitaev magnets on the honeycomb lattice, coupled by Heisenberg exchange in the quantum-dimer phase at strong interlayer coupling. Using the perturbative Continuous Unitary transformation (pCUT) we perform series expansion starting from the fully dimerized limit, to evaluate the elementary excitations, reaching up to and focusing on the two-triplon sector. In stark contrast to conventional bilayer quantum magnets, and because of the broken $SU(2)$-invariance, encoded in the intralayer directional compass-exchange, the bilayer Kitaev magnet is shown to exhib…
The combination of strong spin-orbit coupling and correlations, e.g. in ruthenates and iridates, has been proposed as a means to realize quantum materials with nontrivial topological properties. We discuss here Mott insulators where onsite spin-orbit coupling favors a local $J_{\textrm{tot}}=0$ singlet ground state. We investigate excitations into a low-lying triplet, triplons, and find them to acquire nontrivial band topology in a magnetic field. We also comment on magnetic states resulting from triplon condensation, where we find, in addition to the same ordered phases known from the $J_{\te…
Kitaev-type interactions between neighbouring magnetic moments emerge in the honeycomb material $α$-RuCl3. It is debated however whether these Kitaev interactions are ferromagnetic or antiferromagnetic. With electron energy loss spectroscopy (EELS) we study the lowest excitation across the Mott-Hubbard gap, which involves a d4 triplet in the final state and therefore is sensitive to nearest-neighbor spin-spin correlations. At low temperature the spectral weight of these triplets is strongly enhanced, in accordance with optical data. We show that the magnetic correlation function that determine…
Relationship between doping-induced in-gap states and spin excitations in Kitaev-Hubbard models
Department of Physics, Nanjing University（南京大学物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）；Department of Applied Physics, Nanjing University of Science and Technology（南京理工大学应用物理系）
We construct a class of exactly solvable generalized Kitaev spin-$1/2$ models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-$1/2$ models can be mapped to a gas of free Majorana fermions coupled to static $Z_2$ gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional ($2D$) tetragon-octagon model and a thr…
Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the j = 1/2 Mott insulator in these materials exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here we provide the generic nearest-neighbour spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this com…
In this letter, we propose a local detection scheme for the Majorana zero mode (MZM) carried by a vison in Kitaev's chiral spin liquid (CSL) using scanning tunneling microscopy (STM). The STM introduces a single Majorana into the system through hole/charge injection and the Majorana interacts with the MZM to form a stable composite object. We derive the exact analytical expression of single-hole Green's function in the Mott insulating limit of Kitaev's model and show that the differential conductance has split peaks, as a consequence of resonant tunneling through the vison-hole composite. The …
Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin liquid phase in the Kitaev material $α$-$\mathrm{RuCl}_{3}$. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid's hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to `perfectly' convert electrons from the former into emergent fermions in the latter---thereby enabling variations of tr…
The quest for Kitaev spin liquids in particular three dimensional solids is long sought goal in condensed matter physics, as these states may give rise to exotic new types of quasi-particle excitations carrying fractional quantum numbers namely Majorana Fermionic excitations. Here we report the experimental signature of this characteristic feature of the Kitaev spin liquid via Raman measurements. Sm2ZnIrO6 is a strongly spin orbit coupled Mott insulator, where Jeff = 1/2 controls the physics, which provide striking evidence for this characteristic feature of the Kitaev spin liquid. As the temp…
Mott insulators under sufficiently strong spin-orbit coupling can display quantum spin liquid phases with topological order and fractional excitations. Quantum magnets with pure Kitaev spin exchange interactions can host a gapped quantum spin liquid with a single Majorana edge mode propagating in the counter-clockwise direction when a small positive magnetic field is applied. Here, we show how under a sufficiently strong positive magnetic field a topological transition into a gapped quantum spin liquid with two Majorana edge modes propagating in the clockwise direction occurs. The Dzyaloshinsk…
We present a theoretical study of field-induced magnetic phases in the honeycomb Kitaev-Heisenberg model, which is believed to describe the essential physics of Mott insulators with strong spin-orbit coupling such as $A_2$IrO$_3$ and $α$-RuCl$_3$. We obtain a finite temperature phase diagram based on extensive Monte Carlo simulations and analytical calculations. We show that, while Zeeman coupling favors a symmetric non-coplanar magnetic order, thermal fluctuations enhances the stability of a collinear zigzag phase that breaks the rotational symmetry of the lattice. Our large-scale simulations…
Fractionalized Fermi liquids (FL$^\ast$) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL$^\ast$ phases based on Kitaev's $\mathbb{Z}_2$ spin liquid. We characterize the FL$^\ast$ phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find…
I propose the emergence of the spin-orbital-coupled vector chirality in a non-frustrated Mott insulator with the strong spin-orbit coupling due to $ab$-plane's inversion-symmetry (IS) breaking. I derive the superexchange interactions for a $t_{2g}$-orbital Hubbard model on a square lattice with the strong spin-orbit coupling and the IS-breaking-induced hopping integrals, and explain the microscopic origins of the Dzyaloshinsky-Moriya (DM) -type and the Kitaev-type interactions. Then, by adopting the mean-field approximation to a minimal model including only the Heisenberg-type and the DM-type …
We present an exact solution for a class of one-dimensional compass models which stand for interacting orbital degrees of freedom in a Mott insulator. By employing the Jordan-Wigner transformation we map these models on noninteracting fermions and discuss how spin correlations, high degeneracy of the ground state, and $Z_2$ symmetry in the quantum compass model are visible in the fermionic language. Considering a zigzag chain of ions with singly occupied $e_g$ orbitals ($e_g$ orbital model) we demonstrate that the orbital excitations change qualitatively with increasing transverse field, and t…
We consider a metasurface consisting of a square lattice of cylindrical antidots in a two-dimensional topological insulator (2DTI). Each antidot supports a degenerate Kramer's pair of eigenstates formed by the helical topological edge states. We show that the on-site Coulomb repulsion leads to the onset of the Mott insulator phase in the system in a certain range of experimentally relevant parameters. Intrinsic strong spin-orbit coupling characteristic for the 2DTI supports a rich class of the emerging low-energy spin Hamiltonians which can be emulated in the considered system, which makes it …
In transition-metal compounds with partially filled $4d$ and $5d$ shells spin-orbit entanglement, electronic correlations, and crystal-field effects conspire to give rise to a variety of novel forms of topological quantum matter. This includes Kitaev materials -- a family of spin-orbit assisted Mott insulators, in which local, spin-orbit entangled $j=1/2$ moments form that are subject to strong bond-directional interactions. On a conceptual level, Kitaev materials attract much interest for their unconventional forms of magnetism, such as spin liquid physics in two- and three-dimensional lattic…
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it …
We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, $J$ and $\tilde J$, where $J$ is for the conventional spin and and $\tilde J$ for rotated spin. When $\tilde J=0$, this is the conventional Heisenberg model. When J=0, the system is either in a stripy antiferromagnetic order($\tilde J<0$, ferromagnetic for rotated spin) or a zig-zag antiferromagnetic order ($\tilde J>0$, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or two antiferromagnetic orders induces Kitaev's spin liquid phase characterized by the exactly sol…
Using exact diagonalizations, Green's function Monte Carlo simulations and high-order perturbation theory, we study the low-energy properties of the two-dimensional spin-1/2 compass model on the square lattice defined by the Hamiltonian $H = - \sum_{\bm{r}} (J_x σ_{\bm{r}}^x σ_{\bm{r} + \bm{e}_x}^x + J_z σ_{\bm{r}}^z σ_{\bm{r} + \bm{e}_z}^z)$. When $J_x\ne J_z$, we show that, on clusters of dimension $L\times L$, the low-energy spectrum consists of $2^L$ states which collapse onto each other exponentially fast with $L$, a conclusion that remains true arbitrarily close to $J_x=J_z$. At that poi…
The electronic properties of Mott insulators realized in (111) bilayers of perovskite transition-metal oxides are studied. The low-energy effective Hamiltonians for such Mott insulators are derived in the presence of a strong spin-orbit coupling. These models are characterized by the antiferromagnetic Heisenberg interaction and the anisotropic interaction whose form depends on the $d$ orbital occupancy. From exact diagonalization analyses on finite clusters, the ground state phase diagrams are derived, including a Kitaev spin liquid phase in a narrow parameter regime for $t_{2g}$ systems. Slav…
The exact solution of Kitaev's spin-$1/2$ honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which $\mathrm{Na}_{2}\mathrm{IrO}_{3}$ and $α-\mathrm{RuCl}_{3}$ are prime examples. Subsequently, it has been proposed that also spin-$1$ and spin-$3/2$ analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent $1/S$ expansion, with $S$ being the spin size. We present a comprehensive stu…
We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev model on the hexagonal lattice, which has been suggested to describe the spin-orbital exchange of the effective spin-1/2 momenta in the Mott insulating Iridate Na2IrO3. At zero-temperature this model exhibits magnetically ordered states well beyond the isotropic Heisenberg limit as well as an extended gapless spin liquid phase around the highly anisotropic Kitaev limit. Using a pseudofermion functional renormalization group (RG) approach, we extract both the Curie-Weiss scale and the critical ordering scale (for the magne…
The magnetic field response of the Mott-insulating honeycomb iridate Na$_{2}$IrO$_{3}$ is investigated using torque magnetometry measurements in magnetic fields up to 60 tesla. A peak-dip structure is observed in the torque response at magnetic fields corresponding to an energy scale close to the zigzag ordering ($\approx 15~K$) temperature. Using exact diagonalization calculations, we show that such a distinctive signature in the torque response constrains the effective spin models for these classes of Kitaev materials to ones with dominant ferromagnetic Kitaev interactions, while alternative…
In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of $\mathbb{Z}_2$ quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gaple…
Fractionalization is a hallmark of spin-liquid behavior; it typically leads to response functions consisting of continua instead of sharp modes. However, microscopic processes can enable the formation of short-distance bound states of fractionalized excitations, despite asymptotic deconfinement. Here we study such bound-state formation for the $Z_2$ spin liquid realized in Kitaev's honeycomb compass model, supplemented by a kekule distortion of the lattice. Bound states between flux pairs and Majorana fermions form in the Majorana band gaps. We calculate the dynamic spin susceptibility and sho…
The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet $Li_3Co_2SbO_6$, built of high-spin $\it{d^7}$ ($Co^{2+}$) ions, in contrast to the more typical low-spin $\it{d^5}$ electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of $\it{C_C}2/\…
We study the Kitaev-Heisenberg-$Γ$-$Γ'$ model that describes the magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In strong $[111]$ magnetic fields that bring the system into the fully polarized paramagnetic phase, we find that the spin wave bands carry nontrivial Chern numbers over large regions of the phase diagram implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of magnon number non-conserving terms in the Hamiltonian. Since the effects of int…
