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DOE OSTI2020

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Further, among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl 3 and Na 2 IrO 3 , having an effective $\textit{S}$ = 1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe 3 , that rather possess a $\textit{S}$ = 3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3$\textit{d}$ transition metal compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Fractionalized excitations probed by ultrasound

In this work, we study magnetoelastic interactions by means of ultrasound experiments in 𝛼−RuCl 3 —a prototypical material for the Kitaev spin model on the honeycomb lattice, with a possible spin-liquid state featuring Majorana fermions and ℤ 2 -flux excitations. We present results of the temperature and in-plane magnetic-field dependence of the sound velocity and sound attenuation for several longitudinal and transverse phonon modes propagating along high-symmetry crystallographic directions. A comprehensive data analysis above the magnetically ordered state provides strong evidence of phonon scattering by Majorana fermions. This scattering depends sensitively on the value of the phonon velocities relative to the characteristic velocity of the low-energy fermionic excitations describing the spin dynamics of the underlying Kitaev magnet. Moreover, our data displays a distinct reduction of anisotropy of the sound attenuation, consistent with the presence of thermally excited ℤ 2 visons. Here, we demonstrate the potential of phonon dynamics as a promising probe for uncovering fractionalized excitations in 𝛼−RuCl 3 and provide new insights into the 𝐻−𝑇 phase diagram of this material.

Kitaev magnet↗
DOE OSTI2020

Two-magnon bound states in the Kitaev model in a [111] field

It is now well established that the Kitaev honeycomb model in a magnetic field along the [111] direction harbors an intermediate gapless quantum spin liquid (QSL) phase sandwiched between a gapped non-Abelian QSL at low fields $H < H_{c1}$ and a partially polarized phase at high fields $H > H_{c2}$. Here, we analyze the low-field and high-field phases and phase transitions in terms of single- and two-magnon excitations using exact diagonalization and density matrix renormalization group methods. In this work, we find that the energy to create a bound state of two-magnon $Δ_p$ becomes lower than the energy to create a single spin flip $Δ_s$ near $H_{c2}$. In the entire Kitaev spin liquid, $Δ_p < Δ_s$ and both gaps vanish at $H_{c2}$. We make testable predictions for magnon pairing that could be observable in Raman scattering measurements on Kitaev QSL candidate materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Geometrical frustration versus Kitaev interactions in BaCo 2 (AsO 4 ) 2

Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid (KSL) state. One of the front-runners is BaCo 2 (AsO 4 ) 2 (BCAO), where it was suggested that the exchange processes between Co 2+ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze a comprehensive inelastic neutron scattering (INS) study of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelastic spin structure factor measured in zero magnetic field, we examine two leading theoretical models: the Kitaev-type JK Γ Γ ′ model and the XXZ - J 1 - J 3 model. We show that the existing experimental data can be consistently accounted for by the XXZ - J 1 - J 3 model but not by the JK Γ Γ ′ model, and we discuss the implications of these results for the realization of a spin liquid phase in BCAO and more generally for the realization of the Kitaev model in cobaltates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Strong Kitaev Interaction in BaCo 2⁢ (AsO 4 ) 2

The inelastic neutron scattering results and their analysis unequivocally point to a dominant Kitaev interaction in the honeycomb-lattice cobaltate BaCo 2 ⁢(AsO 4 ) 2 . Our anisotropic-exchange model closely describes all available neutron scattering data in the material’s field-polarized phase. Furthermore, the density-matrix renormalization group results for our model are in close accord with the unusual double-zigzag magnetic order and the low in-plane saturation field of BaCo 2 ⁢(AsO 4 ) 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Temperature evolution of the phonon dynamics in the Kitaev spin liquid

In this work, we present a study of the phonon dynamics in the honeycomb Kitaev spin model at finite temperatures. We show that the fractionalized spin excitations of the Kitaev spin liquid, the itinerant Majorana fermions, and static Z 2 fluxes have distinct effects on the phonon dynamics, which makes the phonon dynamics a promising tool for exploring the Kitaev spin liquid candidate materials. In particular, we focus on the signature of the fractionalized excitations in the thermodynamic behavior of the sound attenuation and the phonon Hall viscosity: the former describes the phonon decay into the fractionalized excitations, and the latter is the leading order time-reversal symmetry breaking effect on the acoustic phonon. We find that the angular dependence of the attenuation coefficient and its magnitude is modified by the thermal excitation of the Z 2 fluxes. The strength of this effect strongly depends on the relative magnitude of the sound velocity and the Fermi velocity characterizing the low-energy Majorana fermions. We also show that the Hall viscosity is strongly suppressed by the increase of the density of the Z 2 fluxes at finite temperatures. All these observations reflect the effects of the emergent disorder on the Majorana fermions introduced by the Z 2 fluxes. Our analysis is based on the complementary analytical calculations in the low-temperature zero-flux sector, and numerical calculations in the inhomogeneous flux sectors at intermediate and high temperatures with stratified Monte Carlo (strMC) method.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Weak-field induced nonmagnetic state in a Co-based honeycomb

Layered honeycomb magnets are of interest as potential realizations of the Kitaev quantum spin liquid (KQSL), a quantum state with long-range spin entanglement and an exactly solvable Hamiltonian. Conventional magnetically ordered states are present for all currently known candidate materials, however, because non-Kitaev terms in the Hamiltonians obscure the Kitaev physics. Current experimental studies of the KQSL are focused on 4 d or 5 d transition metal–based honeycombs, in which strong spin-orbit coupling can be expected, yielding Kitaev interaction that dominates in an applied magnetic field. In contrast, for 3 d -based layered honeycomb magnets, spin-orbit coupling is weak, and thus, Kitaev physics should be substantially less accessible. Here, we report our studies on BaCo 2 (AsO 4 ) 2 , for which we find that the magnetic order associated with the non-Kitaev interactions can be fully suppressed by a relatively low magnetic field, yielding a nonmagnetic material and implying the presence of strong magnetic frustration and weak non-Kitaev interactions.

Science & Technology - Other Topics↗
DOE OSTI2022

Footprints of Kitaev spin liquid in the Fano lineshape of Raman-active optical phonons

We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide observable signatures of fractionalized excitations characteristic of the underlying spin-liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonian based on the D 3d symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low-temperature crossover shows pronounced magnetic-field dependence. We thus identify the observable effect of the Majorana fermions and the Z2 gauge fluxes encoded in the Fano lineshape. Our results are consistent with the phonon Raman scattering experiments in the candidate material α-RuCl 3 .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Unraveling the magnetic ground state in the alkali-metal lanthanide oxide Na 2 ⁢Pr⁡O 3

Here, a comprehensive set of muon spin spectroscopy and neutron scattering measurements supported by ab initio and model Hamiltonian simulations have been used to investigate the magnetic ground state of Na 2 ⁢PrO 3 . μSR reveals a Néel antiferromagnetic order below T N ~ 4.9K, with a small static magnetic moment m static ≤ 0.22 μ B /Pr collinearly aligned along the c axis. Inelastic neutron measurements reveal the full spectrum of crystal field excitations and confirm that the Pr 4+ ground-state wave function deviates significantly from the Γ 7 limit that is relevant to the Kitaev model. Single- and two-magnon excitations are observed in the ordered state below T N =4.6K and are well described by nonlinear spin wave theory from the Néel state using a magnetic Hamiltonian with Heisenberg exchange J=1 meV and symmetric anisotropic exchange Γ/J=0.1, corresponding to an XY model. Intense two magnon excitations are accounted for by g-factor anisotropy g z /g ± = 1.29. A fluctuating moment δm 2 = 0.57 ⁢(22) ⁢μ$^2_B$/Pr extracted from the energy and momentum integrated inelastic neutron signal is reduced from expectations for a local J = 1/2 moment with average g factor g avg ≈ 1.1. Together, the results demonstrate that the small moment in Na 2 ⁢PrO 3 arises from crystal field and covalency effects and the material does not exhibit significant quantum fluctuations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Inverse Faraday effect in Mott insulators

The inverse Faraday effect (IFE), where a static magnetization is induced by circularly polarized light, offers a promising route to ultrafast control of spin states. Here we study the IFE in Mott insulators using the Floquet theory. We find two distinct IFE behavior governed by the inversion symmetry. In the Mott insulators with inversion symmetry, we find that the effective magnetic field induced by the IFE couples ferromagnetically to the neighboring spins. While for the Mott insulators without inversion symmetry, the effective magnetic field due to IFE couples antiferromagnetically to the neighboring spins. We apply the theory to the spin-orbit coupled single- and multiorbital Hubbard model that is relevant for the Kitaev quantum spin liquid material and demonstrate that the magnetic interactions can be tuned by light.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Kitaev physics in the two-dimensional magnet NiPSe 3

The Kitaev interaction, found in candidate materials such as α − RuCl 3 , occurs through the metal ( M )-ligand ( X )-metal ( M ) paths of the edge-sharing octahedra because the large spin-orbit coupling (SOC) on the metal atoms activates directional spin interactions. Here, we show that even in 3 d transition-metal compounds, where the SOC of the metal atom is negligible, heavy ligands can induce bond-dependent Kitaev interactions. In this work, we take as an example the 3 d transition-metal chalcogenophosphate NiPSe 3 and show that the key is found in the presence of a sizable SOC on the Se p orbital, one which mediates the super-exchange between the nearest-neighbor Ni sites. Our study provides a pathway for engineering enhanced Kitaev interactions through the interplay of SOC strength, lattice distortions, and chemical substitutions. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗
DOE OSTI2023

Electronic transport mechanisms in a thin crystal of the Kitaev candidate α -RuCl 3 probed through guarded high impedance measurements

α-RuCl 3 is considered to be the top candidate material for the experimental realization of the celebrated Kitaev model, where ground states are quantum spin liquids with interesting fractionalized excitations. It is, however, known that additional interactions beyond the Kitaev model trigger in α-RuCl 3 a long-range zigzag antiferromagnetic ground state. In this work, we investigate a nanoflake of α-RuCl 3 through guarded high impedance measurements aimed at reaching the regime where the system turns into a zigzag antiferromagnet. We investigated a variety of temperatures (1.45–175 K) and out-of-plane magnetic fields (up to 11 T), finding a clear signature of a structural phase transition at ≈160 K as reported for thin crystals of α-RuCl 3 , as well as a thermally activated behavior at temperatures above ≈30 K, with a characteristic activation energy significantly smaller than the energy gap that we observe for α-RuCl 3 bulk crystals through our angle resolved photoemission spectroscopy (ARPES) experiments. Additionally, we found that below ≈30 K, transport is ruled by Efros–Shklovskii variable range hopping (VRH). Most importantly, our data show that below the magnetic ordering transition known for bulk α-RuCl 3 in the frame of the Kitaev–Heisenberg model (≈7 K), there is a clear deviation from VRH or thermal activation transport mechanisms. Finally, our work demonstrates the possibility of reaching, through specialized high impedance measurements, the thrilling ground states predicted for α-RuCl 3 at low temperatures in the frame of the Kitaev–Heisenberg model and informs about the transport mechanisms in this material in a wide temperature range.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Hydrostatic pressure effect on the Co-based honeycomb magnet BaCo 2 (AsO 4 ) 2

Here the honeycomb antiferromagnet BaCo 2 (AsO 4 ) 2 , in which small in-plane magnetic fields (H1 ≈ 0.26T and H2 ≈ 0.52T at T = 1.8 K < T N ≈ 5.4K) induce two magnetic phase transitions, has attracted attention as a possible candidate material for the realization of Kitaev physics based on the 3d element Co 2+ . Here, we report on the change in the transition temperature T N and the critical fields H1 and H2 of BaCo 2 (AsO 4 ) 2 with hydrostatic pressure up to ~20 kbar, as determined from magnetization and specific heat measurements. Within this pressure range, a marginal increase in the magnetic ordering temperature is observed. At the same time, the critical fields are changed significantly (up to ~25 –35%). Specifically, we find that H1 is increased with hydrostatic pressure, i.e., the antiferromagnetic state is stabilized, whereas H2, which was previously associated with a transition into a proposed Kitaev spin-liquid state, decreases with increasing pressure. We discuss to what extent these results are compatible with suggested models with sizable third-nearest-neighbor exchange. Overall, the results put constraints on the magnetic models that are used to describe the low-temperature magnetic properties of BaCo 2 (AsO 4 ) 2 .

2-dimensional systems↗
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 OSTI2024

Phonon dynamics in the site-disordered Kitaev spin liquid

The Kitaev honeycomb model provides a paradigmatic example of an exactly solvable quantum spin liquid (QSL), where spins fractionalize into itinerant Majorana fermions coupled to a static background of ℤ 2 gauge fluxes. This model has attracted significant interest due to its potential experimental realization in spin-orbit Mott insulators like 𝛼−RuCl 3 . Among various experimental techniques, ultrasound measurements of sound attenuation have emerged as a promising approach to detect spin fractionalization in these materials. However, deviations from the ideal Kitaev model, often due to disorder, introduce localized modes that dominate the low-energy physics. To investigate these effects, we calculate the sound attenuation coefficient in the site-disordered Kitaev honeycomb model under an applied magnetic field that breaks time-reversal symmetry. Our analysis reveals that quasilocalized modes from quasivacancies impact the phonon self-energy, yet the sound attenuation coefficient maintains its sixfold symmetry and linear temperature dependence at low temperatures, even with disorder. This robustness underscores sound attenuation's reliability as a probe for spin fractionalization. As a result, we show that this linear behavior persists under an external field and in the random-flux sector, highlighting the persistent influence of fractionalized excitations, despite disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Scattering Signatures of Bond-Dependent Magnetic Interactions

Bond-dependent magnetic interactions can generate exotic phases such as Kitaev spin-liquid states. Experimentally determining the values of bond-dependent interactions is a challenging but crucial problem. In this paper, I show that each symmetry-allowed nearest-neighbor interaction on triangular and honeycomb lattices has a distinct signature in paramagnetic neutron-diffraction data, and that such data contain sufficient information to determine the spin Hamiltonian unambiguously via unconstrained fits. Moreover, I show that bond-dependent interactions can often be extracted from powder-averaged data. These results facilitate experimental determination of spin Hamiltonians for materials that do not show conventional magnetic ordering.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Cobalt-based pyroxenes: A new playground for Kitaev physics

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe 2 O 6 using a combination of neutron scattering, ab initio methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co 2+ ions. The extended Kitaev–Heisenberg model, including a significant anisotropic bond-dependent exchange term with K/|J| = 0.96, is identified as the key descriptor of the magnetic interactions in SrCoGe 2 O 6 . Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13 T) which shifts the system from a fragile antiferromagnetic ordering with T N = 9 K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended p orbitals, emerge as a platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Competing antiferromagnetic-ferromagnetic states in a d 7 Kitaev honeycomb magnet

The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li 3 Co 2 SbO 6 , built of high-spin d 7 (Co 2+ ) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/m, below T N = 11K at μ 0 H = 0T. The magnetic entropy recovered between T = 2 and 50 K is estimated to be 0.6Rln2, in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C2/m under an applied magnetic field of μ 0 H ≈ 0.7T at T = 2K. Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li 3 Co 2 SbO 6 , and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. Furthermore, this material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗