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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Anisotropic Thermal Conductivity Oscillations in Relation to the Putative Kitaev Spin Liquid Phase of α-RuCl 3

In the presence of an external magnetic field, the Kitaev model could host either gapped topological anyons or gapless Majorana fermions. In α-RuCl 3 , the gapped and gapless cases are only separated by a 30° rotation of the in-plane magnetic field vector. The presence or absence of the spectral gap is key for understanding the thermal transport behavior in α-RuCl 3 . Here, we study the anisotropy of the oscillatory features of thermal conductivity in α-RuCl 3 . We examine the oscillatory features of thermal conductivities (κ / / a, κ / / b) with fixed external fields and find distinct behavior for the gapped (B / / a) and gapless (B / / b) scenarios. Furthermore, we track the evolution of thermal resistivity (λ α ) and its oscillatory features with the rotation of in-plane magnetic fields from B / / b to B / / a. The thermal resistivity λ(B, φ) displays distinct rotational symmetries before and after the emergence of the field-induced Kitaev spin liquid phase. These results suggest that oscillatory features of thermal conductivity in α-RuCl 3 are closely linked to the putative Kitaev spin liquid phase and its excitations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Ultrafast renormalization of the magnetic continuum in the proximal Kitaev quantum spin liquid H 3 LiIr 2 O 6 by tr-RIXS [Invited]

We present the first circularly polarized non-resonant pump time-resolved resonant inelastic X-ray scattering (tr-RIXS) experiment in H 3 LiIr 2 O 6 , an iridium-based Kitaev system. Our calculations and experimental results are consistent with the modification of the low-energy magnetic excitations in H 3 LiIr 2 O 6 only during illumination by the laser pulse. We discuss these results in a cooperative framework between the Floquet engineering of the exchange interactions and the dynamic renormalization of electron-electron correlations. However, the penetration length mismatch between the X-ray probe and laser pump and the intrinsic complexity of Kitaev magnets prevents us from unequivocally extracting towards which ground state H 3 LiIr 2 O 6 is driven. We outline possible solutions to these challenges for light-driven stabilization and observation of the Kitaev quantum spin liquid limit by RIXS.

Kim, Jungho [Argonne National Laboratory (ANL), Ar↗
DOE OSTI2023

Emergent orbital magnetization in Kitaev quantum magnets

Unambiguous identification of the Kitaev quantum spin liquid (QSL) in materials remains a huge challenge despite many encouraging signs from various measurements. To facilitate the experimental detection of the Kiteav QSL, here we propose to use remnant charge response in Mott insulators hosting QSL to identify the key signatures of QSL. We predict an emergent orbital magnetization in a Kitaev system in an external magnetic field. The direction of the orbital magnetization can be flipped by rotating the external magnetic field in the honeycomb plane. The orbital magnetization is demonstrated explicitly through a detailed microscopic analysis of the multiorbital Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture. We first derive the localized electrical loop current operator in terms of the spin degrees of freedom. Thereafter, utilizing the Majorana representation, we estimate the loop currents in the ground state of the chiral Kitaev QSL state, and obtain the consequent current textures, which are responsible for the emergent orbital magnetization. Finally, we discuss the possible experimental techniques to visualize the orbital magnetization which can be considered as the signatures of the underlying excitations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Pressure tuning of Kitaev spin liquid candidate Na$_3$Co$_2$SbO$_6$goo

The search for Kitaev's quantum spin liquid (KQSL) state in real materials has recently expanded with the prediction that honeycomb lattices of divalent, high-spin cobalt ions could host the dominant bond-dependent exchange interactions required to stabilize the elusive entangled quantum state. The layered honeycomb Na$_3$Co$_2$SbO$_6$ has been singled out as a leading candidate provided that the trigonal crystal field acting on Co $3d$ orbitals, which enhances non-Kitaev exchange interactions between $J_{\rm eff}=\frac{1}{2}$ spin-orbital pseudospins, is reduced. We find that applied pressure leads to anisotropic compression of the layered structure, significantly reducing the trigonal distortion of CoO$_6$ octahedra. A strong enhancement of ferromagnetic correlations between pseudospins is observed in the spin-polarized (3 Tesla) phase up to about 60 GPa. Higher pressures drive a spin transition into a low-spin state destroying the $J_{\rm eff}=\frac{1}{2}$ local moments required to map the spin Hamiltonian into Kitaev's model. The spin transition strongly suppresses the low-temperature magnetic susceptibility and appears to stabilize a paramagnetic phase driven by frustration. Although applied pressure fails to realize a KQSL state, the possible emergence of frustrated magnetism of localized, low-spin $S=\frac{1}{2}$ moments opens the door for exploration of novel magnetic quantum states in compressed honeycomb lattices of divalent cobaltates.

FOS: Physical sciences↗
DOE OSTI2022

Sound attenuation in the hyperhoneycomb Kitaev spin liquid

In recent years, it has been shown that the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Furthermore we propose that the sound attenuation measurements allows for the characterization and identification of the Kitaev quantum spin liquid on the hyperhoneycomb lattice, which is particularly interesting since the strong Kitaev interaction was observed in the the hyperhoneycomb magnet β–Li 2 IrO 3 . To this end we consider the low-temperature scattering between acoustic phonons and gapless Majorana fermions with nodal-line band structure. Here, we find that the sound attenuation has a characteristic angular dependence, which is explicitly shown for the high-symmetry planes at temperatures below the flux energy gap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Signatures of fractionalization in the optical phonons of the hyperhoneycomb Kitaev magnet 𝛽−Li 2 ⁢IrO 3

Here, in this study, we propose that the signatures of spin fractionalization in quantum magnets can be identified through a detailed analysis of the temperature dependence of the asymmetric Fano lineshape of optical phonons overlapping with a continuum of spin excitations. We focus on the hyperhoneycomb magnet 𝛽−Li 2 ⁢IrO 3 , a promising candidate for being in proximity to a three-dimensional Kitaev quantum spin liquid. The Raman response in 𝛽−Li 2 ⁢IrO 3 notably displays a distinctive asymmetric Fano lineshape in the 24 meV Raman-active optical phonon. This asymmetry arises from the interaction between the discrete phonon mode and the spin excitation continuum, which could be fractionalized if the material is indeed near a quantum spin-liquid phase. Our theoretical model considers the coupling of this optical phonon to Majorana fermions in the Kitaev model on the hyperhoneycomb lattice. Our findings reveal that the temperature-dependent Fano lineshape is consistent with the fractionalization of spins into Majorana fermions and ℤ ⁢2 fluxes.

Kitaev model↗
DOE OSTI2024

Complex orders and chirality in the classical Kitaev-Γ model

It is well recognized that the low-energy physics of many Kitaev materials is governed by two dominant energy scales, the Ising-type Kitaev coupling 𝐾 and the symmetric off-diagonal Γ coupling. An understanding of the interplay between these two scales is therefore the natural starting point toward a quantitative description that includes subdominant perturbations that are inevitably present in real materials. This study focuses on the classical 𝐾−Γ model on the honeycomb lattice, with a specific emphasis on the region 𝐾< 0 and Γ > 0 , which is the most relevant for the available materials and which remains enigmatic in both quantum and classical limits, despite much effort. We employ large-scale Monte Carlo simulations on specially designed finite-size clusters and unravel the presence of a complex multisublattice magnetic order in a wide region of the phase diagram, whose structure is characterized in detail. We show that this order can be quantified in terms of a coarse-grained scalar-chirality order, featuring a counterrotating modulation on the two spin sublattices. Here, we also provide a comparison to previous studies and discuss the impact of quantum fluctuations on the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Emergence of the isotropic Kitaev honeycomb lattice $α$–RuCl 3 and its magnetic properties

Here, we present a comprehensive investigation of the crystal and magnetic structures of the van der Waals antiferromagnet $α$–RuCl 3 using single crystal x-ray and neutron diffraction. The crystal structure at room temperature is a monoclinic (C2/m). However, with decreasing temperature, a remarkable first-order structural phase transition is observed, leading to the emergence of a rhombohedral ($R\bar3$) structure characterized by three-fold rotational symmetry forming an isotropic honeycomb lattice. On further cooling, a zigzag-type antiferromagnetic order develops below $T_{\textrm{N}} = 6\sim6.6$ K. The critical exponent of the magnetic order parameter was determined to be $\beta = 0.11(1)$, which is close to the two-dimensional Ising model. Additionally, the angular dependence of the magnetic critical field of the zigzag antiferromagnetic order for the polarized ferromagnetic phase reveals a six-fold rotational symmetry within the ab–plane. These findings reflect the symmetry associated with the Ising-like bond-dependent Kitaev spin interactions and underscore the universality of the Kitaev interaction-dominated antiferromagnetic system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Magnetic excitations and interactions in the Kitaev hyperhoneycomb iridate β –Li 2 ⁢IrO 3

Here, we present a thorough experimental study of the three-dimensional hyperhoneycomb Kitaev magnet β –Li 2 ⁢IrO 3 , using a combination of inelastic neutron scattering (INS), time-domain terahertz spectroscopy (TDTS), and heat capacity measurements. The main results include a massive low-temperature reorganization of the INS spectral weight that evolves into a broad peak centered around 12 meV, and a distinctive peak in the terahertz data at 2.8(1) meV. A detailed comparison to powder-averaged spin-wave theory calculations reveals that the positions of these two features are controlled by the anisotropic Γ coupling and the Heisenberg exchange J, respectively. The refined microscopic spin model places β –Li 2 ⁢IrO 3 in close proximity to the Kitaev spin liquid phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Analytic calculation of the vison gap in the Kitaev spin liquid

Although the ground-state energy of the Kitaev spin liquid can be calculated exactly, the associated vison gap energy has to date only been calculated numerically from finite size diagonalization. Here we show that the phase shift for scattering Majorana fermions off a single bond-flip can be calculated analytically, leading to a closed-form expression for the vison gap energy Δ = 0.2633 J . Generalizations of our approach can be applied to Kitaev spin liquids on more complex lattices such as the three dimensional hyper-octagonal lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe 2

The extraordinary properties of the Kitaev model have motivated an intense search for new physics in materials that combine geometrical and bond frustration. In this Letter, we employ inelastic neutron scattering, spin wave theory, and exact diagonalization to study the spin dynamics in the perfect triangular-lattice antiferromagnet (TLAF) CsCeSe 2 . This material orders into a stripe phase, which is demonstrated to arise as a consequence of the off-diagonal bond-dependent terms in the spin Hamiltonian. By studying the spin dynamics at intermediate fields, we identify an interaction between the single-magnon state and the two-magnon continuum that causes decay of coherent magnon excitations, level repulsion, and transfer of spectral weight to the continuum that are controlled by the strength of the magnetic field. Our results provide a microscopic mechanism for the stabilization of the stripe phase in TLAF and show how complex many-body physics can be present in the spin dynamics in a magnet with strong Kitaev coupling even in an ordered ground state. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Review of honeycomb-based Kitaev materials with zigzag magnetic ordering

The search for a Kitaev quantum spin liquid in crystalline magnetic materials has fueled intense interest in the two-dimensional honeycomb systems. Many promising candidate Kitaev systems are characterized by a long-range-ordered magnetic structure with an antiferromagnetic zigzag-type order, where the static moments form alternating ferromagnetic chains. Recent experiments on high-quality single crystals uncovered the existence of intriguing multi-k magnetic structures, which evolved from zigzag structures. Those discoveries have sparked new theoretical developments and amplified interest in these materials. We present an overview of the honeycomb materials known to display this type of magnetic structure and provide detailed crystallographic information for the possible single- and multi-k variants.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Theory of the Kitaev model in a [111] magnetic field

Recent numerical studies indicate that the antiferromagnetic Kitaev honeycomb lattice model undergoes a magnetic-field-induced quantum phase transition into a new spin-liquid phase. This intermediate-field phase has been previously characterized as a gapless spin liquid. By implementing a recently developed variational approach based on the exact fractionalized excitations of the zero-field model, we demonstrate that the field-induced spin liquid is gapped and belongs to Kitaev’s 16-fold way. Specifically, the low-field non-Abelian liquid with Chern number C = ±1 transitions into an Abelian liquid with C = ±4. The critical field and the field-dependent behaviors of key physical quantities are in good quantitative agreement with published numerical results. Furthermore, we derive an effective field theory for the field-induced critical point which readily explains the ostensibly gapless nature of the intermediate-field spin liquid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A j eff = 1/2 Kitaev material on the triangular lattice: the case of NaRuO 2

Motivated by recent reports of a quantum-disordered ground state in the triangular lattice compound NaRuO 2 , we derive a j eff = 1/2 magnetic model for this system by means of first-principles calculations. The pseudospin Hamiltonian is dominated by bond-dependent off-diagonal Γ interactions, complemented by a ferromagnetic Heisenberg exchange and a notably antiferromagnetic Kitaev term. In addition to bilinear interactions, we find a sizable four-spin ring exchange contribution with a strongly anisotropic character, which has been so far overlooked when modeling Kitaev materials. The analysis of the magnetic model, based on the minimization of the classical energy and exact diagonalization of the quantum Hamiltonian, points toward the existence of a rather robust easy-plane ferromagnetic order, which cannot be easily destabilized by physically relevant perturbations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Probing chiral Kitaev spin liquids via dangling boundary fermions

Identifying experimental probes capable of diagnosing extreme quantum behavior is widely regarded as one of the foremost challenges in modern condensed matter physics. Here, we propose a novel approach for detecting chiral Kitaev spin-liquid states through measurements of the local dynamical spin structure factor on the boundary using scanning tunneling microscopy (STM). We specifically focus on unpaired (“dangling”) Majorana fermions, which naturally emerge along boundaries of Kitaev spin liquids, and can serve as indicators of chiral boundary modes under broad conditions, thereby offering a clear signature of these exotic quantum states.

Zhang, Shang-Shun [University of Tennessee, Knoxvi↗
DOE OSTI2025

Probing the Kitaev honeycomb model on a neutral-atom quantum computer

Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, owing to the non-local nature of fermions, such models are challenging to simulate with qubit devices. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays. We utilize a fermion-to-qubit mapping based on Kitaev’s model on a honeycomb lattice, in which fermionic statistics are encoded using long-range entangled states. We prepare these states efficiently using measurement and feedforward, realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram and verify the non-Abelian spin-liquid phase by evaluating an odd Chern number. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study the dynamics of the Fermi–Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry and high-energy physics.

atomic and molecular physics↗
DOE OSTI2023

Signatures of a Majorana-Fermi surface in the Kitaev magnet Ag 3 LiIr 2 O 6

Detecting Majorana fermions in experimental realizations of the Kitaev honeycomb model is often complicated by non-trivial interactions inherent to potential spin liquid candidates. In this work, we identify several distinct thermodynamic signatures of massive, itinerant Majorana fermions within the well-established analytical paradigm of Landau-Fermi liquid theory. We find a qualitative and quantitative agreement between the salient features of our Landau-Majorana liquid theory and the Kitaev spin liquid candidate Ag 3 LiIr 2 O 6 . Our study presents strong evidence for a Fermi liquid-like ground state in the fundamental excitations of a honeycomb iridate, and opens new experimental avenues to detect itinerant Majorana fermions in condensed matter systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Magnon-spinon dichotomy in the Kitaev hyperhoneycomb β-Li 2 IrO 3

The family of edge-sharing tricoordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin-liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually preempted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-one-dimensional spin chains. Here in this paper we present a resonant inelastic x-ray scattering study of the magnetic excitations of the hyperhoneycomb iridate β-Li 2 IrO 3 under a magnetic field with a record-high-resolution spectrometer. At low temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16 meV. A 2 T magnetic field softens the dispersion around Q = 0. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnonlike mode is superimposed by a broad continuum of excitations, centered around 35 meV and extending up to 100 meV. This high-energy continuum survives up to at least 300 K—well above the ordering temperature of 38 K—and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗