Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet α-RuCl3

Field tuning Kitaev systems for spin fractionalization and topological order

The honeycomb Kitaev model describes aZ2spin liquid with topological order and fractionalized excitations consisting of gappedπ-fluxes and free Majorana fermions. Competing interactions, even when not very strong, are known to destabilize the Kitaev spin liquid. Magnetic fields are a convenient parameter for tuning between different phases of the Kitaev systems, and have even been investigated for potentially counteracting the effects of other destabilizing interactions leading to a revival of the topological phase. Here we review the progress in understanding the effects of magnetic fields on some of the perturbed Kitaev systems, particularly on fractionalization and topological order.

Chirality-selective topological magnon phase transition induced by interplay of anisotropic exchange interactions in honeycomb ferromagnet

A variety of distinct anisotropic exchange interactions commonly exist in one magnetic material due to complex crystal, magnetic and orbital symmetries. Here we investigate the effects of multiple anisotropic exchange interactions on topological magnon in a honeycomb ferromagnet, and find a chirality-selective topological magnon phase transition induced by a complicated interplay of Dzyaloshinsky-Moriya interaction and pseudo-dipolar interaction, accompanied by the bulk gap close and reopen with chiral inversion. Moreover, this novel topological phase transition involves band inversion at high symmetry pointsKandK', which can be regarded as a pseudo-orbital reversal, i.e. magnon valley degree of freedom, implying a new manipulation corresponding to a sign change of the magnon thermal Hall conductivity. Indeed, it can be realized in 4dor 5dcorrelated materials with both spin-orbit coupling and orbital localized states, such as iridates and ruthenates,etc.This novel regulation may have potential applications on magnon devices and topological magnonics.

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.

Ultrafast Spin Dynamics and Photoinduced Insulator-to-Metal Transition in α-RuCl3

Laser-induced ultrafast demagnetization is a phenomenon of utmost interest and attracts significant attention because it enables potential applications in ultrafast optoelectronics and spintronics. As a spin-orbit coupling assisted magnetic insulator, α-RuCl3 provides an attractive platform to explore the physics of electronic correlations and unconventional magnetism. Using time-dependent density functional theory, we explore the ultrafast laser-induced dynamics of the electronic and magnetic structures in α-RuCl3. Our study unveils that laser pulses can introduce ultrafast demagnetizations, accompanied by an out-of-equilibrium insulator-to-metal transition in a few tens of femtoseconds. The spin response significantly depends on the laser wavelength and polarization on account of the electron correlations, band renormalizations, and charge redistributions. These findings provide physical insights into the coupling between the electronic and magnetic degrees of freedom in α-RuCl3 and shed light on suppressing the long-range magnetic orders and reaching a proximate spin liquid phase for two-dimensional magnets on an ultrafast time scale.

Possible intermediate quantum spin liquid phase in α-RuCl3 under high magnetic fields up to 100 T

Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material α-RuCl3 has intrigued great research interest recently. A fascinating question is on the possible existence of a field-induced QSL phase in this compound. Here we perform high-field magnetization measurements of α-RuCl3 up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c* axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 35 T and about 83 T, between which lies an intermediate phase as the predicted QSL. This is in sharp contrast to the case with in-plane fields, where a single transition is found at around 7 T and the intermediate QSL phase is absent instead. By measuring the magnetization data with fields tilted from the c* axis up to 90° (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the K-J-Γ-[Formula: see text] model for α-RuCl3 with a large Kitaev term we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.

Disorder-Enriched Magnetic Excitations in a Heisenberg-Kitaev Quantum Magnet Na_{2}Co_{2}TeO_{6}

Using optical magnetospectroscopy, we investigate the magnetic excitations of Na_{2}Co_{2}TeO_{6} in a broad magnetic field range (0  T≤B≤17.5  T) at low temperature. Our measurements reveal rich spectra of in-plane magnetic excitations with a surprisingly large number of modes, even in the high-field spin-polarized state. Theoretical calculations find that the Na-occupation disorder in Na_{2}Co_{2}TeO_{6} plays a crucial role in generating these modes. Our Letter demonstrates the necessity to consider disorder in the spin environment in the search for Kitaev quantum spin liquid states in practicable materials.

Sonication-assisted liquid phase exfoliation of two-dimensional CrTe3 under inert conditions

Liquid phase exfoliation (LPE) has been used for the successful fabrication of nanosheets from a large number of van der Waals materials. While this allows to study fundamental changes of material properties' associated with reduced dimensions, it also changes the chemistry of many materials due to a significant increase of the effective surface area, often accompanied with enhanced reactivity and accelerated oxidation. To prevent material decomposition, LPE and processing in inert atmosphere have been developed, which enables the preparation of pristine nanomaterials, and to systematically study compositional changes over time for different storage conditions. Here, we demonstrate the inert exfoliation of the oxidation-sensitive van der Waals crystal, CrTe3. The pristine nanomaterial was purified and size-selected by centrifugation, nanosheet dimensions in the fractions quantified by atomic force microscopy and studied by Raman, X-ray photoelectron spectroscopy (XPS), energy-dispersive X-ray spectroscopy (EDX) and photo spectroscopic measurements. We find a dependence of the relative intensities of the CrTe3 Raman modes on the propagation direction of the incident light, which prevents a correlation of the Raman spectral profile to the nanosheet dimensions. XPS and EDX reveal that the contribution of surface oxides to the spectra is reduced after exfoliation compared to the bulk material. Further, the decomposition mechanism of the nanosheets was studied by time-dependent extinction measurements after water titration experiments to initially dry solvents, which suggest that water plays a significant role in the material decomposition.

Electronic Structure Manipulation of the Mott Insulator RuCl3 via Single-Crystal to Single-Crystal Topotactic Transformation

The core task for Mott insulators includes how rigid distributions of electrons evolve and how these induce exotic physical phenomena. However, it is highly challenging to chemically dope Mott insulators to tune properties. Herein, we report how to tailor electronic structures of the honeycomb Mott insulator RuCl₃ employing a facile and reversible single-crystal to single-crystal intercalation process. The resulting product (NH₄ )_0.5 RuCl₃ ⋅1.5 H₂ O forms a new hybrid superlattice of alternating RuCl₃ monolayers with NH₄ ⁺ and H₂ O molecules. Its manipulated electronic structure markedly shrinks the Mott-Hubbard gap from 1.2 to 0.7 eV. Its electrical conductivity increases by more than 10³ folds. This arises from concurrently enhanced carrier concentration and mobility in contrary to the general physics rule of their inverse proportionality. We show topotactic and topochemical intercalation chemistry to control Mott insulators, escalating the prospect of discovering exotic physical phenomena.

Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl3

Layered α-RuCl₃ is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this state has been reported under a modest in-plane magnetic field, such behaviour is largely inconsistent with theoretical expectations of spin liquid phases emerging only in out-of-plane fields. These predicted field-induced states have been largely out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations to study the layer-dependent magnons, magnetic anisotropy, structure and exchange coupling in atomically thin samples. Due to picoscale distortions, the sign of the average off-diagonal exchange changes in monolayer α-RuCl₃, leading to a reversal of spin anisotropy to easy-axis anisotropy, while the Kitaev interaction is concomitantly enhanced. Our work opens the door to the possible exploration of Kitaev physics in the true two-dimensional limit.

Identification of a Kitaev quantum spin liquid by magnetic field angle dependence

Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.

Non-Abelian phase of Kitaev quantum spin liquid is promising for topological quantum computation. Here, the authors propose a way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence, providing criteria for such a state for future experiments.

Observation of 4- and 6-Magnon Bound States in the Spin-Anisotropic Frustrated Antiferromagnet FeI_{2}

We observe a wealth of multimagnon bound states in the strongly anisotropic spin-1 triangular antiferromagnet FeI_{2} using time-domain terahertz spectroscopy. These unconventional excitations can arise in ordered magnets due to attractive magnon-magnon interactions and alter their properties. We analyze the energy-magnetic field spectrum via an exact diagonalization method for a dilute gas of interacting magnons and detect up to 4- and 6-magnon bound states, hybridized with single magnons. This zoo of tunable interacting quasiparticles provides a unique platform to study decay and renormalization, reminiscent of the few-body problems found in cold-atom, nuclear, and particle physics.

Bosonic spinons in anisotropic triangular antiferromagnets

Anisotropic triangular antiferromagnets can host two primary spin excitations, namely, spinons and triplons. Here, we utilize polarization-resolved Raman spectroscopy to assess the statistics and dynamics of spinons in Ca₃ReO₅Cl₂. We observe a magnetic Raman continuum consisting of one- and two-pair spinon-antispinon excitations as well as triplon excitations. The twofold rotational symmetry of the spinon and triplon excitations are distinct from magnons. The strong thermal evolution of spinon scattering is compatible with the bosonic spinon scenario. The quasilinear spinon hardening with decreasing temperature is envisaged as the ordering of one-dimensional topological defects. This discovery will enable a fundamental understanding of novel phenomena induced by lowering spatial dimensionality in quantum spin systems.

Spinons are quasisparticles that can appear in anisotropic triangular lattices, however, probing the statistics and dynamics of such excitations is experimentally challenging. Here, Choi et al present Raman spectroscopy measurements of anisotropic triangular lattices, showing a bosonic evolution of the spinon scattering.

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.

Dynamic fingerprint of fractionalized excitations in single-crystalline Cu3Zn(OH)6FBr

Beyond the absence of long-range magnetic orders, the most prominent feature of the elusive quantum spin liquid (QSL) state is the existence of fractionalized spin excitations, i.e., spinons. When the system orders, the spin-wave excitation appears as the bound state of the spinon-antispinon pair. Although scarcely reported, a direct comparison between similar compounds illustrates the evolution from spinon to magnon. Here, we perform the Raman scattering on single crystals of two quantum kagome antiferromagnets, of which one is the kagome QSL candidate Cu₃Zn(OH)₆FBr, and another is an antiferromagnetically ordered compound EuCu₃(OH)₆Cl₃. In Cu₃Zn(OH)₆FBr, we identify a unique one spinon-antispinon pair component in the E_2g magnetic Raman continuum, providing strong evidence for deconfined spinon excitations. In contrast, a sharp magnon peak emerges from the one-pair spinon continuum in the E_g magnetic Raman response once EuCu₃(OH)₆Cl₃ undergoes the antiferromagnetic order transition. From the comparative Raman studies, we can regard the magnon mode as the spinon-antispinon bound state, and the spinon confinement drives the magnetic ordering.

Theoretical scheme for finite-temperature dynamics of Kitaev's spin liquids

In this article, we review the theoretical formulation of finite temperature dynamics of Kitaev's spin liquid. We present the exact analytical solution of the dynamical spin correlation function at the integrable limit of Kitaev's model, on the basis of (2018Phys. Rev. B98220404). By combining the analytical solution with the equilibrium classical Monte-Carlo scheme, we construct a formulation to access the finite temperature dynamics of Kitaev's spin liquid exactly, with a reasonable amount of computational cost. This formulation is based on the real-time representation, which enables us to directly access the experimental observables defined in real frequency, without analytical continuation. The real-time scheme is essential to capturing the resonant features of the spectrum accurately, which occurs e.g. in the chiral spin liquid phase with isolated Majorana zero modes. Accordingly, this scheme provides an effective approach to address the nature of fractional excitations in Kitaev's spin liquid. As an application, we address the detection of zero mode around the site vacancy through the local resonant spectrum and discuss how the character of Kitaev's spin liquid emerges in its dynamical signature.

Thermodynamic Perspective on Field-Induced Behavior of α-RuCl_{3}

Measurements of the magnetic Grüneisen parameter (Γ_{B}) and specific heat on the Kitaev material candidate α-RuCl_{3} are used to access in-plane field and temperature dependence of the entropy up to 12 T and down to 1 K. No signatures corresponding to phase transitions are detected beyond the boundary of the magnetically ordered region, but only a shoulderlike anomaly in Γ_{B}, involving an entropy increment as small as 10^{-5}Rlog2. These observations put into question the presence of a phase transition between the purported quantum spin liquid and the field-polarized state of α-RuCl_{3}. We show theoretically that at low temperatures Γ_{B} is sensitive to crossings in the lowest excitations within gapped phases, and identify the measured shoulderlike anomaly as being of such origin. Exact diagonalization calculations demonstrate that the shoulderlike anomaly can be reproduced in extended Kitaev models that gain proximity to an additional phase at finite field without entering it. We discuss manifestations of this proximity in other measurements.

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.