Unconventional bipartite entanglement in the quantum dimer magnet Yb_2Be_2SiO_7

Domain: chemistry
Published: 2026-03-25
Editorial outcome: minor_revision

Abstract
The quantum dimer magnet, with antiferromagnetic intradimer and interdimer Heisenberg exchange between spin-1/2 moments, is known to host a (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} singlet ground state when the intradimer exchange is dominant. Rare-earth-based quantum dimer systems with strong spin-orbit coupling offer the opportunity for tuning their magnetic properties by using magnetic anisotropy as a control knob. Here, we report bulk characterization and neutron scattering measurements of the quantum dimer magnet Yb2Be2SiO7. We find that the Yb3+ ions can be described by an effective spin-1/2 model at low temperatures and the system does not show signs of magnetic order down to 50 mK. The magnetization, heat capacity, and neutron spectroscopy data can be well-described by an isolated dimer model with highly anisotropic exchange that stabilizes a singlet ground state with a wavefunction (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} or (\uparrow\downarrow + \downarrow\uparrow) / \sqrt{2}. Our results show that strong spin-orbit coupling can induce unusual entangled states of matter in quantum dimer magnets.

Introduction
Insulating magnets devoid of ground states with long-range order and instead characterized by strongly-interacting units featuring quantum entanglement1,2 have attracted intense interest in the field of quantum magnetism. The simplest case consists of a series of dimers with two entangled spins per unit3,4, which is known as a quantum dimer magnet for spin-1/2. The Shastry-Sutherland lattice (SSL) consists of a plane of orthogonal dimers5,6, and it is now known as one of the canonical two-dimensional models that can host entangled spin states. For isotropic Heisenberg spins on the SSL with a sufficiently small ratio of interdimer-to-intradimer exchange interactions \alpha = J2/J1, the Hamiltonian is exactly solvable and the ground state is predicted to be a direct product of entangled spin-singlet states. The gapped elementary excitations associated with this exotic state are known as triplons7,8.

SSL research progressed beyond the initial theoretical studies of the simple toy model with the discovery of SrCu2(BO3)2 9,10, which consists of weakly-coupled planes of S = 1/2 Cu2+ ions with the desired orthogonal dimer geometry11. The \alpha ratio is sufficiently small to generate a spin-singlet ground state9,10, although it is close to the critical value required to produce Neel antiferromagnetic order11,12. This proximity to a quantum phase transition has now been investigated in great detail by both experiment and theory, with a pressure-induced singlet plaquette phase first identified by neutron spectroscopy13 and multiple theoretical studies predicting quantum spin liquid phases in this regime as well14–17. SrCu2(BO3)2 also exhibits striking magnetic-field-induced phenomena, with several magnetization plateaus observed that were first explained by triplon crystallization18–20. The lower-field plateaus were later argued to arise from triplon bound state crystallization instead21.

More recently, the effect of strong spin-orbit-coupling on the magnetic properties of the SSL has received significant attention. Relevant theoretical work has explored the magnetic properties of the Ising or XXZ SSL Hamiltonian22–27, which can be realized for systems with significant magnetic anisotropy. On the experimental side, the RB4 (R=rare earth) family members were initially explored as possible anisotropic SSL systems28–33. Unfortunately, they are itinerant magnets with long-range Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interactions mediated by the conduction electrons34–38, so their magnetic Hamiltonians are more complex than the simple J1-J2 (or nearest-neighbor and next-nearest-neighbor) SSL model. Two insulating families BaR2MX5 (M = Zn, Pd, or Pt; X = O or S)39–46 and R2Be2ZO7 (Z = Ge or Si)47,48 have now come to the forefront as superior model systems for exploring SSL physics in strongly anisotropic magnets. A subset of these rare-earth-based materials host effective spin-1/2 degrees of freedom at sufficiently low temperatures, which arise from a well-isolated crystal field ground state doublet. While ordered ground states have often been identified40,41,43,45,49–51, effective spin-1/2 systems can realize more exotic behavior. Both BaCe2ZnS5 and Yb2Be2GeO7 52,53 are effective spin-1/2 dimer systems with entangled ground states and the latter has emerged as a quantum spin liquid candidate52.

In this work, we report comprehensive bulk characterization and neutron scattering measurements of the quantum dimer magnet Yb2Be2SiO7 with SSL geometry. We find that the Yb3+ ions have effective spin-1/2 degrees of freedom at sufficiently low temperatures below 10 K, and we observe no evidence for magnetic order down to dilution-refrigerator temperatures of 50 mK. The strong magnetic anisotropy of this system generates nearly Ising moments with a strong tendency to align along the [001]-axis. The zero-field neutron spectroscopy and the magnetic-field and temperature-dependence of both the magnetization and specific heat data closely match expectations for a novel entangled dimer state. More specifically, Yb2Be2SiO7 consists of a series of dimers with Sz \neq 0 ground state wavefunctions (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} or (\uparrow\downarrow + \downarrow\uparrow) / \sqrt{2}. The anisotropic intradimer exchange induced by the strong spin-orbit coupling in this system is responsible for stabilizing this exotic state that cannot be realized by the Heisenberg SSL model for spin-1/2 systems.

Results
Yb2Be2SiO7 crystallizes into the tetragonal space group P-42m(113) with room temperature lattice constants a = 7.207(1) Å and c = 4.719(1) Å determined from single crystal x-ray diffraction (see Supplementary Discussion Section I and Supplementary Tables S1, S2 for more details). The eight-fold coordinated Yb3+ ions form an SSL lattice in the ab-plane with intradimer and interdimer distances of 3.239(1) Å and 3.836(1) Å, respectively, as shown in Fig. 1a. Adjacent Yb3+ planes are separated by 4.719(1) Å. A view of the crystal structure along the c-axis with all the atoms shown is depicted in Fig. 1b.

The inverse magnetic susceptibility of single crystalline Yb2Be2SiO7, plotted as field/magnetization H/M, is presented in Fig. 1c between 0.4 K and 300 K. The data was collected in a small magnetic field of 0.1 T applied along the three high-symmetry directions [001], [110], and [100]. The same data is shown in the low-T range between 0.4 K and 1.6 K in Fig. 1d, with the real component of the AC susceptibility data from 0.05 K to 0.65 K also included for two field orientations. There are no clear signatures of long-range magnetic order in this data. Curie–Weiss fits were performed over both high-T (150–300 K) and low-T (1–5 K) ranges. The effective moment values from the high-T fits are broadly consistent with expectations for free Yb3+ ions. The low-T fits return effective moments and Curie–Weiss temperatures of 4.22(5) \muB and -0.10(2) K for H || [001], 1.71(1) \muB and -1.32(1) K for H || [110], and 1.67(1) \muB and -1.21(1) K for H || [100]. The comparatively large effective moment for H || [001] indicates that the moments have a strong preference to align with the crystallographic [001]-axis at low-T and the larger in-plane Curie–Weiss temperatures are consistent with the expected quasi-2D behavior of Yb2Be2SiO7. The small negative Curie–Weiss temperatures are indicative of weak antiferromagnetic interactions in the system under the assumption of isotropic exchange, which is not valid for this system as shown below.

Unpolarized neutron powder diffraction (NPD) patterns collected at 0.25 K and 2 K are presented in Fig. 1e and f, respectively. Both patterns are well-described by nuclear Bragg peaks associated with the Yb2Be2SiO7 crystal structure and the Al sample can. The expected positions of these peaks are indicated by the green and red ticks, respectively. While Rietveld refinements of the data using FULLPROF54 reveal no evidence for oxygen off-stoichiometry in this sample, they do identify ~4.4% Be/Si site mixing. Most importantly, there are no additional Bragg peaks or enhanced peak intensities that can be attributed to long-range magnetic order in Yb2Be2SiO7, even down to 0.25 K. Additional details of the 0.25 K refinement are presented in Supplementary Table S3.

Zero-field specific heat data measured with a single crystal and the corresponding magnetic entropy extracted by integrating Cp/T as a function of temperature are shown in Fig. 2a and its inset, respectively. There are no typical features of magnetic ordering in the heat capacity data. Instead, it is dominated by a broad peak centered near 0.5 K, while the magnetic entropy approaches Rln(2) at 4 K. The entropy result validates the use of an effective spin-1/2 model for the Yb3+ ions at low-T and indicates that the broad peak does not have a crystal field origin. Neutron powder spectroscopy, with the scattering intensity plotted as a function of momentum transfer Q and energy transfer E in Fig. 2b, was used to measure the Yb3+ crystal field spectrum. The magnetic scattering contribution was isolated by subtracting the scattering from the non-magnetic analog Lu2Be2SiO7 measured under the same experimental conditions and scaled appropriately to account for the scattering cross-section difference between Yb and Lu. There is no evidence for low-lying crystal field levels in this data. Instead, there are three excitations centered about 11, 23, and 36 meV as shown in Fig. 2c that likely correspond to the three excited crystal field doublets expected for J=7/2 Kramers Yb3+ ions in a low-symmetry ligand environment. Interestingly, these three excitations are much broader than the instrument energy resolution, which is readily apparent when comparing this data to previous results from Er2Be2SiO7 51 with nearly resolution-limited crystal field levels. This broadening may be a consequence of the Be/Si site mixing that we identified in the Rietveld refinements of the HB-2A data. Interestingly, we confirmed that there is no evidence for Be/Si site mixing in the previously reported HB-2A data for Er2Be2SiO7 51. We also collected Pair-Distribution-Function (PDF) data using the time-of-flight powder diffractometer NOMAD to investigate possible local structural distortions in Yb2Be2SiO7 (see Supplementary Discussion Section I and Supplementary Fig. S1), but the PDF data is explained well by the global structure.

The Yb3+ ions have a monoclinic point group symmetry of Cs with a single mirror plane symmetry element. The crystal field environment of the four Yb3+ ions in the chemical unit cell is different, with the y-axis of the local coordinate system indicated by the orange arrows in Fig. 1b. The local y-axes are parallel to the mirror-plane normals and perpendicular to the intradimer bonds. One principal g-tensor direction lies along the local y-axis. The other two principal g-tensor directions are not constrained by symmetry and make an angle of \beta with the crystallographic [001] and [110] or [1-10] directions. The local coordinate systems sketched in Fig. 1b applies when \beta = 0. Under this assumption, the blue arrows in this same panel denote the local x-axes, which are parallel to the dimer bonds.

Due to the low point symmetry of the Yb3+ ions and the lack of sufficient crystal field observables in the neutron spectroscopy data, it is not feasible to obtain a unique set of crystal field parameters for Yb2Be2SiO7. Half-polarized neutron powder diffraction (pNPD) offers a powerful alternative to probe the single-ion anisotropy of this system via the local site susceptibility approach55. pNPD is performed in the paramagnetic region and therefore the lack of long-range order does not influence the application of this technique. Spin-up and spin-down neutron diffraction patterns with intensities of I+ and I- are measured separately, and then Rietveld refinements of the sum and difference patterns (given by I+ + I- and I+ - I-, respectively) are performed using the software CrysPy55. The Yb3+ local site susceptibility tensor, which provides information on the local anisotropy and principal g-tensor directions and their relative magnitudes, can be extracted from the difference pattern.

The difference pattern I+ - I- measured at 5 K in an applied magnetic field of 1.5 T is shown in Fig. 2d and the sum pattern from the same dataset is shown in Supplementary Fig. S2. In each case, the Rietveld refinement result is superimposed on the data and the fit residual is plotted below the data. The best-fit result of the difference pattern yields a small \beta value of 1.52(3)°, which means that the two principal g-tensor directions not constrained by symmetry are nearly aligned with the crystallographic [001]-axis and the dimer bond direction ([110] and [1-10] for the two dimer sublattices) as illustrated in Fig. 1b. The magnetization ellipsoids’ principal axes have magnitudes of 2.32 \muB/T, 0.14 \muB/T, and 0.10 \muB/T, with the largest value for the pseudo-[001]-axis direction. These results are indicative of an Ising-like anisotropy with small deviations away from the [001]-axis and they are consistent with our Curie–Weiss fitting results described above. The analysis of the 10 K difference pattern measured in the same 1.5 T magnetic field produces similar results. The magnetization ellipsoids calculated from the local site susceptibility analysis are presented in Fig. 2e. CrysPy can also be used to calculate the powder-averaged magnetization from the local-site susceptibility tensor to facilitate a direct comparison to the experimental data as a sanity check. The powder-averaged magnetization at selected temperatures for Yb2Be2SiO7 is presented in Fig. 2f with the measured 1.5 T values shown on the panel. The 5 K and 10 K values calculated from the refined local site susceptibility tensors are 0.53 \muB/Yb and 0.29 \muB/Yb, respectively, which are nearly the same values from our powder-averaged magnetization measurements.

Low-energy neutron powder spectroscopy data were used to investigate the magnetic excitations associated with the collective ground state of Yb2Be2SiO7. A color contour plot of the scattering intensity as a function of Q and E with T = 0.25 K measured on CNCS with Ei = 1.55 meV is presented in Fig. 3a. A simulated scattering pattern based on an isolated dimer model that will be discussed below with Gaussian peak widths (full-width half maximums) that match the expected instrumental energy resolution at the mode positions (i.e. 0.035 meV at 0.11 meV and 0.033 meV at 0.19 meV) is depicted in Fig. 3b. A low-energy band of excitations with minimal dispersion centered at 0.11 meV and an intensity maximum as Q \rightarrow 0 is visible in the data. There is also a second excitation at 0.19 meV that manifests as a shoulder in the data. Both mode energies were determined by fitting the data to a sum of Gaussian functions as shown in Supplementary Fig. S3 and summarized in Supplementary Table S4. Constant-Q cuts at selected temperatures are presented in Supplementary Fig. S4 for the Ei = 1.55 meV dataset and over a wider energy range in Fig. 3c for the Ei = 2.49 meV dataset. The logarithmic intensity scales help to reveal two higher-energy excitation bands centered at 0.7 meV and 1.2 meV. The Q-dependence of the three distinct modes is shown in Fig. 3d. Both the Q and T-dependence of these modes indicate that they are magnetic excitations and their nearly-dispersionless nature suggests that they are associated with isolated or weakly-interacting spin dimers.

Since effective spin-1/2 dimer models with strong intradimer exchange anisotropy can have a maximum of three single-dimer excitations, it is clear that all four modes (at 0.11, 0.19, 0.7 and 1.2 meV) observed here do not have the same origin. We first verified that none of these modes were spurious by measuring them with different incident energies. Zero-field heat capacity only depends on the eigenvalues of these models, so we compared our data shown in Fig. 2a to simulations assuming various energy-level schemes (see Supplementary Fig. S5). The best simulation of the zero-field heat capacity data corresponds to an isolated dimer model with a doubly-degenerate mode at 0.11 meV and a non-degenerate mode at 0.19 meV. This implies that the two higher-energy modes have a different origin. In fact, as shown in Fig. 3d their Q-dependence is well-described by the Yb3+ magnetic form factor squared multiplied by the known structure factor of a triplet excitation for an isolated Heisenberg dimer model56 with the square plaquette distance dnnn = 3.84 Å. Since these higher-energy modes have a negligible contribution to the specific heat, this implies that only a small fraction of Yb3+ ions form longer-ranged dimers in Yb2Be2SiO7, possibly due to the known Be/Si site mixing in this system. We also compared the Q-dependence of these modes to expectations for the lowest-energy excitations of rectangular tetramers56, but this model could not account for the Q-position of their maximum intensities. Finally, we note that higher-energy excitations in SrCu2(BO3)2 have been attributed to singlet bound states consisting of contributions from multiple dimer units57–59 and a similar alternative origin for the higher-energy modes cannot be ruled out in the present case.

With the energy level scheme for a possible isolated dimer model comprised of most Yb3+ ions in the system established, we performed a quantitative analysis of the low-energy neutron spectroscopy data and field-dependent heat capacity and magnetization data. We started by constructing a minimal model based on symmetry analysis46,60. The model Hamiltonian describes a collection of isolated dimers with anisotropic intradimer interactions and Zeeman coupling:

H = \sum_{<i,j>l} \sum_{\alpha\beta} S_{i,l}^{\alpha} J_{l}^{\alpha\beta} S_{j,l}^{\beta} - \sum_{l\alpha} \muB H^{\alpha} g_{l}^{\alpha\beta} S_{i,l}^{\beta} (1)

where the superscript l denotes dimers in sub-lattice A/B, S_i refers to the \alpha (= x, y, z) component of the effective spin 1/2 operator with x=[1,1,0], y=[-1,1,0] and z=[0,0,1], Jl^{\alpha\beta} represents one component of the intradimer exchange tensor for dimers in each sub-lattice, H^{\alpha} is the \alpha component of the applied magnetic field, and gl^{\alpha\beta} represents one component of the g-tensor. Our model is defined in global crystallographic coordinates and it is equivalent to the one defined within the local basis after proper rotations. Constrained by the time-reversal and mirror symmetries, this Hamiltonian takes a diagonal form with an XYZ type of spin anisotropy in the reference frame defined above, and the couplings on the two sub-lattices are related by a 90° rotation about the crystallographic [001]-axis so that JA,xx=yy = JB,yy=xx and JA,zz = JB,zz.

Although off-diagonal g-tensor components are allowed by symmetry, our pNPD results described above suggest they are much smaller than the diagonal ones. We hence take the approximation that the g-tensor follows the same symmetry as the exchange tensor. With the principal g-tensor directions now fixed along high-symmetry crystallographic directions, we estimated the g-tensor values by using the 2 K magnetization data, with the H || [001] and H || [110] measurements presented in Fig. 4a. After subtracting off a linear van-Vleck contribution in the highest-field regime, we obtain gA,xx = 1.64, gA,yy = 1.71, and gA,zz = 4.6.

The energy level scheme established from the neutron spectroscopy and zero-field heat capacity data described above is consistent with 12 different intradimer exchange matrices, which we determined using Supplementary Eq. (S2). We then performed exact diagonalization of these 12 Hamiltonians in zero field to find six solutions with Sz = 0 ground state wavefunctions and six solutions with Sz \neq 0 ground state wavefunctions. We calculated the dimer structure factors for the three excitations of each model using Supplementary Eq. (S4), with the results for three representative models shown in Supplementary Fig. S6. Importantly, all 12 models have one intense mode and two much weaker modes. This common feature allows us to reliably compare the Q-dependence of the intense mode for the models with the neutron spectroscopy data even though neither weak mode is completely resolved from the intense one. The two types of solutions are characterized by intense dimer excitations with very different Q-dependences. In the regime Q \leq 1.6 Å-1, the intense excitation for the Sz = 0 solutions is described by the structure factor,

S(Q) = A [1 - sin(Qd) / Qd] (2)

where A is a constant and d is the intradimer distance. In the same Q-regime, the intense excitation for the Sz \neq 0 solutions is described approximately by the structure factor

S(Q) \approx A [sin(Qd) / Qd] (3)

To narrow down possible intradimer exchange matrices, we examined the Q-dependence of the constant E-cut centered at the intense 0.11 meV mode with an integration range of \pm 0.05 meV shown in Fig. 3d. The data fits well to the expected structure factor for the intense mode of the six Sz \neq 0 solutions. Two of these options can be ruled out because their most intense mode is located at 0.19 meV, which is inconsistent with the neutron spectroscopy data. This leaves four viable solutions and the corresponding simulations for them are presented in Supplementary Fig. S7.

All four remaining candidate models have single-dimer ground states of the form (\uparrow\downarrow + \downarrow\uparrow) / \sqrt{2} or (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} with a dominant contribution from the other Sz \neq 0 wavefunction to the doubly-degenerate first excited state. We note that these two dimer ground states are qualitatively consistent with the low-T magnetic susceptibility data presented in Fig. 1d, which should level off at finite values for all field orientations as T \rightarrow 0 rather than drop to zero as expected for a Heisenberg dimer model. Two of the solutions show superior agreement with the bulk characterization data. Although the Q-dependence of the weak mode intensities from neutron powder spectroscopy is not exactly the same for these two models, our data is not sufficient for differentiating between them conclusively. The exchange parameters for one of these models are Jxx = 0.19 meV, Jyy = -0.03 meV, and Jzz = -0.19 meV and the exchange parameters for the second model are Jxx = -0.03 meV, Jyy = 0.19 meV, and Jzz = -0.19 meV.

Using the Hamiltonian parameters provided above for the first model, the neutron spectroscopy simulation is shown in Fig. 3b and the calculated single crystal magnetization and heat capacity data are superimposed on the corresponding experimental datasets in Fig. 4a–d. It is worth noting that there is no evidence for field-induced magnetic order in the heat capacity measurements down to dilution fridge temperatures. The agreement between experiment and theory is excellent, with the small differences between the H || [001] heat capacity data and the simulation arising from modest sample misalignment that was confirmed by re-measuring the 2 T and 3 T data with coarse temperature steps for T \geq 1.8 K, which are shown as points connected by dashed curves in Fig. 4c. This simulation yields an effective S = 1 dimer state (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} in zero field, which is stabilized by the large ferromagnetic exchange interaction Jzz along the quantization axis. The excited states are doubly degenerate (\uparrow\uparrow + \downarrow\downarrow) / \sqrt{2} and (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} at E = 0.11 meV and (\uparrow\downarrow + \downarrow\uparrow) / \sqrt{2} at E = 0.19 meV, respectively. The second model has a similar eigenvector scheme for its modes, although the two modes swap their eigenvalues so the ground state is (\uparrow\downarrow + \downarrow\uparrow) / \sqrt{2} instead. Both isolated dimer models account for the major experimental features well, including the Q and E-dependence of the dynamical structure factor for the dimer excitations and the temperature and magnetic-field-dependence of the magnetization and specific heat. These results confirm that the interdimer interactions are significantly weaker than the intradimer interactions in Yb2Be2SiO7.

Beyond the qualitative signatures of the Sz \neq 0 dimer ground state in neutron spectroscopy, we also observe an anisotropic magnetization process that is not expected for systems with Sz = 0 dimer ground states. In particular, no low-field magnetization plateaus are observed at 0.4 K when the magnetic field is applied along any high-symmetry crystallographic direction, which is in sharp contrast to expectations for Sz = 0 dimer ground states as shown in Supplementary Fig. S6. Instead, applying a magnetic field along the [001] direction continuously rotates the (\uparrow\downarrow - \downarrow\uparrow) / \sqrt{2} ground state without closing the excitation gap so that the system is immediately magnetized and evolves to the fully-polarized state adiabatically without a transition as shown in the Fig. 4b data and illustrated by the energy level vs field diagram presented in Fig. 4e. On the other hand, applying the field along the [110] direction causes a level crossing for one dimer sublattice as shown in Fig. 4f, which corresponds to a quantum phase transition to an intermediate state as indicated by the peak in dM/dH shown in Fig. 4b. The other dimer sublattice has a similar level crossing when H || [1-10]. It is worth noting that the largest discrepancy in the H || [110] bulk characterization data and the simulations is observed in the fixed-field heat capacity measurements shown in Fig. 4d near the expected critical field for the level crossing. This is likely due to neglecting the appropriate sub-leading interaction in the simulations, which should have the largest effect on the magnetic properties of the system in this regime46. Indeed, neutron powder spectroscopy also suggests that a small additional term should be added to the Hamiltonian to capture the increased bandwidth of the 0.11 meV mode observed in the data, but its accurate determination without single-crystal neutron spectroscopy data is challenging. The nature of this term is not obvious either, as the expected sub-1 K energy scale means it could arise from interdimer exchange or a dipolar interaction. While additional theoretical work on candidate magnetic Hamiltonians for this system and its isostructural family members could help to address this issue, neglecting this extra term does not affect the exotic zero-field magnetic ground state for Yb2Be2SiO7 established here.

Methods
Sample preparation
Polycrystalline samples of Yb2Be2SiO7 were prepared from stoichiometric amounts of Yb2O3, BeO, and SiO2 as detailed in ref. 48. Small single crystals were grown using the floating zone melt method62,63 and oriented via Laue back-diffraction64,65. Detailed structure refinements of single-crystal x-ray diffraction data (XRD) agree well with the previously-reported structure obtained from powder XRD48 and the results are provided in Supplementary Tables S1, S2.

Bulk characterization
Polycrystalline and single-crystal DC magnetization measurements as a function of magnetic field and temperature were performed using an MPMS3 SQUID magnetometer (Quantum Design) equipped with a He-3 insert. For the single crystal measurements, the magnetic fields were applied along high-symmetry crystallographic directions. Specific heat measurements using single crystals were performed with a Quantum Design Physical Property Measurement System (PPMS) equipped with a dilution refrigerator insert. The AC susceptibility measurements were conducted on single crystals with a voltage-controlled current source (Stanford Research, CS580) and lock-in amplifier (Stanford Research, SR830). The phase of the lock-in amplifier was set to measure the first harmonic signal. The RMS amplitude of the AC excitation field was set to be 0.6 Oe with the frequency fixed to be 200 Hz. The measurements were performed in the SCM1 Dilution Refrigerator of the National High Magnetic Field Laboratory, Tallahassee.

Neutron scattering
Neutron powder diffraction (NPD) was performed using the high-resolution HB-2A powder diffractometer66,67 at the High Flux Isotope Reactor (HFIR) of Oak Ridge National Laboratory (ORNL). Unpolarized measurements were conducted with a ~4g polycrystalline sample sealed inside an aluminum can with 1 atm of helium exchange gas. Diffraction patterns were collected at 250 mK and 2 K with a wavelength of 2.41 Å and a collimation of open-open-12’.

A half-polarized neutron powder diffraction (pNPD) experiment was performed using the same HB-2A collimation settings and a V-cavity to generate the polarized beam with a ~13g polycrystalline sample pressed into pellets. The sample was loaded in a larger Al can than the one used for the unpolarized measurements. The polarization state was controlled using a Mezei flipper. Further details of the HB-2A pNPD experimental set-up can be found in ref. 68. Spin-up and spin-down diffraction patterns, with intensities denoted by I+ and I- respectively, were collected in a vertical magnetic field of 1.5 T at temperatures of 5 and 10 K using a wavelength of 2.41 Å.

Time-of-flight neutron powder diffraction data were collected at 100 K on NOMAD67 at the Spallation Neutron Source (SNS) of ORNL using ~4g of powder. Similar measurements were carried out on ~4.5g of crushed single crystals and ~2.3g of polycrystalline Er2Be2SiO7 51.

Neutron powder spectroscopy data were obtained from the direct-geometry time-of-flight instrument SEQUOIA69 at the SNS using ~2.5g of similar Yb2Be2SiO7 powder. The same amount of a non-magnetic reference sample Lu2Be2SiO7 was also measured. All SEQUOIA data were collected at 5 K with an incident energy of 80 meV using the fine Fermi chopper. The T0 frequency, Fermi chopper frequency, and energy resolution at the elastic line (full-width half maximum) were 90 Hz, 480 Hz, and 2.15 meV.

Lower-incident-energy neutron powder spectroscopy data were measured with the direct-geometry time-of-flight instrument CNCS70 at the SNS using the same polycrystalline sample from the unpolarized HB-2A experiment. The CNCS data were collected using incident energies of Ei = 1.55 meV and 2.49 meV in the “high flux” chopper setting mode, which produced energy resolutions of 0.04 meV and 0.06 meV (full-width half maximum) at the elastic line, respectively.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "A Brassington et al reported the possible realization of novel entangled spin dimer state in shastry-sutherland lattice\nYb2Be2SiO7 compound. This class of materials is interesting for investigating the anisotropic spin dimer physics beyond\nisotropic Heisenberg model. The purported conclusion is that the ground states of Yb2Be2SiO7 can be described by an\nisolated dimer model with highly anisotropic exchanges, which is mainly based on the theoretical model but no typical\nexperimental signatures observed in specific heat, magnetization and neutron scattering. The experimental evidence on the\nformation of novel singlet state is quite weak and can’t not support the conclusion, thus it is not reach the level of impact and\nnot enough for publication on Nat. Commun. The comments are listed as below for consideration:\n1) Yb2Be2SiO7 possibly realizes the anisotropic spin dimer physics beyond isotropic Heisenberg model. But, the observed\nanisotropic magnetization behaviors can’t be simply ascribed to the anisotropic exchange interactions since it can be related\nto the single ion effect of Yb3+ ions because similar anisotropy is observed at 2 K far above the energy scale of exchange\ninteractions. Since broad peak centered at 0.5 K, the anisotropic magnetization characterization far below 0.5 K is necessary\nto check whether this is field-induced phase transition, that can identify whether the system is isolated spin dimer or\ninteracted spin dimer. Without this characterization, the authors can’t give the conclusion this is isolated system and exclude\nthe √ 2 (|↑↓⟩ − |↓↑⟩) ground states. Also, in the specific heat data, no experimental data is provided at the field regions\nbetween 0-1T, which can give some information on CEF level crossing for spin dimer. We proposed the authors to\ncharacterize the related properties.\n2) If the ground state is |ψ0⟩ = 1 √ 2 (|↑↑⟩ − |↓↓⟩) singlet state, the magnetic susceptibility should drop down to zero value as\ntemperature approaches zero Kelvin. How about the susceptibility data? The size of energy gap between the singlet state\nand first excited state?\n3) For the Neutron scattering of Yb2Be2SiO7, the powder samples are used that cannot give the dispersion relation of spin\nexcitation, as presented in Figs. 2 and 3. The experimental data is enough to determine the CEF levels, the resolution is not\nhigh enough that the dispersionless nature of excitation can not be concluded based on the present data. And, how to\nunderstand the double mode at 0.11 meV and 0.19 meV, the related experimental measurements on single crystal is\nappreciated to clarify this experimental behavior. Only in that case, the excite states can be fully confirmed alongside their\nproposed model.\n4) The spin dimer physics in Ce/Yb based SSL compounds included the proposed singlet state have been discussed in the\nsimilar compounds BaCe2ZnS5 [arXiv:2412.17913,2024] and Yb2Be2GeO7 [Phys. Rev. B 110, 144445 (2024)]. The similar\nclaim is reported, the related work should be cited.\n5) In Figure S7 of supporting information, we don’t observe the double broad peaks in the specific heat near critical field for\nclosing the gap of spin dimer. While, the proposed theoretical model yield the two humps in Cp(T) curves, this contradicts\nwith the formation of isolated spin dimer, how to explain this controversy.", "reviewer_2": "Novel entangled dimer state in the Shastry-Sutherland magnet Yb2Be2SiO7\nThe authors present a thorough experimental investigation of the material Yb2Be2SiO7 by using a combination of low-\ntemperature neutron scattering, bulk magnetometry and specific heat measurements. It is argued in the paper that the\nmaterial realizes an anisotropic variant of the Shastry-Sutherland model (SSM) in the weakly-interacting interdimer regime.\nThe SSM is a quintessential model in quantum magnetism and the results presented in the paper, if correct, would cement\nYb2Be2SiO7 as a novel material in which anisotropic SSM physics could be further explored in e.g. future single-crystal\ninelastic neutron scattering (INS) studies. Although the agreement between the model calculations and the experimental\ndata is overall excellent and demonstrates a deep and accurate interpretation of the physics of Yb2Be2SiO7, we find that the\nquality of the presentation of these results has room for improvement in order to be understandable by a broad audience not\nfamiliar with the plethora of neutron scattering techniques used in the paper. In addition, the potential impact that these new\nresults have, could be motivated further, especially given the wealth of literature on SSM physics and other recent\nexperimental efforts on crystal systems featuring SSM physics. For these general reasons we suggest that the authors\nrework the paper before we can support it for publication.\nOn the results:\n-Abstract: Revise the sentence “a singlet ground state with the symmetric wavefunction”\n-Introduction and conclusions: link results to existing theoretical work\nPage 5: It is not stated in the text how the inelastic neutron scattering data (proportional to S(Q,E)) is compared to equations\n(2) and (3). Is the partially Q-integrated powder data integrated along E in order to yield the total scattering intensity S(Q)? In\nRef. [48] the term ``exclusive structure factor” is used to refer to the Q-dependence of S(Q,E) at a fixed E corresponding to a\nselected transition from the ground state. Is this definition adopted in the paper? If so it should be made explicit.\nEquation (2) is derived in Ref. [48]. The authors do not derive explicitly nor provide a reference that leads to a Q-dependence\nof the form shown in Eq. (3) (Eq. (6) in the SM). Is this equation rather a phenomenological structure factor that goes to a\nconstant value as Q->0 as seen in experiment?\nIs there a physical reason why the intradimer xx-exchange is ferromagnetic whereas the zz-exchange is\nantiferromagnetic? Could the sign of the exchange tensor elements be determined from the data that entered the fit? In other\nwords, did the fit procedure allow to determine whether the exchange is AF or AFM?\nA discussion on the results put in the context of Refs [39, 49 and 51] would be beneficial. Especially given that the ground\nstate wavefunction of Yb2Be2SiO7 deduced from the heat capacity and INS data appears identical to the one found by the\nauthors of Ref. [39] for their model system.\nPage 4: specify quantitatively how good the agreement is between the measured polycrystalline magnetization and the\ncalculated powder-averaged magnetization.\nOn the presentation:\nDiscussion regarding the g-tensor in page 2 can be left for after the pNDP results and discussion.\nFig.2(f) clarify meaning of values (0.28,0.52,1.03) in figure caption.\nAs measurements were made both in powder and single crystal samples, specify the sample form for the results in the main\ntext, eg. “Powder neutron spectroscopy” instead of “Neutron spectroscopy”\nSpecify instrumental energy resolution for/or in Fig.2(c)\nFor the published version, the paper would benefit greatly from higher-quality (higher-DPI) figures throughout the text. The\nxyz coordinate axes in Fig. 1 for example are barely legible in a printed version of the paper.\nSupplement, section II. The equation relating the local susceptibility tensor to the magnetization and applied field should be\nwritten in component form to avoid a notation that implies division by a vector.\nSupplement, figure S6. The x-label for panels (a), (c) and (e) should read Q (Å-1).", "reviewer_3": "The authors have presented a comprehensive study of the magnet Yb₂Be₂SiO₇ with a Shastry-Sutherland lattice structure.\nThe main finding of the manuscript is that this compound can be described well by isolated dimers where the ground state of\neach dimer is an effective S=1 state (|↑↑>-|↓↓>)/√2. This conclusion is firmly established via thermodynamic measurements,\ninelastic neutron scattering (to obtain CEF scheme), half-polarized neutron diffraction (to obtain the magnetic anisotropy),\nand a model using isolated dimers. In particular, I am quite impressed by the authors’ effort of using the half-polarized\nneutron powder diffraction to clarify the magnetic anisotropy of the compound, which is a crucial step for accurately\ndetermining the model. Overall, this manuscript appears to be a very solid work.\nHowever, I am not in a positive position in supporting the publication of the manuscript in Nature Communications, at least\nnot in the current form. In fact, in contradiction to what the authors have claimed in the title, the results of this manuscript\nshow that this compound has “boring disentangled” dimer state, and despite the lattice structure the physics of this material\nhas almost NOTHING to do with “Shastry-Sutherland” physics. As the authors have successfully demonstrated, the physics\nof this material is a simple “molecular”-like paramagnet, which can be described by isolated (disentangled) dimers\n(molecules).\nI believe that both the authors and the editor would agree with me that reporting negative results is also a helpful way in\nmaintaining the healthy growth of the scientific community. I understand that the authors were trying to find a fancy title so the\nmanuscript could have a higher chance in glossy journals like the Nature series. However, in this particular case, it seems to\nme it does not hurt to publish this paper with an unbiased title in Nature Communications. Due to the increasing interest in\nfinding novel Shastry-Sutherland physics in rare-earth based systems, this paper could save the global research community\nworking on related compounds a lot of money/time, by simply letting people know that there is no Shastry-Sutherland\nphysics in this particular compound (and likely also in sibling compounds). In this sense, publishing this paper with an\nunbiased message in Nature Communications will be greatly helpful to the community. My suggestion is to modify the title\nand the discussions of the paper to unbiasedly reflect the physics of this material, although it is in some sense a “negative”\nresult.\nAnother minor note: I am confused by comparing Fig. 4(f) with H//[-1 1 0] and Fig. 4(b) with H//[1 1 0], and related discussions\nin the paragraph before “In summary”. In particular, the level crossing observed in Fig. 4(f) near 1.5T was associated to the\npeak in Fig. 4(b) by the authors, however the magnetic fields are along different directions. Are the authors mixing the\ndirections of the fields, or am I simply mis-reading the authors’ message?"}, "author_response": "Response to Referees\nWe thank the referees for their constructive and unique reports. We address their criticisms and outline\nthe changes that we made to the manuscript in point form here:\nReferee 1:\n1) Yb2Be2SiO7 possibly realizes the anisotropic spin dimer physics beyond isotropic Heisenberg model.\nBut, the observed anisotropic magnetization behaviors can’t be simply ascribed to the anisotropic\nexchange interactions since it can be related to the single ion effect of Yb3+ ions because similar\nanisotropy is observed at 2 K far above the energy scale of exchange interactions. Since broad peak\ncentered at 0.5 K, the anisotropic magnetization characterization far below 0.5 K is necessary to check\nwhether this is field-induced phase transition, that can identify whether the system is isolated spin dimer\nor interacted spin dimer. Without this characterization, the authors can’t give the conclusion this is\nisolated system and exclude the √ 2 (|↑↓ − |↓↑ ) ground states. Also, in the specific heat data, no\nexperimental data is provided at the field regions between 0-1T, which can give some information on CEF\nlevel crossing for spin dimer. We propose⟩d the au⟩thors to characterize the related properties.\nThere may be some confusion here between spin-1/2 and effective spin-1/2 quantum dimer magnets,\nwhich can have very different properties. To help alleviate this confusion, we have briefly commented\non the differences between these two cases in the introduction of the revised manuscript and we have\nadded a separate discussion section at the end of the paper where we go through this comparison more\nthoroughly.\nIn the pure spin-1/2 case, the dominant energy scale will be intradimer Heisenberg exchange which is\nusually antiferromagnetic. This isolated dimer Hamiltonian yields the familiar (|↑↓ − |↓↑ )\nentangled ground state. Effective spin-1/2 moments are generated in materials with strong crystal field\n⟩ ⟩\neffects where the single ion ground state doublet is well-separated from the first excited level. For rare\nearth systems, the ground state doublet wavefunctions are a linear superposition of the different J basis\nz\nstates. These wavefunctions generate an anisotropic g-tensor, which leads to the anisotropic\nmagnetization that persists above 2 K for Yb Be SiO . The effective spin-1/2 moments interact via an\n2 2 7\nanisotropic exchange Hamiltonian rather than the more familiar Heisenberg Hamiltonian. The\nanisotropic intradimer exchange is usually the second-highest energy scale for effective spin-1/2\nquantum dimer systems, so its effect on the magnetic properties is not apparent until lower\ntemperatures. For example, the dimer level crossing observed in the magnetization data for Yb Be SiO\n2 2 7\nis only observed in the 0.4 K data when the temperature is cooled below the energy scale for the\nanisotropic intradimer exchange.\nWe investigated the origin of the broad peak centered at 0.5 K in the heat capacity data by measuring\nneutron powder diffraction patterns both above and below this temperature. The main results are\npresented in Fig. 1 (e) and (f) of the main manuscript. As we discuss in the text, there is no evidence for\nmagnetic Bragg peaks in our data at 0.25 K and therefore we have ruled out the possibility of a phase\ntransition to a ground state with long-range magnetic order. Neutron diffraction is an effective\ntechnique for ruling out the presence of low-temperature long-range magnetic order because it is a\nvolume-integrated probe that is insensitive to small magnetic impurities. We also note that neutron\nspectroscopy is an effective technique for establishing an isolated (or weakly interacting) vs strongly\ninteracting dimer system and low-T magnetic susceptibility data is not required for this purpose. Finally,\nwe did not collect additional specific heat data between 0 and 1 T because there is no evidence of\nanything exotic (e.g. a dimer level crossing) happening in this regime from both our 0.4 K magnetization\ndata and our energy level diagrams presented in Fig. 4(b) and Figs. 4(e-g) respectively.\n2) If the ground state is |ψ0 = 1 √ 2 (|↑↑ − |↓↓ ) singlet state, the magnetic susceptibility should\ndrop down to zero value as temperature approaches zero Kelvin. How about the susceptibility data? The\nsize of energy gap betwee⟩n the singlet sta⟩te and fi⟩rst excited state?\nThis is not true. Instead, the magnetic susceptibility will level off at a finite value as T => 0 K regardless of\nthe field direction. This behavior is related to the lack of a low-field magnetization plateau for this dimer\nground state. The referee is correct that the magnetic susceptibility will go to zero as T => 0 K, regardless\nof the field direction, for the more familiar (|↑↓ − |↓↑ ) dimer ground state. The (|↑↓ + |↓↑ )\nstate makes an interesting comparison, since it exhibits hybrid behavior between these two cases. To\n⟩ ⟩ ⟩ ⟩\nensure that these three possibilities are discussed in the manuscript, we have added panels to Fig. S6\nthat present the simulated low-T susceptibility data for three models with different dimer ground states.\nWe have also revised Fig. 1(d) to plot chi vs T in the lowest-T regime, which includes new AC\nsusceptibility data down to 50 mK, since this format makes it more obvious that the susceptibility data\nfor Yb Be SiO does not match qualitative expectations for a (|↑↓ − |↓↑ ) dimer ground state. The\n2 2 7\nenergy gap between the singlet state and the first excited state is 0.11 meV, which was measured\n⟩ ⟩\ndirectly by neutron spectroscopy.\n3) For the Neutron scattering of Yb2Be2SiO7, the powder samples are used that cannot give the\ndispersion relation of spin excitation, as presented in Figs. 2 and 3. The experimental data is enough to\ndetermine the CEF levels, the resolution is not high enough that the dispersionless nature of excitation\ncan not be concluded based on the present data. And, how to understand the double mode at 0.11 meV\nand 0.19 meV, the related experimental measurements on single crystal is appreciated to clarify this\nexperimental behavior. Only in that case, the excite states can be fully confirmed alongside their\nproposed model.\nThe referee is correct that powder samples cannot be used to measure dispersion relations of spin\nexcitations. For quantum dimer systems measured by neutron spectroscopy, a common approach is to\nmodel the data with an isolated dimer Hamiltonian first. This is exactly what we did in this manuscript.\nThe agreement between the powder-averaged data and the simulation with instrumental energy\nresolution included, presented in Fig. 4(a) and (b) respectively, is excellent. This implies that our isolated\ndimer Hamiltonian describes the physics of Yb Be SiO well and additional terms (i.e. interdimer and/or\n2 2 7\ndipolar interactions) will be small by comparison. We attribute the double-mode at 0.11 meV and 0.19\nmeV to two different single dimer excitations with degeneracies of 2 and 1 respectively. This eigenvalue\nscheme is further supported by our zero-field heat capacity simulations, as it explains the broad\nmaximum in this data perfectly [see Fig. S5(b)]. The XYZ dimer model for effective spin-1/2 quantum\ndimer magnets can yield up to three magnetic excitations in neutron spectroscopy, unlike the more\nfamiliar Heisenberg model which will only yield one mode with a degeneracy of 3.\n4) The spin dimer physics in Ce/Yb based SSL compounds included the proposed singlet state have been\ndiscussed in the similar compounds BaCe2ZnS5 [arXiv:2412.17913,2024] and Yb2Be2GeO7 [Phys. Rev. B\n110, 144445 (2024)]. The similar claim is reported, the related work should be cited.\nWe thank the referee for identifying these two important references. While we had already cited the\nBaCe ZnS manuscript in our work, we missed the PRB paper on Yb Be GeO . We have now cited this\n2 5 2 2 7\npaper in our manuscript and briefly discussed the results presented there.\n5) In Figure S7 of supporting information, we don’t observe the double broad peaks in the specific heat\nnear critical field for closing the gap of spin dimer. While, the proposed theoretical model yield the two\nhumps in Cp(T) curves, this contradicts with the formation of isolated spin dimer, how to explain this\ncontroversy.\nThe referee is correct that our isolated dimer model does not describe the in-field heat capacity data\nnear the 1.5 T level-crossing for H || ab-plane very well. This discrepancy arises from our failure to\nidentify the appropriate sub-leading longer-range interaction term in our Hamiltonian, which could be\ndue to interdimer exchange or a dipolar interaction. Since the neutron powder spectroscopy and the\nother bulk characterization data is described well by the isolated dimer model, we are confident that\nthis longer-range interaction term will be a perturbation to our isolated dimer Hamiltonian. The best\nway to establish the form and magnitude of this interaction is to perform single crystal neutron\nspectroscopy on Yb Be SiO , which is beyond the scope of the current manuscript. Our inability to say\n2 2 7\nmore about this weak term does not affect the major conclusions of our paper, which are that\nYb Be SiO hosts a novel dimer ground state due to strong spin-orbit coupling. In other words, the\n2 2 7\naddition of a sub-leading term to our magnetic Hamiltonian will not alter the zero-field magnetic ground\nstate of this system, which is the most important finding in our paper. A new, separate discussion\nsection near the end of our manuscript provides more information on how this exotic, entangled state-\nof-matter is stabilized and how its identification in this system has broad implications for other rare-\nearth-based quantum dimer magnets, including Shastry-Sutherland systems, which are currently a\nsubject of great interest in the condensed matter physics community.\nReferee 2:\nWe find that the quality of the presentation of these results has room for improvement in order to be\nunderstandable by a broad audience not familiar with the plethora of neutron scattering techniques used\nin the paper. In addition, the potential impact that these new results have, could be motivated further,\nespecially given the wealth of literature on SSM physics and other recent experimental efforts on crystal\nsystems featuring SSM physics. For these general reasons we suggest that the authors rework the paper\nbefore we can support it for publication.\nWe thank the referee for his/her constructive review and the valuable suggestions on how to improve\nthe quality of the manuscript. For the first comment, we are assuming that the referee would like us to\nimplement the recommended changes below so that’s what we have done. We have also added some\ndiscussion to the manuscript that describes the difference between true spin-1/2 vs effective spin-1/2\nquantum dimer systems since we’ve realized now that this would help a broad audience understand the\nsignificance of our results more easily. As for the second comment, it is an excellent point. We have\nadded some discussion near the end of the manuscript that explains why our results are important and\nrelevant for the plethora of recent work on rare-earth-based Shastry Sutherland magnets.\nOn the results:\n-Abstract: Revise the sentence “a singlet ground state with the symmetric wavefunction”\nWe have modified this sentence, so it now presents the wavefunction in the less ambiguous form\n(|↑↓ − |↓↑ ).\n-Introdu⟩ction and⟩ conclusions: link results to existing theoretical work\nWe have added some theory references to the introduction which discuss Hamiltonians (i.e. Ising and\nXXZ models) relevant for anisotropic SSL systems. We have also added a separate discussion section to\nthe end of the paper that explains the difference between spin-1/2 and effective spin-1/2 quantum\ndimer magnets, provides more details of the XYZ dimer theory relevant to our material, and explains\nhow our results are relevant for all effective spin-1/2 quantum dimer magnets including many new rare-\nearth-based SSL systems.\nPage 5: It is not stated in the text how the inelastic neutron scattering data (proportional to S(Q,E)) is\ncompared to equations (2) and (3). Is the partially Q-integrated powder data integrated along E in order\nto yield the total scattering intensity S(Q)? In Ref. [48] the term ``exclusive structure factor” is used to\nrefer to the Q-dependence of S(Q,E) at a fixed E corresponding to a selected transition from the ground\nstate. Is this definition adopted in the paper? If so it should be made explicit.\nThis is a good point. We have rewritten this section of the manuscript to clarify how we compared the\ntwo different dimer structure factors to the most intense mode of the neutron spectroscopy data. We\ntook a constant-E cut of the E = 1.55 meV data centered at 0.11 meV with an integration range of +/-\ni\n0.05 meV and found that the Q-dependence fit much better to the expected structure factor for the six\nS ≠ 0 solutions. This is compelling evidence that Yb Be SiO does not have a (|↑↓ − |↓↑ ) dimer\nz 2 2 7\nground state. We are not familiar with the term “exclusive structure factor” and it is not commonly used\n⟩ ⟩\nby the neutron scattering community, so we have chosen not to adopt it here.\nEquation (2) is derived in Ref. [48]. The authors do not derive explicitly nor provide a reference that leads\nto a Q-dependence of the form shown in Eq. (3) (Eq. (6) in the SM). Is this equation rather a\nphenomenological structure factor that goes to a constant value as Q->0 as seen in experiment?\nThis is another good point. Upon review of our discussion related to those two equations, we agree with\nthe referee that it was misleading and unnecessarily vague. We have rewritten this section of the\nmanuscript to improve clarity. For the XYZ dimer model, the Q-dependence of the most intense\nexcitation is not described by an analytical function over a broad Q-range. However, for the 12 XYZ\ndimer models being considered in this work the Q-dependence of this excitation is well-described by\neither Eq. (2) or Eq. (3) in the low-Q regime (≤ 1.6 Å-1). Examining the Q-dependence of the most intense\nmode in the neutron spectroscopy carefully allows us to reduce the number of viable solutions from 12\nto 6. When working to address this point, we found an error in our code for powder-averaging the dimer\nstructure factors. We have now corrected this error and re-generated Fig. 3, Fig. S6, and Fig. S7. We\nhave validated the accuracy of our new powder-averaged results by using the community software\nSunny (https://github.com/SunnySuite/Sunny.jl) to reproduce the calculations with our own code. After\ncorrecting this powder-averaging error, we are now convinced that we can no longer use our neutron\npowder spectroscopy data to determine the magnetic Hamiltonian of Yb Be SiO unambiguously. There\n2 2 7\nare two different models that show similar agreement between the simulations and our bulk\ncharacterization and neutron powder spectroscopy data. Nonetheless, they both have Sz ≠ 0 dimer\nground states so our major finding that Yb Be SiO hosts a magnetic ground state with novel bipartite\n2 2 7\nentanglement is unaffected. We have modified the manuscript in the appropriate places to ensure that\nour modified conclusions are properly communicated.\nIs there a physical reason why the intradimer xx-exchange is ferromagnetic whereas the zz-exchange is\nantiferromagnetic? Could the sign of the exchange tensor elements be determined from the data that\nentered the fit? In other words, did the fit procedure allow to determine whether the exchange is AF or\nAFM?\nThis is a good question. Phrased more generally, one could ask if there are simple physical explanations\nfor the relative magnitudes and signs of each component in an anisotropic exchange matrix. We are not\naware of straightforward connections between the crystal structure, single ion properties, and an\nanisotropic exchange matrix along the lines of Goodenough-Kanamori rules for isotropic exchange in\ntransition metal magnets. The second question is easier to answer. There are only 12 anisotropic\nintradimer exchange matrices consistent with the eigenvalue scheme determined from neutron\nspectroscopy and zero-field heat capacity data. In other words, the three components of these matrices\nsatisfy Supplementary Eq. S2. Each solution has two larger components with equal magnitudes and a\nsmaller component. The signs of the different components are variable. Therefore, our procedure for\nidentifying the best solution from these 12 possibilities does indeed allow us to determine if each\ncomponent (J , J , and J ) is antiferromagnetic or ferromagnetic. In fact, the sign of these terms helps\nxx yy zz\nto establish the single dimer ground state of the system.\nA discussion on the results put in the context of Refs [39, 49 and 51] would be beneficial. Especially given\nthat the ground state wavefunction of Yb2Be2SiO7 deduced from the heat capacity and INS data appears\nidentical to the one found by the authors of Ref. [39] for their model system.\nThis is a great suggestion. We have now added a discussion section with this content near the end of the\nmanuscript.\nPage 4: specify quantitatively how good the agreement is between the measured polycrystalline\nmagnetization and the calculated powder-averaged magnetization.\nThe refined values from the local site susceptibility measurement are nearly the same as the values from\nour powder-averaged magnetization measurements. We have now compared the two sets of values\ndirectly in the manuscript.\nOn the presentation:\nDiscussion regarding the g-tensor in page 2 can be left for after the pNDP results and discussion.\nThis is another good point. We have moved the g-tensor discussion to the single ion properties section\nof the paper to help explain why the local site susceptibility measurement was useful for this system.\nFig.2(f) clarify meaning of values (0.28,0.52,1.03) in figure caption.\nThese are the measured values from the powder-averaged magnetization. We have now stated this\nexplicitly in the figure caption.\nAs measurements were made both in powder and single crystal samples, specify the sample form for the\nresults in the main text, eg. “Powder neutron spectroscopy” instead of “Neutron spectroscopy”\nWe have now specified if each measurement was made on powders or single crystals the first time it is\nmentioned in the manuscript. We have also provided these details in the methods section.\nSpecify instrumental energy resolution for/or in Fig.2(c)\nWe now explicitly state in the manuscript text that the Er Be SiO crystal field levels shown in Fig. 2(c)\n2 2 7\nare nearly resolution limited. We also revised Fig. 2(c) to plot the correct constant-Q cut for Er Be SiO\n2 2 7\nto facilitate a direct comparison to the Yb Be SiO dataset collected under the same experimental\n2 2 7\nconditions. Finally, we provided instrumental energy resolution information used to generate the\nsimulation shown in Fig. 3(b). While the referee did not explicitly ask for this last change, we realize that\nit was an oversight not to provide this information previously.\nFor the published version, the paper would benefit greatly from higher-quality (higher-DPI) figures\nthroughout the text. The xyz coordinate axes in Fig. 1 for example are barely legible in a printed version\nof the paper.\nYes, this is a good point. We have re-generated all the figures with a DPI of 300.\nSupplement, section II. The equation relating the local susceptibility tensor to the magnetization and\napplied field should be written in component form to avoid a notation that implies division by a vector.\nSupplement, figure S6. The x-label for panels (a), (c) and (e) should read Q (Å-1).\nThanks for pointing out these two errors. They have been corrected in the revised manuscript.\nReferee 3:\nHowever, I am not in a positive position in supporting the publication of the manuscript in Nature\nCommunications, at least not in the current form. In fact, in contradiction to what the authors have\nclaimed in the title, the results of this manuscript show that this compound has “boring disentangled”\ndimer state, and despite the lattice structure the physics of this material has almost NOTHING to do with\n“Shastry-Sutherland” physics. As the authors have successfully demonstrated, the physics of this material\nis a simple “molecular”-like paramagnet, which can be described by isolated (disentangled) dimers\n(molecules).\nI believe that both the authors and the editor would agree with me that reporting negative results is also\na helpful way in maintaining the healthy growth of the scientific community. I understand that the\nauthors were trying to find a fancy title so the manuscript could have a higher chance in glossy journals\nlike the Nature series. However, in this particular case, it seems to me it does not hurt to publish this\npaper with an unbiased title in Nature Communications. Due to the increasing interest in finding novel\nShastry-Sutherland physics in rare-earth based systems, this paper could save the global research\ncommunity working on related compounds a lot of money/time, by simply letting people know that there\nis no Shastry-Sutherland physics in this particular compound (and likely also in sibling compounds). In this\nsense, publishing this paper with an unbiased message in Nature Communications will be greatly helpful\nto the community. My suggestion is to modify the title and the discussions of the paper to unbiasedly\nreflect the physics of this material, although it is in some sense a “negative” result.\nWe sincerely thank the referee for his/her overall positive review of our work. While the referee seems\nto understand our general rationale for trying to publish this work in a high-profile journal like Nature\nCommunications, our choice of some unfortunate language has led to his/her main criticism. We realize\nnow that the term ‘entangled dimer state’ is misleading as it could imply that there is entanglement\nbetween dimers, which would be a more exotic state-of-matter than the one we have found for\nYb Be SiO here. It was not our intention to convey this message in our paper as it is not supported by\n2 2 7\nour experimental data or our simulations. To improve clarity, we have modified our title to make it clear\nthat we have intradimer (or ‘bipartite’) entanglement in our system only. We think that this entangled\nstate-of-matter is still quite novel as it has only been observed in one other quantum dimer magnet\nquite recently (the manuscript is still unpublished) and many condensed matter physicists still don’t\nseem to appreciate that it can be stabilized in effective spin-1/2 quantum dimer magnets by anisotropic\nintradimer exchange. Instead, it is often assumed that all quantum dimer magnets must have (|↑↓ −\n⟩\n|↓↑ ) dimer ground states due to the plethora of true spin-1/2 systems with antiferromagnetic\nHeisenberg exchange that have been characterized.\n⟩\nRegarding the referee’s related comment about Shastry-Sutherland physics, we agree that the\napplicability of the J -J SSL Hamiltonian to Yb Be SiO is an open question since our work shows that\n1 2 2 2 7\nthis system is very close to the isolated dimer limit. Since the simple isolated dimer model does not\ndescribe all our data perfectly, we know that we are missing a sub-leading term in the Hamiltonian that\nmay arise from interdimer exchange (i.e. J in the SSL model) or a dipolar interaction. However, it is\n2\nbeyond the scope of our work to conclusively determine the nature of this term, and it is not relevant\nfor our main conclusions that the referee stated in his/her review. To address the referee’s concern, we\nhave decided not to explicitly call Yb Be SiO a Shastry-Sutherland magnet in the manuscript and instead\n2 2 7\nwe refer to it as a ‘quantum dimer magnet’ now. Our understanding is that a quantum dimer magnet is\nany system with structural dimers where the pairs of spins entangle to form a singlet state, which is\ncertainly true in the present case. This modification also allowed us to discuss the difference between\npure spin-1/2 and effective spin-1/2 quantum dimer magnets in the introduction and a new discussion\nsection of our manuscript and explain the significance of our results more clearly in the same discussion\nsection.\nAnother minor note: I am confused by comparing Fig. 4(f) with H//[-1 1 0] and Fig. 4(b) with H//[1 1 0],\nand related discussions in the paragraph before “In summary”. In particular, the level crossing observed\nin Fig. 4(f) near 1.5T was associated to the peak in Fig. 4(b) by the authors, however the magnetic fields\nare along different directions. Are the authors mixing the directions of the fields, or am I simply mis-\nreading the authors’ message?\nThanks for catching this issue. There are two dimer sublattices with the same H || [001] energy level\ndiagrams and opposite behavior along the H || [110] and H || [-110] directions. We have now plotted\nthe energy level diagrams for the other sublattice since the level crossing then occurs when H || [110],\nwhich agrees with the field direction convention we chose for plotting the bulk characterization data.\nWe have also tried to clarify the sublattice-dependent level crossing behavior in the manuscript text.\nExtra correction:\nOne additional correction we made not related to any referee comment was to revise Fig. S5. We\naccidentally included a variable scale factor in the heat capacity simulations presented in the previous\nversion of this figure, which doesn’t make physical sense since the simulation result should be in\nabsolute units. Now that this error has been corrected, most of the models we previously discarded\nusing Fig. S5 have even larger discrepancies with the experimental data. Resolving this issue does not\naffect any of our conclusions.\nThanks again to the referees for their careful reviews of our work, which helped to significantly\nstrengthen the revised manuscript.\nSincerely,\nDr. Adam Aczel, Corresponding Author"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have replied part of questions mentioned in the initial review, the manuscripts are improved but they still did not\nreply the concerned questions:\n1) Since the exotic magnetic behaviors of Yb2Be2SiO7 is located at temperature below 0.5 K and field (B< 1T), the\nanisotropic magnetization and specific heat characterizations at T< 0.5 K and B< 1T are necessary to check whether this\nexists field-induced phase transition, that can identify whether the system is a pure isolated spin dimer or interacted spin\ndimer. Even the neutron diffraction is measured but it is under zero field. The authors neglected this issue in their revision, I\nstill proposed the authors to characterize the related properties.\nAs pointed by Reviewer 3, if this is a pure isolated spin dimer, the present results are trivial. But, the key is to investigate the\nmagnetic behaviors at lower fields, while most of experimental results are missing.\n2) The proposed dimer state is not convincing. In Fig. S7, one can not distinguish between model 2 and model 4. Moreover,\nboth models cannot reproduce the specific data satisfactorily, especially in nonzero magnetic fields. The poor resolution, or\nintrinsic broadening of the spectra renders a separation of the 0.11 and 0.19 meV excitations nearly impossible. Therefore, a\ncomparison of the Q dependence of these excitations is not convincing. The origin of the excitations at 0.7 and 1.2 meV\nremains elusive. Could that be observed with different Eis?\n3) The Weiss temperature along the [110] direction is very large compared to that along the [001] direction. But the extract\nexchange parameters show a larger Jz than Jy. How to reconcile these results?\nSome minor points:\n1) in Fig. S3, the 0.19 meV peak seems to locate above 0.2 meV by eye. Is the fit reliable?\n2) Also, the peak width seems to be Q dependent, see Fig. 3. Is the large integration range in Fig. S3 justified?", "reviewer_3": "I have reviewed the authors' response along with the updated manuscript, and found the changes to be satisfactory.\nTherefore, I now fully support the publication of this paper without reservation."}, "author_response": "Response to Referees\nWe thank the two referees for their second round of reports. We address Referee 1’s remaining\ncriticisms and outline the changes that we made to the manuscript in point form here:\nReferee 1:\n1) Since the exotic magnetic behaviors of Yb2Be2SiO7 is located at temperature below 0.5 K and field (B<\n1T), the anisotropic magnetization and specific heat characterizations at T< 0.5 K and B< 1T are\nnecessary to check whether this exists field-induced phase transition, that can identify whether the\nsystem is a pure isolated spin dimer or interacted spin dimer. Even the neutron diffraction is measured\nbut it is under zero field. The authors neglected this issue in their revision, I still proposed the authors to\ncharacterize the related properties. As pointed by Reviewer 3, if this is a pure isolated spin dimer, the\npresent results are trivial. But, the key is to investigate the magnetic behaviors at lower fields, while most\nof experimental results are missing.\nDuring the first round of revisions, we already added anisotropic magnetization data plotted as  = M/H\nbelow 0.5 K (see revised Fig. 1d). In the initial manuscript, we also included 0 T heat capacity data down\nto dilution fridge temperatures. Both datasets find no evidence for long-range magnetic order in zero\nfield and their T-dependence is consistent with the bipartite-entangled dimer ground state that we have\nproposed in this work. We also have dilution fridge heat capacity data in selected magnetic fields (1 T, 2\nT, 3 T) for various sample orientations that show no evidence for field-induced magnetic order. We have\nadded one sentence to the second revision of the manuscript on p. 6-7 to make this clear, which states:\n“It is worth noting that there is no evidence for field-induced magnetic order in the heat capacity\nmeasurements down to dilution fridge temperatures.”\nWe assume that the referee is focused on the search for field-induced order between 0 and 1 T due to\nthe small discrepancy between the H || [110] heat capacity data and the isolated dimer simulation for 1\nand 2 T. As we have already pointed out in our first referee response letter and the first revision of the\nmanuscript on p.7, we attribute these discrepancies to the proximity of that heat capacity data to the 1.5\nT level crossing identified in both our magnetization data and the isolated dimer modeling. This is\nprecisely the regime where one expects the heat capacity of an isolated dimer model and a weakly-\ninteracting dimer model to have the largest discrepancies, as the spin gap between the two lowest\ndimer levels becomes comparable to the weak interdimer interaction. The nearly perfect agreement\nbetween the 0 T and 3 T H || [110] heat capacity data and simulations, where we are far away from the\nlevel crossing, validates this point. Note that the differences between the H-T phase diagrams of the\nisolated and weakly-interacting dimer models have been investigated extensively in pure spin-1/2\nquantum dimer magnets. For good review articles, please see Giamarchi et al, Nature Physics 4, 199\n(2008) and Zapf et al, Rev. Mod. Phys. 86, 563 (2014). The relevant text in the manuscript states: “It is\nworth noting that the largest discrepancy in the H || [110] bulk characterization data and the\nsimulations is observed in the fixed-field heat capacity measurements shown in Fig. 4(d) near the\nexpected critical field for the level crossing. This is likely due to neglecting the appropriate sub-leading\ninteraction in the simulations, which should have the largest effect on the magnetic properties of the\nsystem in this regime. Indeed, neutron powder spectroscopy also suggests that a small additional term\nshould be added to the Hamiltonian to capture the increased bandwidth of the 0.11 meV mode\nobserved in the data, but its accurate determination without single-crystal neutron spectroscopy data is\nchallenging. The nature of this term is not obvious either, as the expected sub-1 K energy scale means it\ncould arise from interdimer exchange or a dipolar interaction. While additional theoretical work on\ncandidate magnetic Hamiltonians for this system and its isostructural family members could help to\naddress this issue, neglecting this extra term does not affect the novel zero-field magnetic ground state\nfor Yb2Be2SiO7 established here.”\nThe small deviations between the H || [110] heat capacity data and simulations at 1 and 2 T show that\nYb2Be2SiO7 is likely a weakly-interacting dimer system, which we already acknowledged in the first\nrevision of the manuscript in several places. We are hesitant to include an interdimer term in our\nHamiltonian for the simulations because it is very weak, its origin is unclear from our data (i.e. in-plane\nexchange, out-of-plane exchange, dipolar interaction, or some combination of these terms) and it would\nnot be possible to solve the revised Hamiltonian exactly, so we would have to resort to more\ncomplicated numerical approaches for the simulations that wouldn’t add significant value to the paper\nand instead likely reduce the credibility of our analysis instead. Importantly, the main conclusion of our\nwork is that Yb2Be2SiO7 has an exotic, entangled dimer ground state in zero field. This is true for both\nisolated dimer and weakly-interacting dimer scenarios. Identifying field-induced magnetic order in a\nsmall region of the H-T phase diagram (most likely between 1 and 2 T for H || [110]) doesn’t affect\nthis conclusion and we don’t consider it to be a very impactful result. We also don’t expect to observe\nfield-induced order for any applied field. Beyond the lack of experimental evidence for this field-induced\norder via our heat capacity measurements in selected applied magnetic fields, the out-of-plane Curie-\nWeiss temperature is only -0.1 K, which implies that the energy scale for the out-of-plane interdimer\nexchange term necessary for this 3D field-induced order is barely above the lowest experimentally\naccessible temperature provided by a dilution fridge. This suggests that Yb2Be2SiO7 is a weakly-\ninteracting dimer system with the largest interdimer term likely arising from in-plane exchange as\nexpected for the 2D Shastry-Sutherland model. Note that not all weakly-interacting dimer models\ngenerate magnetic order somewhere in their H-T phase diagrams.\nAs we already described in the first revision of the manuscript, particularly in the discussion section, the\nzero-field dimer ground state of Yb2Be2SiO7 is far from trivial. In fact, we think that this entangled state-\nof-matter is quite novel and precisely what makes this work worthy of publication in Nature\nCommunications. It has only been observed/proposed in one other quantum dimer magnet quite\nrecently (the manuscript is still unpublished) and many condensed matter physicists still don’t\nseem to appreciate that it can be stabilized in effective spin-1/2 quantum dimer magnets by anisotropic\nintradimer exchange. Instead, it is often assumed that all quantum dimer magnets must have (|↑↓⟩ −\n|↓↑⟩) dimer ground states due to the plethora of true spin-1/2 systems with antiferromagnetic\nHeisenberg exchange that have been characterized. This confusion has led to significant challenges with\ncharacterizing new dimer systems with strong spin-orbit-coupling, which have come to the forefront as a\ntopical research area in the field. In fact, some researchers are proposing materials in this family as new\nquantum spin liquid candidates that may not order for similar reasons to Yb2Be2SiO7 instead.\n2) The proposed dimer state is not convincing. In Fig. S7, one cannot distinguish between model 2 and\nmodel 4. Moreover, both models cannot reproduce the specific data satisfactorily, especially in nonzero\nmagnetic fields. The poor resolution, or intrinsic broadening of the spectra renders a separation of the\n0.11 and 0.19 meV excitations nearly impossible. Therefore, a comparison of the Q dependence of these\nexcitations is not convincing. The origin of the excitations at 0.7 and 1.2 meV remains elusive. Could that\nbe observed with different Eis?\nWe’ll assume that the referee doesn’t think the proposed dimer state is convincing for the specific\nreasons given here and address each of these points in turn.\nFirst point - In the first revision of the manuscript on p. 6, we had already acknowledged that the data\npresented in our paper cannot be used to distinguish between models 2 and 4. As shown in Fig. S7, the\nsimulated bulk characterization data (magnetization and specific heat) looks the same, as expected. The\nstrongest mode in neutron spectroscopy is also the same for the two models. It turns out that the only\nway to differentiate between these two models is via the Q-dependence of the two weak modes in\nneutron spectroscopy, but one weak mode is at the same energy transfer as the strong mode (0.11\nmeV) and the second weak mode (0.19 meV) is not sufficiently well-separated for us to draw any\nconclusions from it. Despite both models providing equivalent descriptions of our data, our main\nconclusion shown above in the first bold sentence is still robust. The only drawback now is that we are\nnot certain if the dimer ground state of the system is |↑↑⟩ − |↓↓⟩ or |↑↑⟩ + |↓↓⟩. We don’t think\nthat this diminishes the impact of our work. The relevant manuscript text states: “Two of the solutions\nshow superior agreement with the bulk characterization data. Although the Q-dependence of the weak\nmode intensities from neutron powder spectroscopy is not exactly the same for these two models, our\ndata is not sufficient for differentiating between them conclusively.”\nSecond point - The two models explain the 0 T heat capacity data and the H || [110] heat capacity data\nat 3 T very well. There are two separate issues leading to small discrepancies between the intermediate\nfield H || [110] heat capacity data and the models and the H || [001] heat capacity data and the models.\nBoth issues were already discussed in the first revision of the manuscript on p. 7. The reason for the first\ndiscrepancy along the H || [110] direction is also provided in our response to (1) above. The reason for\nthe second discrepancy along the H || [001] direction is that there was a modest misorientation of the\nsample for that measurement. To verify this, we had already collected additional H || [001] heat\ncapacity data over a limited temperature range at 2 T and 3 T. The associated text on p. 7 of the revised\nmanuscript read as follows: “The agreement between experiment and theory is excellent, with the small\ndifferences between the H || [001] heat capacity data and the simulation arising from modest sample\nmisalignment that was confirmed by re-measuring the 2 T and 3 T data with coarse temperature steps\nfor T  1.8 K.” To emphasize this new data further, we have now added the following to the end of this\nsentence: “…which are shown as points connected by dashed curves in Fig. 4(c).” We have also referred\nto this new heat capacity data explicitly in the figure caption.\nThird point – We agree with the referee that the neutron spectroscopy experiment does not have\nsufficient energy resolution to separate the modes at 0.11 meV and 0.19 meV to examine their Q-\ndependences independently. The critical point here is that the simulated intensity of one mode is\nsignificantly larger than the intensity of the other two modes for all 12 isolated dimer models with the\nappropriate eigenvalues (see Fig. S6 for three examples), so we can compare the simulated Q-\ndependence of this intense mode to the experimental data quite accurately. We use both the measured\n0.11 meV eigenvalue and the Q-dependence of the intense mode to eliminate 8 of the 12 isolated dimer\nmodels from consideration. We have added two sentences to the manuscript to explain how the Q-\ndependence of the intense mode can be compared between experiment and theory, which read as\nfollows: “Importantly, all 12 models have one intense mode and two much weaker modes. This common\nfeature allows us to reliably compare the Q-dependence of the intense mode for the models with the\nneutron spectroscopy data even though neither weak mode is completely resolved from the intense\none.”\nFourth point – We agree with the referee that we couldn’t conclusively identify the origin of the weak\n0.7 and 1.2 meV magnetic excitations. They are not spurious, as the 0.7 meV mode was observed in both\nthe Ei = 1.55 meV and 2.49 meV data shown in Fig. S4 and Fig. 3(c) respectively. We added one sentence\nto the second revision of the manuscript to make this more explicit now: “We first verified that none of\nthese modes were spurious by measuring them with different incident energies.” We already discussed\nthe possible origin of these modes at length in the first revision of the manuscript on p. 5. The manuscript\ntext reads as follows: “Since effective spin-1/2 dimer models with strong intradimer exchange\nanisotropy can have a maximum of three single-dimer excitations, it is clear that all four modes (at 0.11,\n0.19, 0.7 and 1.2 meV) observed here do not have the same origin. Zero-field heat capacity only\ndepends on the eigenvalues of these models, so we compared our data shown in Fig. 2(a) to simulations\nassuming various energy-level schemes (see Supplementary Fig. S5). The best simulation of the zero-\nfield heat capacity data corresponds to an isolated dimer model with a doubly-degenerate mode at 0.11\nmeV and a non-degenerate mode at 0.19 meV. This implies that the two higher-energy modes have a\ndifferent origin. In fact, as shown in Fig. 3(d) their Q-dependence is well-described by the Yb^{3+}\nmagnetic form factor squared multiplied by the known structure factor of a singlet-triplet transition for\nan isolated Heisenberg dimer model with the square plaquette distance d_{nnn} = 3.84 \\AA. Since these\nhigher-energy modes have a negligible contribution to the specific heat, this implies that only a small\nfraction of Yb^{3+} ions form longer-range dimers in Yb2Be2SiO7, possibly due to the known Be/Si site\nmixing in this system. We also compared the Q-dependence of these modes to expectations for the\nlowest-energy excitations of rectangular tetramers, but this model could not account for the Q-position\nof their maximum intensities. Finally, we note that higher-energy excitations in SrCu2(BO3)2 have been\nattributed to singlet bound states consisting of contributions from multiple dimer units and a similar\nalternative origin for the higher-energy modes cannot be ruled out in the present case.”\n3) The Weiss temperature along the [110] direction is very large compared to that along the [001]\ndirection. But the extract exchange parameters show a larger Jz than Jy. How to reconcile these results?\nThere may be some confusion here between different types of anisotropic exchange interactions. One\ncommon type of exchange anisotropy arises in 2D magnets, where the in-plane exchange interactions\nare stronger than the out-of-plane interactions. Another type of exchange anisotropy occurs between a\nsingle pair of magnetic ions due to strong spin-orbit-coupling, where the exchange interaction needs to\nbe described by a tensor rather than a single value that is appropriate for the Heisenberg case. Both\ntypes of anisotropic exchange play a role in Yb2Be2SiO7. Since the Yb ions form a Shastry-Sutherland\nlattice, the system is expected to be quasi-2D in nature. The measured Curie-Weiss temperatures are\nconsistent with this scenario since the in-plane values are much larger than the out-of-plane value. The\nanisotropic intradimer exchange, given by the parameters J_{xx}, J_{yy}, and J_{zz}, is the driving force\nfor the exotic entangled dimer ground state of the system. To help alleviate some of this confusion, we\nhave added the following text to the manuscript on p. 3: “…and the larger in-plane Curie-Weiss\ntemperatures are consistent with the expected quasi-2D behavior of Yb2Be2SiO7. The small negative\nCurie-Weiss temperatures are indicative of weak antiferromagnetic interactions in the system under the\nassumption of isotropic exchange, which is not valid for this system as shown below.”\n4) in Fig. S3, the 0.19 meV peak seems to locate above 0.2 meV by eye. Is the fit reliable?\nThe 0.19 meV peak position is deceiving by eye because this feature shows up as a shoulder in the data,\nwhich leads to a sizable error in the peak center value (see Table S4). We are confident that the fit is\nreliable though because the zero-field heat capacity data is described almost perfectly by a single dimer\nmodel with a doubly-degenerate excitation at 0.11 meV and a single excitation at 0.19 meV, as\nillustrated in Fig. S5b. If the 0.19 meV shoulder is not included in the heat capacity simulation, the\nagreement with the data is reduced significantly as shown in Fig. S5a.\n5) Also, the peak width seems to be Q dependent, see Fig. 3. Is the large integration range in Fig. S3\njustified?\nThere is essentially no dispersion in the intense, low-energy magnetic excitation, as expected for an\nisolated dimer or very weakly-interacting dimer model. This ensures that our constant Q-cut with a\nrelatively large Q integration range can be used to accurately determine the 0.11 and 0.19 meV peak\npositions. The excellent agreement between the zero-field heat capacity data and the simulation with\nthis dimer energy scheme further validates our approach.\nThanks again to Referee 1 for his/her review of our work.\nSincerely,\nDr. Adam Aczel, Corresponding Author"}]

Decision letter