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All sourcesNASA NTRSDOE OSTI
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

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 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 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

Magnetic field effects on the quantum spin liquid behaviors of NaYbS 2

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides NaYbCh 2 (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between Na + and Yb 3+ ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the Yb 3+ ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Pressure tuning of Kitaev spin liquid candidate Na 3 Co 2 SbO 6

The search for Kitaev’s quantum spin liquid 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 $J$ eff = $\frac{1}{2}$ spin-orbital pseudospins, is reduced. Here we show that applied pressure leads to anisotropic compression of the layered structure, significantly reducing the trigonal distortion of CoO 6 octahedra. Ferromagnetic correlations between pseudospins are enhanced in the spin-polarized (3 Tesla) phase up to about 60 GPa. Higher pressures drive a high-spin to low-spin transition destroying the $J$ eff = $\frac{1}{2}$ 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. The possible emergence of frustrated magnetism of localized $S$ = $\frac{1}{2}$ moments opens the door for exploration of novel magnetic quantum states in compressed honeycomb lattices of divalent cobaltates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Evidence for field induced quantum spin liquid behavior in a spin-1/2 honeycomb magnet

One of the most important issues in modern condensed matter physics is the realization of fractionalized excitations, such as the Majorana excitations in the Kitaev quantum spin liquid. To this aim, the 3d-based Kitaev material Na 2 Co 2 TeO 6 is a promising candidate whose magnetic phase diagram of B // a* contains a field-induced intermediate magnetically disordered phase within 7.5 T < |B| < 10 T. The experimental observations, including the restoration of the crystalline point group symmetry in the angle-dependent torque and the coexisting magnon excitations and spinon-continuum in the inelastic neutron scattering spectrum, provide strong evidence that this disordered phase is a field induced quantum spin liquid with partially polarized spins. Our variational Monte Carlo simulation with the effective K-J 1 -Γ-Γ'-J 3 model reproduces the experimental data and further supports this conclusion.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Magnetoelastic coupling anisotropy in the Kitaev material α-RuCl 3

Here we show that the Kitaev material α-RuCl 3 is among the most prominent candidates to host a quantum spin-liquid state endowed with fractionalized excitations. Recent experimental and theoretical investigations have separately revealed the importance of both the magnetoelastic coupling and the magnetic anisotropy in dependence of the applied magnetic-field direction. In this combined theoretical and experimental research, we investigate the anisotropic magnetic and magnetoelastic properties for magnetic fields applied along the main crystallographic axes as well as for fields canted out of the honeycomb plane. We found that the magnetostriction anisotropy is unusually large compared to the anisotropy of the magnetization, which is related to the strong magnetoelastic $\tilde{Γ}'$-type coupling in our ab-initio derived model. We observed large, nonsymmetric magnetic anisotropy for magnetic fields canted out of the honeycomb ab plane in opposite directions, namely, toward the +c* or -c* axes, respectively. The observed directional anisotropy is explained by considering the relative orientation of the magnetic field with respect to the coaligned RuCl 6 octahedra. Magnetostriction measurements in canted fields support this nonsymmetric magnetic anisotropy; however, these experiments are affected by magnetic torque effects. Comparison of theoretical predictions with experimental findings allow us to recognize the significant contribution of torque effects in experimental setups where α-RuCl 3 is placed in canted magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effective J eff = 1/2 magnetic moments. This includes, but not limited to, 5d 5 iridates, 4d 5 ruthenates and 3d 7 cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Lastly, we highlight some of the key questions in the field as well as future directions.

Kitaev materials↗
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 OSTI2024

Vacancy Spectroscopy of Non-Abelian Kitaev Spin Liquids

Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. In this study, our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This “quasi-zero-voltage peak” is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid. Our proposed signatures are within reach of current experiments on the candidate material α-RuCl 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 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↗
DOE OSTI2020

Tunneling Spectroscopy of Quantum Spin Liquids

Here, we examine the spectroscopic signatures of tunneling through a Kitaev quantum spin liquid (QSL) barrier in a number of experimentally relevant geometries. We combine contributions from elastic and inelastic tunneling processes and find that spin-flip scattering at the itinerant spinon modes gives rise to a gapped contribution to the tunneling conductance spectrum. We address the spectral modifications that arise in a magnetic field, which is applied to drive the candidate material α-RuCl 3 into a QSL phase, and we propose a lateral 1D tunnel junction as a viable setup in this regime. The characteristic spin gap is an unambiguous signature of the fractionalized QSL excitations, distinguishing it from magnons or phonons. We discuss the generalization of our results to a wide variety of QSLs with gapped and gapless spin correlators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2026

Disorder-induced spin-cluster magnetism in a doped kagome spin liquid candidate

The search for new quantum spin liquid materials relies on systems with strong frustration such as spins on an ideal kagome lattice. However, lattice imperfections can have substantial effects which are as yet not well understood. In recent work, the two-dimensional kagome system YCu 3 ⁢(OH) 6 ⁢[(Cl 𝑥 ⁢Br (1−𝑥) ) 3−𝑦 ⁢(OH) 𝑦 ] has emerged as a leading candidate hosting a Dirac spin liquid which appears to survive at least for 𝑥 < 0.4, associated with alternating-bond-hexagon (ABH) disorder. Here in magnetic samples with 𝑥 = 0.58, 𝑦 = 0.1 we report unusual in-plane ferromagnetic canting (FM) of the in-plane antiferromagnet (AFM), with an unusually wide regime of short-ranged order, and propose theoretical models to explain this behavior. First, we show that Kitaev-type exchanges naturally arise on the kagome lattice to second order in the known Dzyaloshinskii-Moriya exchanges, and that these interactions can produce the unusual in-plane FM canting from antichiral AFM. Second, we propose a phenomenological model of weakly FM-canted spin clusters to describe the short-ranged regime and analyze quantum fluctuations in an ABH toy model to show how ABH disorder can stabilize this regime. Here, the combination of experimental observation and theory suggests that kagome-Kitaev interactions and ABH disorder are necessary for describing the magnetic fluctuations in this family of materials, with potential implications for the proposed proximate spin liquid phase.

Seth, Arnab [Georgia Institute of Technology, Atla↗