Probing the quantum noise of the spinon Fermi surface with NV centers
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36 MATERIALS SCIENCE↗
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Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3
Here, we report a detailed study of the specific heat and magnetic susceptibility of single crystals of a spin-liquid candidate: the hyperhoneycomb Cu oxalate framework compound [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3 . The specific heat shows no anomaly associated with a magnetic transition at low temperatures down to T ~ 180 mK in zero magnetic field. We observe a large linear-in-T contribution to the specific heat γT, γ = 98 (1) mJ / mol K 2 , at low temperatures, indicative of the presence of fermionic excitations despite the Mott insulating state. The low-T specific heat is strongly suppressed by applied magnetic fields H, which induce an energy gap, Δ(H), in the spin-excitation spectrum. We use the four-component relativistic density-functional theory (DFT) to calculate the magnetic interactions, including the Dzyaloshinskii-Moriya antisymmetric exchange, which causes an effective staggered field acting on one copper sublattice. The magnitude and field dependence of the field-induced gap, Δ (H) ∝ H 2/3 , are accurately predicted by the soliton mass calculated from the sine-Gordon model of weakly coupled antiferromagnetic Heisenberg chains with all parameters determined by our DFT calculations. Thus our experiment and calculations are entirely consistent with a model of [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3 in which anisotropic magnetic exchange interactions due to Jahn-Teller distortion cause one copper sublattice to dimerize, leaving a second sublattice of weakly coupled antiferromagnetic chains. We also show that this model quantitatively accounts for the measured temperature-dependent magnetic susceptibility. Thus [(C 2 H 5 ) 3 NH] 2 Cu 2 (C 2 O 4 ) 3 is a canonical example of a one-dimensional spin-1/2 Heisenberg antiferromagnet and not a resonating-valence-bond quantum spin liquid, as previously proposed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Competition of spinon Fermi surface and heavy Fermi liquid states from the periodic Anderson to the Hubbard model
Not Available
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Extracting spinon self-energies from two-dimensional coherent spectroscopy
Two-dimensional coherent spectroscopy (2DCS) is a nonlinear spectroscopy technique capable of identifying whether apparent continua in linear response are made out of multiplets of sharp deconfined quasiparticles. This makes it a potent tool for experimental identification of fractionalized phases. Previous discussions have focused on limits where the quasiparticles in question are infinitely long lived. In this paper we discuss 2DCS in the regime where the fractionalized quasiparticles can themselves decay. We introduce a powerful path-integral-based approach, whereby the computation of nonlinear susceptibilities reduces to an efficient exercise in diagrammatic perturbation theory. Here, we apply this method to compute the 2DCS response of the one-dimensional transverse field Ising model, in the presence of integrability-breaking perturbations. We discuss aspects of the self-energy of the fractionalized quasiparticles that may be extracted via 2DCS, such as the momentum-dependent decay rate.
1-dimensional spin chains↗
Spinon Fermi Surface Spin Liquid in a Triangular Lattice Antiferromagnet NaYbSe 2
Not Available
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Dynamic fingerprint of fractionalized excitations in single-crystalline Cu3Zn(OH)6FBr
Abstract 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 Cu 3 Zn(OH) 6 FBr, and another is an antiferromagnetically ordered compound EuCu 3 (OH) 6 Cl 3 . In Cu 3 Zn(OH) 6 FBr, 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 EuCu 3 (OH) 6 Cl 3 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.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe 2 from scanning tunnelling microscopy
Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. In this work, we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe 2 . We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe 2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe 2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Structure of domain walls in chiral spin liquids
The chiral spin liquid is a canonical state of quantum spins combining topological and symmetry-breaking order, and possible experimental realizations have attracted growing interest. We examine the physics at interfaces between chiral spin liquid domains of opposite chirality. We show that a self-consistent mean-field description of spinons remains possible in the vicinity of a domain wall and use this to formulate a Ginzburg–Landau theory of the domain wall. The bulk of a chiral spin liquid contains gapped spinon excitations and gauge fluctuations, set by a finite spinon mass and a nonzero spinon Chern number. A third class of excitations consists of amplitude fluctuations of the spinon hoppings, which admit a geometric interpretation in terms of effective vielbein fields. These fluctuations are usually neglected because they are irrelevant for a homogeneous chiral spin liquid and are suppressed in standard large- N treatments. Going beyond the purely topological Chern–Simons limit, we incorporate these fluctuations into an effective field theoretic framework and show that they generate momentum-dependent corrections, including Chern–Simons-like linear terms and higher-order contributions, beyond the universal topological limit. We then analyze nontopological properties, including domain wall tension and edge velocity, and explain how they modify observables relative to the uniform case. These results connect measurable, nonuniversal quantities such as domain wall width, domain wall tension, and edge velocity to microscopic parameters and provide concrete targets for experiments.
domain walls↗
Detecting fractionalization in critical spin liquids using color centers
Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024
Takei, So (ORCID:0000000191771895)↗
Dirac Node Pinning from Dzyaloshinskii-Moriya Interactions in a Kagome Spin Liquid
Recent experiments on the Kagome spin liquid candidate material YCu 3 (OH) 6 Br 2 [Br 1−𝑦 (OH) 𝑦 ] suggest the presence of Dirac fermionic spinons near the magnetization plateau at 1/9. Theories suggest that the spinons are charge neutral spin-1/2 excitations, in a 2𝜋/3 flux, which triples the unit cell. Generally a gap is expected, and there is no symmetry protection for the Dirac nodes in this system. The question arises as to what causes the nodes and stabilizes them. In this work, we propose a node-creation and node-pinning mechanism driven by Dzyaloshinskii-Moriya (DM) interactions. Employing Gutzwiller-projected variational Monte Carlo calculations, we demonstrate that DM interactions induce a band closing phase transition in the spinon spectrum. There is a change in the Chern number when the bands are inverted. Together with the DM-generated internal gauge flux, the coupling to the spinon orbital magnetization counteracts the band reopening. Furthermore, this interplay energetically pins the Dirac nodes over a range of parameters, resulting in a pinning mechanism distinct from the usual one from symmetry protection.
Kagome lattice↗
Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal
Highlights: • We look at the role played by generic scale invariance (GSI) in the phase transition between a U(1) spin liquid and a Fermi liquid. • We identify dangerously irrelevant operators in the renormalization group transformation, involved with the GSI. • We highlight novel mean-field dynamics of this Mott quantum criticality, resulting from the GSI. We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality. We discuss physical implications of effective one-dimensional spin dynamics and extremely overdamped gauge dynamics at the Mott quantum criticality.
36 MATERIALS SCIENCE↗
Symmetric U(1) and Z 2 spin liquids on the pyrochlore lattice
The geometrically frustrated three-dimensional pyrochlore lattice has been long predicted to host a quantum spin liquid, an intrinsic long-range entangled state with fractionalized excitations. To date, most proposals for pyrochlore materials have focused on quantum spin ice, a U(1) quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. Here, we explore the possibility of finding pyrochlore quantum spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric U ( 1 ) and Z 2 spin liquids on the pyrochlore lattice within the projective symmetry group framework for fermionic spinons. We find 18 U ( 1 ) spin liquids and 28 Z 2 spin liquids that preserve pyrochlore space-group symmetry while, upon further imposing time-reversal symmetry, the numbers of classes become 16 and 48, respectively. For each class, the most general symmetry-allowed spinon mean-field Hamiltonian is given. Interestingly, we find that several U(1) spin liquid classes possess an unusual gapless multi-nodal-line structure (“nodal star”) in the spinon bands, which is protected by the projective actions of the threefold rotation and screw symmetries of the pyrochlore space group. Through a simple model, we study the effect of gauge fluctuations on such a nodal star spin liquid and propose that the leading terms in the low temperature specific heat have the scaling form C / T ~ T + T / ln T , in contrast to the form C / T ~ T 2 of the standard U(1) pyrochlore spin liquid with gapped spinons.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Unraveling higher-order contributions to spin excitations probed using resonant inelastic x-ray scattering
Resonant inelastic x-ray scattering (RIXS) is an evolving tool for investigating the spin dynamics of strongly correlated materials, which complements inelastic neutron scattering. In isotropic spin-$\frac{1}{2}$ Heisenberg antiferromagnetic (HAFM) spin chains, both techniques have observed non-spin-conserving (NSC) excitations confined to the two-spinon phase space. However, a recent O K-edge RIXS study of the one-dimensional HAFM Sr 2 CuO 3 observed spin-conserving (SC) four-spinon excitations outside the two-spinon phase space. Here, we demonstrate that analogous four-spinon excitations can also be accessed at the Cu L 3 edge in the related material SrCuO 2 . Through detailed modeling, we establish that these excitations appear in both the SC and NSC channels of the Cu L 3 edge, and are only captured by higher-order terms in the ultrashort core-hole lifetime expansion. Finally, since these terms encode information about spin-spin correlations extending beyond nearest neighbors, our results offer different possibilities for studying nonlocal spin correlations in quantum magnets.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Cyclotron resonance in a kagome spin liquid candidate material
We propose cyclotron resonance as an optical probe for emergent fractionalized excitations in U(1) quantum spin liquids, focusing on kagome antiferromagnets. In contrast to conventional systems, where cyclotron resonance directly couples to charged carriers, spinons in spin liquids are charge-neutral and interact only through an emergent gauge field, making direct probing challenging. We identify two key mechanisms by which an external physical electromagnetic field induces emergent electric and magnetic fields, enabling indirect coupling to spinons. Using these mechanisms, we compute the absorption rate of the cyclotron resonance response for Dirac spinons forming Landau levels. Our analysis shows that, although the absorption per layer is small, the absence of a skin-depth limitation in insulating spin liquids allows for cumulative absorption comparable to graphene in realistic sample sizes for the recently discovered spin-liquid candidate material YCu 3 (OH) 6 Br 2 [Br 1−𝑦 (OH) 𝑦 ]. Furthermore, our proposed cyclotron-resonance measurement is a decisive, practical test for spinon Landau levels, providing quantitative expectations where clear experimental evidence has so far been lacking.
Dzyaloshinskii-Moriya interaction↗
Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. Furthermore, the linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Magnetic field effects in an octupolar quantum spin liquid candidate
Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to an external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here, in this study, we use neutron scattering to show that the application of a large external magnetic field to Ce 2 Zr 2 O 7 , an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wave vectors in Ce 2 Sn 2 O 7 pyrochlore, and its absence in Ce 2 Zr 2 O 7 . Therefore, our results identify Ce 2 Zr 2 O 7 as a strong candidate for an octupolar U(1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quasiparticle description of angle-resolved photoemission spectroscopy for SrCuO 2
SrCuO 2 has long been considered a near-archetypal realization of a quasi-one-dimensional (1D) system of interacting electrons with short-range interactions. Within this framework, experimental observations - interpreted through the lens of the 1D Hubbard model - suggest that electron and hole excitations decay into two types of (unphysical) collective bosonic modes: "spinons", which carry the spin degree of freedom, and "holons", which carry the charge degree of freedom. This model, known as spin-charge separation, is most directly evidenced by angle-resolved photoemission spectroscopy (ARPES), where a photo-induced hole decays into a continuum of these excitations. Here we present an alternative perspective grounded in first-principles, self-consistent, and parameter-free many-body perturbation theory. In this revised quasiparticle framework, ARPES can be understood as a one-body effect arising from mild disorder in a long-range antiferromagnetic ground state. the emergence of the so-called spinon branch arises naturally from spin disorder, the anomalous linewidths are accurately captured, and we provide a compelling explanation for the spectral weight observed at the non-magnetic zone boundary. This reinterpretation provides a unified explanation for key experimental signatures previously attributed to spin-charge separation, including features observed in optical conductivity. Additionally, we show that SrCuO 2 exhibits a nontrivial interchain coupling that significantly influences both its one-particle and two-particle spectral functions. By comparing the spectral features of SrCuO 2 with those of La 2 CuO 4 , we argue that SrCuO 2 shares notable similarities with the two-dimensional cuprates-both being rooted in a common CuO 4 plaquette-based molecular orbital framework.
1D cuprates↗