Session L37: Iridates -- Honeycomb Lattice and Other Geometries

Anomalous Magnetic Torque Signal in a Kitaev Spin Liquid Candidate

The honeycomb iridates have received much attention as potential material realization of Kitaev's exactly solvable honeycomb model, which predicts a quantum spin liquid ground state with fractionalized Majorana excitations. While the presence of magnetic order at low temperature makes the Kitaev nature of the iridates less apparent, it may still be possible to detect high-temperature signatures of the spin liquid state. In this study, we present data on a unique high-temperature phase of lithium iridate as measured by torque magnetometry.   

Magnetic excitation spectra of hyper-honeycomb iridate β-Li2IrO3

A unique feature of 5d materials is the fact that spin-orbit coupling, Coulomb interactions, and crystal electric field effects are of comparable strength. In the edge-sharing honeycomb iridates, this competition of energy scales leads to a strongly anisotropic, Ising-like exchange between neighboring isospin-1/2 moments. Such interactions couple each spin to orthogonal components of the three neighboring spins and, as a consequence, no single exchange direction can be simultaneously satisfied, leading to strong frustration closely approximated by the Kitaev Hamiltonian. So far, most potential Kitaev materials have been found to order at low temperatures, eluding the sought-after QSL state. Nonetheless, experiments suggest that Kitaev exchange is the dominant spin interaction in these systems, with additional small contributions from a direct Heisenberg and a symmetric off-diagonal exchange term. We previously showed that a magnetic field completely suppresses the complex incommensurate spiral order in β-Li₂IrO₃, while stabilizing a commensurate zig-zag component similar to the ground state observed in Na₂IrO₃. In this work, we present the magnon excitation spectra of β-Li₂IrO₃ in zero and finite magnetic field, at zone centers corresponding to both coexisting states.   

Spin-Glass Behavior in Hole-Doped Lithium Iridates

Honeycomb iridates have been proposed to host a quantum spin liquid ground state described by the Kitaev model. In these materials, the edge-sharing environment between neighboring isospin-1/2 moments favors strongly anisotropic bond-directional interactions. This creates three orthogonal planes of interaction which cannot be simultaneously satisfied, leading to strong frustration and an emergent spin liquid state. Though most candidate materials order at low temperatures, Kitaev interactions dominate. The three-dimensional β and γ phases of the lithium iridates, Li₂IrO₃, show an unusual incommensurate antiferromagnetic order at T_i~38K. Previous studies have suppressed magnetic order by applying weak magnetic fields and hydrostatic pressure; however, the role that frustration plays in these systems is still debated. Theory predicts that chemical substitution on magnetic sites can induce a spin-glass state in these materials, reflecting frustrated interactions. In this work, we report spin-glass behavior in hole-doped Li₂IrO₃ at low substitution levels, indicating the fragility and tunability of the incommensurate order and indicating the strength frustration.   

Kitaev iridates in 3D: magnetic and structural instabilities

Recent efforts were focused on the search for honeycomb antiferromagnets that realize Kitaev model in two dimensions. Despite showing sizable Kitaev couplings, Na₂IrO₃ and α-Li₂IrO₃ undergo long-range magnetic ordering at low temperatures and prove hard to be tuned by pressure, as compression leads to a dimerization instability and renders α-Li₂IrO₃ non-magnetic above 3.7 GPa.

Here, I will present recent results on the pressurized hyperhoneycomb iridate β-Li₂IrO₃ and argue that this compound can be tuned to a classical spin liquid state triggered by the reduction in the nearest-neighbor Kitaev term K and the enhancement of the off-diagonal anisotropy Γ. We find that above 1.4 GPa pressurized β-Li₂IrO₃ separates into a mixture of dynamic and frozen spins representing a partially frozen spin liquid, as expected in a system where spin dynamics is supported by thermal rather than quantum fluctuations.

I will further show how Kitaev magnetism is realized in three-dimensional frameworks of Ir⁴⁺ hexahalides that can be chemically tuned even at ambient pressure, thus giving rise to a variety of intertwined structural and magnetic instabilities.   

NQR investigation of low frequency spin dynamics in Kitaev spin liquid candidate material Cu2IrO3 in zero magntic field

Cu₂IrO₃ [1] is a Kitaev spin liquid candidate material with nearly ideal honeycomb planes consisting of Ir magnetic moments, and does not exhibit a bulk magnetic long range order. We report ^63,65Cu Nuclear Quadrupole Resonance (NQR) investigation of Cu₂IrO₃ in zero external magnetic field [2]. Unlike the case of the celebrated sister compound Na₂IrO₃ or α-RuCl₃ with a bulk antiferromagnetic ground state below T_N, spin dynamics reflected on the NMR relaxation rate 1/T₁ does not show a divergent behavior caused by conventional magnons. We can therefore probe the intrinsic low energy spin excitations of the Kitaev planes using NQR in zero magnetic field in a broad window of temperature.

[1] M. Abramchuk, F. Tafti et al., JACS 139, 15371 (2017).
[2] S. K. Takahashi, J. Wang et al., preprint (to be published).   

NMR investigation of Kitaev spin liquid candidate material Cu2IrO3

Cu₂IrO₃ is a Kitaev spin liquid candidate material [1]. In this talk, we report ^63,65Cu high-field Nuclear Magnetic Resonance (NMR) measurements of Cu₂IrO₃ [2]. We probed the intrinsic spin susceptibility based on ^63,65Cu Knight shift, and the magnetic field effects on paramagnetic spin dynamics based on NMR relaxation rate 1/T₁.

[1] M. Abramchuk, F. Tafti et al., JACS 139, 15371 (2017).
[2] S. K. Takahashi, J. Wang et al., preprint (to be published).   

Competition between static and dynamic magnetism in the Kitaev spin liquid material Cu2IrO3.

Cu₂IrO₃ is a new honeycomb iridate without thermodynamic signatures of long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of Cu₂IrO₃. We find a two-component depolarization with slow and fast relaxation rates corresponding to distinct regions with dynamic and static magnetism, respectively. X-ray absorption spectroscopy and first principles calculations identify a mixed copper valence as the origin of this behavior. Our results suggest that a minority of Cu²⁺ ions nucleate regions of static magnetism whereas the majority of Cu⁺/Ir⁴⁺ on the honeycomb lattice give rise to a Kitaev spin liquid.   

Neutron Scattering Study of Kitaev Spin-Liquid Candidate H3LiIr2O6

A central theme of condensed matter physics in recent years has been the realization of materials that exhibit a quantum spin-liquid state beyond one dimension. The exactly solvable Kitaev model of a quantum spin liquid consists of a 2D honeycomb lattice of J_eff = ½ magnetic ions with bond dependant interactions. NMR and bulk sample characterization has suggested that H₃LiIr₂O₆ could be a spin-liquid [1]. The structure consists of a honeycomb lattice of Ir⁴⁺ ions with strong spin-orbit coupling to support the bond dependent exchange interactions required in the Kitaev model. While previous litium irdates have all been found to magnetically order at low temperature, specific heat and magnetization measurements show no order in this material down to low temperature. Using inelastic neutron scattering on SEQUOIA at ORNL, we probed the material magnetic excitations in D₃⁷Li¹⁹³Ir₂O₆. We describe features in neutron scattering which are consistent with those of a KSL. Through a first moment analysis of the scattering data we determine the range of interactions and an estimate for the ground state energy.
[1]K. Kitagawa, T. Takayama, Y. Matsumotot, A. Kato, R. Takano, Y. Kishimoto, S. Bette, R. Dinnebier, G. Jackeli, H. Takagi, Nature 554, 25482 (2018)   

Crystal electric field and structural study of Jeff = 1/2 K2IrX6 (X = Cl, Br)

Strong spin orbit coupling in 5d materials has been a focus of research due to the wide variety of exotic phases which can exist in these systems. Of particular interest are systems with octahedral coordination, the triply degenerate t_2g state will split into the occupied J_eff = 3/2 and the partially occupied J_eff = ½ states. It is this J_eff = ½ state that can host a large range of exotic phases such as quantum spin liquids and superconductivity. Here we present detailed data on two Iridium halide materials, K₂IrX₆, X = Cl, Br, which have the antifluorite structure and the Ir atom inside separated halide octahedra. Powder X-ray scattering study show a newly observed structural transition in the Br compound at T_c=180K. Resonant inelastic X-ray scattering data and X-ray absorption data are combined with quantum chemistry calculations to study the crystal electric field levels, and show that these materials show record proximity to the ideal Jeff = ½ state at all temperatures down to T=5K.   

Multi-scale Quantum Criticality driven by Kondo-lattice Coupling in Pyrochlore Systems

Pyrochlore systems with local moments and 5d conduction electrons offer excellent material platforms for the discovery of exotic quantum many-body ground states. Notable examples include U(1) quantum spin liquid (QSL) and semimetallic non-Fermi liquid state. Here we investigate emergent quantum phases and their transitions driven by the Kondo-lattice couplings. Using the renormalization group method, we show that weak Kondo-lattice coupling is irrelevant, leading to a fractionalized semimetal phase with decoupled local moments and conduction electrons. Upon increasing the Kondo-lattice coupling, this phase is unstable to the formation of broken symmetry states. The important thing is the opposing influence of the Kondo-lattice coupling and long-range Coulomb interaction. The former prefers to break the particle-hole symmetry while the latter tends to restore it. The characteristic competition leads to multiple phase transitions, first from a fractionalized semimetal phase to a fractionalized Fermi surface state with particle-hole pockets, followed by the second transition to a fractionalized ferromagnetic state. Multi-scale quantum critical behaviors appear at non-zero temperatures and with the external magnetic field near such quantum phase transitions.   

Observing spin fractionalization of the Kitaev spin liquid via temperature evolution of the K-edge RIXS response

A prominent feature of the Kitaev quantum spin liquid is fractionalization of the spin degree of freedom. Here we propose that the temperature evolution of the fractionalization in the Kitaev honeycomb model can be studied by
the resonant inelastic X-ray scattering (RIXS). We calculate the RIXS response of the Kitaev honeycomb model and show how
the momentum-energy map of the fractionalization varies with temperature. We also suggest that the indirect RIXS process at Ru K-edge which allows for sub-meV resolution can provide important insights about the structure of the excitation spectrum in $\alpha$-RuCl$_3$.   

Understanding counter-rotating spiral ordering in three dimensional Kitaev materials

The counter-rotating spiral ordering found in three-dimensional (3D) iridate Kitaev candidates suggest frustration of spin interactions and raise a possibility of nearby spin liquid phases. Understanding the microscopic mechanism of this ordering may provide routes to 3D Kitaev spin liquids. We study a minimal 3D model including Kitaev K and a symmetric off-diagonal bond-dependent Γ interaction on the hyperhoneycomb lattice by using exact diagonalization (ED). An ED cluster was chosen to satisfy a hidden SU(2) symmetry. The magnetic ordering in the transformed basis then generically maps to the counter-rotating noncoplanar spiral order of the original spin when the moment is pinned along a certain direction. When K and Γ are negative, a small positive Heisenberg interaction favours the (1,1,0) direction consistent with the reported spiral order in β-Li₂IrO₃. Our findings offer a relevant set of microscopic parameters, which in turn guides a way to approach possible Kitaev spin liquids.