Session S22: Quantum Spin Liquids III: Triangular and Honeycomb Systems

Probing short-range magnetism in candidate quantum spin liquids and related materials with a "both-and" approach to diffuse neutron scattering data

Extracting the maximum possible information from diffuse neutron scattering data is an important objective that supports efforts to gain a deeper understanding of the entangled ground states of quantum spin liquids and related materials. Significant progress has been made in the recent past by modeling diffuse magnetic scattering either in reciprocal space or real space using either big-box (e.g. reverse Monte Carlo) or small-box (e.g. magnetic unit cell) models. However, this "either-or" approach may not be as effective as a "both-and" approach that considers the data in both reciprocal space and real space and makes use of both big-box and small-box models in a complementary fashion. The power of the "both-and" approach is highlighted in recent studies of two triangular lattice antiferromagnets: TmMgGaO₄, which is thought to host a Kosterlitz-Thouless phase, and NaYbO₂, a candidate quantum spin liquid. We present diffuse neutron scattering data on both of these systems and demonstrate how the use of complementary modes of analysis reveals important details about the local magnetic correlations that could otherwise be easily missed. In addition to shedding light on the physics of these two interesting systems, this work motivates future "both-and" studies of candidate quantum spin liquids and related materials.   

New Quantum Spin Liquid Candidates Based on a Tm triangular lattice

Quantum spin liquids are exotic states of matter where the electron spins are highly entangled but do not display any long-range magnetic order even at zero temperature. They contain fractionalized excitations and could lead to high-temperature superconductivity as well as applications in quantum computation. Therefore, the experimental realization of quantum spin liquids has been a long-sought goal of condensed matter physics. Several triangular lattice rare earth compounds have been proposed as quantum spin liquid candidates thus far. The rare earth ions in these compounds have small spins and form a triangular lattice which can lead to exotic ground states due to geometric frustration brought about by the lattice symmetry. In this talk, I will discuss our results from single crystal thermodynamic measurements (field-dependent heat capacity, magnetization, ac susceptibility) and powder inelastic neutron scattering measurements on Tm-based triangular lattice compounds. No long-range order is observed down to 50 mK. The magnetic susceptibility indicates a high degree of frustration with a Curie-Weiss temperature of -14 K. These are all indications of a quantum spin liquid ground state.   

How many bodies are many-body? Characterizing the effect of lattice sizes on many-body entanglements through thermal conductivity measurements on NaYbxLu1-xSe2

Quantum spin liquid (QSL) is an intriguing many-body phase of matter characterized by its anomalously high degree of entanglement. While new crystal candidates hosting QSL are synthesized continually, in recent years, simulating QSLs with Rydberg-atom-array-based quantum simulators [Semeghini 2021] has gained considerable momentum. To characterize such an inherently many-body phase as QSL, infinitely large lattices of perfect geometric order are needed theoretically. In experimental practices, however, quantum simulators are limited to a few hundred sites, and lattice disorders are inevitable in crystal growths. Both limitations could drastically alter the intended QSL phases simulated or hosted [de la Torre 2023]. Therefore, it is crucial to investigate how lattice size and boundary conditions would affect the formation of QSL, attempting to answer the fundamental question of “how many bodies are many-body?” To do this, we synthesized compositions of NaYb_xLu_1-xSe₂, where by increasing the doping x, we can form a collection of antiferromagnetic triangular lattices of Jeff = 1/2 Yb³⁺ ions with growing sizes and connections. We then characterize this series via thermal transport measurements under extremely low temperatures, focusing on the behavior changes across the percolation transition at x = 0.5 when isolated lattices join to form networks of infinity size.   

Room temperature excitation continuum in the Rare-Earth Magnetic Insulator RInO3

Mott insulators have the capacity to support various unique ground states, and one of the most intriguing systems among them is a quantum spin liquid that comprises highly entangled spins. It is established that such an entangled system can host novel non-local excitations, like the continuum excitation known as a spinon. Using terahertz time-domain spectroscopy, we have detected a continuum excitation in the magnetic insulators RInO₃ (where R stands for Tb³⁺ and Gd³⁺). This continuum excitation exhibits optical conductivity proportional to the square of frequency, even at room temperature. Furthermore, a Fano distortion observed in the lowest optical phonon mode suggests a pronounced interaction with the continuum excitation. In the case of TbInO₃, the proportional frequency-dependent optical conductivity remains robust and is unaffected by external magnetic fields of up to 7 T, persisting at low temperatures as low as 1.5 K. Conversely, the continuum excitation in GdInO₃ diminishes as the temperature decreases. Our results propose the existence of an emergent charge excitation, even in a wide-bandgap Mott insulator, and hint at the potential for achieving a highly entangled many-body state at room temperature.   

First-principles derivation of magnetic interactions in the triangular quantum spin liquid candidates KYbCh2 (Ch=S, Se, Te) and AYbSe2 (A=Na, Rb)

The AYbCh₂ (A=alkali metal, Ch=chalcogen) delafossites hold great promise for the realization of the triangular quantum spin liquid state because of their defect-minimized growth and lack of magnetic ordering down to extremely low temperature. Here we use ab initio computations and strong coupling perturbation theory to evaluate the exchange couplings of the delafossites and examine the influence of chemical substitution on promoting the development of a quantum spin liquid state.   

Bond-dependent anisotropy and magnon decay in cobalt-based Kitaev triangular antiferromagnet

The Kitaev model, a honeycomb network of spins with bond-dependent anisotropic interactions, is a rare example that gives the quantum spin liquid state as an exact solution. Although most Kitaev model candidate materials eventually order magnetically due to additional non-Kitaev interactions, their bond-dependent anisotropy manifests in unusual spin dynamics. It has recently been suggested that bond-dependent anisotropy can stabilize exotic magnetic phases on the geometrically frustrated triangular lattice. Unfortunately, few materials have been identified with simultaneous geometric frustration and bond-dependent anisotropy. In this talk, I will present spin dynamics of iodine-based van der Waals triangular antiferromagnet CoI₂. We found evidence of finite bond-dependent anisotropy in CoI­₂ using inelastic neutron scattering. From the paramagnetic scattering and observed magnetic structure, we conclude that the Kitaev interaction plays an essential role in explaining. Moreover, momentum and energy-resolved inelastic neutron scattering measurements show substantial magnon decay and level repulsion in CoI₂. Our results provide the basis for future studies of the interplay between Kitaev magnetism and geometric frustration.   

Ab initio study for heterostructures of a Kitaev magnet α-RuCl3 and CrX3 (X=Cl and I)

The Kitaev model is a honeycomb spin model with bond-dependent anisotropic interactions, whose ground state features a quantum spin liquid with fractional excitations. Beyond the theoretical interest, it has also attracted much attention for the feasibility in real materials toward topological quantum computing. However, it remains a challenge to materialize the Kitaev spin liquid, especially at zero magnetic field, due to parasitic interactions beyond the Kitaev model. For instance, a prime candidate α-RuCl₃ exhibits a zigzag-type antiferromagnetic order at low temperature, albeit the hallmarks of the Kitaev spin liquid were observed only within a specific region in an applied magnetic field. Here, we propose a possible realization of the Kitaev spin liquid at zero field, by making van der Waals heterostructures of α-RuCl₃ and a ferromagnet CrX₃ (X=Cl and I). Using ab initio calculations, we find that in the case of X=Cl, the spin-orbit coupled Mott insulating state, which is a key to realizing the Kitaev-type interactions, is preserved in the heterostructure and the zigzag order is suppressed at zero field by the proximity of the XY ferromagnet CrX₃. In contrast, in the case of X=I, the Mott gap is almost closing, suggesting that the α-RuCl₃ layer is on the verge of an insulator-metal transition in the spin-orbit coupled bands. Our results indicate that van der Waals heterostructures provide a new platform for studying not only magnetic but also electronic properties of the Kitaev spin liquids.   

Topological and magnetic phase transitions in bilayer Kitaev-Ising model

We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising inter-layer interactions via Majorana mean field theory and perturbative analysis. We show that a diverse array of magnetic and topological phase transitions occur with inter-layer exchange depending on the direction of the Ising interaction and the relative sign of the Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin-liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite sign of the Kitaev interaction, we observe a notable weakening of the magnetic tendencies and the Kitaev spin liquid survives up to a remarkably larger inter-layer exchange. Our analysis identifies the emergence of an intermediate gapped Ζ₂ spin liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated 120° compass model. We conclude with a discussion on the perturbative analysis when the Ising axis lie along z-axis or in the xy-plane. In both cases, our analysis reveals the formation of 1D Ising chains, which intriguingly remain decoupled up to the sixth order in perturbation theory. Our results highlight the interplay between topological order and magnetic tendencies in bilayer quantum spin liquids.   

Ground-state phase diagram of an extended Kitaev-Gamma model on a honeycomb lattice

Abstract: Alpha-RuCl3 has been studied extensively due to the possible realization of Kitaev spin liquid physics. The Kitaev-Gamma (KGamma) model on the honeycomb lattice has been proposed as a minimal model of alpha-RuCl3. So far, the KGamma model has mostly been studied considering equal coupling strength along the three bond directions of the honeycomb lattice. However, the details of the ground states have been under debate. In this study, we extended the model to include an additional parameter that controls the coupling strength on one of the bonds; we connect the limit of isolated KGamma chains to the isotropically interacting two-dimensional (2d) model. We investigate the ground-state phase diagram by using numerical exact diagonalizations and density-matrix renormalization group methods. We find that TLL appearing in the chain limit [2] persist for finite interchain couplings. In this proximate TLL phase, the low-energy excitation is characterized by spinon-like gapless excitation that is similar to that is observed in S=1/2 antiferromagnetic Heisenberg chain. In contrast, D4 magnetically ordered state [2] in the spin chain limit becomes 90-degree non-coplanar ordered state in the 2d model. Furthermore, we find that two magnetically ordered states seem to exist near the limit of the antiferromagnetic Kitaev spin chain. These two states also become corresponding ordered states in the 2d model.

 

[1] J. G. Rau, E. Lee, and H.-Y. Kee, Phys. Rev. Lett. 112, 077204 (2014).

[2] W. Yang, et al., Phys. Rev. Lett. 124, 147205 (2020).   

Exotic Spin Liquid phases in Generalized Kitaev JKΓΓ' model on honeycomb lattice

Employing a gauge invariant Majorana fermion decomposition of spin, we derive a renormalized mean-field theory (RMFT) for the Generalized Kitaev JKΓΓ' model under magnetic fields on a honeycomb lattice. We allow for the most general mean field parameters permitted by the projected symmetry group. Our RMFT approach provides good results compared with other numerical methods such as DMRG and VMC on the same model, e.g., reproducing the 8-,14-,20-cone quantum spin-liquid (QSL) states in the KΓmodel and under fields. Therefore, we are confident that this RMFT approach provides an economic way to investigate the mean-field spinon band structure properties (Chern number etc.) and complex vortices structure in JKΓΓ' model under field in arbitrary directions.

    By using our RMFT, we find several new stable QSL states which are not found by early VMC works. In particular, a new exotic 2-cone state with negative Wilson loop values and Chern number ν=±1 is found. In the presence of magnetic fields along ab plane, this 2-cone state holds opposite Chern number compared to the Kitaev spin liquid, and is thus a new state that is distinct from the Kitaev spin liquid. Furthermore, it displays non-Abelian statistics in weak magnetic fields when gap is opened, which provides a new perspective to examine experimental results