Abstract
Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between and ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120° antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.
Similar content being viewed by others
Avoid common mistakes on your manuscript.
1 Introduction
Quantum spin liquid (QSL) is a long-range entangled “quantum liquid” state of interacting spins [1–3], which is believed not only to be a platform for obtaining the original driving force of the high-temperature superconductivity but also to be a basic unit for the quantum data storage and computation. Although there has been much theoretical effort on different models of QSL, a firm experimental establishment of this exciting and exotic phase in a real compound is still lacking. Although limited behaviors have been confirmed and actively investigated on a few spin liquid candidate compounds, such as the organic materials [4–7] κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, kagomé herbertsmithite [8, 9] ZnCu3(OH)6Cl2, the cluster Mott insulator [10, 11] 1T-TaS2 in the commensurate charge density wave phase, the honeycomb Kitaev materia [12–16], and the pyrochlore spin ice materials [17–27], there is always some unexpected factors observed in these candidate materials, such as the distorted lattice, relatively low-energy scale of the spin interactions, anti-site ionic disordering, and restricted experimental resolution, and the intrinsic magnetic behaviors might be shaded. Therefore, investigating an ideal compound and revealing the intrinsic quantum and magnetic properties related to QSLs is crucial to both material and physics research.
Previously, part of us and many others have worked on a rare-earth triangular lattice magnet [28–48] where the Yb3+ ions form a perfect triangular lattice with spin-orbit-entangled effective spin-1/2 local moments. Thus, is likely to be the first spin liquid candidate in the strong spin-orbit-coupled Mott-insulators with odd electron fillings [29, 30, 49] and goes beyond the conventional Oshikawa-Hastings-Lieb-Schultz-Mattis theorem [50–53] that requires the U(1) spin rotational symmetry. However, the potential issue of is the Mg-Ga disorder in the non-magnetic layers. To what extent the non-magnetic disorder in the non-magnetic layer would impact the intrinsic magnetic properties of the system may require further scrutiny. Instead of delving with , we turn to a different route. This is motivated by the robustness of QSLs and the principle of universality. If the QSL ground state is relevant for , similar QSL state could likely be realized in other triangular lattice rare-earth magnets. On the other hand, other triangular lattice rare-earth magnets could potentially eliminate the non-magnetic disorder issue that was suggested for . Indeed, a series of rare-earth chalcogenides was recently identified [54, 56–67] as candidates for QSLs, and apparently, there is no structural disorder like the Mg/Ga ions in YbMgGaO4. Therefore, we combine the experimental measurements and theoretical analysis and propose NaYbS2 likely to be a gapless QSL candidate. The field- and temperature-dependence of magnetization, specific heat, neutron diffraction, and inelastic neutron scattering measurements demonstrate several field-induced magnetic transitions in this QSL ground state system. Moreover, we provide extra theoretical results and suggestions for further experimental verification of the QSL state in the isostructural compounds.
2 Samples and experimental techniques
The polycrystalline and single crystals of were synthesized by the high-temperature solid-state reaction and the -flux method, respectively [54]. Around 0.5 g single crystals of NaYbS2 were co-aligned in the (HHL) scattering plane on a copper plate, and the single-crystal neutron diffraction data were collected at the Australia Nuclear Science and Technology Organisation (ANSTO), using a cold neutron triple-axis diffractometer, Sika [55]. An 8 T vertical magnetic field cryostat with a dilution refrigerator insert was applied to collect magnetic field data at 0 T, 3 T, 4 T, 5 T, and 8 T at 0.1 K. The magnetic field was applied along [1 −1 0], and the data were collected with final energy as \(\mathrm{E}_{f}\sim 5\) meV. Rietveld refinement was performed with the SARAh software and the magnetic symmetry approach at the Bilbao Crystallographic Server. The fitted data are shown in Fig. 1 at 300 K and 1.6 K. The inelastic neutron-scattering powder data were collected at the Swiss Spallation Neutron Source (SINQ), the Paul Scherrer Institut (PSI), using a disc chopper spectrometer, FOCUS, in a 10 T magnetic field with a dilution insert. Incident neutrons with 5 Åwavelength were used with the medium-resolution chopper setting.
Specific heat measurements were performed for sintered pellets of down to 0.3 K at zero-field on a physical property measurement system (PPMS, Quantum Design), and the He-3 refrigerator insert was applied for temperatures below 1.8 K. Moreover, data under 3 T, 4 T, 5 T, 6 T, 7 T, 8 T, and 9 T applied fields were also collected. The magnetic signal of specific heat was determined by subtracting the data of non-magnetic compound between 1.8 K and 30 K. The calculated magnetic entropy was obtained by integrating Cmag/T between 0.3 K and 20 K.
Magnetic properties were measured by using several different instruments. Isothermal DC magnetization up to 9 T was collected on a PPMS with a vibrating sample magnetometer insert, and isothermal AC susceptibility in applied fields up to 7 T from 0.5 K to 20 K was obtained on a magnetic property measurement system (MPMS3, Quantum Design). The DC magnetic susceptibilities versus H up to 18 T at 0.8 K were collected at Wuhan National High Magnetic Field Center. Torque magnetometry was performed at the University of Michigan using a self-built capacitive cantilever setup mounted inside a dilution refrigerator.
3 Neutron diffraction and magnetic structure
The rare-earth ions in the chalcogenides (Ch = O, S, Se) have an ideal triangular lattice structure with the magnetic ions localized at the center of chalcogenide octahedra, Fig. 1(a), and the triangular layers are well separated by the non-magnetic octahedra. Since the difference between the and ionic sizes is large, the anti-site disorder is eliminated. The single-crystal XRD data have confirmed that the anti-site disorder between them is less than 4%. has a perfect triangular lattice, and the intrinsic properties of the QSL, if there exists any, would be more clearly presented. We perform the neutron powder diffraction on NaYbS2 and compare the results at 50 mK and 300 mK, Fig. 1(b). From the labeled lattice reflections, the overplotting agreement suggests no long-range magnetic ordering down to 50 mK in this system. The space groups of is \(R\bar{3}\)m, which is same as and different to the P-lattice type triangular oxides with a rotation axis \(C_{3}\) or \(C_{6}\) of the \(Z_{3}\) symmetry, such as and [68, 69]. Meanwhile, the external magnetic field could break the degenerated ground state and induce complicated magnetic structures ([57] and see Additional file 1).
To determine the magnetic structure of new phases under the field, single-crystal neutron diffraction was applied, Fig. 1(c). Although up-up-down (uud) plateau phase has been reported to be induced by the magnetic field in the isostructure [57] and has the similar powder neutron diffraction spectra except an extra reflection at \(\boldsymbol{q}\approx 1.2429\) Å−1 (see Additional file 1), surprisingly, the reflections of \((1/3,1/3,1)\) and \((1/3,1/3,2)\) were too weak to be observed under the field, which is different to the powder data of ([57] and see Additional file 1). Based on the program SARAh [70] and the magnetic symmetry approach at the Bilbao Crystallographic Server [71], the magnetic Yb3+ ions spiral upwards with a 120° state and the equivalent reflections of \((2/3,-1/3,1)\) and \((2/3,-1/3,-2)\) are instead of \((1/3,1/3,1)\) and \((1/3,1/3,2)\), Fig. 1(d). Therefore, the magnetic wave vector is \((1/3,1/3,0)\). As the magnetic field increased, the reflections of \((1/3,1/3,0)\) and \((1/3,1/3,3)\) disappeared above 8 T. Since this high field phase does not have the wave vector of \((1/3,1/3)\) in ab-plane, it is disappointed to minimize the possibility of reported \(uud\) plateau in .
Compared to the M(H) measurements with the van Vleck correction, the saturated magnetization is 1.0\(\mu _{B}\) per ion and the moment of the intermediate phase is 0.5\(\mu _{B}\) per ion with a constant dM/dH, Fig. 2(a). The plateau phase has been predicted by Ye et al. as an up-up-up-down (uuud) state and breaks either \(Z_{3}\) orientational symmetry or \(Z_{4}\) sublattice symmetry with the competition of the magnetic field and quantum fluctuations [72]. Therefore, the subsequent state above the 120° state is an uuud state, which has been realized on the triangular lattice antiferromagnet Fe1/3NbS2 [73] and [74], and the stabilization of such a state requires further neighbor exchange interaction. A recent study on the diamond lattice antiferromagnet does suggest the importance of the second neighbor exchange interaction [75]. Moreover, the magnetic wave vector of \(uuud\) phase shifts from \((1/3,1/3,0)\) to \((0,1/2,0)\) in [76, 77]. On further increasing the magnetic field, the \(uuud\) phase undergoes a second-order phase transition to a high-field oblique phase, commonly to be observed in triangular lattices [72].
4 Thermodynamic data at finite temperature and phase diagram
To reveal the magnetic phases in detail, the DC and AC magnetizations and the torque magnetometry were measured. For zero field, the Curie-Weiss temperatures of \({\Theta _{\text{CW},\perp}= -13.5 \text{ K}}\) and \({\Theta _{\text{CW},\parallel}=-4.5 \text{ K}}\) for the in-plane and out-of-plane susceptibility measurements [56] present the related frustration parameters as \(f>|\Theta _{\text{CW},\perp}|/(0.05 \text{ K})\approx 270\) for the in-plane value and \({f>|\Theta _{\text{CW},\parallel}|/(0.05 \text{ K})\approx 90}\) for the out-of-plane value. Meanwhile, the larger in-plane Curie-Weiss temperature expects to enhance the spin correlation between the in-plane spin components and contribute mostly to the diffusive scattering peak. The exchange energy scale of NaYbS2 is a couple times larger than the ones in YbMgGaO4, consistent with the enhanced Curie-Weiss temperatures. This advantage allows a broader temperature window to explore the QSL physics in this system. Furthermore, it is noted that the magnetic susceptibility in the zero field limit is constant. Although it seems to be consistent with a spinon Fermi surface state, this is expected from the fact that the total magnetization is not a conserved quantity. Thus, the constant spin susceptibility cannot be used to identify the QSL ground state for this material and other materials. Unlike NaYbO2, NaYbS2 demonstrates quite rich phases with a higher saturated magnetization field (up to ∼ 16.0 T), Fig. 2: there are four transition fields for DC susceptibility at 0.8 K, ∼ 3.3 T, 6.1 T, 10.2 T, and 14.8 T, respectively, and are consistent with the transition fields by the AC susceptibility very well (see Additional file 1). Figure 2(b) presented the torque magnetometry measurements by applying the field in the ab-plane. The dM/dH curves between 30 mK and 600 mK show two peaks on the lower and upper critical fields. As the temperature increases, this derivative becomes weaker and finally disappears around \({T=1}\) K. Finally, the sublattice spins are aligned along the applied field and saturated.
The low-temperature specific heat measurements on were performed down to 0.3 K at zero-field, Fig. 2(c). As the neutron powder diffraction measurement, no signature of magnetic transition is observed, and a broad peak occurs at about 1 K, a typical phenomenon of the QSL candidate materials. The lattice phonon contribution to the specific heat is obtained from the isostructural non-magnetic material and could be almost negligible below 3 K, Fig. 2(c). The entropy release for from 0.3 K to 20 K saturates up to 92% of the \(R\ln 2\) entropy (where R is the ideal gas constant), and an effective spin-1/2 description of the local moments is obtained. Unlike , \(C_{P}/T\) of NaYbS2 does not diverge at low temperatures, while the divergence in is interpreted as the signature of U(1) gauge fluctuations [29, 30]. The intercept of \(C_{P}/T\) on the \({T=0}\) axis is slightly larger than the one for , and the specific heat fits well with a \(T^{2}\) behavior below 0.7 K, the inset in Fig. 2(c), which is consistent with a gapless QSL and the Lorentz invariance guarantees. A residual density of states that contribute to the small intercept could be regarded [78] as the tail of the contributions of nuclear spin and becomes more and more significant below 0.1 K.
As the external magnetic field is applied, the specific heat demonstrates a series of highly tunable states, which relate to the quantum and thermal fluctuations, Fig. 2(d): a broad peak starts to be observed at 3 T, then a sharp peak appears at 5 T around ∼ 1.3 K and turns to be suppressed gradually with the increasing field. Finally another broad peak is split from the sharp peak and shifts to the lower temperature at 7 T. Those transitions could also be recognized by the magnetic entropy, which decreases from 92% (0 T) to 86% (3 T), then increases 88% (5 T), and drops again to 83% (9 T). Meanwhile, the low-temperature specific heat below the peak temperature is strongly suppressed, and \(C_{P}/T\) actually goes to zero in the zero temperature limit. Hence, the magnetic field breaks the QSL ground state and induces a range of intermediate states before the magnetic ions in are fully saturated.
The temperature versus magnetic field diagram is plotted in Fig. 2(e). The phase transitions are determined by combining different techniques, and the various exotic states from 120° to the \(uuud\) Ms/2 anomaly-phase to oblique phases were decided. Especially, the thermal effect is realized in the system even at low temperatures, ∼ 0.8 K, with the S-shape transition between the Ms/2- or Ms/3- anomaly phase and oblique phases.
5 Inelastic neutron scattering and gapless spin liquid
We perform the inelastic neutron scattering (INS) measurements on both at \(H=0 \text{ T}\) and 6 T at 50 mK. This measurement contains the dynamical energy-momentum information about the magnetic excitations in the system. In Fig. 3(a), highly dispersive signals are revealed. It is proposed a U(1) spinon Fermi surface spin liquid in with a clear V-shape at Γ point [30]. Several key features can be lost for the powder sample of due to the lack of angular momentum information. However, there still exits a cone feature that can be distinguished at \(|\boldsymbol{Q}|\approx 1.24\) Å−1 from Fig. 3(a), which should correspond to the cone-like feature of the Dirac spin liquid. The inter-Dirac cone scattering and intra-Dirac cone scattering processes would present these characters at low energies. Meanwhile, for the spinon Fermi surface states, a large amount of low-energy intensity is expected in a wider momentum range, which is clearly incompatible with the experimental data. For example, [79] is a quantum spin liquid candidate with spinon Fermi surface states. With magnetic field \(H=6 \text{ T}\), as depicted in Fig. 3(b) and the insets of constant-energy and -moment cuts in Fig. 3(c) and (d), the low-energy spectral weight is mostly transferred to higher energies, consistent with specific heat data that this field-induced state should be gapped due to the anisotropic spin interactions between the local moments, which is different to with the bigger ion on the Ch-site. Moreover, the temperature dependence of the energy- and moment-integrated intensities, Fig. 3(c) and (d), clearly presented that the V-shape magnetic signals start to be observed around 8 K.
Furthermore, was also suggested as a gapless quantum spin liquid by longitudinal field (LF) muon spin relaxation (μSR) [80]. At 0.1 K, an indicator as the spin relaxation rate, \(\lambda _{LF}\), was applied to describe the spin dynamics and obtained from LF-μSR experimental data of . As the magnetic field increased to 1000 G, \(\lambda _{LF}\) was almost close to zero, significantly different from the LF-μSR spin relaxation rate \(\lambda _{LF}\) of quantum spin liquids with spinon Fermi surface state. For example, the quantum spin liquid material demonstrated a spinon Fermi surface state [79], and the spin relaxation rate \(\lambda _{LF}\) maintained a constant value of ∼0.2 \(\mu s^{-1}\) at 0.1 K and the magnetic field of 1000 G [80]. Although both and had magnetic ground states with quantum spin liquid states, and the crystallographic structures were close, the spinon excitation characteristics were significantly different. Therefore, the substitution of the oxychloride element effect was clearly demonstrated, and the crystal electric field played an important role in regulating quantum spin liquids [81].
6 Summary
Comparing to , the bigger ion on the Ch-site not only prevents crystallographic site-mixing, but also inceases the interlayer distances via the mediating cation, therefore the layer distance along the c axis is reduced significantly in with the slightly larger a axis and leads to the \(c/a\) ratio for (5.1) is more closer to (7.4) than (4.9). Rather than a pure two-dimensional model with anisotropic exchanges, a more precise theoretical analysis should naturally include other factors, such as the interlayer couplings [57]. Although the spins in the oxide are expected to be more localized than in sulfide, the quantum effects from both spin- and thermal-fluctuations in the latter are more complicated. Additionally, the ground state of can be driven into a magnetically ordered state in intermediate magnetic fields. Due to the strong easy-plane exchange anisotropy of , the numerical studies suggest a canted 120° state or an incommensurate state rather than an \(uud\) state in , which is also confirmed by the magnetization and neutron diffraction measurements.
Our experiments demonstrate that the nearly ideal triangular lattice of Yb ions in strongly spin-orbit-coupled materials can realize various exotic ground states. Especially, both the thermodynamic and the neutron scattering measurements suggest realizes a gapless spin liquid state. According to the fermion doubling theorem, there cannot be a single Dirac cone in a lattice system, and the cones must at least come in pairs. INS experiments measure the dynamical spin structural factor, which corresponds to the particle-hole pair of spinon excitations, and the intra-cone scattering will contribute to low energy spin excitations near Γ point. In contrast, the inter-cone scattering corresponds to low energy spin excitations at finite momentum [30, 49]. Furthermore, the scenario of staggered π-flux Dirac spin liquid would double the unit cell of spinons. This results in an enhanced periodicity of the dynamical spin structure factor despite the lack of magnetic ordering, which can be identified as a sharp feature to distinguish this peculiar fractionalized state from trivial spin glass. Although the density-of-state decided the moment-dependence of the spin dynamics and no gap above 0.1 meV, the clear feature of enhanced periodicity is smeared out due to lack of angular resolution, and more experimental efforts on single crystals are highly desired to distinguish if this system really hosts this π-flux gapless (or Dirac) spin liquid state.
Availability of data and materials
All data generated or analyzed during this study are included in this article and its supplementary information files.
Change history
02 December 2022
The original version of this article was revised: the author contribution section was updated.
05 December 2022
A Correction to this paper has been published: https://doi.org/10.1007/s44214-022-00024-8
References
Lee PA (2008) An end to the drought of quantum spin liquids. Science 321:1306–1307
Balents L (2010) Spin liquids in frustrated magnets. Nature 464:199–208
Savary L, Balents L (2016) Quantum spin liquids: a review. Rep Prog Phys 80:016502
Shimizu Y, Miyagawa K, Kanoda K, Maesato M, Saito G (2003) Spin liquid state in an organic Mott insulator with a triangular lattice. Phys Rev Lett 91:107001
Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K (2008) Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt. Nat Phys 4:459–462
Itou T, Oyamada A, Maegawa S, Tamura M, Kato R (2007) Spin-liquid state in an organic spin-1/2 system on a triangular lattice, EtMe3Sb[Pd(dmit)2]2. J Phys Condens Matter 19:145247
Itou T, Oyamada A, Maegawa S, Tamura M, Kato R (2008) Quantum spin liquid in the spin-1/2 triangular antiferromagnet EtMe3Sb[Pd(dmit)2]2. Phys Rev B 77:104413
Helton JS, Matan K, Shores MP, Nytko EA, Bartlett BM, Yoshida Y, Takano Y, Suslov A, Qiu Y, Chung J-H, Nocera DG, Lee YS (2007) Spin dynamics of the spin-\(1/2\) kagome lattice antiferromagnet ZnCu3(OH)6Cl2. Phys Rev Lett 98:107204
Han T-H, Helton JS, Chu S, Nocera DG, Rodriguez-Rivera JA, Broholm C, Lee YS (2012) Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492:406–410
He W-Y, Xu XY, Chen G, Law KT, Lee PA (2018) Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS2. Phys Rev Lett 121:046401
Law KT, Lee PA (2017) 1T-TaS2 as a quantum spin liquid. Proc Natl Acad Sci 114:6996–7000
Kasahara Y, Sugii K, Ohnishi T, Shimozawa M, Yamashita M, Kurita N, Tanaka H, Nasu J, Motome Y, Shibauchi T, Matsuda Y (2018) Unusual thermal Hall effect in a Kitaev spin liquid candidate α-RuCl3. Phys Rev Lett 120:217205
Banerjee A, Bridges CA, Yan J-Q, Aczel AA, Li L, Stone MB, Granroth GE, Lumsden MD, Yiu Y, Knolle J, Bhattacharjee S, Kovrizhin DL, Moessner R, Tennant DA, Mandrus DG, Nagler SE (2016) Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. Nat Mater 15:733–740
Banerjee A, Yan J, Knolle J, Bridges CA, Stone MB, Lumsden MD, Mandrus DG, Tennant DA, Moessner R, Nagler SE (2017) Neutron scattering in the proximate quantum spin liquid α-RuCl3. Science 356:1055–1059
Kasahara Y, Ohnishi T, Mizukami Y, Tanaka O, Ma S, Sugii K, Kurita N, Tanaka H, Nasu J, Motome Y, Shibauchi T, Matsuda Y (2018) Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid. Nature 559:227–231
Plumb KW, Clancy JP, Sandilands LJ, Shankar VV, Hu YF, Burch KS, Kee H-Y, Kim Y-J (2014) α-RuCl3: a spin-orbit assisted Mott insulator on a honeycomb lattice. Phys Rev B 90:041112
Molavian HR, Gingras MJP, Canals B (2007) Dynamically induced frustration as a route to a quantum spin ice state in Tb2Ti2O7 via virtual crystal field excitations and quantum many-body effects. Phys Rev Lett 98:157204
Ross KA, Savary L, Gaulin BD, Balents L (2011) Quantum excitations in quantum spin ice. Phys Rev X 1:021002
Gingras MJP, McClarty PA (2014) Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Rep Prog Phys 77:056501
Sibille R, Gauthier N, Yan H, Hatnean MC, Ollivier J, Winn B, Filges U, Balakrishnan G, Kenzelmann M, Shannon N, Fennell T (2018) Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7. Nat Phys 14:711–715
Tokiwa Y, Yamashita T, Terazawa D, Kimura K, Kasahara Y, Onishi T, Kato Y, Halim M, Gegenwart P, Shibauchi T, Nakatsuji S, Moon E-G, Matsuda Y (2018) Discovery of emergent photon and monopoles in a quantum spin liquid. J Phys Soc Jpn 87:064702
Petit S, Lhotel E, Guitteny S, Florea O, Robert J, Bonville P, Mirebeau I, Ollivier J, Mutka H, Ressouche E, Decorse C, Hatnean MC, Balakrishnan G (2016) Antiferroquadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7. Phys Rev B 94:165153
Chen G (2016) “magnetic monopole” condensation of the pyrochlore ice U(1) quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7. Phys Rev B 94:205107
MacLaughlin DE, Bernal OO, Shu L, Ishikawa J, Matsumoto Y, Wen J-J, Mourigal M, Stock C, Ehlers G, Broholm CL, Machida Y, Kimura K, Nakatsuji S, Shimura Y, Sakakibara T (2015) Unstable spin-ice order in the stuffed metallic pyrochlore \(\mathrm{Pr}_{2+x}\mathrm{Ir}_{2-x}\mathrm{O}_{7-\delta}\). Phys Rev B 92:054432
Sibille R, Lhotel E, Pomjakushin V, Baines C, Fennell T, Kenzelmann M (2015) Candidate quantum spin liquid in the Ce3+ pyrochlore stannate Ce2Sn2O7. Phys Rev Lett 115:097202
Gaudet J, Smith EM, Dudemaine J, Beare J, Buhariwalla CRC, Butch NP, Stone MB, Kolesnikov AI, Xu G, Yahne DR, Ross KA, Marjerrison CA, Garrett JD, Luke GM, Bianchi AD, Gaulin BD (2019) Quantum spin ice dynamics in the dipole-octupole pyrochlore magnet Ce2Zr2O7. Phys Rev Lett 122:187201
Gao B, Chen T, Tam DW, Huang C-L, Sasmal K, Adroja DT, Ye F, Cao H, Sala G, Stone MB, Baines C, Verezhak JAT, Hu H, Chung J-H, Xu X, Cheong S-W, Nallaiyan M, Spagna S, Maple MB, Nevidomskyy AH, Morosan E, Chen G, Dai P (2019) Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore. Nat Phys 15:1052–1057
Li Y, Liao H, Zhang Z, Li S, Jin F, Ling L, Zhang L, Zou Y, Pi L, Yang Z, Wang J, Wu Z, Zhang Q (2015) Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet ybmggao4. Sci Rep 5:16419
Li Y, Chen G, Tong W, Pi L, Liu J, Yang Z, Wang X, Zhang Q (2015) Rare-Earth triangular lattice spin liquid: a single-crystal study of YbMgGaO4. Phys Rev Lett 115:167203
Shen Y, Li Y-D, Wo H, Li Y, Shen S, Pan B, Wang Q, Walker HC, Steffens P, Boehm M, Hao Y, Quintero-Castro DL, Harriger LW, Frontzek MD, Hao L, Meng S, Zhang Q, Chen G, Zhao J (2016) Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540:559–562
Li Y-D, Wang X, Chen G (2016) Anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets. Phys Rev B 94:035107
Li Y, Adroja D, Biswas PK, Baker PJ, Zhang Q, Liu J, Tsirlin AA, Gegenwart P, Zhang Q (2016) Muon spin relaxation evidence for the U(1) quantum spin-liquid ground state in the triangular antiferromagnet YbMgGaO4. Phys Rev Lett 117:097201
Xu Y, Zhang J, Li YS, Yu YJ, Hong XC, Zhang QM, Li SY (2016) Absence of magnetic thermal conductivity in the quantum spin-liquid candidate YbMgGaO4. Phys Rev Lett 117:267202
Li Y-D, Chen G (2017) Detecting spin fractionalization in a spinon Fermi surface spin liquid. Phys Rev B 96:075105
Li Y, Adroja D, Voneshen D, Bewley RI, Zhang Q, Tsirlin AA, Gegenwart P (2017) Nearest-neighbour resonating valence bonds in YbMgGaO4. Nat Commun 8:15814
Li Y, Adroja D, Bewley RI, Voneshen D, Tsirlin AA, Gegenwart P, Zhang Q (2017) Crystalline electric-field randomness in the triangular lattice spin-liquid YbMgGaO4. Phys Rev Lett 118:107202
Tóth S, Rolfs K, Wildes AR, Rüegg C (2017) Strong exchange anisotropy in YbMgGaO4 from polarized neutron diffraction. arXiv:1705.05699 [cond-mat.str-el]
Paddison JAM, Daum M, Dun Z, Ehlers G, Liu Y, Stone MB, Zhou H, Mourigal M (2017) Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Nat Phys 13:117–122
Shen Y, Li Y-D, Walker HC, Steffens P, Boehm M, Zhang X, Shen S, Wo H, Chen G, Zhao J (2018) Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4. Nat Commun 9:4138
Li Y-D, Shen Y, Li Y, Zhao J, Chen G (2018) Effect of spin-orbit coupling on the effective-spin correlation in YbMgGaO4. Phys Rev B 97:125105
Zhang X, Mahmood F, Daum M, Dun Z, Paddison JAM, Laurita NJ, Hong T, Zhou H, Armitage NP, Mourigal M (2018) Hierarchy of exchange interactions in the triangular-lattice spin liquid YbMgGaO4. Phys Rev X 8:031001
Luo Z-X, Lake E, Mei J-W, Starykh OA (2018) Spinon magnetic resonance of quantum spin liquids. Phys Rev Lett 120:037204
Zhu Z, Maksimov PA, White SR, Chernyshev AL (2017) Disorder-induced mimicry of a spin liquid in YbMgGaO4. Phys Rev Lett 119:157201
Zhu Z, Maksimov PA, White SR, Chernyshev AL (2018) Topography of spin liquids on a triangular lattice. Phys Rev Lett 120:207203
Maksimov PA, Zhu Z, White SR, Chernyshev AL (2019) Anisotropic-exchange magnets on a triangular lattice: spin waves, accidental degeneracies, and dual spin liquids. Phys Rev X 9:021017
Kimchi I, Nahum A, Senthil T (2018) Valence bonds in random quantum magnets: theory and application to YbMgGaO4. Phys Rev X 8:031028
Liu C, Yu R, Wang X (2016) Semiclassical ground-state phase diagram and multi-q phase of a spin-orbit-coupled model on triangular lattice. Phys Rev B 94:174424
Luo Q, Hu S, Xi B, Zhao J, Wang X (2017) Ground-state phase diagram of an anisotropic spin-\(\frac{1}{2}\) model on the triangular lattice. Phys Rev B 95:165110
Li Y-D, Lu Y-M, Chen G (2017) Spinon Fermi surface U(1) spin liquid in the spin-orbit-coupled triangular-lattice Mott insulator YbMgGaO4. Phys Rev B 96:054445
Masaki O (2000) Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice. Phys Rev Lett 84:1535–1538
Hastings MB (2004) Lieb-schultz-mattis in higher dimensions. Phys Rev B 69:104431
Lieb E, Schultz T, Mattis D (1961) Two soluble models of an antiferromagnetic chain. Ann Phys 16:407–466
Watanabe H, Po HC, Vishwanath A, Zaletel M (2015) Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals. Proc Natl Acad Sci 112:14551–14556
Liu W, Zhang Z, Ji J, Liu Y, Li J, Wang X, Lei H, Chen G, Zhang Q (2018) Rare-earth chalcogenides: a large family of triangular lattice spin liquid candidates. Chin Phys Lett 35:117501
Wu C-M, Deng G, Gardner JS, Vorderwisch P, Li W-H, Yano S, Peng J-C, Imamovic E, (2016) SIKA–the multiplexing cold-neutron triple-axis spectrometer at ANSTO. J Instrum 11:10009
Baenitz M, Schlender P, Sichelschmidt J, Onykiienko YA, Zangeneh Z, Ranjith KM, Sarkar R, Hozoi L, Walker HC, Orain J-C, Yasuoka H, van den Brink J, Klauss HH, Inosov DS, Doert T (2018) NaYbS2: a planar spin-\(\frac{1}{2}\) triangular-lattice magnet and putative spin liquid. Phys Rev B 98:220409
Bordelon MM, Kenney E, Liu C, Hogan T, Posthuma L, Kavand M, Lyu Y, Sherwin M, Butch NP, Brown C, Graf MJ, Balents L, Wilson SD (2019) Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet NaYbO2. Nat Phys 15:1058–1064
Ranjith KM, Dmytriieva D, Khim S, Sichelschmidt J, Luther S, Ehlers D, Yasuoka H, Wosnitza J, Tsirlin AA, Kühne H, Baenitz M (2019) Field-induced instability of the quantum spin liquid ground state in the \({J}_{\mathrm{eff}}=\frac{1}{2}\) triangular-lattice compound NaYbO2. Phys Rev B 99:180401
Ding L, Manuel P, Bachus S, Grußler F, Gegenwart P, Singleton J, Johnson RD, Walker HC, Adroja DT, Hillier AD, Tsirlin AA (2019) Gapless spin-liquid state in the structurally disorder-free triangular antiferromagnet NaYbO2. Phys Rev B 100:144432
Xing J, Sanjeewa LD, Kim J, Meier WR, May AF, Zheng Q, Custelcean R, Stewart GR, Sefat AS (2019) Synthesis, magnetization, and heat capacity of triangular lattice materials NaErSe2 and KErSe2. Phys Rev Mater 3:114413
Zangeneh Z, Avdoshenko S, van den Brink J, Hozoi L (2019) Single-site magnetic anisotropy governed by interlayer cation charge imbalance in triangular-lattice AYbX2. Phys Rev B 100:174436
Xing J, Sanjeewa LD, Kim J, Stewart GR, Podlesnyak A, Sefat AS (2019) Field-induced magnetic transition and spin fluctuations in the quantum spin-liquid candidate CsYbSe2. Phys Rev B 100:220407
Ranjith KM, Luther S, Reimann T, Schmidt B, Schlender P, Sichelschmidt J, Yasuoka H, Strydom AM, Skourski Y, Wosnitza J, Kühne H, Doert T, Baenitz M (2019) Anisotropic field-induced ordering in the triangular-lattice quantum spin liquid NaYbSe2. Phys Rev B 100:224417
Sarkar R, Schlender P, Grinenko V, Haeussler E, Baker PJ, Doert T, Klauss H-H (2019) Quantum spin liquid ground state in the disorder free triangular lattice NaYbS2. Phys Rev B 100:241116
Xing J, Sanjeewa LD, Kim J, Stewart GR, Du M-H, Reboredo FA, Custelcean R, Sefat AS (2020) Crystal synthesis and frustrated magnetism in triangular lattice CsRESe2 (RE = La-Lu): quantum spin liquid candidates CsCeSe2 and CsYbSe2. ACS Mater Lett 2:71–75
Gao S, Xiao F, Kamazawa K, Ikeuchi K, Biner D, Krämer KW, Rüegg C, Arima T (2020) Crystal electric field excitations in the quantum spin liquid candidate NaErS2. Phys Rev B 102:024424
Scheie A, Garlea VO, Sanjeewa LD, Xing J, Sefat AS (2020) Crystal-field Hamiltonian and anisotropy in KErSe2 and CsErSe2. Phys Rev B 101:144432
Ma J, Kamiya Y, Hong T, Cao HB, Ehlers G, Tian W, Batista CD, Dun ZL, Zhou HD, Matsuda M (2016) Static and dynamical properties of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba3CoSb2O9. Phys Rev Lett 116:087201
Garlea VO, Sanjeewa LD, McGuire MA, Batista CD, Samarakoon AM, Graf D, Winn B, Ye F, Hoffmann C, Kolis JW (2019) Exotic magnetic field-induced spin-superstructures in a mixed honeycomb-triangular lattice system. Phys Rev X 9:011038
Wills AS (2000) A new protocol for the determination of magnetic structures using simulated annealing and representational analysis (sarah). Physica B: Condensed Matter 276–278:680–681
Perez-Mato JM, Gallego SV, Tasci ES, Elcoro L, de la Flor G, Aroyo MI (2015) Symmetry-based computational tools for magnetic crystallography. Annual Review of Materials Research 45:217–248
Ye M, Chubukov AV (2017) Half-magnetization plateau in a Heisenberg antiferromagnet on a triangular lattice. Phys Rev B 96:140406
Haley SC, Weber SF, Cookmeyer T, Parker DE, Maniv E, Maksimovic N, John C, Doyle S, Maniv A, Ramakrishna SK, Reyes AP, Singleton J, Moore JE, Neaton JB, Analytis JG (2020) Half-magnetization plateau and the origin of threefold symmetry breaking in an electrically switchable triangular antiferromagnet. Phys Rev Research 2:043020
Bachus S, Iakovlev IA, Li Y, Wörl A, Tokiwa Y, Ling L, Zhang Q, Mazurenko VV, Gegenwart P, Tsirlin AA (2020) Field evolution of the spin-liquid candidate YbMgGaO4. Phys Rev B 102:104433
Bordelon MM, Liu C, Posthuma L, Kenney E, Graf MJ, Butch NP, Banerjee A, Calder S, Balents L, Wilson SD (2021) Frustrated Heisenberg \({J}_{1}- {J}_{2}\) model within the stretched diamond lattice of LiYbO2. Phys Rev B 103:014420
Wawrzyńska E, Coldea R, Wheeler EM, Sörgel T, Jansen M, Ibberson RM, Radaelli PG, Koza MM (2008) Charge disproportionation and collinear magnetic order in the frustrated triangular antiferromagnet AgNiO2. Phys Rev B 77:094439
Coldea AI, Seabra L, McCollam A, Carrington A, Malone L, Bangura AF, Vignolles D, van Rhee PG, McDonald RD, Sörgel T, Jansen M, Shannon N, Coldea R (2014) Cascade of field-induced magnetic transitions in a frustrated antiferromagnetic metal. Phys Rev B 90:020401
Durst AC, Lee PA (2000) Impurity-induced quasiparticle transport and universal-limit Wiedemann-franz violation in d-wave superconductors. Phys Rev B 62:1270–1290
Dai P-L, Zhang G, Xie Y, Duan C, Gao Y, Zhu Z, Feng E, Tao Z, Huang C-L, Cao H, Podlesnyak A, Granroth GE, Everett MS, Neuefeind JC, Voneshen D, Wang S, Tan G, Morosan E, Wang X, Lin H-Q, Shu L, Chen G, Guo Y, Lu X, Dai P (2021) Spinon Fermi surface spin liquid in a triangular lattice antiferromagnet NaYbSe2. Phys Rev X 11:021044
Zhang Z, Li J, Xie M, Zhuo W, Adroja DT, Baker PJ, Perring TG, Zhang A, Jin F, Ji J, Wang X, Ma J, Zhang Q (2021) Low-energy spin dynamics of quantum spin liquid candidate NaYbSe2. cond-mat.str-el. arXiv:2112.07199
Zhang Z, Ma X, Li J, Wang G, Adroja DT, Perring TP, Liu W, Jin F, Ji J, Wang Y, Kamiya Y, Wang X, Ma J, Zhang Q (2021) Crystalline electric field excitations in the quantum spin liquid candidate NaYbSe2. Phys Rev B 103:035144
Acknowledgements
J.M. and X.Q.W. acknowledge additional support from a Shanghai talent program. Q.M.Z. acknowledges the support from Users with Excellence Program of Hefei Science Center and High Magnetic Field Facility, CAS and the synergetic Extreme Condition User Facility (SECUF), CAS. Q.H. and H.Z. thank the support from NSF-DMR-2003117. F.Z., E.F. and Y.S. thank the support of the OCPC-HGF Postdoctoral Fellowship. The torque magnetometry work at Michigan was supported by the U.S. Department of Energy (DOE) under Award No. DE-SC0020184. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida.
Funding
This work is supported by the Ministry of Science and Technology of China (Grant No. 2022YFA1402700, 2018YFGH000095), the NSF of China (Grant No. U2032213, 11774223, 12274186, 11774352, 11974244, U1832214, and U1932215), the interdisciplinary program Wuhan National High Magnetic Field Center (Grant No. WHMFC 202122), Huazhong University of Science and Technology, and the Research Grants Council of Hong Kong with General Research Fund Grant No. 17303819 and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010100). Open Access funding provided by Shanghai Jiao Tong University.
Author information
Authors and Affiliations
Contributions
QMZ and JM conducted the study. JSL and ZZ grew NaYbS2 polycrystalline samples and single crystals. GCD, YW and EXF carried out the neutron powder diffraction of NaYbS2 and analyzed the data. ZW, ZQ, RC, JFW, QH, ESC, and HDZ performed magnetization measurements. ZX, LC and LL performed torque magnetometry measurements. JTW, QH, HDZ and JM performed specific heat measurements. JTW, QR, FFZ, EXF, JE and ES carried out inelastic neutron scattering of NaYbS2 and analyzed the data. GC performed the Monte Carlo calculation of the proposed spin model. JTW, ZZ, GC, QMZ, and JM prepared the manuscript and the supplementary materials. All authors read and approved the final manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
The original version of this article was revised: the author contribution section was updated.
Jiangtao Wu, Jianshu Li and Zheng Zhang contributed equally to this work.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Wu, J., Li, J., Zhang, Z. et al. Magnetic field effects on the quantum spin liquid behaviors of NaYbS2. Quantum Front 1, 13 (2022). https://doi.org/10.1007/s44214-022-00011-z
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s44214-022-00011-z