We show how Raman spectroscopy can serve as a valuable tool for diagnosing quantum spin liquids (QSL). We find that the Raman response of the gapless QSL of the Kitaev-Heisenberg model exhibits signatures of spin fractionalization into Majorana fermions, which give rise to a broad signal reflecting their density of states, and Z(2) gauge fluxes, which also contribute a sharp feature. We discuss the current experimental situation and explore more generally the effect of breaking the integrability on response functions of Kitaev spin liquids.
In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A2IrO3 includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We also find that, while the Heisenberg and the Kitaev interactions between nearest neighbors are correspondingly antiferro-and ferromagnetic, they both change sign for the next-nearest neighbors. Using classical Monte Carlo simulations we examine the magnetic phase diagram of the derived super-exchange model. Zigzag-type antiferromagnetic order is found to occupy a large part of the phase diagram of the model and, for ferromagnetic next-nearest neighbor Heisenberg interaction relevant for Na2IrO3, it can be stabilized even in the absence of third nearest neighbor coupling. Our results suggest that a natural physical origin of the zigzag phase experimentally observed in Na2IrO3 is due to the interplay of the Kitaev anisotropic interactions between nearest and next-nearest neighbors.
We present a theoretical study of the static and dynamical properties of the three-dimensional, hyperhoneycomb Kitaev magnet β-Li2IrO3. We argue that the observed incommensurate order can be understood in terms of a long-wavelength twisting of a nearby commensurate period-3 state, with the same key qualitatively features. The period-3 state shows very different structure when either the Kitaev interaction K or the off-diagonal exchange anisotropy Γ is dominant. A comparison of the associated static spin structure factors with reported scattering expoeriments in zero and finite fields gives strong evidence that β-Li2IrO3 lies in the regime of dominant Kitaev coupling, and that the Heisenberg exchange J is much weaker than both K and Γ. Our predictions for the magnon excitation spectra, the dynamical spin structure factors and their polarization dependence provide additional distinctive fingerprints that can be checked experimentally. arXiv:1801.00874v3 [cond-mat.str-el]
Motivated by recent neutron and x-ray observations in V2O3, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t2g states containing two electrons coupled to spin S = 1, and use it to re-examine the low-temperature ground-state properties of this compound. An axial trigonal distortion of the cubic states is also taken into account. Since there are no assumptions about the symmetry properties of the hopping integrals involved, the resulting spin-orbital Hamiltonian can be generally applied to any crystallographic configuration of the transition metal ion giving rise to degenerate t2g orbitals.Specializing to the case of V2O3 we consider the low temperature antiferromagnetic insulating phase. We find two variational regimes, depending on the relative size of the correlation energy of the vertical pairs and the in-plane interaction energy. The former favors the formation of stable molecules throughout the crystal, while the latter tends to break this correlated state. Using the appropriate variational wave functions we determine in both cases the minimizing orbital solutions for various spin configurations, compare their energies and draw the corresponding phase diagrams in the space of the relevant parameters of the problem. We find that none of the symmetry-breaking stable phases with the real spin structure presents an orbital ordering compatible with the magnetic space group indicated by very recent observations of non-reciprocal x-ray gyrotropy in V2O3. We do however find a compatible solution with very small excitation energy in two distinct regions of the phase space, which might turn into the true ground state of V2O3 due to the favorable coupling with the lattice. We illustrate merits and drawbacks of the various solutions and discuss them in relation to the present experimental evidence.
We show that the off-diagonal exchange anisotropy drives Mott insulators with strong spin-orbit coupling to a classical spin liquid regime, characterized by an infinite number of ground states and Ising variables living on closed or open strings. Depending on the sign of the anisotropy, quantum fluctuations either fail to lift the degeneracy down to very low temperatures, or select non-coplanar magnetic states with unconventional spin correlations. The results apply to all 2D and 3D tri-coordinated materials with bond-directional anisotropy, and provide a consistent interpretation of the suppression of the x-ray magnetic circular dichroism signal reported recently for β-Li2IrO3 under pressure. The key ingredients for the desired degree of frustration in the JKK systems is the three-fold coordination and the compass-like, nearest-neighbor (NN) Ising interactions along bond-dependent quantization axes. [7,[30][31][32][33][34][35][36][37][38][39] While this socalled Kitaev anisotropy is the dominant interaction, all JKK materials show magnetic order at sufficiently low temperatures, [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] consistent with predictions that Kitaev QSLs are fragile against perturbations. [7,8,30,[40][41][42][43][44] Nevertheless, the aspiration for spin liquid physics in JKK systems still stands. The new experimental direction is to use external perturbations, such as magnetic field, [45] chemical substitution, [46] and pressure. Introduction -[28] For β-Li 2 IrO 3 , for example, x-ray magnetic circular dichroism (XMCD) experiments show a strong reduction of the signal with pressure, and a complete suppression around 2 GPa.[28] Since the system remains insulating under pressure, the authors suggest that the system is driven into a spin-liquid regime, and naturally the Kitaev QSL is the first suspect. Surprisingly, however, according to two independent ab initio studies, [39,47] pressure pushes the system further away from the ideal Kitaev model, and the interaction becoming increasingly relevant is the symmetric off-diagonal exchange Γ. [30-32, 37, 38, 42] Motivated by these reports, we set out to investigate the physics of the JKK systems in the region where Γ is the dominant coupling. Remarkably, the qualitative results are shared by all 2D and 3D JKK systems. The Γ coupling drives these
The 5d-electron honeycomb compound H3LiIr2O6 [K. Kitagawa et al., Nature 554, 341-345 (2018)] exhibits an apparent quantum spin liquid (QSL) state. In this intercalated spin-orbital compound, a remarkable pile up of low-energy states was experimentally observed in specific heat and nuclear magnetic (NMR) spin relaxation. We show that a bond disordered Kitaev model can naturally account for this phenomenon, suggesting that disorder plays an essential role in its theoretical description. In the exactly soluble Kitaev model, we obtain, via spin fractionalization, a random bipartite hopping problem of Majorana fermions in a random flux background. This has a divergent low-energy density of states (DOS) of the required power-law form N (E) ∝ E −ν with a drifting exponent which takes on the value ν ≈ 1/2 for relatively strong bond disorder.Breaking timereversal symmetry removes the divergence of the density of states, as does applying a magnetic field in experiment. We discuss the implication of our scenario, both for future experiments and from a broader perspective.
We study the critical properties of the Kitaev-Heisenberg (KH) model on the honeycomb lattice at finite temperatures that might describe the physics of the quasi two-dimensional (2D) compounds, Na2IrO3 and Li2IrO3. The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by the order-by-disorder mechanism. This magnetically ordered state with a spontaneously broken Z6 symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature, ordered phase and the high-temperature, disordered phase. Finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless (KT) phase with continuously variable exponents. We argue that the intermediate phase has been observed above the low-temperature, magnetically ordered phase in Na2IrO3, and also likely exists in Li2IrO3.Introduction. The Ir-based transition metal oxides, in which the orbital degeneracy is accompanied by a strong relativistic spin-orbit coupling (SOC), have recently attracted a lot of theoretical and experimental attention [1][2][3][4][5][6][7][8]. This is because the strong SOC creates a different, and frequently novel, set of magnetic and orbital states due to the unusual anisotropic exchange interactions between localized moments which are in turn determined by the combination of spin and lattice symmetries. The spin-orbital models that describe the low-energy physics of iridium systems often include anisotropic terms that do not reduce to the conventional easy-plane and easy-axis anisotropies because they involve the products of different components of multiple spin operators. These terms are responsible for exotic Mott-insulating states [3], topological insulators [10,11], spin-orbital liquid states [1, 2], and non-trivial long-range magnetic orders [3,4,6].A prominent example of such an anisotropic spinorbital model is the KH model on the honeycomb lattice [12,13] which likely describes the low-energy physics of the quasi 2D compounds, Na 2 IrO 3 and Li 2 IrO 3 . In these compounds, Ir 4+ ions are in a low spin 5d 5 configuration and form weakly coupled hexagonal layers [4,6,8]. Due to strong SOC, the atomic ground state is a doublet where the spin and orbital angular momenta of Ir 4+ ions are coupled into J eff = 1/2. It was suggested [12,13] that the interactions between these effective moments can be described by a spin Hamiltonian containing two competing nearest neighbor (NN) interactions: an isotropic antiferromagnetic (AF) Heisenberg exchange interaction and a highly anisotropic ferromagnetic (FM) Kitaev exchange interaction [14]. This competition can be described with the parameter, 0 ≤ α ≤ 1, which sets the relative strength of these two interactions. At α = 0, the coupling corresponds to the AF Heisenberg interaction, and at α = 1, it corresponds to the Kitaev interaction.This model immediately attracted a lot of attention; several theoretical studies were publis...
Motivated by recent theoretical and experimental controversy, we present a theoretical study to clarify the orbital symmetry of the ground state of vanadium spinel oxides AV2O4 (A=Zn, Mg, Cd). The study is based on an effective Hamiltonian with spin-orbital superexchange interaction and a local spin-orbit coupling term. We construct a classical phase-diagram and prove the complex orbital nature of the ground state. Remarkably, with our new analysis we predict correctly also the coherent tetragonal flattening of oxygen octahedra. Finally, through analytical considerations as well as numerical ab-initio simulations, we propose how to detect the predicted complex orbital ordering through vanadium K edge resonant x-ray scattering.PACS numbers: 75.10. Jm, 75.30.Et Vanadium and titanium spinels, AB 2 O 4 (B=Ti 3+ , or V 3+ ), belong to a class of frustrated antiferromagnets where magnetic B-ions are characterized by orbital degeneracy due to partial occupancy of t 2g -orbitals (n t2g =1 for titanates and n t2g =2 for vanadates). Recently these spinels were thoroughly studied from both experimental [1,2,3] and theoretical [4,5,6] points of view. While the ground state of Ti-based spinels can be explained in terms of orbitally-driven superexchange interactions on the frustrated pyrochlore lattice [6], the situation seems not so fluid for vanadium spinels, as two conflicting theoretical works appeared to explain their structural and magnetic properties [4,5].In AV 2 O 4 , magnetically active V 3+ -ions form a pyrochlore lattice and are characterized by two 3d electrons in t 2g -orbitals, while A is a divalent ion like Cd 2+ , or Zn 2+ , or Mg 2+ . All compounds show qualitatively similar structural and magnetic behavior with a structural transition at a higher temperature T S and an antiferromagnetic (AFM) transition at a slightly lower temperature T N [7]. These findings have been interpreted by Tsunetsugu and Motome [4] as an interplay of ddσ superexchange (SE) interaction and geometrical frustration: they showed that ordering of orbitals can partially remove magnetic frustration and explain the experimentally observed magnetic structure which is composed of AFM chains running in [110] and [110] directions. The ground state orbital ordering suggested in Ref.[4] consists of stacked ab planes with alternating d xz and d yz vanadium hole orbitals (hereafter referred to as ROO).On the other side Tchernyshyov [5] pointed out that the ground state symmetry I4 1 /a of ROO solution seems at odds with x-ray and neutron diffraction data, indicating a I4 1 /amd space symmetry. Thus, he proposed a purely ionic model where spin-orbit (SO) coupling plays the major role and the V hole occupies (predetermining the sign of Jahn-Teller (JT) distortion) a complex linear combination of xz and yz orbitals: (d xz ± id yz )/ √ 2. (We shall refer to this orbital order as COO).Actually, the correct space group of the system is still elusive. The tetragonal I4 1 /amd space group was found in Ref.[1], while the authors of the neutron scatter...
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