Antiferromagnetic Resonance and Terahertz Continuum in α-RuCl_{3}

Continuous Spin Excitations in the Three-Dimensional Frustrated Magnet K_{2}Ni_{2}(SO_{4})_{3}

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K_{2}Ni_{2}(SO_{4})_{3}, which consists of two sets of intersected spin-1 (Ni^{2+}) trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-Gaussian-approximation method, we determine that the fourth- and fifth-nearest-neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as a "hypertrillium" lattice. Our results provide direct evidence for the existence of QSL features in K_{2}Ni_{2}(SO_{4})_{3} and highlight the potential for the hypertrillium lattice to host frustrated quantum magnetism.

Phonon Anharmonicity and Spin-Phonon Coupling in CrI3

We report on the far-infrared, temperature-dependent optical properties of a CrI3 transition metal halide single crystal, a van der Waals ferromagnet (FM) with a Curie temperature of 61 K. In addition to the expected phonon modes determined by the crystalline symmetry, the optical reflectance and transmittance spectra of CrI3 single crystals show many other excitations as a function of temperature as a consequence of the combination of a strong lattice anharmonicity and spin-phonon coupling. This complex vibrational spectrum highlights the presence of entangled interactions among the different degrees of freedom in CrI3.

A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo₂(AsO₄)₂, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo₂(AsO₄)₂ is a promising QSL candidate.

Direct observation of the Mottness and p-d orbital hybridization in the epitaxial monolayer α-RuCl3

α-RuCl₃, a promising material to accomplish the Kitaev honeycomb model, has attracted enormous interest recently. Mottness and p-d bonds play vital roles in generating Kitaev interactions and underpinning the potential exotic states of quantum magnets, and the van der Waals monolayer is considered to be a better platform to approach a two-dimensional Kitaev model than the bulk. Here, we worked out the growth art of an α-RuCl₃ monolayer on a graphite substrate and studied its electronic structure, particularly the delicate orbital occupations, through scanning tunneling microscopy and spectroscopy. An in-plane lattice expansion of 2.67 ± 0.83% is observed and the pronounced t_2g-p_π and e_g-p_σ hybridization are visualized. The Mott nature is unveiled by an ∼0.6 eV full gap at the Fermi level located inside the t_2g-p_π manifold which is further verified by the density functional theory calculations. The monolayer phase of α-RuCl₃ fulfills the a priori criteria of recent theoretical predictions of tuning the relevant properties in this material and provides a novel platform to explore the Kitaev physics.

Liquid-Phase Exfoliation of Magnetically and Optoelectronically Active Ruthenium Trichloride Nanosheets

α-RuCl₃ is a layered transition metal halide that possesses a range of exotic magnetic, optical, and electronic properties including fractional excitations indicative of a proximate Kitaev quantum spin liquid (QSL). While previous reports have explored these properties on idealized single crystals or mechanically exfoliated samples, the scalable production of α-RuCl₃ nanosheets has not yet been demonstrated. Here, we perform liquid-phase exfoliation (LPE) of α-RuCl₃ through an electrochemically assisted approach, which yields ultrathin, electron-doped α-RuCl₃ nanosheets that are then assembled into electrically conductive large-area thin films. The crystalline integrity of the α-RuCl₃ nanosheets following LPE is confirmed through a wide range of structural and chemical analyses. Moreover, the physical properties of the LPE α-RuCl₃ nanosheets are investigated through electrical, optical, and magnetic characterization methods, which reveal a structural phase transition at 230 K that is consistent with the onset of Kitaev paramagnetism in addition to an antiferromagnetic transition at 2.6 K. Intercalated ions from the electrochemical LPE protocol favorably alter the optical response of the α-RuCl₃ nanosheets, enabling large-area Mott insulator photodetectors that operate at telecommunications-relevant infrared wavelengths near 1.55 μm. These photodetectors show a linear photocurrent response as a function of incident power, which suggests negligible trap-mediated recombination or photothermal effects, ultimately resulting in a photoresponsivity of ≈2 mA/W.

Low energy electrodynamics of CrI3 layered ferromagnet

We report on the optical properties from terahertz (THz) to Near-Infrared (NIR) of the layered magnetic compound CrI3 at various temperatures, both in the paramagnetic and ferromagnetic phase. In the NIR spectral range, we observe an insulating electronic gap around 1.1 eV which strongly hardens with decreasing temperature. The blue shift observed represents a record in insulating materials and it is a fingerprint of a strong electron-phonon interaction. Moreover, a further gap hardening is observed below the Curie temperature, indicating the establishment of an effective interaction between electrons and magnetic degrees of freedom in the ferromagnetic phase. Similar interactions are confirmed by the disappearance of some phonon modes in the same phase, as expected from a spin-lattice interaction theory. Therefore, the optical properties of CrI3 reveal a complex interaction among electronic, phononic and magnetic degrees of freedom, opening many possibilities for its use in 2-Dimensional heterostructures.

Magnon-phonon hybridization in 2D antiferromagnet MnPSe3

Magnetic excitations in van der Waals (vdW) materials, especially in the two-dimensional (2D) limit, are an exciting research topic from both the fundamental and applied perspectives. Using temperature-dependent, magneto-Raman spectroscopy, we identify the hybridization of two-magnon excitations with two phonons in manganese phosphorus triselenide (MnPSe3), a magnetic vdW material that hosts in-plane antiferromagnetism. Results from first-principles calculations of the phonon and magnon spectra further support our identification. The Raman spectra’s rich temperature dependence through the magnetic transition displays an avoided crossing behavior in the phonons’ frequency and a concurrent decrease in their lifetimes. We construct a model based on the interaction between a discrete level and a continuum that reproduces these observations. Our results imply a strong hybridization between each phonon and a two-magnon continuum. This work demonstrates that the magnon-phonon interactions can be observed directly in Raman scattering and provides deep insight into these interactions in 2D magnetic materials.

On the proximate Kitaev quantum-spin liquid α-RuCl3: thermodynamics, excitations and continua

This topical review provides an overview over recent thermodynamic, infrared, and THz results on the proximate Kitaev spin-liquid. Quantum-spin liquids are exotic phases characterized by the absence of magnetic ordering even at the lowest temperatures and by the occurrence of fractionalized spin excitations. Among those, Kitaev spin liquids are most fascinating as they belong to the rare class of model systems, that can be solved analytically by decomposing localized spinsS= 1/2 into Majorana fermions. The main aim of this review is to summarize experimental evidence obtained by THz spectroscopy and utilizing heat-capacity experiments, which point to the existence of fractionalized excitations in the spin-liquid state, which in α-RuCl₃exists at temperatures just above the onset of magnetic order or at in-plane magnetic fields just beyond the quantum-critical point where antiferromagnetic order becomes suppressed. Thermodynamic and spectroscopic results are compared to theoretical predictions and model calculations. In addition, we document recent progress in elucidating the sub-gap (<1 eV) electronic structure of the 4d⁵ruthenium electrons to characterize their local electronic configuration. The on-site excitation spectra of thedelectrons below the optical gap can be consistently explained using a spin-orbit coupling constant of ∼170 meV and the concept of multiple spin-orbital excitations. Furthermore, we discuss the phonon spectra of the title compound including rigid-plane shear and compression modes of the single molecular layers. In recent theoretical concepts it has been shown that phonons can couple to Majorana fermions and may play a substantial role in establishing the half-integer thermal quantum Hall effect observed in this material.

Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl3

The frustrated magnet α-RuCl3 constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in α-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on α-RuCl3.

Time-domain terahertz spectroscopy in high magnetic fields

There are a variety of elementary and collective terahertz-frequency excitations in condensed matter whose magnetic field dependence contains significant insight into the states and dynamics of the electrons involved. Often, determining the frequency, temperature, and magnetic field dependence of the optical conductivity tensor, especially in high magnetic fields, can clarify the microscopic physics behind complex many-body behaviors of solids. While there are advanced terahertz spectroscopy techniques as well as high magnetic field generation techniques available, a combination of the two has only been realized relatively recently. Here, we review the current state of terahertz time-domain spectroscopy (THz-TDS) experiments in high magnetic fields. We start with an overview of time-domain terahertz detection schemes with a special focus on how they have been incorporated into optically accessible high-field magnets. Advantages and disadvantages of different types of magnets in performing THz-TDS experiments are also discussed. Finally, we highlight some of the new fascinating physical phenomena that have been revealed by THz-TDS in high magnetic fields.

Tunneling Spectroscopy of Quantum Spin Liquids

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.

Electrical Access to Ising Anyons in Kitaev Spin Liquids

We show that spin-spin correlations in a non-Abelian Kitaev spin liquid are associated with a characteristic inhomogeneous charge density distribution in the vicinity of Z_{2} vortices. This density profile and the corresponding local electric fields are observable, e.g., by means of surface probe techniques. Conversely, by applying bias voltages to several probe tips, one can stabilize Ising anyons (Z_{2} vortices harboring a Majorana zero mode) at designated positions, where we predict a clear Majorana signature in energy absorption spectroscopy.

Nature of Magnetic Excitations in the High-Field Phase of α-RuCl_{3}

We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of α-RuCl_{3}, a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identified most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered region is dominated by single- and two-particle processes with magnons as elementary excitations. The peculiarities of the excitation spectrum in the vicinity of the critical field are discussed.

Heisenberg-Kitaev physics in magnetic fields

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators [Formula: see text]-RuCl₃ and Na₂IrO₃, which are believed to realize this fascinating physics.

Proposal to Detect Dark Matter using Axionic Topological Antiferromagnets

Antiferromagnetically doped topological insulators (ATI) are among the candidates to host dynamical axion fields and axion polaritons, weakly interacting quasiparticles that are analogous to the dark axion, a long sought after candidate dark matter particle. Here we demonstrate that using the axion quasiparticle antiferromagnetic resonance in ATIs in conjunction with low-noise methods of detecting THz photons presents a viable route to detect axion dark matter with a mass of 0.7 to 3.5 meV, a range currently inaccessible to other dark matter detection experiments and proposals. The benefits of this method at high frequency are the tunability of the resonance with applied magnetic field, and the use of ATI samples with volumes much larger than 1  mm^{3}.

Sawtooth Torque in Anisotropic j_{eff}=1/2 Magnets: Application to α-RuCl_{3}

The so-called "Kitaev candidate" materials based on 4d^{5} and 5d^{5} metals have recently emerged as magnetic systems displaying strongly anisotropic exchange interactions reminiscent of the Kitaev's honeycomb model. Recently, these materials have been shown to commonly display a distinct sawtooth angular dependence of the magnetic torque over a wide range of magnetic fields. While higher order chiral spin interactions have been considered as a source of this observation, we show here that bilinear anisotropic interactions and/or g anisotropy are each sufficient to explain the observed torque response, which may be distinguished on the basis of high-field measurements. These findings unify the understanding of magnetic torque experiments in a variety of Kitaev candidate materials.

Quasi-degenerate magnetic states in α-RuCl3

Exploring quantum spin liquid (QSL) state has both fundamental scientific value and realistic application potential. Recently, α-RuCl₃ was experimentally observed to hold in-plane zigzag antiferromagnetic (AFM) order at low temperature, which was further proposed to be proximate to a Kitaev QSL ground state. We have studied the magnetic properties of α-RuCl₃ in the framework of electronic structure calculation based on density functional theory (DFT) with Hubbard U correction (DFT+U) and spin-orbit coupling. When the intra-orbital Hubbard interaction U and the inter-orbital Hund's coupling J adopt the commonly accepted values of U = 2.0 eV and J = 0.4 eV, the zigzag AFM order indeed owns the minimum energy, consistent with the experimental observation. More importantly, we find that compared with the ferromagnetic order in the previous theoretical studies, there exist a series of magnetic configurations energetically even closer to the zigzag AFM ground state. The further calculations and analysis indicate that these low-energy magnetic states are closely related to the electronic correlation effect of Ru 4d orbitals. By decreasing U and increasing J with just about 0.2 eV, they become energetically degenerate with the zigzag AFM order, inducing strong magnetic frustration and then yielding a state without long-range magnetic order but with nonzero local moments. Considering the facts that theoretically the pressure usually reduces the intra-orbital Hubbard interaction and meanwhile enhances the inter-orbital Hund's coupling, while experimentally the pressure drives α-RuCl₃ into a quantum disordered phase, our results provide a perspective to understand the exotic magnetic behaviors of α-RuCl₃.

Screening Magnetic Two-Dimensional Atomic Crystals with Nontrivial Electronic Topology

To date, only a few two-dimensional (2D) magnetic crystals have been experimentally confirmed, such as CrI₃ and CrGeTe₃, all with very low Curie temperatures ( T_C). High-throughput first-principles screening over a large set of materials yields 89 magnetic monolayers including 56 ferromagnetic (FM) and 33 antiferromagnetic compounds. Among them, 24 FM monolayers are promising candidates possessing T_C higher than that of CrI₃. High T_C monolayers with fascinating electronic phases are identified: (i) quantum anomalous Hall and valley Hall effects coexist in a single material RuCl₃ or VCl₃, leading to a valley-polarized quantum anomalous Hall state; (ii) TiBr₃, Co₂NiO₆, and V₂H₃O₅ are revealed to be half-metals. More importantly, a new type of fermion dubbed type-II Weyl ring is discovered in ScCl. Our work provides a database of 2D magnetic materials, which could guide experimental realization of high-temperature magnetic monolayers with exotic electronic states for future spintronics and quantum computing applications.

Sub-gap optical response in the Kitaev spin-liquid candidate α-RuCl3

We report detailed optical experiments on the layered compound α-RuCl₃ focusing on the THz and sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where the stacking sequence of the molecular layers is changed. This type of phase transition is characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase exhibits the higher symmetry. One motivation is to unravel the microscopic nature of THz and spin-orbital excitations via a study of temperature and symmetry-induced changes. The optical studies are complemented by thermal expansion experiments. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. A complex dielectric loss spectrum in the THz regime, which could indicate remnants of Kitaev physics. Orbital excitations, which cannot be explained based on recent models, and an electronic excitation, which appears in a narrow temperature range just across the structural phase transition. Despite significant symmetry changes across the monoclinic to rhombohedral phase transition and a change of the stacking sequence, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, the symmetry of a single molecular layer determines the eigenfrequencies of most of these excitations. Only one mode at THz frequencies, which becomes suppressed in the high-temperature monoclinic phase and one phonon mode experience changes in symmetry and stacking. Finally, from this combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (<1 eV) electronic structure of the ruthenium 4d ⁵ electrons in α-RuCl₃.

Néel Spin-Orbit Torque Driven Antiferromagnetic Resonance in Mn_{2}Au Probed by Time-Domain THz Spectroscopy

We observe the excitation of collective modes in the terahertz (THz) range driven by the recently discovered Néel spin-orbit torques (NSOTs) in the metallic antiferromagnet Mn_{2}Au. Temperature-dependent THz spectroscopy reveals a strong absorption mode centered near 1 THz, which upon heating from 4 to 450 K softens and loses intensity. A comparison with the estimated eigenmode frequencies implies that the observed mode is an in-plane antiferromagnetic resonance (AFMR). The AFMR absorption strength exceeds those found in antiferromagnetic insulators, driven by the magnetic field of the THz radiation, by 3 orders of magnitude. Based on this and the agreement with our theory modeling, we infer that the driving mechanism for the observed mode is the current-induced NSOT. Here the electric field component of the THz pulse drives an ac current in the metal, which subsequently drives the AFMR. This electric manipulation of the Néel order parameter at high frequencies makes Mn_{2}Au a prime candidate for antiferromagnetic ultrafast memory applications.

Electrical Transport Signature of the Magnetic Fluctuation-Structure Relation in α-RuCl3 Nanoflakes

The small gap semiconductor α-RuCl₃ has emerged as a promising candidate for quantum spin liquid materials. Thus far, Raman spectroscopy, neutron scattering, and magnetization measurements have provided valuable hints for collective spin behavior in α-RuCl₃ bulk crystals. However, the goal of implementing α-RuCl₃ into spintronic devices would strongly benefit from the possibility of electrically probing these phenomena. To address this, we first investigated nanoflakes of α-RuCl₃ by Raman spectroscopy and observed similar behavior as in the case of the bulk material, including the signatures of possible fractionalized excitations. In complementary experiments, we investigated the electrical charge transport properties of individual α-RuCl₃ nanoflakes in the temperature range between 120 and 290 K. The observed temperature-dependent electrical resistivity is consistent with variable range hopping behavior and exhibits a transition at about 180 K, close to the onset temperature observed in our Raman measurements. In conjunction with the established relation between structure and magnetism in the bulk, we interpret this transition to coincide with the emergence of fractionalized excitations due to the Kitaev interactions in the nanoflakes. Compared to the bulk samples, the transition temperature of the underlying structural change is larger in the nanoflakes. This difference is tentatively attributed to the dimensionality of the nanoflakes as well as the formation of stacking faults during mechanical exfoliation. The demonstrated devices open up novel perspectives toward manipulating the Kitaev-phase in α-RuCl₃ via electrical means.

Spinon Magnetic Resonance of Quantum Spin Liquids

We describe electron spin resonance in a quantum spin liquid with significant spin-orbit coupling. We find that the resonance directly probes spinon continuum, which makes it an efficient and informative probe of exotic excitations of the spin liquid. Specifically, we consider spinon resonance of three different spinon mean-field Hamiltonians, obtained with the help of projective symmetry group analysis, which model a putative quantum spin liquid state of the triangular rare-earth antiferromagnet YbMgGaO_{4}. The band of absorption is found to be very broad and exhibit strong van Hove singularities of single spinon spectrum as well as pronounced polarization dependence.