Session R61: Towards realizing Kitaev physics and other topological phases

Heisenberg-Kitaev physics in magnetic fields

Kitaev's bond-anisotropic spin model on the honeycomb lattice describes an exactly solvable quantum spin liquid with emergent gauge fields and fractionalized excitations. By now, a number of honeycomb-lattice magnets have been proposed to host sizeable Kitaev interactions, driven by strong spin-orbit coupling, among them Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃. Given the strong spin anisotropies, their response to applied magnetic fields is particularly rich. In this talk, I will describe the behavior of the relevant Heisenberg-Kitaev models and their extensions in applied field, with focus on field-induced exotic phases and their experimental signatures. I will also discuss phases of the hyperhoneycomb-lattice extended Kitaev models relevant for β-Li₂IrO₃ and a mapping connecting them to their two-dimensional counterparts.   

Emergence of a field-driven U(1) spin liquid in spin-1 Kitaev systems

Recent proposals for spin-1 Kitaev materials, such as Na3Ni2SbO6, have shown that these compounds naturally realize antiferromagentic (AFM) Kitaev couplings. Interest in such AFM Kitaev systems has recently sparked by the observation of a transition to a gapless U(1) spin liquid at intermediate field strengths in the AFM spin-1/2 Kitaev model. However, all known spin-1/2 Kitaev materials exhibit ferromagnetic bond-directional exchanges. Here we discuss the physics of the spin-1 Kitaev model in a magnetic field and show, by extensive numerical analysis, that for AFM couplings it exhibits an extended gapless U(1) quantum spin liquid at intermediate field strengths. The close analogy to its spin-1/2 counterpart suggests that this gapless spin liquid exhibits a spinon Fermi surface.   

Ground-state phase diagram of the Kitaev-Γ model on a honeycomb lattice

We investigate the ground-state phase diagram of the Kitaev-Γ model on a honeycomb lattice by utilizing several numerical methods, such as the numerical exact-diagonalization method and the density-matrix-renormalization-group method. In this study, we focus on the effect of the anisotropic interaction; we connect the isolated dimer limit and the spin-chain limit by changing the coupling constants. From the numerical results, we find that there are three kinds of phases, namely the Tomonaga-Luttinger (TL) liquid phase and two kinds of magnetic ordered states, in the spin-chain limit. When the Γ interaction is positive and the Kitaev interaction is negative, the TL liquid is stable against the interchain couplings, which implies that the TL liquid survives up to the vicinity of the isotropic point or shows a crossover behavior. The dimer phases also survive in the vicinity of the isotopic limit. We expect that many states are competing around the isotropic point.
  

Large off-diagonal exchange coupling driven magnetic anisotropy and spin liquid states in the C3-symmetric iridate K2IrO3

Honeycomb lattice spin-orbit insulators are promising candidates for realization of quantum spin liquid states. The iridate oxide K₂IrO₃ is an end member of the recently synthesized iridate family K_xIr_yO₂, and features a C₃ point-group symmetry at the Ir sites. Using ab-initio techniques, we investigate the magnetic couplings in the proposed structural model for K₂IrO₃. We find that the higher point-group symmetry leads to strong magnetic anisotropy driven by the unusually large off-diagonal exchange couplings (Γ's) as opposed to other spin liquid candidates considered so far. High magnetic frustration and large quantum fluctuations imply lack of magnetic ordering consistent with the experiments. Exact diagonalization calculations for the fully anisotropic K−J−Γ Hamiltonian reveal a rich phase diagram with competing magnetic as well as spin liquid states. Our study points out the importance of the Γ's in stabilizing a spin liquid state and highlights an alternative route to stabilize spin liquid states for ferromagnetic K.

References:
[1] R. Yadav, et al. Phys. Rev. B 100, 144422 (2019).   

Chemical tuning between triangular and honeycomb structures in a 5d spin-orbit Mott insulator

We report structural studies of the spin-orbit Mott insulator family KxIryO2 , with triangular layers of edge-sharing IrO6 octahedra bonded by potassium ions. The potassium content acts as a chemical tuning parameter to control the amount of charge in the Ir-O layers. Unlike the isostructural families with Ir replaced by Co or Rh (y = 1), which are metallic over a range of potassium compositions x, we instead find insulating behaviour with charge neutrality achieved via iridium vacancies, which order in a honeycomb supercell above a critical composition x_c . By performing density functional theory calculations we attribute the observed behaviour to a subtle interplay of crystal-field environment, local electronic correlations and strong spin-orbit interaction at the Ir 4+ sites, making this structural family a candidate to display Kitaev magnetism in the experimentally unexplored regime that interpolates between triangular and honeycomb structures.   

Raman Scattering Investigation of a New Candidate for a Quantum Spin Liquid, the Magnetic Insulator, Ba3Ir4O10

The insulator Ba₃Ir₄O₁₀ is a new candidate for a frustrated quantum spin liquid, which was reported to have a stabilized quantum spin liquid state down to 0.2 K. The frustration parameter of around 3800 is extremely high. The spin liquid is also extraordinarily sensitive to changes in the lattice parameters as shown with the effects from strontium doping. The replacement of approximately 2% of barium with strontium readily lifts the frustration parameter and this doped material has long-range order from an antiferromagnetic transition at 130 K. Raman spectroscopy results show that both materials are also strongly anisotropic. We will present a comparison of the results of Raman scattering experiments on Sr-doped and undoped samples of Ba₃Ir₄O₁₀.   

Ab-Initio insight into non-local charge fluctuations in optical conductivity for α-RuCl3 through a Wannier basis: Highlighting the role of chemistry in correlated electron systems

α-RuCl₃ is one of the top contenders for hosting a quantum spin liquid as its exact ground state by possibly being a real material realization of Kitaev's anisotropic spin model. While there is still no consensus for the magnetic ground state, there is plenty of rich physics in the electronic excitations (i.e optical conductivity). We simulate the optical excitations of α-RuCl₃, by invoking a parameter-free treatment of the Random Phase Approximation (RPA) to exact Time Dependent Density Functional Theory (TD-DFT) implemented using a Wannier basis. The calculated optical peak for α-RuCl₃ (peak at ~1eV) is in very good agreement in location and absolute units with experiment. There are two key findings using this implementation. The first is the origin of the insulating gap in the ground state appears to be due to the interplay between relativity (spin-orbit coupling) and correlation (Hubbard U). The second finding is the surprising result that to converge the optical peak in the calculation, there are sizable Ru-Ru electron-hole pairs of Wannier d-like orbitals spanning beyond neighboring sites. This is determined due to the strong covalency built into the underlying solid state electronic structure of the underlying α-RuCl₃, in particular the hexagonal arrangement of Ru atoms.   

New magnetic order revealed in α-RuCl3 at intermediate magnetic fields using neutron diffraction

It is well-known that an external magnetic field can induce a transition in α-RuCl₃ from a magnetically ordered state to a disordered state that may be related to the Kitaev quantum spin liquid. The overall temperature - magnetic field phase diagram of α-RuCl₃ is currently under intense scrutiny, and presently there is no universal agreement on the number of field induced phase transitions between the zero-field state and the high field polarized paramagnet. Single crystals with minimal stacking faults show a transition near T_N = 7 K at B = 0 T to a low temperature ordered phase that has a zigzag AFM structure in a single honeycomb layer, with a 3-fold periodicity perpendicular to the planes. For fields applied in the honeycomb plane perpendicular to a Ru-Ru bond there is evidence from magnetization, AC susceptibility, thermal transport [1], and magnetocaloric effect [2] data for an intermediate-field phase with a different magnetic order that precedes the disordered phase. Here we discuss neutron diffraction data that clarifies the magnetic structure in this phase. The intermediate ordered phase puts additional constraints on the minimal model magnetic Hamiltonian for α-RuCl₃.
[1] P. Lampen-Kelley et al, arXiv:1807.06192 (2018).
[2] C. Balz et al, Phys. Rev. B 100, 060405 (2019).   

Phononic Structure of Kitaev Quantum Spin Liquid Candidate Material alpha-RuCl3

While many studies have focused on the magnetic excitations in alpha-RuCl3, its vibrational excitation spectrum has remained relatively unexplored. However, understanding phonons in RuCl3 is important for example to analyze the controversial observation of the half-integer thermal quantum Hall effect. We investigate the phononic structure of alpha-RuCl3 via Density Functional Theory calculations and Inelastic Neutron Scattering experiments.   

X-ray scattering studies of elementary excitations of α-RuCl3

We investigated the Kitaeuv quantum spin liquid candidate α-RuCl₃ using resonant inelsatic x-ray scattering (RIXS) and inelastic x-ray scattering (IXS). Our room temperature M₃-edge RIXS results revealed a spin-orbit exciton from which we extracted values for the spin-orbit coupling constant and trigonal distortion field energy which support the j_eff = 1/2 nature of α-RuCl₃ [1]. I will discuss the potential of M₃-edge RIXS to study 4d transition metal systems and perspectives on low temperature measurements on α-RuCl₃. Finally, I will present our IXS measurements of the dispersion of acoustic phonons in α-RuCl₃ measured at 5 K.

[1] B.W. Lebert, S. Kim, V. Bisogni, I. Jarrige, A.M Barbour, Y.-J. Kim. Resonant inelastic x-ray scattering study of α-RuCl₃: a progress report. arXiv:1908.01190   

Raman scattering response in the Kitaev magnet beta-Li2IrO3 and its evolution in the magnetic field

Raman scattering has been proven to be a powerful dynamical probe to study magnetic excitations in various frustrated magnets. Here we analyze theoretically the one- and two-magnon Raman scattering intensity in the Kitaev magnet beta-Li2IrO3 and its evolution in the magnetic field. Our analysis shows that the response is very sensitive to the polarization of light and the direction of the external magnetic field, reflecting a peculiar spin dynamics of this compound which arises due to the competition between anisotropic exchange interactions and applied magnetic field.   

Giant linearly-polarized photogalvanic effect and second harmonic generation in zero-plateau quantum anomalous Hall systems

Combining quantum perturbation theory and first-principles simulation, we predict giant nonlinear optical responses (NLOs) in even septuple layers of MnBi₂Te₄ family materials (MBTs), which are the zero-plateau quantum anomalous Hall systems (QAHs). The interlayer antiferromagnetic order breaks the inversion symmetry, and the amplitudes of injection current and second harmonic generation can be about one order of magnitude larger than those of the ferroelectrics, such as LiNbO₃ and BiFeO₃. Moreover, unlike the injection current in ferroelectrics, we find that the injection photocurrent only emerges under a linearly polarized light in MBTs. Our analysis indicates that these giant linearly-polarized second-order NLOs are resulted from the parity-time symmetry, three-fold rotation symmetry, and large spin-orbit coupling. These enhanced NLOs are valuable for characterizing subtle magnetic orders in QAHs and shed light on photo-detecting and photovoltaic applications based on emerging magnetic topological materials.   

Berry Curvature Engineering by Gating Two-Dimensional Antiferromagnets

Recent advances in tuning electronic, magnetic, and topological properties of two-dimensional (2D) magnets have opened a new frontier in the study of quantum physics and promised exciting possibilities for future quantum technologies. In this study, we find that the dual gate technology can well tune the electronic and topological properties of antiferromagnetic (AFM) even septuple-layer (SL) MnBi2Te4 thin films. Under an out-of-plane electric field that breaks PT symmetry, the Berry curvature of the thin film could be engineered efficiently, resulting in a huge change of anomalous Hall (AH) signal. Beyond the critical electric field, the double-SL MnBi2Te4 thin film becomes a Chern insulator with a high Chern number of 3. We further demonstrate that such 2D material can be used as an AFM switch via electric-field control of the AH signal. These discoveries inspire the design of low-power memory prototype for future AFM spintronic applications.