Room Temperature Relaxometry of Single Nitrogen Vacancy Centers in Proximity to α-RuCl3 Nanoflakes

Nitrogen vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use the longitudinal relaxation time T1 of single NV centers to investigate the spin dynamics of nanometer-thin flakes of α-RuCl3 at room temperature. We observe a significant reduction in the T1 in the presence of α-RuCl3 in the proximity of NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal planes. Furthermore, the T1 time exhibits a monotonic increase with an applied magnetic field. We associate this trend with the alteration of the spin and charge noise in α-RuCl3 under an external magnetic field. These findings suggest that the influence of the spin dynamics of α-RuCl3 on the T1 of the NV center can be used to gain information about the material itself and the technique to be used on other 2D materials.

Angular-Momentum Transfer Mediated by a Vibronic-Bound-State

The notion that phonons can carry pseudo-angular momentum has many major consequences, including topologically protected phonon chirality, Berry curvature of phonon band structure, and the phonon Hall effect. When a phonon is resonantly coupled to an orbital state split by its crystal field environment, a so-called vibronic bound state forms. Here, a vibronic bound state is observed in NaYbSe2 , a quantum spin liquid candidate. In addition, field and polarization dependent Raman microscopy is used to probe an angular momentum transfer of ΔJz = ±ℏ between phonons and the crystalline electric field mediated by the vibronic bound stat. This angular momentum transfer between electronic and lattice subsystems provides new pathways for selective optical addressability of phononic angular momentum via electronic ancillary states.

Frustrated magnetism of the spin-1 kagome antiferromagnetβ-BaNi3(VO4)2(OH)2

We propose the newly synthesizedβ-BaNi3(VO4)2(OH)2(space group:R3‾m) as a candidate for the spin-1 kagome Heisenberg antiferromagnet (KHA). The compound features a uniform kagome lattice of Ni2+(S= 1) ions with a large interlayer distance. High-field measurements at low temperatures reveal a susceptibility local minimum at ∼9 T, resembling a 1/3 magnetization plateau as predicted by the pureS= 1 KHA model. Below ∼6 K, approximately 1% of the spins exhibit spin-glass order, which may be attributed to the nanocrystalline grain size of ∼50 nm. Despite the antiferromagnetic exchange coupling strength of ∼7 K, the majority of spins remain disordered down to ∼0.1 K as indicated by the observed power-law behaviors in magnetic specific heatCm∝T1.4. Our results demonstrate that the low-energy magnetic excitations inβ-BaNi3(VO4)2(OH)2are gapless, which contradicts the current theoretical expectations of the ideal model.

Fluctuating magnetic droplets immersed in a sea of quantum spin liquid

The search of quantum spin liquid (QSL), an exotic magnetic state with strongly fluctuating and highly entangled spins down to zero temperature, is a main theme in current condensed matter physics. However, there is no smoking gun evidence for deconfined spinons in any QSL candidate so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report comprehensive and systematic measurements of the magnetic susceptibility, ultralow-temperature specific heat, muon spin relaxation (μSR), nuclear magnetic resonance (NMR), and thermal conductivity for NaYbSe2 single crystals, in which Yb3+ ions with effective spin-1/2 form a perfect triangular lattice. All these complementary techniques find no evidence of long-range magnetic order down to their respective base temperatures. Instead, specific heat, μSR, and NMR measurements suggest the coexistence of quasi-static and dynamic spins in NaYbSe2. The scattering from these quasi-static spins may cause the absence of magnetic thermal conductivity. Thus, we propose a scenario of fluctuating ferrimagnetic droplets immersed in a sea of QSL. This may be quite common on the way pursuing an ideal QSL, and provides a brand new platform to study how a QSL state survives impurities and coexists with other magnetically ordered states.

Possible realization of three-dimensional quantum spin liquid behavior in HoVO4

The study of geometrically frustrated magnetic systems with unusual crystal field ground states offers a possibility of realizing the new aspects of physics of disordered systems. In this study, we report our results of structural, magnetic susceptibility, heat capacity measurements, along with density functional theory (DFT) calculations on HoVO₄; a compound in which the presence of a distorted kind of HoO₈polyhedral leads to multiple magnetic interaction paths. The observed broad maximum below 10 K in the temperature response of DC susceptibility curves implies the presence of short-range correlations. AC susceptibility rules out the possibility of any kind of spin freezing. Temperature dependent heat capacity measurement at zero field indicate towards the absence of long-range ordering, along with the presence of a broad maximum centered around 14 K. The residual heat capacity exhibits a characteristic power-law (T^α) behavior with the exponentαnearly equal to 2, which is analogous to that observed for other three-dimensional (3D) quantum spin liquid (QSL) systems. The DFT calculations signify the presence of dominant second and third nearest neighbor interactions, which in turn lead to magnetic frustration in our system. Our investigations suggest that HoVO₄can be a candidate for realizing a 3D QSL state.

Unraveling the Electrical and Magnetic Properties of Layered Conductive Metal-Organic Framework With Atomic Precision

This paper describes structural elucidation of a layered conductive metal-organic framework (MOF) material Cu₃ (C₆ O₆ )₂ by microcrystal electron diffraction with sub-angstrom precision. This insight enables the first identification of an unusual π-stacking interaction in a layered MOF material characterized by an extremely short (2.73 Å) close packing of the ligand arising from pancake bonding and ordered water clusters within pores. Band structure analysis suggests semiconductive properties of the MOF, which are likely related to the localized nature of pancake bonds and the formation of a singlet dimer of the ligand. The spin of Cu^II within the Kagomé arrangement dominates the paramagnetism of the MOF, leading to strong geometrical magnetic frustration.

Antiferromagnetic Kitaev interaction inJeff1/2 cobalt honeycomb materials Na3Co2SbO6and Na2Co2TeO6

Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue for quantum magnetism research. We conclude that Na₃Co₂SbO₆and Na₂Co₂TeO₆are new honeycomb cobalt-based systems with AFM Kitaev interaction by carrying out inelastic neutron scattering experiments and subsequent analysis. The spin-orbit excitons observed at 20-28 meV in both compounds strongly support the idea that Co²⁺ions of both compounds have a spin-orbital entangledJ_eff= 1/2 state. Furthermore, we found that a generalized Kitaev-Heisenberg Hamiltonian can describe the spin-wave excitations of both compounds with additional 3rd nearest-neighbor interaction. Our best-fit parameters show significant AFM Kitaev terms and off-diagonal symmetric anisotropy terms of a similar magnitude in both compounds. We also found a strong magnon-damping effect at the higher energy part of the spin waves, entirely consistent with observations in other Kitaev magnets. Our work suggests Na₃Co₂SbO₆and Na₂Co₂TeO₆as rare examples of the AFM Kitaev magnets based on the systematic studies of the spin waves and analysis.

Spin-orbital entangled state and realization of Kitaev physics in 3dcobalt compounds: a progress report

The realization of Kitaev's honeycomb magnetic model in real materials has become one of the most pursued topics in condensed matter physics and materials science. If found, it is expected to host exotic quantum phases of matter and offers potential realizations of fault-tolerant quantum computations. Over the past years, much effort has been made on 4d- or 5d-heavy transition metal compounds because of their intrinsic strong spin-orbit coupling. But more recently, there have been growing shreds of evidence that the Kitaev model could also be realized in 3d-transition metal systems with much weaker spin-orbit coupling. This review intends to serve as a guide to this fast-developing field focusing on systems withd⁷transition metal occupation. It overviews the current theoretical and experimental progress on realizing the Kitaev model in those systems. We examine the recent experimental observations of candidate materials with Co²⁺ions: e.g., CoPS₃, Na₃Co₂SbO₆, and Na₂Co₂TeO₆, followed by a brief review of theoretical backgrounds. We conclude this article by comparing experimental observations with density functional theory calculations. We stress the importance of inter-t_2ghopping channels and Hund's coupling in the realization of Kitaev interactions in Co-based compounds, which has been overlooked in previous studies. This review suggests future directions in the search for Kitaev physics in 3dcobalt compounds and beyond.

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.

Why the Schwinger boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?

We find that the Schwinger boson mean field theory (SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1) spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2) There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3) There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-12TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.

Quantum spin-liquid states in an organic magnetic layer and molecular rotor hybrid

The exotic properties of quantum spin liquids (QSLs) have continually been of interest since Anderson's 1973 ground-breaking idea. Geometrical frustration, quantum fluctuations, and low dimensionality are the most often evoked material's characteristics that favor the long-range fluctuating spin state without freezing into an ordered magnet or a spin glass at low temperatures. Among the few known QSL candidates, organic crystals have the advantage of having rich chemistry capable of finely tuning their microscopic parameters. Here, we demonstrate the emergence of a QSL state in [EDT-TTF-CONH₂]₂ ⁺[[Formula: see text]] (EDT-BCO), where the EDT molecules with spin-1/2 on a triangular lattice form layers which are separated by a sublattice of BCO molecular rotors. By several magnetic measurements, we show that the subtle random potential of frozen BCO Brownian rotors suppresses magnetic order down to the lowest temperatures. Our study identifies the relevance of disorder in the stabilization of QSLs.

Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism

The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar interactions can be yielded by the synergy of spin-orbit coupling and electron correlations for specific electron configuration and lattice geometry, which is known as the Jackeli-Khaliullin mechanism. Based on this mechanism, there has been a fierce race for the materialization of the Kitaev spin liquid over the last decade, but the candidates have been still limited mostly to 4d- and 5d-electron compounds including cations with the low-spind5electron configuration, such as Ir4+and Ru3+. Here we discuss recent efforts to extend the material perspective beyond the Jackeli-Khaliullin mechanism, by carefully reexamining the two requisites, formation of thejeff= 1/2 doublet and quantum interference between the exchange processes, for not onlyd- but alsof-electron systems. We present three examples: the systems including Co2+and Ni3+with the high-spind7electron configuration, Pr4+with thef1-electron configuration, and polar asymmetry in the lattice structure. In particular, the latter two are intriguing since they may realize the antiferromagnetic Kitaev interactions, in contrast to the ferromagnetic ones in the existing candidates. This partial overview would stimulate further material exploration of the Kitaev spin liquids and its topological properties due to fractional excitations.

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

The Kitaev model with an applied magnetic field in the [Formula: see text] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at [Formula: see text] and a second transition at a higher field [Formula: see text] to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function [Formula: see text] and the Fermi surface [Formula: see text] of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.

Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice

A spin-[Formula: see text] lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the [Formula: see text] point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.