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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Pairing tendencies in the doped Kitaev-Heisenberg model

Here, we study the impact of hole doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a t - J - K model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the Néel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely, a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Static and dynamical magnetic properties of the extended Kitaev-Heisenberg model with spin vacancies

Motivated by the potential to suppress antiferromagnetic long-range order in favor of the long-sought-after Kitaev quantum spin liquid state, we study the effect of spin vacancies in the extended Kitaev-Heisenberg model. In particular, we focus on a realistic model obtained from fitting inelastic neutron scattering on α–RuCl 3 . We observe that the long-range zigzag magnetic ordered state only survives when the doping concentration is smaller than 5%. Upon further increasing the spin vacancy concentration, the ground state becomes a short-range ordered state at low temperatures. Compared with experiments, our classical solution overstabilizes the zigzag correlation in the presence of spin vacancies. Here, our theoretical results provide guidance toward interpreting inelastic neutron scattering experiments on magnetically diluted Kitaev candidate materials

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Easy-plane anisotropic-exchange magnets on a honeycomb lattice: Quantum effects and dealing with them

We provide analytical and numerical insights into the phase diagram and other properties of the extended Kitaev-Heisenberg model on the honeycomb lattice in the easy-plane limit, in which interactions are only between spin components that belong to the plane of magnetic ions. This parameter subspace allows for a much-needed systematic quantitative investigation of spin excitations in the ordered phases and of their generic features. Specifically, we demonstrate that in this limit one can consistently take into account magnon interactions in both zero-field zigzag and field-polarized phases. For the nominally polarized phase, we propose a regularization of the unphysical divergences that occur at the critical field and are plaguing the 1/S approximation in this class of models. For the explored parameter subspace, all symmetry-allowed terms of the standard parametrization of the extended Kitaev-Heisenberg model, such as K, J, and Γ, are significant, making the offered consideration relevant to a much wider parameter space. Furthermore, the dynamical structure factor near the paramagnetic critical point illustrates this relevance by showing features that are reminiscent of the ones observed in α–RuCl 3 , underscoring that they are not unique and should be common to a wide range of parameters of the model and, by extension, to other materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Rethinking 𝛼−RuCl 3 : Parameters, models, and phase diagram

RuCl 3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44 Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form 𝛼−RuCl 3 rose to exceptional prominence. This “rediscovery” of 𝛼−RuCl 3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of 𝛼−RuCl 3 , and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the nontrivial physical properties of this material. These constraints allow one to focus on the relevant region of the multidimensional phase diagram of the 𝛼−RuCl 3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the 𝛼−RuCl 3 parameter space using quasiclassical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization-group methods, demonstrating a remarkably close quantitative accord between them on the general structure and hierarchy of the phases, with the zigzag, ferromagnetic, and incommensurate phases that are proximate to each other. As a result, one of the highlights is the detailed agreement on the nature of the incommensurate phases that realize two distinct counterrotating helical states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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

Static and dynamic magnetic properties of honeycomb lattice antiferromagnets Na 2 M 2 TeO 6 , M = Co and Ni

The magnetic structures and spin dynamics of Na 2 CO 2 TeO 6 and Na 2 Ni 2 TeO 6 are investigated by means of elastic and inelastic neutron scattering measurements and the results are discussed in the context of a generalized Kitaev-Heisenberg model on a honeycomb lattice with strong spin-orbit coupling. The large number of parameters involved in the Hamiltonian model is evaluated by using an iterative optimization algorithm capable of extracting model solutions and simultaneously estimating their uncertainty. The analyses indicate that both Co 2+ (d 7 ) and Ni 2+ (d 8 ) antiferromagnets realize bond-dependent anisotropic nearest-neighbor interactions and support the theoretical predictions for the realization of Kitaev physics in 3 d electron systems with effective spins S = 1/2 and 1. By studying the Na-doped system Na 2.4 Ni 2 TeO 6 , we show that the control of Na content can provide an effective route for fine-tuning the magnetic lattice dimensionality, as well as to controlling the bond-dependent anisotropic interactions.

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 OSTI2021

Single-ion anisotropy is necessary and appropriate to study the magnetic behavior of ${\mathrm{Tb}}^{3+}$ moments with ${J}_{\text{eff}}=\frac{1}{2}$ on the honeycomb lattice in ${\mathrm{Tb}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Ga}}_{9}$

By developing models of increasing complexity, we show that a model without single-ion anisotropy (SIA) cannot explain the magnetic properties of J eff = 1 / 2 Tb 3+ moments in the orthorhombically distorted, honeycomb material Tb 2 Ir 3 Ga 9 . In four different models for the magnetization of a single honeycomb layer, the only sources of anisotropy are symmetric exchange interactions J nαβ = J nβα along three different bonds n , an anisotropic $\underline{g}$ tensor, and a Dzyalloshinskii-Moriya interaction (asymmetric exchange) that produces the observed canted moment along b . With 21 parameters, the best such model yields χ 2 = 0.065 , which is substantially smaller than χ 2 = 0.112 obtained using a Heisenberg model containing six parameters including easy-axis anisotropy. However, models without SIA fail to reproduce the linear dependence of the magnetization with a field perpendicular to the Ising axis while predicting a saturation magnetization that is far too low. Due to the complex crystal-field environments, we argue that SIA is necessary to study low-symmetry, three-dimensional J eff = 1 / 2 materials containing Tb 3+ ions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Impurity-induced moment freezing in NaFe x⁢ Ru 1–x O 2

We report the impact of magnetic impurity substitution on the quantum disordered magnetic ground state of NaRuO 2 . Local S = 5/2 moments are introduced into the frustrated triangular lattice of J eff = 1/2 Ru moments via Fe substitution in NaFe x⁢ Ru 1–x O 2 , and the evolution of the magnetic ground state is reported. Local spin freezing associated with conventional spin-glass behavior is observed upon Fe substitution, marking an impurity-induced freezing of the primarily dynamic magnetic ground state in NaRuO 2 . Furthermore, local Fe moments induce a Curie-Weiss magnetic behavior in the uniform magnetic susceptibility, and the local moment magnitude is best described by dynamic Ru moments polarized about impurity sites. Furthermore, our results establish an impurity-doping phenomenology consistent with inherently dynamic moments in NaRuO 2 that are pinned by local magnetic impurities, similar to “swiss cheese” models of impurity-substituted copper oxides.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Collective excitations in the tetravalent lanthanide honeycomb antiferromagnet

Thermomagnetic and inelastic neutron-scattering measurements on Na 2 PrO 3 are reported. This material is an antiferromagnetic honeycomb magnet based on the tetravalent lanthanide Pr 4+ and has been proposed to host dominant antiferromagnetic Kitaev interactions. These measurements reveal magnetic fluctuations in Na 2 PrO 3 below an energy of 2 meV as well as crystal-field excitations around 230 meV. Furthermore, the latter energy is comparable to the scale of the spin-orbit interaction and explains both the very small effective moment of around 1.0μB per Pr 4+ and the difficulty to uncover any static magnetic scattering below the ordering transition at T N = 4.6 K. By comparing the low-energy magnetic excitations in Na 2 PrO 3 to those of the isostructural spin-only compound, Na 2 TbO 3 , a microscopic model of exchange interactions is developed that implicates dominant and surprisingly large Heisenberg exchange interactions J≈1.1(1) meV. Although antiferromagnetic Kitaev interactions with K≤0.2J cannot be excluded, the inelastic neutron-scattering data of Na 2 PrO 3 is best explained with a Δ=1.22 easy-axis XXZ exchange anisotropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Enhanced hybridization in the electronic ground state of the intercalated honeycomb iridate Ag 3 LiIr 2 O 6

In this work, we use x-ray spectroscopy at the Ir L 3 /L 2 absorption edge to study powder samples of the intercalated honeycomb magnet Ag 3 LiIr 2 O 6 . Based on x-ray absorption and resonant inelastic x-ray scattering measurements, and exact diagonalization calculations including nearest-neighbor Ir-Ir electron hopping integrals, we argue that the intercalation of Ag atoms results in a delocalized electronic structure with enhanced Ir-O hybridization, departing from the local relativistic j eff =1/2 state. We find that the relative orbital contribution to the magnetic moment is increased and the magnetization density is spatially extended and asymmetric in this hybridized state. Our results confirm the importance of metal-ligand hybridization in the magnetism of transition metal oxides and provide empirical guidance for understanding the collective magnetism in intercalated honeycomb iridates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Resolution of zigzag magnetic correlations in Na-deficient Na x IrO 3 without long-range ordering

The materials search for Kitaev quantum spin liquids led to the discovery of many honeycomb lattice materials. Much attention has been paid to materials without magnetic order down to the lowest temperatures. The newly synthesized Na-deficient Na x IrO 3 has been found to bear no sign of long-range magnetic order above 1 K from physical property measurements. In this paper, we report momentum-and energy-resolved excitation spectra in Na-deficient Na x IrO 3 measured using a resonant inelastic x-ray scattering spectrometer. Orbital excitation spectra show that the octahedral and trigonal crystal field splittings are larger in Na x IrO 3 than in Na 2 IrO 3 . On the other hand, the low-energy spectrum at low temperature shows a wave-vector dispersion and a spectral weight distribution that are similar to those of Na 2 IrO 3 , revealing that the two-dimensional zigzag magnetic correlations in Na x IrO 3 are similar to those in Na 2 IrO 3 in terms of the ordered magnetic moment direction and three dynamically fluctuating zigzag orders. The azimuth angle dependence of the low-energy spectrum corroborates these results. The two-dimensional zigzag magnetic correlations rapidly weaken until 50 K. At high temperatures, the spectral weight distribution of the low-energy excitation resembles that of the pure Kitaev model, indicating that the Kitaev interaction dominates the dynamic magnetic response at high temperature. Here we suggest that the larger crystal field and distortion and the weakened longer-range Heisenberg exchange interactions due to the Na deficiency in Na x IrO 3 contribute to bring Na x IrO 3 away from the zigzag long-range magnetic order phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Frustrated magnetic cycloidal structure and emergent Potts nematicity in CaMn 2 P 2

We report neutron-diffraction results on single-crystal CaMn 2 P 2 containing corrugated Mn honeycomb layers, and we determine its ground-state magnetic structure. The diffraction patterns consist of prominent (1/6,1/6, L ) reciprocal-lattice unit (r.l.u.; L = integer) magnetic Bragg reflections, whose temperature-dependent intensities are consistent with a first-order antiferromagnetic phase transition at the Néel temperature T N = 70 (1) K. Our analysis of the diffraction patterns reveals an in-plane 6 × 6 magnetic unit cell with ordered spins that in the principal-axis directions rotate by 60°steps between nearest neighbors on each sublattice that forms the honeycomb structure, consistent with the P A c magnetic space group. We find that a few other magnetic subgroup symmetries (P A 2 /c, P C 2/m, P S 1, P C 2, P C m, P S 1) of the paramagnetic $P\bar{3}m11'$ crystal symmetry are consistent with the observed diffraction pattern. We relate our findings to frustrated J 1 -J 2 -J 3 Heisenberg honeycomb antiferromagnets with single-ion anisotropy and the emergence of Potts nematicity.

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

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↗