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arXiv:1703.01876 · Physical review. B./Physical review. B

Detecting spin fractionalization in a spinon Fermi surface spin liquid

Yaodong Li, Gang Chen

Published Aug 2, 2017• 54 citations
arXivHTMLPDF

Abstract

Motivated by the recent proposal that several candidate materials such as ${\mathrm{YbMgGaO}}_{4}$ could be spinon Fermi surface spin liquids, we explore the experimental consequences of the external magnetic fields on this exotic state. Specifically, we focus on the weak field regime where the spin-liquid state is well preserved and the spinon remains to be a good description of the magnetic excitations. From the spin-1/2 nature of the spinon excitation, we predict the unique features of the spinon continuum when the weak magnetic field is applied to the system. Due to the small energy scale of the exchange interactions between the local moments in the spin-liquid candidate like ${\mathrm{YbMgGaO}}_{4}$, our proposal for the spectral weight shifts and spectral crossing in the magnetic fields can be immediately tested by inelastic neutron scattering experiments. Several other experimental aspects about the spinon Fermi surface and the spinon excitations are discussed and proposed. Our work provides an experimental scheme to examine the fractionalized spinon excitation and the candidate spin-liquid states in ${\mathrm{YbMgGaO}}_{4}$, the 6H-B phase of ${\mathrm{Ba}}_{3}{\mathrm{NiSb}}_{2}{\mathrm{O}}_{9}$, and other relevant materials.

DOI
10.1103/physrevb.96.075105

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Motivated by the recent proposal that several candidate materials such as YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ could be spinon Fermi surface spin liquids, we explore the experimental consequences of the external magnetic fields on this exotic state. Specifically, we focus on the weak field regime where the spin-liquid state is well preserved and the spinon remains to be a good description of the magnetic excitations. From the spin-1/2 nature of the spinon excitation, we predict the unique features of the spinon continuum when the weak magnetic field is applied to the system. Due to the small energy scale of the exchange interactions between the local moments in the spin-liquid candidate like YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, our proposal for the spectral weight shifts and spectral crossing in the magnetic fields can be immediately tested by inelastic neutron scattering experiments. Several other experimental aspects about the spinon Fermi surface and the spinon excitations are discussed and proposed. Our work provides an experimental scheme to examine the fractionalized spinon excitation and the candidate spin-liquid states in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, the 6H-B phase of Ba3NiSb2O9{\mathrm{Ba}}_{3}{\mathrm{NiSb}}_{2}{\mathrm{O}}_{9}Ba3​NiSb2​O9​, and other relevant materials.
Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor S(q,ω)S(\mathbf{q},ω)S(q,ω) of spin liquid states on the kagome lattice. Spin-1 excited states in spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). FSL and RSL have low energy peaks in S(q,ω)S(\mathbf{q},ω)S(q,ω) at KKK points in the extended magnetic Brillouin zone, in contrast to experiments where low energy peaks are found at MMM points. There is no obviuos contradiction between DSL and neutron scattering measurements. Besides a fractionalized spin (i.e. spin-1/2), spinons in DSL carry a fractionalized crystal momentum which is potentially detectable in SWC in the neutron scattering measurements.
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
We study the transverse dynamical spin susceptibility of the two-dimensional U(1) spinon Fermi-surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed noninteracting spinon approximation. The short-range part of the interaction lead to a collective ``spinon spin wave'' mode, which splits off from the two-spinon continuum at a small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing nonzero power-law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as B2/3{B}^{2/3}B2/3 with magnetic field BBB at low temperatures. Our results form the basis for a theory of inelastic neutron scattering, ESR, and resonant inelastic x-ray scattering studies of this quantum spin-liquid state.
Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, we carry out a systematic projective symmetry group analysis and mean-field study of candidate U(1)U(1)U(1) spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight U(1)U(1)U(1) spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​. Further connection of this spinon Fermi surface U(1)U(1)U(1) spin liquid with YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.
Recently, thermal Hall effect has been observed in the paramagnetic state of volborthite, which consists of distorted kagome layers with S=1/2S=1/2S=1/2 local moments. Despite the appearance of magnetic order below 1K1\phantom{\rule{0.28em}{0ex}}\mathrm{K}1K, the response to external magnetic field and unusual properties of the paramagnetic state above 1K1\phantom{\rule{0.28em}{0ex}}\mathrm{K}1K suggest possible realization of exotic quantum phases. Motivated by these discoveries, we investigate possible spin liquid phases with fermionic spinon excitations in a nonsymmorphic version of the kagome lattice, which belongs to the two-dimensional crystallographic group p2ggp2ggp2gg. This nonsymmorphic structure is consistent with the spin model obtained in the density functional theory calculation. Using projective symmetry group analysis and fermionic parton mean field theory, we identify twelve distinct Z2{\mathbb{Z}}_{2}Z2​ spin liquid states, four of which are found to have correspondence in the eight Schwinger boson spin liquid states we classified earlier. We focus on the four fermionic states with bosonic counterpart and find that the spectrum of their corresponding root U(1)U(1)U(1) states features spinon Fermi surface. The existence of spinon Fermi surface in candidate spin liquid states may offer a possible explanation of the finite thermal Hall conductivity observed in volborthite.
Motivated by the rapid experimental progress of quantum spin ice materials, we study the dynamical properties of pyrochlore spin ice in the U(1) spin liquid phases. In particular, we focus on the spinon excitations that appear at high energies and show up as an excitation continuum in the dynamic spin structure factor. The keen connection between the crystal symmetry fractionalization of the spinons and the spectral periodicity of the spinon continuum is emphasized and explicitly demonstrated. When the spinon experiences a background $\ensuremath{\pi}$ flux and the spinon continuum exhibits an enhanced spectral periodicity with a folded Brillouin zone, this spectral property can then be used to detect the spin quantum number fractionalization and U(1) spin liquid. Our prediction can be immediately examined by inelastic neutron-scattering experiments among quantum spin ice materials with Kramers' doublets. Further application to the non-Kramers' doublets is discussed.