Spin Liquid Research Articles

Response functions for electric field induced two-dimensional nonlinear spectroscopy in a Kitaev magnet

We study the dynamical response functions relevant for electric field induced two-dimensional (2D) coherent nonlinear optical spectroscopy in a Kitaev magnet at finite temperature. We show that these response functions are susceptible to both types of fractional quasiparticles of this quantum spin-liquid, i.e. fermions and flux visons. Focusing on the second order response, we find a strong antidiagonal feature in the 2D frequency plane, related to the galvanoelectric effect of the fractional fermions. Perpendicular to the antidiagonal, the width of this feature is set by quasiparticle relaxation rates beyond the bare Kitaev magnet, thereby providing access to single-particle characteristics within a multi-particle continuum. While the 2D spectrum of the response is set by the fermionic quasiparticles and displays Fermi blocking versus temperature, the emergent bond randomness which arises due to thermally populated visons strongly modifies the fermionic spectrum. Therefore also the presence of gauge excitations is manifest in the 2D nonlinear response as the temperature is increased beyond the flux proliferation crossover.

Phonon dynamics in the site-disordered Kitaev spin liquid

Phonon dynamics in the site-disordered Kitaev spin liquid

Probing Majorana Wave Functions in Kitaev Honeycomb Spin Liquids with Second-Order Two-Dimensional Spectroscopy.

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.

Exploring rare-earth Kitaev magnets by massive-scale computational analysis

The Kitaev honeycomb model plays a pivotal role in the quest for quantum spin liquids, in which fractional quasiparticles would provide applications in decoherence-free topological quantum computing. The key ingredient is the bond-dependent Ising-type interactions, dubbed the Kitaev interactions, which require strong entanglement between spin and orbital degrees of freedom. Here we investigate the identification and design of rare-earth materials displaying robust Kitaev interactions. We scrutinize all possible 4f electron configurations, which require up to 6+ million intermediate states in the perturbation processes, by developing a parallel computational program designed for massive-scale calculations. Our analysis reveals a predominant interplay between the isotropic Heisenberg J and anisotropic Kitaev K interactions across all realizations of the Kramers doublets. Remarkably, instances featuring 4f3 and 4f11 configurations showcase the prevalence of K over J, presenting unexpected prospects for exploring the Kitaev quantum spin liquids in compounds, including Nd3+ and Er3+, respectively.

Pressure-tuning of α-RuCl3 towards a quantum spin liquid

The layered material α-RuCl3 is a promising candidate to realize the Kitaev quantum spin liquid (QSL) state. However, at ambient pressure, deviations from the perfect Kitaev geometry prevent the existence of the QSL state at low temperatures. Here we present the discovery of a pressure-induced high-symmetry phase in α-RuCl3, which creates close to ideal conditions for the emergence of a QSL. Employing a novel approach based on Bragg and diffuse scattering of synchrotron radiation, we reveal a pressure-induced reorganization of the RuCl3-layers. Most importantly, this reorganization affects the structure of the layers themselves, which acquire a high trigonal symmetry. For this trigonal phase the largest ratio between the Kitaev (K) and the Heisenberg exchange (J) ever encountered is found: K/J = 124. Additionally, we demonstrate that this phase can also be stabilized by a slight biaxial pressure. This not only resolves the conflicting reports of low-temperature structures in the literature, but also facilitates the investigation of the high-symmetry phase and its potential QSL using a range of experimental techniques.

Inside Back Cover

Metal−organic frameworks (MOFs) offer a versatile platform to investigate emergent physics, the collective behavior of condensed matter stemming from many‐body interactions, thanks to their atomic‐level designability and high spatial ordering. Strong correlations, superconductivity, charge density wave, long‐range magnetic order, and quantum spin liquid phenomena in MOFs have been evidenced recently. These pioneering studies demonstrate the great potential of MOFs as quantum materials yet reveal challenges for their deep physical characterizations. More details are discussed in the Emerging Topic by Wang et al. on page 2514—2519.image

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets.

Spin liquids are a paradigmatic example of a nontrivial state of matter. The search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration-where the geometry of the net that the spins occupy precludes the generation of a simple ordered state-is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this paper, we investigate the high symmetry nets-those which are both vertex- and edge-transitive-for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identify two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases.

Structural Distortions and Short‐Range Magnetism in a Honeycomb Iridate Cu3ZnIr2O6

Layered honeycomb iridates receive significant attention in the materials chemistry and physics fields due to the relevance of their crystal structures to the Kitaev model of a quantum spin liquid (QSL). In quest of liquid‐like magnetic ground state signatures, first‐generation alkali metal iridates A2IrO3 ≡ A3[AIr2]O6 (A = Li, Na) and second‐generation iridates T3[AIr2]O6 (T = Cu, Ag, H) are developed. T3[AIr2]O6 is synthesized from A3[AIr2]O6 via metathesis reactions replacing alkali ions located between honeycomb layers. Herein, the next level of chemical and structural complexity is introduced by synthesizing the honeycomb iridate, Cu3ZnIr2O6, in which alkali ions between and within the honeycomb layers are both selectively exchanged with two different transition metals. Analysis of powder X‐Ray diffraction data reveals corrugation of the honeycomb layers in Cu3ZnIr2O6 that hinders complete magnetic frustration and results in a spin glass behavior observed from magnetization and specific heat data. Thus, Cu3ZnIr2O6 represents yet another model, which broadens understanding of intricate relationships between intralayer distortions and magnetism of prospective Kitaev QSL compounds.

Observation of magnetic dimers in the diluted triangular-lattice spin liquid candidate NaYbO2

The triangular-lattice spin liquid (QSL) candidate NaYbO2 is magnetically diluted by Lu doping, forming homogeneous solid solutions NaYb1-xLuxO2 (0≤ x<1.0). A combination of structural, magnetic, and pulsed high-field electron spin resonance analysis shows that the lattice parameters and the Curie-Weiss temperature θCW vary almost linearly with x, and the crystal electric field environment of the Yb/Lu ions persists during the Lu doping. The statistical distribution analysis of clusters and the deduced linear θCW ∼ x relation indicate that the nearest neighbor exchange J does not change with magnetic dilution. Interestingly, with the magnetization measurement at 0.39 K, we have observed Seff = 1/2 antiferromagnetic Yb-Yb dimers in NaYb0.02Lu0.98O2, which is manifested as a magnetization step at μ0Hc = 2.68 T due to the transition between singlet and triplet states. Thus, the intradimer interaction is directly determined as J/kB = −5.15 K. Surprisingly, this value is close to the interaction of undoped NaYbO2, supporting the theoretical analysis of clusters. Our study provides a method of estimating the magnetic interaction of QSL materials through magnetic dilution. The statistical distribution analysis of magnetic clusters suggests that through a small amount of Lu doping (x < 0.5), the QSL state in NaYbO2 can continue to be maintained.

Kinetic ferromagnetism and topological magnons of the hole-doped Kitaev spin liquid

We study the effect of hole doping on the Kitaev spin liquid (KSL) and find that for ferromagnetic (FM) Kitaev exchange K the system is very susceptible to the formation of a FM spin polarization. Through density matrix renormalization group simulations on finite systems, we uncover that the introduction of a single hole, corresponding to ≈1% hole doping for the system size we consider, with a hopping strength of just t ~ 0.28K is enough to disrupt fractionalization and polarize the spins in the [001] direction due to an order-by-disorder mechanism. Taking into account a material relevant FM anisotropic exchange Γ drives the polarization towards the [111] direction via a transition into a topological FM state with chiral magnon excitations. We develop a parton mean-field theory incorporating fermionic holons and bosonic magnons, which accounts for the doping induced FM phases and topological magnon excitations. We discuss experimental implications for Kitaev candidate materials.

Competing gauge fields and entropically driven spin liquid to spin liquid transition in non-Kramers pyrochlores.

Gauge theories are powerful theoretical physics tools that allow complex phenomena to be reduced to simple principles and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behavior at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and tensor gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the tensor gauge field, rendering the system spin-ice-like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and tensor gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers magnetic pyrochlore materials.

Field‐Induced Butterfly‐Like Anisotropic Magnetoresistance in a Kagome Semimetal Co3In2S2

AbstractWith the interplay between magnetism and topological bands, magnetic kagome semimetals provide promising platforms for exploring exotic correlated electronic states and quantum phenomena such as anomalous Hall effect, quantum spin liquid, and unconventional magnetoresistance, as well as driving advances in electronic and spintronic applications. Here, a field‐induced butterfly‐like anomalous anisotropic magnetoresistance (AMR) effect in an intriguing kagome semimetal Co3In2S2 is reported. The kagome‐lattice Co3In2S2 single crystals are synthesized via a polycrystal‐source chemical vapor transport approach, possessing a high carrier mobility reaching 104 cm2V−1s−1. The Co3In2S2 single crystal exhibits a canted antiferromagnetic state below 5 K, but intriguingly, it is easily transformed into a ferromagnetic state under a small external magnetic field. Furthermore, the planar Hall effect (PHE) is detected, stemming from the complex contribution of field‐induced ferromagnetism and orbital magnetoresistance. Remarkably, as the magnetic field increases, the low‐temperature magnetoresistance behavior of the Co3In2S2 reveals a butterfly‐like AMR effect with a maximum value of 850%, exhibiting a superposition of the two‐, four‐, and six‐fold AMR terms. Band structure calculations suggest that such a field‐induced butterfly‐like AMR effect may originate from the modulations of the electronic structure near the Fermi level by the magnetic moment. The findings offer a valuable platform for understanding the anomalous AMR effect and for the development of advanced spintronic devices.

Detecting symmetry fractionalization in gapped quantum spin liquids by magnetic impurities

Detecting symmetry fractionalization in gapped quantum spin liquids by magnetic impurities

Irrational Moments and Signatures of Higher-Rank Gauge Theories in Diluted Classical Spin Liquids

Classical spin liquids (CSLs) have proved to be a fruitful setting for the emergence of exotic gauge theories. Vacancy clusters in CSLs can introduce gauge charges into the system, and the resulting behavior in turn reveals the nature of the underlying theory. We study these effects for a series of CSLs on the honeycomb lattice. We find that dilution leads to the emergence of effective free spins with tuneable, and generally irrational, size. For a specific higher-rank CSL, described by a symmetric tensor gauge fields, dilution produces spin textures with a characteristic quadrupolar angular structure and infinite-ranged interactions between dilution clusters. Published by the American Physical Society 2024

Josephson dynamics and localization revivals in ultradilute quantum liquids

Josephson dynamics and localization revivals in ultradilute quantum liquids

Anomalous Hall effect and electronic correlation in a spin-reoriented kagome antiferromagnet LuFe6Sn6

Abstract The kagome lattice system has been identified as a fertile ground for the emergence of a number of new quantum states, including superconductivity, quantum spin liquids, and topological electronic states. This has attracted significant interest within the field of condensed matter physics. Here, we present the observation of an anomalous Hall effect in an iron-based kagome antiferromagnet LuFe6Sn6, which implies a non-zero Berry curvature in this compound. By means of extensive magnetic measurements, a high Neel temperature, T N = 552 K, and a spin reorientation behavior were identified and a simple temperature-field phase diagram was constructed. Furthermore, this compound was found to exhibit a large Sommerfeld coefficient of γ = 87 mJ⋅mol−1⋅K−2, suggesting the presence of a strong electronic correlation effect. Our research indicates that LuFe6Sn6 is an intriguing compound that may exhibit magnetism, strong correlation, and topological states.

Finite Temperature Magnetism in the Triangular Lattice Antiferromagnet KErTe2

Abstract After the discovery of the ARECh2 (A = alkali or monovalent ions, RE = rare-earth, Ch = chalcogen) triangular lattice quantum spin liquid (QSL) family, a series of its oxide, sulfide, and selenide counterparts has been consistently reported and extensively investigated. While KErTe2 represents the initial synthesized telluride member, preserving its triangular spin lattice, it was anticipated that the substantial tellurium ions could impart more pronounced magnetic attributes and electronic structures to this material class. This study delves into the magnetism of KErTe2 at finite temperatures through magnetization and electron spin resonance (ESR) measurements. Based on the angular momentum J ^ after spin-orbit coupling (SOC) and symmetry analysis, we obtain the magnetic effective Hamiltonian to describe the magnetism of Er3+ in R 3 ¯ m space group. Applying the mean-field approximation to the Hamiltonian, we can simulate the magnetization and magnetic heat capacity of KErTe2 in paramagnetic state and determine the crystalline electric field (CEF) parameters and partial exchange interactions. The relatively narrow energy gaps between the CEF ground state and excited states exert a significant influence on the magnetism. For example, small CEF excitations can result in a significant broadening of the ESR linewidth at 2 K. For the fitted exchange interactions, although the values are small, given a large angular momentum J = 15/2 after SOC, they still have a noticeable effect at finite temperatures. Notably, the heat capacity data under different magnetic fields along the c axis direction also roughly match our calculated results, further validating the reliability of our analytical approach. These derived parameters serve as crucial tools for future investigations into the ground state magnetism of KErTe2. The findings presented herein lay a foundation for exploration of the intricate magnetism within the triangular-lattice delafossite family.

Nematic Ising superconductivity with hidden magnetism in few-layer 6R-TaS2

In van der Waals heterostructures (vdWHs), the manipulation of interlayer stacking/coupling allows for the construction of customizable quantum systems exhibiting exotic physics. An illustrative example is the diverse range of states of matter achieved through varying the proximity coupling between two-dimensional (2D) quantum spin liquid (QSL) and superconductors within the TaS2 family. This study presents a demonstration of the intertwined physics of spontaneous rotational symmetry breaking, hidden magnetism, and Ising superconductivity (SC) in the three-fold rotationally symmetric, non-magnetic natural vdWHs 6R-TaS2. A distinctive phase emerges in 6R-TaS2 below a characteristic temperature (T*) of approximately 30 K, which is characterized by a remarkable set of features, including a giant extrinsic anomalous Hall effect (AHE), Kondo screening, magnetic field-tunable thermal hysteresis, and nematic magneto-resistance. At lower temperatures, a coexistence of nematicity and Kondo screening with Ising superconductivity is observed, providing compelling evidence of hidden magnetism within a superconductor. This research not only sheds light on unexpected emergent physics resulting from the coupling of itinerant electrons and localized/correlated electrons in natural vdWHs but also emphasizes the potential for tailoring exotic quantum states through the manipulation of interlayer interactions.

Variational MonteCarlo Study of the 1/9-Magnetization Plateau in Kagome Antiferromagnets.

Motivated by very recent experimental observations of the 1/9-magnetization plateaus in YCu_{3}(OH)_{6+x}Br_{3-x} and YCu_{3}(OD)_{6+x}Br_{3-x}, our study delves into the magnetic-field-induced phase transitions in the nearest-neighbor antiferromagnetic Heisenberg model on the kagome lattice using the variational MonteCarlo technique. We uncover a phase transition from a zero-field Dirac spin liquid to a field-induced magnetically disordered phase that exhibits the 1/9-magnetization plateau. Through a comprehensive analysis encompassing the magnetization distribution, spin correlations, chiral order parameter, topological entanglement entropy, ground-state degeneracy, Chern number, and excitation spectrum, we pinpoint the phase associated with this magnetization plateau as a chiral Z_{3} topological quantum spin liquid and elucidate its diverse physical properties.

Giant Anisotropic Magnetoresistance in Few-Layer α-RuCl3 Tunnel Junctions.

The spin-orbit-assisted Mott insulator α-RuCl3 is proximate to the coveted quantum spin liquid (QSL) predicted by the Kitaev model. In the search for the pure Kitaev QSL, reducing the dimensionality of this frustrated magnet by exfoliation has been proposed as a way to enhance magnetic fluctuations and Kitaev interactions. Here, we perform angle-dependent tunneling magnetoresistance (TMR) measurements on ultrathin α-RuCl3 crystals with various layer numbers to probe their magnetic, electronic, and crystal structures. We observe a giant change in resistance, as large as ∼2500%, when the magnetic field rotates either within or out of the α-RuCl3 plane, a manifestation of the strongly anisotropic spin interactions in this material. In combination with scanning transmission electron microscopy, this tunneling anisotropic magnetoresistance (TAMR) reveals that few-layer α-RuCl3 crystals remain in the high-temperature monoclinic phase at low temperatures. It also shows the presence of a zigzag antiferromagnetic order below the critical temperature TN ≃ 14 K, which is twice the one typically observed in bulk samples with rhombohedral stacking. Our work offers valuable insights into the relation between the stacking order and magnetic properties of this material, which helps lay the groundwork for creating and electrically probing exotic magnetic phases such as QSLs via van der Waals engineering.