Introduction

Frustration effects in low-dimensional quantum spin systems lead to the suppression of long-range order and non-trivial ground states1. A typical example of such a frustrated quantum spin system is the S = 1/2 zigzag chain with competition between the nearest-neighbor and next-nearest neighbor exchange interaction2,3. In this system, a variety of non-trivial quantum phenomena such as spin dimerization, a 1/3-magnetization plateau, and vector chirality have been theoretically suggested4,5,6 and experimentally confirmed in (N2H5)CuCl3, Rb2Cu2Mo3O12, and so on7,8,9,10.

Recently, there have been much attention and interest in frustrated spin systems with rare-earth elements (Ln). The strong spin–orbit coupling (SOC) and crystalline electric field (CEF) associated with 4f electrons of rare-earth ions lead to highly anisotropic exchange interactions, which gives rise to exotic states and phenomena not expected in simple S = 1/2 Hisenberg theoretical models.

In particular, Yb-based frustrated insulators have been intensively studied11,12,13,14,15,16,17,18,19,20,21,22,23,24,25. Since the Yb3+ ion has the nearly filled (4f)13 configuration, the ionic states and magnetic interactions become simpler than those in a typical rare-earth ion. In addition, the CEF energy scale is relatively large, yielding an isolated CEF doublet ground state, making it suitable for exploring the physics of frustrated magnet11. For example, YbMgGaO412,13,14 and NaYbSe215,16,17 with a triangular structure exhibit an unusual ground state. Even though the ground state of the S = 1/2 Heisenberg triangular antiferromagnets is known to be a 120o Neel ordered state theoretically, the spin–orbital-entangled local moments originating from Yb3+ ions in these compounds may host strong quantum fluctuations, stabilizing the quantum spin liquid state; a Z2 spin liquid, a Dirac-like spin liquid, or a spinon Fermi surface18,19,20. Moreover, Yb-based systems show often a unique ground state compared to other Ln-based systems. In fact, after the study in various LnCuS2 systems21,22, it was found that YbCuS2 has larger magnetic interactions between magnetic ions compared to other rare-earth ions. Furthermore, this compound exhibits peculiar magnetic phase diagrams such as magnetic-field-robust phase transitions and 1/3 plateaus, which are not seen in other rare-earth zigzag-chain materials. Quite recently, various Yb-based compounds such as YbCl3 with honeycomb lattices23, CdYb2S4 with pyrochlore lattices24, SrYb2O4 with zigzag chains arranged in honeycomb lattices25 have also been under intense investigation.

YbCuS2 is an above-mentioned Yb-based frustrated system. Figure 1a shows the crystal structure of YbCuS2, which has an orthorhombic structure with the space group P212121 (No. 19, \({D}_{2}^{4}\)). In YbCuS2, Yb atoms form the zigzag chains along the a-axis26. The electrical resistivity of YbCuS2 shows semiconducting behavior with an activation energy of 0.08–0.28 eV27. From the Curie–Weiss behavior of the magnetic susceptibility χ(T), the effective magnetic moment μeff was estimated to be 4.62μB, which is close to the value of the free Yb3+ ion (4.54μB). In general, the CEF level is important for understanding high-temperature and high-field magnetic responses in rare-earth systems. However, the low-temperature properties are governed by only the CEF ground state which was reported to be an isolated Kramers doublet with an energy separation of about 300 K from the first excited state in YbCuS221,22. The negative Weiss temperature θp = −31.6 K considering the CEF effect indicates the antiferromagnetic (AFM) interaction between the Yb magnetic moments, which is comparable to some Yb-based systems25,28. The magnetic specific heat divided by the temperature Cm/T shows a sharp peak at TO ~ 0.95 K, suggesting a first-order (FO) phase transition. Since the transition temperature TO is much lower than θp, YbCuS2 is expected to be a frustrated spin system. Below 20 K, the magnetic entropy decreased from R ln 2 expected for the Kramers doublet ground state. Here, R is the gas constant. The value of the magnetic entropy was only 20% of R ln 2 at TO, suggesting that the phase transition is suppressed by the frustration effect and it causes short-range ordering above TO.

Fig. 1: Crystal structure.
figure 1

a Crystal structure of YbCuS2 with the space group P212121. The black sticks represent the principal axis of the electric field gradient tensor determined by calculation using the WIEN2k package58. b View from the b-axis: zigzag chains along the a-axis are formed by Yb atoms. The black box represents the unit cell. The structural image was produced using the VESTA program59.

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In addition, the unusual magnetic field H dependence of TO was reported22. TO is independent of H up to 4 T and has a maximum at approximately 7 T. There are three anomalies in the H-swept AC susceptibility measured at low temperatures up to 18 T. These results suggest that a nontrivial ground state is realized in YbCuS2.

To investigate the physical properties, particularly the origin of the TO transition, from a microscopic point of view, we performed 63/65Cu-nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements on polycrystalline samples of YbCuS2. Our NQR results indicate that the FO AFM transition occurs at TO. Moreover, the nuclear spin-lattice relaxation rate 1/T1 of 63Cu at zero fields abruptly decreases below TO and exhibits T-linear behavior below 0.5 K, suggesting the presence of gapless fermionic excitations. The gapless excitations were also confirmed by the low-temperature specific-heat measurements. We discuss the possible origin of the fermionic excitation.

Results

63/65Cu-NMR/NQR spectrum

Figure 2a shows the H-swept 63/65Cu-NMR spectrum measured at 4.2 K on the powdered sample. From this powder pattern of the NMR spectrum, the quadrupole parameters νzz and η, which are explained subsequently, can be estimated by fitting the H-swept NMR spectrum to the calculated theoretical spectrum. In general, the total effective NMR Hamiltonian of a nucleus in H is given by

$${{{{{{{\mathcal{H}}}}}}}}= \, {{{{{{{{\mathcal{H}}}}}}}}}_{{{{{{{{\rm{Z}}}}}}}}}+{{{{{{{{\mathcal{H}}}}}}}}}_{{{{{{{{\rm{Q}}}}}}}}}=-\frac{\gamma }{2\pi }h(1+K){{{{{{{\boldsymbol{I}}}}}}}}\cdot {{{{{{{\boldsymbol{H}}}}}}}}\\ +\frac{h{\nu }_{zz}}{6}\left\{\left(3{I}_{z}^{2}-{I}^{2}\right)+\frac{1}{2}\eta \left({I}_{+}^{2}+{I}_{-}^{2}\right)\right\},$$
(1)

where γ is the nuclear gyromagnetic ratio, K is the Knight shift, h is the Planck constant, and I± are the ladder operators of the nuclear spin I, which are defined as I± = Ix ± iIy. νzz( ∝ Vzz) is the quadrupole frequency along the principal axis of the electric field gradient (EFG) and is defined as νzz ≡ 3eVzzQ/2I(2I − 1) with the electric quadrupole moment Q. η is an asymmetry parameter of the EFG defined as η ≡ (Vxx − Vyy)/Vzz, where Vii is the second derivative of the electric potential V (\({V}_{ii}={\partial }^{2}V/\partial {x}_{i}^{2}\)). Since the NMR signal of each grain depends on the angle between the principal axis of the EFG in each grain and the direction of the magnetic field, the sum of the NMR signals for all solid angles could be observed in the non-oriented powder samples. The NMR spectrum was well fitted by the simulation with K = 1.0%, 63νzz = 9.14 MHz, 65νzz = 8.48 MHz, and η = 0.32, as shown by the dashed line in Fig. 2a.

Fig. 2: 63/65Cu-NMR/NQR spectrum.
figure 2

a NMR spectrum at a fixed frequency of 19.5 MHz and 4.2 K: the black solid and red dashed curves are the experimental result and the simulation of the NMR spectrum, respectively. The three narrow lines in the NMR spectrum are signals from the Cu coil used for the NMR measurements and Al as an impurity arising from the NMR probe. b 63/65Cu-NQR spectra at 4.2 and 0.075 K: the pink curve represents the 63Cu signals scaled by 65γ/63γ and shifted to the observed 65Cu signals. The inset shows the temperature variations of the 63Cu-NQR spectrum for 0.7 ≤ T ≤ 1.0 K. c Temperature dependence of the internal fields Hint estimated by simulation of the NQR spectra: the red dashed curve represents the relation \({H}_{{{{{{{{\rm{int}}}}}}}}}(T)={H}_{{{{{{{{\rm{int}}}}}}}}}(0){[({T}_{{{{{{{{\rm{O}}}}}}}}}-T)/{T}_{{{{{{{{\rm{O}}}}}}}}}]}^{\beta }\) with β = 0.05. The inset shows the 63/65Cu-NQR spectrum at 0.075 K, and the red solid curve is the simulation of the NQR spectrum.

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We observed sharp 63/65Cu-NQR signals at 63νQ = 9.28 MHz and 65νQ = 8.59 MHz, as shown in the upper panel of Fig. 2b. The spectra were obtained by the frequency-swept method at 4.2 K without an external field. The obtained 63/65Cu-NQR frequencies νQ at 4.2 K were consistently reproduced by \({\nu }_{{{{{{{{\rm{Q}}}}}}}}}={\nu }_{zz}\sqrt{1+{\eta }^{2}/3}\) with the quadrupole parameters obtained above.

The occurrence of the AFM transition at TO was concluded from the following NQR results. The lower panel of Fig. 2b shows the frequency-swept 63/65Cu-NQR spectra measured at 0.075 K. Each paramagnetic (PM) peak splits into six peaks [(A1)–(A6) for 63Cu and (B1)–(B6) for 65Cu]. The 63Cu signals for (A1) and (A2) overlap with the 65Cu signals for (B5) and (B6), respectively. As shown in Fig. 2b, the observed 65Cu peaks almost coincide with the 63Cu signals scaled by the isotope ratio of the nuclear gyromagnetic ratio 65γ/63γ = 1.07, not by that of the quadrupole moment 65Q/63Q = 0.93. In addition, since the 63νQ does not change across TO, the EFG parameters seem to be unchanged below TO (see Supplementary Note 1). Therefore, the NQR signals are split due to the appearance of internal magnetic fields at the Cu site rather than to the change of electric factors such as charge density wave, charge-ordered, or structural transitions.

We performed spectrum simulations to estimate the magnitude of the internal magnetic fields and their orientation with respect to the principal axis of the EFG at 0.075 K. As shown in the inset of Fig. 2c, the eight clearly visible peaks (A2)–(A5) and (B2)–(B5) can be fitted by the simulation with μ0Hint = 0.021 T, θ = 77°, and ϕ = 0°, where μ0Hint is the absolute value of the internal fields, θ is the polar angle, and ϕ is the azimuthal angle of the internal fields from the principal axis of the EFG. The small internal field at the Cu site suggests the tiny Yb-ordered moment (see Supplementary Note 2). However, the peaks (A1), (A6), (B1), and (B6) cannot be fitted by the above parameters: these peaks can be reproduced by assuming a slightly larger internal field. Moreover, the presence of non-zero intensity between the peaks indicates the distribution of the internal fields (see Supplementary Note 2). The wide distribution of the internal fields suggests that the ground state is incommensurate spiral or spin-density wave (SDW)-type magnetic order. Thus, to determine the realized magnetic structure, elastic neutron scattering measurements are necessary.

The inset of Fig. 2b shows the temperature variations in the 63Cu-NQR spectra below 1.0 K. Multi-peaks appear below TO ~ 0.95 K and coexist with the PM peak of νQ = 9.28 MHz. The PM peak is not visible below 0.85 K. As shown in the main figure of Fig. 2c, the internal field evaluated with the above simulation of the NQR spectra increases discontinuously below TO, and the critical exponent β derived by fitting the relation \({H}_{{{{{{{{\rm{int}}}}}}}}}(T)={H}_{{{{{{{{\rm{int}}}}}}}}}(0){[({T}_{{{{{{{{\rm{O}}}}}}}}}-T)/{T}_{{{{{{{{\rm{O}}}}}}}}}]}^{\beta }\) is 0.05, which is substantially smaller than the conventional mean-field value (0.5). These results indicate that the AFM transition is an FO phase transition, which is consistent with the sharp peak at TO in the specific heat22. The FO AFM transition is unusual and has been observed when the AFM transition and structural transition occur simultaneously29,30. In YbCuS2, since the NQR parameters are unchanged below TO, a structural transition is unlikely. Therefore, the FO AFM transition is likely to be related to magnetic frustration. In fact, fluctuation-induced FO AFM transitions have been proposed from theoretical studies31,32 and several frustrated magnets such as EuPtSi show an FO AFM transition without a structural phase transition33,34. The magnetic properties of YbCuS2 deserve further investigation with various measurements.

Nuclear spin-lattice relaxation rate 1/T 1

The nuclear spin-lattice relaxation rate 1/T1 of 63/65Cu-NQR was measured in order to investigate the magnetic fluctuations at low temperatures. Figure 3 shows the typical relaxation curves R(t) ≡ 1−M(t)/M0 of the nuclear magnetization M(t) at (a) T = 1.6 K (>TO) and (b) T ≤ 0.4 K (<TO), and the fitting for T1 determination. As shown in Fig. 3a, the single exponential function of

$$R(t)=\exp \left(-\frac{3t}{{T}_{1}}\right)$$
(2)

was used as the fitting function above TO. R(t) has not only a major slow component but also a minor fast component below TO as shown in Fig. 3b. The two components seem to originate from the distribution of the relaxation in the magnetically ordered state. The slow and fast components were determined by fitting two decay regions of R(t) with the single exponential function (the fast component was determined with the decay from R(0) to 0.7R(0) as shown in Supplementary Note 3). As the fraction of the slowest component become dominant below TO, we picked up the slow component fitted by the single exponential function below 0.7R(0), and we plotted the 1/T1 data.

Fig. 3: 63Cu relaxation curve.
figure 3

63Cu relaxation curve R(t) at a T = 1.6 K (>TO) and b T ≤ 0.4 K (<TO). The dashed line represents the fitting of the slow component.

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Figure 4 shows the temperature dependence of the nuclear spin-lattice relaxation rate 1/T1 measured at the 63Cu signal of YbCuS2. Below TO, 1/T1 was measured at the two peaks shown in the inset. To investigate contributions other than the 4f electrons, we also measured 1/T1 of a nonmagnetic reference compound LuCuS2 and plot the results. For LuCuS2, the isotopic ratio of 1/T1 [65(1/T1)/63(1/T1)] is 0.88, which is close to the square of the quadrupole-moment ratio \({\left.\right(}^{65}Q{/}^{63}Q\))2 ~ 0.86. This indicates that in LuCuS2, 1/T1 is determined by the electric quadrupole relaxation originating from the phonon dynamics. The low-temperature 1/T1 of LuCuS2 is quite small. In contrast, for YbCuS2, the isotopic ratio of 1/T1 ~ 1.14 coincides with the square of the gyromagnetic ratios \({\left.\right(}^{65}\gamma {/}^{63}\gamma\))2 ~ 1.15, indicating that 1/T1 is determined by the magnetic relaxation from the Yb3+ moments. 1/T1 exhibits a broad maximum at ~50 K, where the magnetic entropy reaches \(R\ln 2\), as expected for the Kramers doublet ground state in specific-heat measurements. Note that 1/T1 gradually decreases below 50 K. This may be related to the entropy release observed in the specific-heat measurements, which is described later. Below 5 K, 1/T1 becomes constant, suggesting that the local moments fluctuate with a short-range correlation. This behavior agrees with the theoretical prediction for the one-dimensional (1-D) spin chain35, and it was observed in the S = 1/2 1-D cuprate antiferromagnet36,37. On the other hand, the absence of the critical slowing down behavior around TO is in sharp contrast to the divergence behavior of 1/T1 observed in the zigzag chain compound CaV2O438 and the above 1-D cuprate antiferromagnets near TN36,37, where the magnetic order occurs due to interchain coupling. The absence of the slowing down behavior is likely to be related to the character of the FO phase transition30.

Fig. 4: Nuclear spin-lattice relaxation rate 1/T1.
figure 4

Temperature dependence of the nuclear spin-lattice relaxation rates 1/T1 of YbCuS2 and a nonmagnetic reference compound LuCuS2: the circles denote the 63Cu-NQR 1/T1 in the PM state of YbCuS2. The diamonds and squares represent 1/T1 in the AFM state of YbCuS2. The black triangles indicate 63Cu-NMR 1/T1 in LuCuS2 for μ0H = 9.8 T. The gray solid line denotes 1/T1 in a Cu-metal47. The dashed curve represents \(1/{T}_{1} \sim \exp (-\Delta /T)\) in conventional semiconducting antiferromagnets with a spin gap. The inset shows the 63Cu-NQR spectra measured at 4.2 and 0.075 K. The spectrum peaks at which 1/T1 was measured are denoted by the symbols. Error bars are standard deviations.

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Below TO, 1/T1 decreases rapidly; it is roughly proportional to T5 down to 0.5 K. In general, 1/T1 of local-moment frustrated systems, such as the triangular Heisenberg antiferromagnet, is determined by the two-magnon process. It can be expressed as 1/T1 ∝ T2D−1 for T ≫ Δ, where Δ is the spin gap, and D (=3 or 2) is the dimensionality of the spin-wave dispersion39,40,41,42. In YbCuS2, D = 3 is likely. Conversely, peculiar T-linear behavior was observed below 0.5 K. Theoretically, 1/T1 decreases exponentially [\(1/{T}_{1} \sim \exp (-\Delta /T)\)] for T ≪ Δ at low temperatures in conventional semiconducting antiferromagnets with a spin gap39,40. Thus, the T-linear behavior suggests the presence of gapless excitation, which makes YbCuS2 quite different from conventional antiferromagnets.

Specific heat

In addition to the previous study of the magnetic susceptibility22, we further studied the CEF levels and magnetic interaction from the magnetic specific heat Cm and the magnetic entropy Sm by using the specific heat of LuCuS2. The specific heat of LuCuS2 would be more reliable and accurate for the lattice contribution than that of YCuS2 in the previous study22, because the ionic radius of Lu is closer to that of Yb than that of Y. As shown in the inset of Fig. 5, a broad maximum of Cm/T was also observed near 100 K, which is reproduced by a two-level model with the energy separations of 300 K from the doublet ground state to the first excited quartet. Moreover, the magnetic entropy Sm reaches \(R\ln 2\) at higher temperatures near 50 K, which is likely related to a broad maximum near 50 K of 1/T1 in the NQR measurement. Theoretically, 1/T1 increases towards the temperature corresponding to the energy scale of the interaction43. Hence, the isolated CEF doublet ground state and the strong interactions between Yb moments are convincing in YbCuS2.

Fig. 5: Specific heat and entropy.
figure 5

Temperature dependence of magnetic specific heat Cm divided by the temperature (left-hand scale) and magnetic entropy Sm (right-hand scale) for YbCuS2. Cm was estimated by the subtraction of the lattice contribution measured in LuCuS2. The inset shows the temperature dependence of magnetic specific heat Cm. The blue solid line is a fit with a two-level model with the energy separations of 300 K from the doublet ground state to the first excited quartet.

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The presence of the gapless excitation was also confirmed from the low-T specific-heat measurements. The specific heat measurements and the analysis of the residual T-linear term γel of specific heat were performed down to 0.08 K as shown in Fig. 6. Cm can be fitted by

$$\frac{{C}_{{{{{{{{\rm{m}}}}}}}}}}{T}={\gamma }_{{{{{{{{\rm{res}}}}}}}}}+\frac{{C}_{{{{{{{{\rm{AFM}}}}}}}}}}{T}+\frac{{C}_{{{{{{{{\rm{Sch}}}}}}}}}}{T}.$$
(3)

Here, the second term represents AFM magnon excitations with an energy gap Δm44

$$\frac{{C}_{{{{{{{{\rm{AFM}}}}}}}}}}{T}=\beta {T}^{2}\exp \left(-\frac{{\Delta }_{{{{{{{{\rm{m}}}}}}}}}}{T}\right).$$
(4)

The third term is the two-level nuclear Schottky term

$$\frac{C_{{{{{{{\mathrm{Sch}}}}}}}}}{T}= \frac{R {{\Delta}}_{{{{{{{\mathrm{Cu}}}}}}}}{\,}^2}{T^3} \frac{{{{{{\mathrm{e}}}}}}^{-{{\Delta}}_{{{{{{{\mathrm{Cu}}}}}}}} / T}}{\left(1+{{{{{\mathrm{e}}}}}}^{-{{\Delta}}_{{{{{{{\mathrm{Cu}}}}}}}} / T}\right)^2} \\ +\frac{R {{\Delta}}_{{{{{{{\mathrm{nuc}}}}}}}}{\,}^2}{T^3} \frac{{{{{{\mathrm{e}}}}}}^{-{{\Delta}}_{{{{{{{\mathrm{nuc}}}}}}}} / T}}{\left(1+{{{{{\mathrm{e}}}}}}^{-{{\Delta}}_{{{{{{{\mathrm{nuc}}}}}}}} / T}\right)^2},$$
(5)

where ΔCu and Δnuc are the corresponding energy splitting of Cu nucleus and other nucleus (Yb and S), respectively. Using the energy splitting of Cu nucleus ΔCu = 4.37 mK estimated from NQR measurements, this analysis yields the parameters as listed in Table 1. This analysis shows the residual term \({\gamma }_{{{{{{{{\rm{res}}}}}}}}}=14\) mJ K−2 mol−1. While \({\gamma }_{{{{{{{{\rm{res}}}}}}}}}\) term is usually defined as an electronic specific-heat term in metallic compounds, it may be attributed to gapless excitation with a pseudo-Fermi surface.

Fig. 6: Low-temperature specific heat.
figure 6

Temperature dependence of magnetic specific heat Cm divided by temperature. The black solid, blue solid, and black dashed curves represent the total fitting, the residual term \({\gamma }_{{{{{{{{\rm{res}}}}}}}}}\) + AFM magnon contribution, and the Schottky contribution, respectively.

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Table 1 Parameters obtained from the specific heat analysis at low temperatures.
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Discussion

The presence of gapless quasiparticle excitation on an incommensurate antiferromagnetic ordered state with a tiny ordered moment in YbCuS2 is not consistent with the simple S = 1/2 Heisenberg zigzag-chain antiferromagnet model, in which a Tomonaga–Luttinger liquid or a gapped dimer phase were expected at zero magnetic field4,5,6. There is a possibility that exotic ground state and quasiparticle excitation in YbCuS2 originate from the anisotropic interactions unique to the effect of SOC and CEF of 4f electrons. The specific heat and 1/T1 measurements under magnetic fields to investigate the low-T properties are interesting since the peculiar magnetic field-temperature phase diagram was reported.

Here, we discuss the origin of the gapless excitation. The similar T-linear behavior of 1/T1 was reported in kagomé systems, Zn-brochantite ZnCu3(OH)6SO4 below the nonmagnetic phase transition45 and volborthite Cu3V2O7(OH)2 ⋅ 2H2O below the magnetic phase transition46. To explain these behaviors, particle-hole excitations by spinons (fermionic elementary excitations), which are analogous to metallic excitations, were proposed45,46. In fact, we point out that the experimental value of 1/T1T in YbCuS2 at 0.1 K (~14 s−1 K−1) is larger than that in a Cu-metal (~0.83 s−1 K−1)47 by more than one order of magnitude.

Another possibility is phason excitation48,49,50,51. T-linear 1/T1 was observed in the temperature region just below TSDW in organic quasi 1-D metallic (TMTSF)2PF6, and this 1/T1 behavior was interpreted with the gapless phason contribution in the incommensurate SDW state48,49,50. Here, the phason is elementary excitation corresponding to phase mode51. There is a possibility that the gapless excitation in YbCuS2 originates from such an unusual excitation, but it is surprising that such behavior was observed in semiconducting YbCuS2.

Quite recently, gapless excitation has been observed in Yb-based semiconducting Kondo-lattice materials such as YbB1252,53,54 and YbIr3Si755. In these compounds, although the band gap opens at low temperatures due to the hybridization between the localized f and the conduction electrons, quantum oscillation at high fields and the finite residual term in the specific heat and thermal conductivity experiments were observed53,55. These results suggest the presence of gapless and charge-neutral excitations in the bulk properties, which are proposed to result in a quantum spin liquid with a spinon Fermi surface and the Majorana Fermi liquid56,57. We note the possibility that the large gapless excitation observed at low temperatures in YbCuS2 might arise from such exotic Fermi liquid states, although YbCuS2 is a conventional semiconductor. To confirm this possibility, it is crucially important to prepare high-quality single crystals for the measurements of thermal conductivity and quantum oscillation.

Conclusion

In conclusion, we performed 63/65Cu-NMR/NQR and specific-heat measurements on polycrystalline samples of YbCuS2 in which the Yb ions form a zigzag chain along the orthorhombic a-axis. Below TO ~ 0.95 K, multi-peaks affected by the internal magnetic fields appear; they coexist with the PM signal down to 0.85 K, indicating that the FO AFM phase transition occurs at TO. In addition, 1/T1 decreases abruptly below TO and exhibits T-linear behavior below 0.5 K. The significantly large 1/T1T value—more than one order of magnitude larger than that for metallic Cu suggests the presence of gapless spin excitation originating from exotic fermions, which was also confirmed by the low-T specific heat measurements. Our finding of the large gapless excitation unveils the presence of unknown fermionic quasiparticles in frustrated magnets.

Methods

63/65Cu-NMR/NQR measurements

Polycrystalline samples of YbCuS2 were synthesized by the melt-growth method21,22. The polycrystalline samples were coarsely powdered to increase the surface area for better thermal contact. The powdered sample was mixed with GE 7031 varnish and solidified at zero magnetic fields to avoid the preferential orientation of crystals for the NMR measurements and contact between crystals for the NQR measurements. A conventional spin-echo technique was used for the NMR and NQR measurements. A 3He–4He dilution refrigerator was used for the NQR measurements down to 0.075 K. The stability of the temperature is about ± 5 mK, and the typical measurement time for one spectrum is about 2–3 h. The NQR measurement was performed in the cooling process. 63/65Cu-NMR spectra (with nuclear gyromagnetic ratios of 63γ/2π = 11.289 and 65γ/2π = 12.093 MHz T−1, respectively, and both with the nuclear spin I = 3/2) were obtained as a function of H at the frequency f = 19.5 MHz. The principal axis of the EFG at the Cu site was determined by WIEN2k calculation using the density functional theory58 since the principal axis was not determined experimentally due to a lack of a single crystal sample. The principal axis is represented by the black sticks in Fig. 1a. 63/65Cu-1/T1 was measured in YbCuS2 and a reference compound LuCuS2 to estimate the lattice contribution. 1/T1 was evaluated by fitting the relaxation curve of the nuclear magnetization after the saturation to a theoretical function for the nuclear spin I = 3/2. 1/T1 can be determined by a single relaxation component down to TO. However, a short component appears in the relaxation curve below TO, thus, we picked up the slowest components.

Specific-heat measurements

Specific-heat measurements were performed on a polycrystalline sample of 4.74 mg down to 0.08 K by the thermal relaxation method with a Quantum Design PPMS and mF-ADR-100s.