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 E2g 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 Eg 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.


I. INTRODUCTION
When subject to strong quantum fluctuation and geometrical frustration, the quantum spin system may not develop into a magnetically ordered state [1,2], but a quantum spin liquid (QSL) ground state at zero temperature.[3][4][5][6] QSL has no classic counterpart as it exhibits various topological orders characterized by the long-range entanglement pattern.[7][8][9] The lattice of the spin-1/2 kagome network of cornersharing triangles is a long-sought platform for antiferromagnetically interacting spins to host a QSL ground state.[10][11][12][13][14][15][16] Herbersmithite [ZnCu 3 (OH) 6 Cl 2 ] is the first promising kagome QSL candidate, [3,[16][17][18][19][20][21][22][23] in which no long-range magnetic order was detected down to low temperature, [17,18] and inelastic neutron scattering on single crystals revealed a magnetic continuum, as a hallmark of fractionalized spin excitations.[20,22] Up to date, most, if not all, experimental information on the nature of kagome QSL relies on a single compound of Herbertsmithite.Considering the fact that a lattice distortion away from a perfect kagome structure has recently been confirmed in Herbersmithite, [24,25] which stimulates investigations on the subtle magneto-elastic effect in the kagome materials, [26,27] an alternative realization of the QSL compound with the ideal kagome lattice is still in urgent need.Zn-Barlowite [Cu 3 Zn(OH) 6 FBr] is such a can-didate for a kagome QSL ground state [28][29][30][31][32][33][34][35][36][37][38] with no lattice distortion being reported yet.Measurements on the powder samples of Zn-Barlowite indicate the absence of longrange magnetic order or spin freezing down to temperatures of 0.02 K, four orders of magnitude lower than the Curie-Weiss temperature.[30,32] Besides the absence of long-range magnetic order down to low temperature, the fractionalized spin excitations, i.e. spinons, in the spectroscopy is essential evidence for the long-range entanglement pattern in QSL.However, spectroscopic evidence for the deconfined spinon excitations in Zn-Barlowite is still lacking, in part due to unavailable single-crystal samples.Note that for Zn-Barlowite Cu 4 -x Zn x (OH) 6 FBr the doping parameter x ≤ 0.56, in the previously reported Zn-Barlowite single crystal samples, does not belong to the QSL regime.[33-35, 37, 38] In this work, we report the synthesis of the single crystals of Cu 4 -x Zn x (OH) 6 FBr (x = 0.82) of millimeter size, which is in the QSL regime, and the spin dynamics revealed by the inelastic light scattering on these samples.We confirm the ideal kagome-lattice structure by the angle-resolved polarized Raman responses and second-harmonic-generation (SHG), and observe a magnetic Raman continuum in our crystal samples.Raman scattering has previously been reported for Herbertsmithite, [19] and the overall continuum agreed with that in Zn-Barlowite.Although it was not discussed, the lattice distortion in Herbertsmithite was evident by the anisotropic angle dependent Raman responses [19] and may account for the difference from our results in details.In the theory the Raman spectrum of the kagome QSL contains the one-pair component of spinon-antispinon excitations with a peculiar power-law behavior at low frequency, serving as the fingerprint of spinons.[39] Our measured magnetic Raman continuum agrees well with the theoretical prediction, revealing the fractionalized spin excitation in Cu 3.18 Zn 0.82 (OH) 6 FBr.
To demonstrate the one-pair spinon dynamics in the kagome QSL even more evidently, we perform a control experiment on a kagome antiferromagnet EuCu 3 (OH) 6 Cl 3 , which suffers a spinon confinement as a transition taking places from a paramagnetic phase to a q = 0 type 120 • non-collinear antiferromagnetic order (AFM) ground state below the Néel temperature T N = 17 K. [40][41][42] We observe a magnon peak in the AFM state, which can be regarded as the spinon confinement in the magnetically ordered state as schematically summarized in Fig. 1.The magnon excitation emerges from the one-pair continuum, firstly reported in our work, and can be regarded as the bound state of the spinonantispinon excitations.
To study changes in the crystal structures of Cu3Zn and Cu4, we track the temperature evolution of Raman spectra in the two compounds.Cu3Zn and Cu4 at high temperature crystallize the same space group P 6 3 /mmc.[28,30] We didn't observe the structural phase transition in Cu3Zn from the Raman scattering down to low temperature (Supplementary Sec-tion2 and 3).Cu4 transforms to orthorhombic Pnma below 265 K, characterized by changes in the relative occupancies of the interlayer Cu 2+ site.[31,[33][34][35] The splitting of phonon peaks in Cu4 due to the superlattice folding in the orthorhombic Pnma phase is resolved for several modes [Supplementary Fig. S4].Cu3Zn displays sharp E 2g modes at 125 cm −1 for in-plane relative movements of Zn 2+ .The corresponding modes for the interlayer Cu 2+ in Cu4 are broad at 290 K due to the randomly distributed interlayer Cu 2+ and split into two peaks below the structural transition temperature.Cu3Zn has no Raman-active mode related to the kagome Cu 2+ vibra-tions, indicating the kagome layer remains substantially intact as the inversion center of Cu 2+ sites is evident.The kagome layers in Cu4 are distorted, signaled by a new phonon mode for the kagome Cu 2+ vibration at 62 cm −1 .Besides sharp phonon modes, we observe a Raman continuum background in Cu3Zn, particularly at low frequency, signifying substantial magnetic excitations.
Previous X-ray and neutron refinements of the crystal structure suggest ideal kagome planes in Cu3Zn.SHG confirmed the parity symmetry of the crystallographic structure in Barlowite 2 Cu 4 (OH) 6 FBr and Zn-Barlowite Cu 3.66 Zn 0.33 (OH) 6 FBr.In Supplementary Section7, we also reveal the inversion symmetry by SHG in our single crystals of Cu3Zn.To further exclude subtle local symmetry lowering or lattice distortions, we perform the angle-resolved polarization-dependent Raman measurements of Cu3Zn for magnetic and lattice vibration modes.[44,45] The threefold rotation symmetry of the kagome lattice leads to isotropic angle dependence in the XX configuration both for A 1g and E 2g components, XY and X-only configurations for the E 2g component; it also gives rise to the angle θ dependence of cos 2 θ in the X-only configuration for the A 1g component.We find that the angle dependence of Raman responses, in particular for the magnetic continuum at low frequency, the Br − E 2g phonon, and O 2− A 1g phonon modes, fit the theoretical curves very well [Supplementary Section4], confirming the threefold rotational symmetry of the kagome lattice in the dynamical Raman responses of the lattice vibrations and magnetic excitations.Combining the X-ray and neutron refinement, [30][31][32]38] we conclude that Cu3Zn manifests a structurally ideal realization of layered spin-1/2 Cu 2+ kagome-lattice planes.
Having established the absence of a sharp anomaly in the thermodynamic properties [Supplementary Section1] and the lack of an emergent magnetic order with the weak symmetry breaking in the angle-dependent polarized Raman response, which is the first step to a QSL, we now present our main results of the magnetic Raman continuum in Cu3Zn with subtracting phonon contribution, as shown in Fig. 2. The susceptibility is related to the Raman intensity I(ω) = (1 + n(ω))χ (ω) with the bosonic temperature factor n(ω). Fig. 2a, b and c are the A 1g magnetic Raman response in Cu3Zn, which measures the thermal fluctuation of the interacting spins on the kagome lattice.[46][47][48] We can see that the A 1g channel is activated only at high temperatures, disappears at low temperatures, behaving as the thermally activated excitations.At high temperatures, the Raman spectra exhibit the quasielastic scattering that is common in the inelastic light scattering for the spin systems.[48] The maximum in the Raman response function decreases from 60 cm −1 at room temperature to 30 cm −1 at 110 K, and the magnetic intensity becomes hardly resolved at low temperatures below 50 K.The integrated Raman susceptibility χ (T ) in Fig. 2b fits the thermally activated function, ∝ e −ω * /T with ω * = 53 cm −1 , different from the power-law temperature dependence of the quasielastic scattering in Herbertsmithite.[19] The temperature dependence of the A 1g magnetic Raman susceptibilities χ A1g (ω, T ) in Cu3Zn distributes the main spectral weight among the frequency region less than 400 cm −1 and the tem-perature range above 50 K in Fig. 2c.
Different from the A 1g channel, the pronounced E 2g magnetic Raman continuum in Cu3Zn persists at low temperatures (Fig. 2d), indicating the quantum fluctuation of the kagome spin-1/2 system.Along with the theoretical work, [39] we schematically decompose the E 2g Raman continuum into two components, which have the maximum around 150 cm −1 and the higher one around 400 cm −1 , respectively.We denote them as spin excitations for one spin-antispinon pair (one-pair) and two spinon-antispinon pair (two-pair) excitations, respectively.[39] Like the two-magnon scattering in the antiferromagnet, [48,49] the two-pair component doesn't show a significantly non-monotonic temperature dependence as reducing temperatures.The substantial low energy one-pair component has a more pronounced non-monotonic temperature dependence.It increases with the temperature decreasing from 290 K to 50 K and decreases with further temperature reduce as shown in Figs.2d, e, and f.The frequency and temperature dependence of the E 2g magnetic Raman susceptibilities χ E2g (ω, T ) distributes the main spectral weight among the frequency region less than 400 cm −1 , and reaches the maximum at around 150 cm −1 and 50 K, as shown in Fig. 2f.We also observed the Fano effect for the E 2g F − phonon peak at 173 cm −1 in Cu3Zn [Supplementary Section3], whose asymmetric lineshape provides an additional probe of the magnetic continuum.
The one-pair component in the E 2g Raman continuum is crucial as it has an origin in the spinon excitation in the kagome QSL from the perspective of theory.[39] With the incoming and outgoing light polarizations êin and êout , magnetic Raman scattering measures the spin-pair (two-spin-flip) dynamics in terms of the Raman tensor [39,44,50,51] where the summation runs over ij for the nearest neighbor bonds r ij for the S i and S j on the kagome lattice.At zero temperature, the magnetic Raman susceptibility is given as denotes the matrix element for the transition between the ground state |0 and the excited state |f .
denotes the density of state (DOS) for the Raman tensor associated excitations.Introducing the spinon operator f iσ in QSL, the spin-pair operator in the Raman tensor is rewritten in terms of two pairs of spinon-antispinon excitations Besides the two-pair excitation, the magnetic Raman continuum contains the one-pair spinon ex- , where χ = f † iσ f jσ is the spinon mean-field hopping amplitude.[39] As shown in Fig. 2d, the one-pair component in the measured Raman susceptibility in the E 2g has the maximum at 150 cm −1 (J), and extends up to 400 cm −1 (2.6J) at low temperatures.The twopair component has the maximum at 400 cm −1 (2.6 J) and the cut-off around 750 cm −1 (4.9 J).In totality, the mentioned features (maxima and cut-offs) of one-and two-pair excitations in the E 2g measured Raman response in Cu3Zn (Fig. 2  d) overall agree well with the theoretical calculation for the kagome QSL state.[39] In more detail, the one-pair component dominates the E 2g magnetic Raman continuum at low frequency.It displays the power-law behavior up to 70 cm −1 , with a significantly nonmonotonic temperature dependence, as shown in Figs. 3. As lowering the temperature, the E 2g continuum at low frequency increases above 50 K and decreases below 50 K.The lowenergy continuum evolves from a sublinear behavior T α with α < 1 to a superlinear one T α with α > 1 as reducing the temperature.A central question for the kagome spin liquid is whether a spin gap exist.The results of the spin gap in Herbertsmithite are controversial due to the difficulty of singling out the kagome susceptibility.[21,23] Previous results on the powder samples of Cu3Zn suggest a small spin gap, [30,32] and measurements on the single-crystal samples would be of great interest.If such a gap exists, the power-law behavior of the E 2g magnetic Raman continua sets an upper bound for the spin gap of 2 meV.
The temperature-dependent magnetic continua of Cu3Zn in Figs.2d, e, and f, and Fig. 3 imply the maximal spin fluctuations at the characteristic temperature 50 K.The maximum of the kagome spin fluctuations in Cu3Zn signifies the spin singlet forming, [2,52] but is masked by the inter-layer Cu 2+ moments in the thermodynamic properties [Supplementary Section1].It can be revealed by the Knight shift related to the kagome spins in the nuclear magnetic resonace measurements.[30] In contrast to significant energy dependence in magnetic Raman continuum in Cu3Zn in Figs. 2  and 3, the scattered neutron signal in Herbertsmithite is overall insensitive to energy transfer, rather flat above 1.5 meV, but increases significantly at low-energy scattering due to the interlayer Cu 2+ ions.[20,22] The interlayer Cu 2+ ions distribute spatially away from each other, and the spin-pair magnitude among themselves and between them and kagome spins is weak, giving rise to a negligible matrix element in Raman tensors.So different from the neutron scattering, the Raman scattering is not sensitive to the inter-layer Cu 2+ at low energies, advantageous to the detection of kagome spins.Furthermore, inelastic neutron scattering in Herbertsmithite measures the magnetic continuum up to 2-3 J, [20] the same energy range as the one-pair Raman component in Cu3Zn.These results suggest that the magnetic Raman continuum originates from the kagome-plane spins, and the onepair component has an origin of spinon excitations.
The theoretical calculation for kagome Dirac spin liquid (DSL) predicts the power-law behavior for the Raman susceptibility in the E 2g channel at low frequency.[39] The onepair spinon excitation in DSL gives the linear density of state D 1P ∝ ω.The matrix element turns out to be exactly zero for all one-pair excitations in the mean field Dirac Hamiltonian.As a result a Raman spectrum that scales as ω 3 was predicted.[39] However, the vanishing of the matrix element is somewhat accidental and depends on the assumption of a DSL in a Heisenberg model in an ideal kagome lattice.Any deviation from the ideal DSL state, e.g. a small gap in the ground state, [30,32] DM interactions, or other effects of perturbations, [26,53] changes the wave functions and may result in a constant matrix element M (ω).In that case, the Raman spectrum will be simply proportional to the DOS of the one-pair component D 1P which is linear in ω.From our fitting for Cu3Zn in Fig. 3, we find that α = 1.3 when approaching zero temperature.The existence of a small gap in the spinon spectrum may explain this discrepancy.We also note that according to the theory [39] the A 1g and A 2g contributions to the one-pair continuum are the forth-order effect, much smaller than the E 2g contributions.This explains the invisible one-pair continuum in the A 1g and A 2g channels.
Figure 4 presents a control Raman study on the magnetic ordered kagome antiferromagnet EuCu3, which has the antiferromagnetic superexchange J 10 meV, half of the value in Cu3Zn.EuCu3 belongs to the atacamite family with the perfect kagome lattice and has the q = 0 type 120 • ordered spin configuration below T N due to a large Dzyaloshinski-Moriya (DM) interaction [Supplementary Section8].[40,42,[54][55][56] Above the ordering temperature T N = 17 K, the magnetic Raman continuum in the E g channel displays the extended continuum, similar to that in Zn-Barlowite at 4 K as shown in Fig. S10 in Supplementary Section6.This indicates the strong magnetic fluctuations in EuCu3.The less pronounced lowenergy continuum excitations in EuCu 3 (OH) 6 Cl 3 indicate the suppression of the quantum fluctuation due to a large DM interaction.The low energy excitation in the ordered state is the spin-wave excitation, i.e. magnon, and the E g Raman scatter-ing measures one-and two-magnon excitations for the noncollinear 120 • spin configuration as detailed in the Methods section, leading to a sharp magnon peak at 72 cm −1 superimposing on the two-magnon continuum.In this sense, the AFM transition may be thought of as a confinement transition.The comparative studies between Cu3Zn and EuCu3 are sketched in Fig. 1, demonstrating the spinon deconfinement and confinement, respectively, in the different ground states.

III. CONCLUSIONS
Our Raman scattering studies compare the spin dynamics in the kagome QSL compound Cu3Zn and magnetically ordered antiferromagnet EuCu3.In contrast to a sharp magnon peak in EuCu3, the overall magnetic Raman scattering in Cu3Zn agrees well with the theoretical prediction for a spin liquid state.The spinon continuum is evident, providing the strongest evidence yet for the kagome QSL ground state in Cu3Zn.On the material side, Zn-Barlowite provides an ideal structural realization of the kagome lattice, and the available single crystal samples stimulate future systematical studies of the kagome QSL.Along with Herbertsmithite, the singlecrystalline Zn-Barlowite stands able to provide considerable insight into singling out the intrinsic properties of the intrinsic nature of the kagome QSL, without deceiving by the material chemistry details.

METHODS
Sample preparation and characterization.High qualified single crystals of Zn-Barlowite was grown by a hydrothermal method similar to crystal growth of herbertsmithite.[57,58] CuO (0.6 g), ZnBr 2 (3 g), and NH 4 F (0.5 g) and 18 ml deionized water were sealed in a quartz tube and heated between 200 • C and 140 • C by a two-zone furnace.After three months, we obtained millimeter-sized single crystal samples.The value of x in Cu 4 -x Zn x (OH) 6 FBr has been determined as 0.82 by Inductively Coupled Plasma-Atomic Emission Spectroscopy (ICP-AES).The single-crystal X-ray diffraction has been carried out at room temperature by using Cu source radiation ( λ = 1.54178Å) and solved by the Olex2.PC suite programs.[59] The structure and cell parameters of Cu 4 -x Zn x (OH) 6 FBr are in coincidence with the previous report on polycrystalline samples.[30,32] For Barlowite(Cu 4 (OH) 6 FBr), the mixture of CuO (0.6 g), MgBr 2 (1.2 g), and NH 4 F (0.5 g) was transferred into Teflon-lined autoclave with 10 ml water.The autoclave was heated up to 260 • C and cooled to 140 • C after two weeks.A similar growth condition to Barlowite was applied for the growth of EuCu 3 (OH) 6 Cl 3 with staring materials of EuCl 3 • 6 H 2 O (2 g) and CuO (0.6 g).
Measurement methods.Our thermodynamical measure-ments were carried out on the Physical Properties Measurement System (PPMS, Quantum Design) and the Magnetic Property Measurement System (MPMS3, Quantum Design).
The temperature-dependent Raman spectra are measured in a backscattering geometry using a home-modified Jobin-Yvon HR800 Raman system equipped with an electron-multiplying charged-coupled detector (CCD) and a 50× objective with long working distance and numerical aperture of 0.45.The laser excitation wavelength is 514 nm from an Ar + laser.The laser-plasma lines are removed using a BragGrate bandpass filter (OptiGrate Corp.), while the Rayleigh line is suppressed using three BragGrate notch filters (BNFs) with an optical density 4 and a spectral bandwidth ∼5-10 cm −1 .The 1800 lines/mm grating enables each CCD pixel to cover 0.6 cm −1 .The samples are cooled down to 30 K using a Montana cryostat system under a vacuum of 0.4 mTorr and down to 4 K using an attoDRY 1000 cryogenic system.All the measurements are performed with a laser power below 1 mW to avoid sample heating.The temperature is calibrated by the Stocksanti-Stocks relation for the magnetic Raman continuum and phonon peaks.The intensities in two cryostat systems are matched by the Raman susceptibility.The polarized Raman measurements with light polarized in the ab kagome plane of samples were performed in parallel (XX), perpendicular (XY ), and X-only polarization configurations [Supplementary Section4].
SHG measurements were performed using a homemade confocal microscope in a back-scattering geometry.A fundamental wave centered at 800 nm was used as excitation source, which was generated from a Ti-sapphire oscillator (Chameleon Ultra II) with an 80 MHz repetition frequency and a 150 fs pulse width.After passing through a 50x objective, the pump beam was focused on the sample with a diameter of 2 µm.The scattering SHG signals at 400 nm were collected by the same objective and led to the entrance slit of a spectrometer equipped with a thermoelectrically cooled CCD.Two shortpass filters were employed to cut the fundamental wave.
Magnon peak in Raman response for q = 0 AFM state.We consider a kagome lattice antiferromagnet with the DM interaction where summation runs over nearest neighbor bonds ij of the kagome lattice, and the DM interaction is assumed to be of the out-of-plane type.With a large DM interaction D, the kagome antiferromagnet devoleps a q = 0 type 120 • AFM order at low temperature in EuCu3.[40][41][42][60][61][62] In terms of the local basis for the AFM order, we rewrite the Hamiltonian as with where θ ij is an angle between two neighboring spins.The effective linear spin wave Hamiltonian is given as for which the Holstein-Primakoff representation for spin operators in the local basis was applied and the energy dispersion was obtained in Ref. [63].The Raman tensor in the XY configuration is given as In the local spin basis, we have the Raman tensor is given as In the spin-pair operator S i S j in Eq. ( 4), there are twomagnon contribution in terms of S x i S x j + cos(θ ij )(S y i S y j + S z i S z j ), and one-and three-magnon contributions in terms of sin(θ ij )(S z i S y j − S y i S z j ).For the q = 0 spin configuration, we find that τ xy R in Eq. 7 has the non-vanished one magnon contributions.For the √ 3 × √ 3 AFM state, τ xy R has no onemagnon contribution.The observed one-magnon peak in the E g channel in EuCu 3 provides evidence for the q = 0 spin ordering at low temperatures.In the linear spin-wave theory, we take S z in the local basis as a constant, S z i = S z = 1/2, and the XY Raman tensor is given as in terms of the local basis, directly measuring the one magnon excitation.For EuCu3, we have the estimation for the interaction parameters, J = 10 meV, D/J = 0.3, and the magnon peak position is ∆ sw = 1.1J = 88 cm −1 , very close to the measured value 72 cm −1 in our Raman measurement of the one-magnon peak.
FIG. 1. Schematical comparative Raman responses for the AFM and QSL states.With a large DM interaction D, the kagome antiferromagnet develops a 120 • non-collinear AFM ground state with the wave vector q = 0 below TN .[60][61][62] Increasing J/D, the fluctuation of the kagome system increases, driving the system into the QSL state.By increasing the temperature, the thermal fluctuation melts the magnetic order and turns the system into the classic paramagnetic state at high temperatures.By the first-principle calculations in Supplementary Sec-tion8, Cu3Zn and EuCu3 have the values of D/J as 0.05 and 0.3, and thus correspond to the QSL and AFM ground states, respectively.In the middle, the elementary excited states of AFM and QSL states are the magnon and spinon, respectively, resulting in different magnetic Raman spectra shown at the bottom.Here 1P and 2P denote the one-pair and two-pair spinon excitations, respectively.1M and 2M in magnetically ordered state denote the one-and two-magnon excitations, respectively.The 1M Raman peak in AFM measures the magnon [Methods Section] while the 1P Raman continuum in QSL probes the spinon excitations.[39] The shadow background of the 1M peak, marked as '1P', denotes the continuum above TN in EuCu3, mimicking the 1P continuum in the QSL state [Supplementary Section6].So the magnon excitation below TN emerges from the one-pair continuum and can be regarded as the bound state of the spinon-antispinon excitations.The transition between QSL and AFM can be thought to be driven by the spinon confinement.

IV. ANGLE-RESOLVED LIGHT POLARIZATION DEPENDENT RAMAN RESPONSE FOR Cu3Zn
Two typical polarization configurations were utilized to measure the angle-resolved polarized Raman spectra: i) a half-wave plate was put after the polarizer in the incident path to vary the angles between the polarization of incident laser and the analyzer with the fixed vertical polarization, which can be denoted as the X-only configuration; ii) a polarizer is allocated in the common path of the incident and scattered light to simultaneously vary their polarization directions, while the polarizations of incident laser and analyzer were parallel or perpendicular to each other.By rotating the fast axis of the half-wave plate with an angle of θ/2, the polarization of incident and/or scattered light is rotated by θ.
FIG. S6.Three polarization configurations in the angle dependent Raman response.In the XX (XY ) configuration, the incoming and outgoing light polarizations are parallel (perpendicular) and we rotate both of them simultaneously.In the X-only configuration, the outgoing light polarization is fixed and we rotate the incoming light polarization only.For Eu 3+ , we observe the A2g excitation of the 4f 6 configuration with the transition from 7 FJ=0 to 7 FJ=1.EuCu3@4 K EuCu3@10 K EuCu3@19 K EuCu3@23 K EuCu3@32.5K EuCu3@50 K EuCu3@100 K Cu3Zn@4 K FIG.S10.Magnetic Raman susceptibility in the XY configuration of EuCu3 above the Néel temperature.We present the XY magnetic Raman continuum in EuCu3 below 100 K. Above TN = 17 K, the Raman response has the substantial magnetic continuum below 50 K.
For a comparison, we also plot the XY magnetic Raman continuum in Cu3Zn at 4 K.The Raman shift frequency of Cu3Zn is divided by 1.9, the ratio of the super-exchange strength of two compounds.We can see that above TN , the profile of the Raman susceptibility in EuCu3 mimic that in Cu3Zn, suggesting the spinon contribution.There are less pronounced low-energy continuum excitations in EuCu3 than those in Cu3Zn, probably due to the large DM interaction which suppresses the low-energy quantum fluctuations.The maximum of the continuum excitations above TN in EuCu3 has the same energy scale as the magnon peak below TN , which suggests that the magnon peak can be taken as the bound state of spinon-antispinon pair.

FIG. 2 .
FIG. 2. Temperature dependence of the Raman susceptibilities in Cu3Zn.(a) The A1g Raman susceptibility χ A 1g = χ XX − χ XY .The solid lines are a guide to the eye.(b) Temperature dependence of the static Raman susceptibility in A1g channel χ A 1g (T ) = 2 π 400 cm −1 10 χ A 1g (ω) ω dω.The solid line is a thermally activated function.(c) Color map of the temperature dependence of the magnetic Raman continuum χ A 1g (ω, T ).(d) The E2g Raman response function χ E 2g = χ XY .The solid lines are a guide to the eye.We schematically decompose the E2g magnetic Raman continuum into two components of spin excitations for one and two spin-antispinon pair excitations, respectively.Here 1P and 2P represent one-and two-pair, respectively.(e) Temperature dependence of the static Raman susceptibility in E2g channel χ E 2g = 2 π 780 cm −1 10 χ E 2g (ω) ω dω.The solid line is a guide to the eye.(f) Color map of the temperature dependence of the magnetic Raman continuum χ E 2g (ω, T ).

2 FIG. 3 .
FIG. 3. Power-law behavior for the E2g Raman continua at low frequency in Cu3Zn.(a) and (b) Power-law fitting of χ E 2g (ω) ∝ ω α at low and high temperatures, respectively, in Cu3Zn.(c) Temperature dependent exponent α for the power-law fittings in cu3zn.

FIG. 4 .FIG. S2 .
FIG. 4. temperature dependence of the eg raman susceptibilities in eucu3.(a) the eg raman susceptibility χ eg = χ xy .the solid lines are a guide to the eye.a sharp magnon peak appears in the eg magnetic raman continuum below the magnetic transition temperature tn = 17 k.(b) temperature dependence of the static raman susceptibility in eg channel χ eg = 2 π 780 cm −1 10 χ eg (ω) ω dω. the solid line is a guide to the eye.(c) Color map of the temperature dependence of the magnetic Raman continuum χ Eg (ω, T ).A sharp magnon peak is observed below TN .

FIG. S3 .
FIG. S3.Raman spectra in Cu3Zn at different temperatures.(a) Unpolarized Raman spectra in Cu3Zn.(b) Raman spectra in the XX configuration in Cu3Zn which contains the A1g and E2g channel.(c) Raman spectra in the XY configuration which contains the E2g channel in Cu3Zn.

FIG. S4 .
FIG. S4.Raman spectral evolution from Cu4 to Cu3Zn (a) Unpolarized Raman spectra for Cu4 and Cu3Zn at selected temperatures.Comparison for phonon modes between 40 cm −1 and 90 cm −1 in (b), and between 100 cm −1 and 250 cm −1 in (c) for Cu4 and Cu3Zn.The Cu4 spectra in (a), (b) and (c) have been offset vertically for clarity.The phonon evolution from Cu4 to Cu3Zn displays the difference by substituting Cu4 interlayer Cu 2+ site with Zn 2+ in Cu3Zn.The parent Barlowite Cu4 transforms to orthorhombic Pnma below T ≈ 265 K, characterized by changes in the relative occupancies of the interlayer Cu 2+ site.Between 300 cm −1 and 600 cm −1 , there are several phonon peaks associated with O 2− vibrations in Cu4 and Cu3Zn.Cu3Zn displays the Br − in-plane relative mode (E2g) at 75 cm −1 , and has no active Raman mode related to the kagome Cu 2+ vibrations since Cu 2+ is the inversion center.The Br − phonon mode changes into two peaks in Cu4 due to the superlattice folding in the orthorhombic Pnma phase at low temperature.An additional Br − peak at 85 cm −1 appears in Cu4, related to the Br vibrations along the c-axis.The kagome layers in Cu4 are distorted, signaled by a new phonon mode for the kagome Cu 2+ vibration at 62 cm −1 .Cu3Zn displays sharp E2g modes at 125 cm −1 and 173 cm −1 correspond to in-plane relative movements for Zn 2+ and F − , respectively.The corresponding modes (interlayer Cu 2+ and F − ) in Cu4 are broad at 290 K due to the randomly distributed interlayer Cu 2+ and split into two peaks at 200 K.

FIG. S7 .
FIG. S7.Rotation symmetry of Raman dynamics for lattice vibrations and magnetic excitations in Cu3Zn.(a) We monitor three selected modes (both continua and phonon peaks).(b) Angle dependence of the integrated Raman susceptibility χR = 2 π 60 cm −1 10 χ (ω) ωdω.In X-only configuration, the continua at 290 K follows the cos 2 (θ) for the A1g channel, while at other configurations, the continua remain constant.(c) Angle dependence of the Br E2g phonon (75 cm −1 ) scattering intensity.The lines are constant functions.(d) Angle dependence of the O 2− A1g phonon (429 cm −1 ) scattering intensity.The Raman intensity of O 2− A1g mode exhibits a cos 2 (θ) behavior in the X-only configuration at both room temperature and low temperature, and keeps constant in XX and XY configurations.
FIG. S8.Raman spectra in EuCu3 at different temperatures.(a) Unpolarized Raman spectra in EuCu3.(b) Raman spectra in the XX configuration in EuCu3 which has the Ag and Eg channel.(c) Raman spectra in the XY configuration which contains the Eg and A2g channel.For Eu 3+ , we observe the A2g excitation of the 4f 6 configuration with the transition from 7 FJ=0 to 7 FJ=1.

FIG. S9 .
FIG. S9.Rotation symmetry of Raman dynamics for lattice vibrations and magnetic excitations in EuCu3.We monitor the selected magnetic continuum at low frequency and the O 2− Eg mode in (a).(b)Angle dependence of the integrated Raman continuum from 9-80 cm −1 .The continua at 290 K follows cos 2 (θ) for the A1g channel, while others remain constant.(c) Angle dependence of the O 2− Eg phonon (487 cm −1 ) scattering intensity.Its Raman intensities are independent of θ.

6 FIG. S12 .
FIG.S12.SHG in Cu3Zn at 300 K with different laser powers.(a) and (b) represent the successive SHG measurements in the same point of sample taken every 5 seconds with excitation powers at 25 mW and 32 mW, respectively.There are no SHG signals at the excitation power of 25 mW, whereas strong SHG signals appear at the excitation power above 32 mW after a 10 second exposure.By comparison, damage or degradation in crystal structure under high power excitation induces a detectable SHG signal, implying that inversion symmetry presents in undamaged Cu3Zn at room temperature.The lines have been offset vertically for clarity.

TABLE S1 .
Mode assignment for Cu3Zn.Cu3Zn crystallizes the space group P 63/mmc (No. 194) and has Raman active A1g, E1g, and E2g modes according to the point group representation of D 6h (6/mmm).E1g is not visible when the light polarization lies in the kagome ab plane, and we have Raman active phonon modes ΓRaman = 4A1g + 9E2g.
Raman spectra in EuCu3 at different temperatures.
SHG in Cu3Zn at 26 K with different laser powers.(a) SHG measurements in the same spot of sample taken every 5 seconds (from #1 to #6).At 23 mW, SHG signals in Cu3Zn sample are absent, implying that inversion symmetry remains preserved.(b) A series of SHG measurements under the excitation power of 32 mW in the same point of the sample taken every 5 seconds (from #1 to #12).A remarkable SHG signal at 400 nm is detectable after a 10 second exposure, which dramatically enhances as the time increases.Due to the damage or degradation of Cu3Zn under high power excitation, the inversion symmetry breaking induces a strong SHG signals in sample.By comparison, we conclude that undamaged Cu3Zn single crystal presents spatial inversion symmetry at low temperature.The lines have been offset vertically clarity.