Long-range magnetic order with disordered spin orientations in a high-entropy antiferromagnet

Domain: chemistry
Published: 2026-03-06
Editorial outcome: major_revision

Abstract
Disorder in magnetic systems typically suppresses long-range order, promoting short-range states such as spin glasses and magnetic clusters. This is particularly prominent in high-entropy materials, characterized by the random distributions of local magnetic entities and exchange interactions. However, in rare exceptions, long-range magnetic order can persist in high-entropy systems, while the microscopic characters and underlying mechanisms remain elusive, especially the magnetic behaviors of individual elements. Here, combining neutron diffraction and resonant soft x-ray scattering, we have conducted an element-specific investigation into the magnetic order of a high-entropy honeycomb-lattice van der Waals material (Mn1/4Fe1/4Co1/4Ni1/4)PS3. Despite significant atomic disorder, long-range zigzag antiferromagnetic order is observed below 72 K, with all four transition-metal elements participating in a unified phase transition. However, the spin orientations of various elements are distinct, attributed to the competition between single-ion anisotropies and exchange interactions. Our findings showcase a novel form of long-range magnetic order with disordered spin orientations, which is synergically stabilized by distinct magnetic elements in a high entropy magnet, offering a new paradigm for understanding complex magnetic systems.

Introduction
Conventionally, magnetism is characterized by order parameters indicative of symmetry breaking and features a repeating pattern of magnetic moments. Disorder can be introduced through chemical substitution, which is commonly treated as local perturbations when its effects are weak. However, when disorder becomes significant — such as when dopant concentrations approach those of the host material — the periodic spin arrangement can be entirely disrupted, leading to dramatically weakened magnetic correlations. In classical magnetic systems, such disordered states with short-range order are generally understood within the framework of spin glass theory [1, 2].

Such is the case for the magnetism in high-entropy (HE) materials—such as alloys [3–7], ceramics [8], oxides [9, 10], and van der Waals compounds [11–13]. These materials feature multiple principal elements randomly distributed at comparable concentrations, yielding exceptionally high configurational entropy. They can exhibit highly tunable properties, novel topological electronic structures [14], and outstanding performance in applications [15–17]. Regarding magnetic properties, the substantial disorder arising from randomly distributed magnetic moments and exchange interactions is expected to suppress long-range magnetic order. Indeed, glass-like magnetic behaviors are commonly observed in HE magnets [18, 19], where spin moments are frozen in random directions, pinned by local lattice distortions. Yet, in some rare cases, long-range magnetic order can persist [20–23], presenting a fundamental paradox given the inherent disorder of the system, and the nature of such ordering remains unresolved. For instance, it is often presumed that once magnetic order is established in HE magnets, it uniformly affects all constituent elements with identical transition temperatures and spin orientations, even though each element, with its distinct orbital filling, could contribute its unique magnetic characteristics such as spin magnitudes and single-ion anisotropies. In fact, the magnetic behaviors of individual magnetic elements have never been thoroughly explored in HE materials. The lack of HE single crystals poses an additional barrier for detailed studies of their magnetic properties.

In this regard, HEPS3, short for (Mn1/4Fe1/4Co1/4Ni1/4)PS3, emerges as a pivotal candidate to address this gap [11]. As a newly discovered HE van der Waals material, it features a slightly distorted two-dimensional (2D) honeycomb lattice with the monoclinic space group C2/m and lattice constants of a=5.9321 Å, b=10.2737 Å, c=6.7061 Å, α=γ=90° and β ≈107° (Supplementary Note 1), belonging to the TMPX3 family (TM: transition metal, X: S/Se) [24–30]. For the non-HE individual TMPX3 members, as shown in Fig. 1a–d, MnPS3 exhibits N´eel-type magnetic order with a propagation vector k=(0,0,0), while FePS3, CoPS3, and NiPS3 display zigzag antiferromagnetic (AFM) order with a propagation vector k=(0,1,L) where L varies with the specific TM element (Table I). The magnetic moments in these materials are confined to the ac* plane (Fig. 1e), and their precise orientations are also element-dependent (Table I). Here, a, b, and c represent the real-space vectors, while a*, b*, and c* denote reciprocal vectors. Note that c* is orthogonal to a, and b* is parallel to b. For HEPS3, which incorporates four different TM elements in equal concentrations, long-range magnetic order is hinted by magnetic susceptibility measurements at low temperatures [11], presenting a unique instance of magnetic order within a highly disordered system. Furthermore, the availability of HEPS3 single crystals enables detailed exploration of its magnetic properties.

Here, combining neutron diffraction and resonant soft x-ray scattering (RSXS) techniques, we have comprehensively investigated the magnetic ordering in HEPS3 single crystals. Neutron diffraction is a powerful tool for detecting various forms of magnetic order, including long-range and short-range types, with greater access to reciprocal space. In contrast, resonant soft x-ray scattering (RSXS), despite its limited reciprocal space coverage, achieves element-specific resolution by tuning the incident photon energy to the resonant edge of the target element. Our neutron diffraction experiments reveal the presence of three-dimensional (3D) long-range magnetic order, with a N´eel temperature of TN ≈ 72 K, coexisting with 2D magnetic signals. RSXS measurements further confirm that all four TM elements participate in the magnetic ordering through a unified phase transition. The resulting magnetic structure features element-dependent spin orientations, attributed to the competition between single-ion anisotropies and exchange interactions.

Results
Sample characterization
First, we verify the random distribution of TM elements in HEPS3 through atomic-resolved elemental mapping using scanning transmission electron microscopy (STEM) on an exfoliated HEPS3 thin flake. The sample, with a thickness of dozens of unit cells, enables the STEM mapping to be interpreted as spatial averages across multiple stacked honeycomb layers. As shown in Fig. 1f, the images reveal a homogeneous intensity distribution for each element, indicating that all elements are randomly distributed throughout the lattice. While a high-entropy scenario is well established, an anomaly indicative of magnetic phase transition is observed in the magnetic susceptibility measurements of HEPS3 at T =TN ≈72 K, followed by another transition taking place at T ≈40 K, below which the zero-field-cooling (ZFC) and field-cooling (FC) profiles split (Fig. 1g). This second transition likely originates from glassy behaviors or spin reorientations (Supplementary Note 2). Note that TN observed in HEPS3 is very close to that of non-HE MnPS3 (TN ≈78 K, see Table I). Above 80 K, the susceptibility follows Curie-Weiss behavior with a Curie-Weiss temperature of -43 K and an effective moment of 3.03 µB/site, corresponding to a saturated moment of 2.19 µB/site assuming a g-factor of 2 (Supplementary Note 2). Intriguingly, in binary or ternary TMPX3 compounds, where disorder is expected to be less significant than in HEPS3, the anomaly related to TN is more rounded, suggesting reduced correlation lengths (Fig. 1g). This observation underscores the importance of high configurational entropy in stabilizing the long-range magnetic order in HEPS3.

Neutron diffraction
To elucidate the origin of the magnetic susceptibility anomaly at TN, we conducted neutron diffraction measurements on HEPS3 single crystals. At 6 K, additional collection of Bragg peaks can be observed in the diffraction patterns alongside structural nuclear peaks that are also available at 250 K, demonstrating the emergence of magnetic ordering (Fig. 2a–d). These magnetic reflections can be described by a single propagation vector k = (0,1,0), with three equivalent domains arising from the honeycomb lattice within each van der Waals layer [31]. Detailed examination of the H and K dependence reveals that the in-plane magnetic peak widths are comparable to those of the nuclear reflections, confirming the establishment of long-range magnetic order (Fig. 2e, f). In contrast, along the L direction, in addition to the sharp peaks corresponding to 3D magnetic order, diffuse scattering is also observed (Fig. 2d, g), suggesting the simultaneous presence of 2D magnetic ordering. Note that the in-plane k vector is identical for both 3D and 2D magnetic signals, implying that the 2D signals maintain the same in-plane spin configuration and correlation characteristics as the 3D ones. The primary distinction between the 2D and 3D magnetic order is the reduced interlayer correlations. For the 3D magnetic order, adjacent layers are strongly coupled with parallel alignment of magnetic moments between neighboring planes. In contrast, the 2D magnetic order exhibits reduced or essentially decoupled layers, where the spin arrangement in one layer weakly affects neighboring layers. While stacking faults may play a role here, they cannot completely explain the observed 2D signals (Supplementary Note 3).

Regarding the temperature dependence, the intensity of the 3D magnetic signals decreases with increasing temperature, and a phase transition takes place at TN ≈ 72 K (Fig. 2h), consistent with the susceptibility measurements. The temperature dependence was fitted using I −BG ∝ (T −T)2β (BG: background), yielding a critical exponent β =0.40(5). Meanwhile, the 2D magnetic signals remain detectable above TN, persisting weakly at 90 K (Fig. 2g) before vanishing around that temperature (Fig. 2h). Through a global magnetic refinement of the 3D signals (Supplementary Note 4), we determined the preliminary spin structure of HEPS3, which exhibits zigzag magnetic order with Θ=49°, where Θ denotes the angle between spin moment and lattice a direction (Fig. 2i). The refined moment magnitude is 1.51(1) µB/site, much smaller than the average value of the non-HE individual counterparts (Table I). The reduced moment is partially attributed to the presence of 2D magnetic signals, which account for a substantial portion of the spectral weight. To make a quantitative estimation of the total static moment, we integrated the intensity of Q=(0,1,0) over L between -0.5 and 0.5, capturing both the 2D and 3D contributions (Fig. 2g). We find that the 3D signal spectral weight, obtained by fitting with a Gaussian profile, accounts for 67% of the total spectral weight. Since neutron diffraction intensity is proportional to the squared static moment, we estimate the total static moment to be around 1.85 µB/site, slightly smaller than that derived from the magnetic susceptibility (2.19 µB/site). The discrepancy may arise from fluctuating moments or element-specific spin orientations, which will be discussed subsequently. Overall, these analyses suggest that the long-range order is mostly homogeneous across the sample.

Resonant soft x-ray scattering
While long-range magnetic order in HEPS3 is confirmed by neutron diffraction, the microscopic properties, particularly the behaviors of individual TM elements, remain unclear. Note that neutron diffraction averages contributions from disordered elements, masking element-specific magnetic properties. To overcome this limitation, we employed RSXS measurements at the TM L edges, during which process 2p core electrons are resonantly excited to 3d valence orbitals and then de-excite [32]. By tuning incident photon energy to the resonance edge of the target element, we can selectively probe the magnetic signals of a specific element in the samples. This is evident in the x-ray absorption spectrum (XAS) data, which also reveals that all TM elements in HEPS3 adopt a divalent state (Supplementary Fig.11). Moreover, as the HEPS3 sample is very thin with an ab cleavage surface, 3D magnetic signals at Q=(0,1,0) were inaccessible. However, we successfully resolved 2D magnetic signals at Q=(0,1,L) with finite L (Fig. 3a). Figure 3b–e depict the RSXS scans across the 2D magnetic signals for each TM element in HEPS3. These scans reveal well-defined peak-like structures centered around K = 1 at low temperatures, which disappear as the temperature increases, consistent with the magnetic phase transition. The magnetic signals of Ni exhibit sharper peak profiles (Fig. 3e, see also Supplementary Fig. 10). However, it should be noted that Q resolution varies for different elements due to the various incident energy, penetration depth, and beam footprint. A detailed investigation of the temperature-dependent RSXS signals shows a unified magnetic phase transition, whose behaviors are in good agreement with the neutron diffraction measurements on the 2D signals (Fig. 3f). This suggests that all TM elements in HEPS3 undergo a simultaneous magnetic phase transition at the same temperature. Note that the amplitudes of the magnetic signals are affected by multiple factors, including the azimuthal angle, incident photon energy, number of electrons in the valence band, and self-absorption effects, making direct intensity comparisons between elements unreliable. While XAS data exhibit negligible L linear dichroism for all four TM elements (Supplementary Fig. 11), their magnetic signals show distinct polarization-dependent energy profiles (Fig. 3g–j). Given the strong RSXS cross-section dependence on spin orientation, these distinct behaviors imply different spin orientations for each element.

To verify these observations and quantitatively determine the spin orientations of each TM element in HEPS3, we examined the azimuthal dependence of the 2D magnetic signals by rotating the sample about the Q vector (Fig. 3a). Upon rotation, the cross-sectional profile of the magnetic RSXS signals changes for both polarization channels [33, 34]. As shown in Fig. 4, each TM element displays unique azimuthal intensity modulations, directly indicating distinct spin orientations even without theoretical modeling. Although the azimuthal scan range is restricted by hardware limitations, we can model the intensity modulation by assuming that the spin moments rotate within the ac* plane. This assumption is validated by the observed spin structures in the non-HE TMPX3 counterparts and the aforementioned neutron diffraction measurements on HEPS3. By simultaneously fitting the azimuthal dependence in both polarization channels (Methods), we derived the best fit for each TM element, the results of which are presented in Fig. 4. The resulting inclined angles, Θ, vary among elements and deviate from those observed in the non-HE TMPX3 materials (Table I). Notably, the average Θ across the four TM elements (47°) closely matches the neutron refinement result (49°), highlighting the consistency between neutron and RSXS measurements. Furthermore, the element-specific spin orientation may contribute to the reduced net spin moment derived from neutron diffraction refinement, an analysis that is based on an average spin structure.

Methods
Sample synthesis and characterization
Single-crystalline (Mn1/4Fe1/4Co1/4Ni1/4)PS3 (HEPS3) samples, as well as the binary and ternary TMPX3 compounds, were grown using the chemical vapor transport (CVT) method as detailed in the previous report [11]. Atomic-resolved EDS mapping was performed using an aberration-corrected STEM (JEM NEOARM), operated at 200 kV. As mentioned in the main text, the STEM mapping is interpreted as an average result of multiple stacked honeycomb layers, leading to a triangular arrangement considering ABC stacking. Consequently, elements that are randomly distributed throughout the lattice will display uniform intensity at each site.

Neutron diffraction experiment
All neutron diffraction measurements were conducted using the CORELLI instrument at Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL) [45, 46]. One piece of single crystal (27 mg in weight; 6×3 mm in size) was aligned first in the H0L scattering plane and subsequently in the 0KL scattering plane, utilizing monoclinic notation. Diffraction patterns were collected at 6 K, 90 K, and 250 K by rotating the sample with a fixed tilting angle. For the temperature dependence measurements, the sample position and orientations were unchanged; data were acquired with a 5 min counting time per temperature point with a step of 2 K.

RSXS experiments
The RSXS experiments were performed at the REIXS (10ID-2) beamline of the Canadian Light Source (CLS) [47] and 13-3 beamline of the Stanford Synchrotron Radiation Lightsource (SSRL) at the SLAC National Accelerator Laboratory [48]. Both have an in-vacuum 4-circle diffractometer to access the magnetic signals.

For the REIXS experiment, XAS data were collected using a silicon drift detector (SDD) at a fixed position, while RSXS signals were measured with another SDD equipped at the goniometer arm at the peak position of the L edge for each transition-metal element in HEPS3 (Supplementary Fig. 11). RSXS scans were conducted by rotating the sample at a fixed scattering angle 2θ, considering that the signal is independent of L within a small range. The x-ray energies were chosen to be 639.3 eV, 706.9 eV, 777.7 eV, and 851.9 eV for the Mn, Fe, Co, and Ni L edges, respectively. The intensity was normalized to the incoming x-ray flux. Background subtraction was performed using high-temperature data for all RSXS scans (Supplementary Fig. 12).

In the 13-3 experiment, a 2D CCD detector was employed, covering a finite range of Q. The collected signals were normalized by electron current. In Fig. 4, the data were further normalized by fluorescence to account for variations in measurement efficiency, particularly due to self-absorption effects and changes in the x-ray footprint on the sample, which is not relevant in the energy dependence presented in Fig. 3g–j. Furthermore, for the energy-dependent measurements, all diffraction angles, including the scattering angle 2θ, were fixed. Although Q varies slightly with energy, the large area of the CCD detector ensured that magnetic signals were still captured, enabling equivalent fix-Q energy scans. The azimuthal-dependent measurements shown in Fig. 4 were conducted at the peak position of the L edge (Supplementary Fig. 13). To be more specific, the x-ray energies are 638.4 eV, 707 eV, 779 eV, and 853.9 eV for the Mn, Fe, Co, and Ni L edges, respectively. For each azimuthal angle, a RSXS scan was performed by rotating the sample. The magnetic signals in the HK plane were fitted with a 2D Lorentzian function to determine the peak height. The signals along the L direction were averaged as they exhibited no significant dependence on L within the small L range investigated.

Simulation of the azimuthal dependence
Considering that the linear dichroism is negligible in HEPS3, we use a simplified model based on spherical symmetry to simulate the azimuthal dependence of the magnetic signals:
F =κ·ϵ×ϵ′·M (1)
where κ is a scale factor, ϵ and ϵ′ are the incident and emission photon polarization, respectively, and M is the spin moment. The magnetic RSXS cross-section can be obtained as I = F2. M is confined within the ac* plane and the fitting results are presented in Fig. 4. Note that for each element, a unified scale factor κ is used for different polarizations. The outgoing photon polarization is not distinguished. Thus, the simulated signals are summed over two polarization channels, σ′ and π′, for the outgoing photons. Note that magnetic signals will contribute to the σ-π′, π-π′, and π-σ′ channels but not σ-σ′ channel. The full-range calculation results for the azimuthal dependence are presented in Supplementary Fig. 14, which are simulated based on calculated motor positions, while for Fig. 4, experimental motor positions are used. The discrepancy is negligible.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper reports neutron diffraction and RSXS measurements on the high-entropy magnetic compound (Mn₁/₄Fe₁/₄Co₁/₄Ni₁/₄)PS₃. The authors find that despite strong chemical disorder, this material develops long-range zigzag antiferromagnetic order below 72 K. RSXS reveals element-specific spin orientations, showing that different transition-metal ions settle into distinct magnetic configurations. They speculate that this could be due to a competition between exchange interactions and single-ion anisotropy. The main finding is that this magnetic order lacks a periodic spin pattern but remains long-range and collective. This is potentially important for understanding magnetism in disordered or high-entropy systems. The manuscript is very well written, clear and interesting. The data is of very high quality, and the topic is relevant in the context of understanding complex magnetic orders in high-entropy materials. I am inclined to recommend this for publication in Nature Communications, but there are certain aspects that require more rigor, in order to meet the standards of a high-impact publication.\n1. From a high level, I have an issue with the title of the paper, which is misleading. If sharp magnetic Bragg peaks are observed, there is a periodicity. It may well be the case that spins of different sublattices are pointing in different directions, but they are still ordered in the same way. They all have a well-defined propagation vector. A similar situation could be found in a material with domains that have different orientation, in which case it would not be labeled as “non-periodic”. Please change the title to something more straightforward.\n2. In regards to the temperature dependence of diffuse scattering via neutrons, the diffuse component observed along L in Fig. 2e should be plotted as a function of temperature. It is unclear whether the 2D correlations persist above T_N, and whether they evolve gradually or abruptly. A temperature series of (0,1,L) cuts would help clarify this. Present it on a log scale to expose the faint tails.\n3. Along similar lines, neutron cuts should be plotted along other directions. All presented diffuse scattering is along L. Cuts along H or K, in log scale for comparison with the cut along L, would clarify if the diffuse component is genuinely 2D or anisotropic.\n4. Please show a plot that compares the widths of magnetic and structural Bragg peaks in the neutron data. Are magnetic peaks resolution-limited? If not, this would suggest a finite correlation length and should be discussed.\n5. Is there any signature of structural disorder or local distortions in diffuse x-ray diffraction? A comparison of diffuse intensity around Bragg peaks in x-ray diffraction would support the structural homogeneity assumption.\n6. The neutron refinement yields a moment of 1.51 µB, but this is an average quantity. A more nuanced discussion of how much spectral weight is in the diffuse versus 3D component, and whether the long-range order is homogeneous across the sample, is needed. This moment size should be compared to the ones obtained in magnetization curves, since these are both averaged measurements.\n7. A comparison of the magnetic Bragg peak widths between the resonant x-ray and neutron data would be very beneficial. Are the x-ray peaks broader, as one would expect because they only probe the specific element’s domains? Can this give a sense of the domain sizes of each elemental composition?\n8. Since this may be a highly variable system, data on more samples needs to be obtained and shown. For example, only one susceptibility curve is shown per composition. Please show magnetization data for multiple crystals to demonstrate sample reproducibility. Are T₁ and T₂ always present and the same? Are the anomalies consistent across several crystals? If needed, the quantities in Table 1 should be stated as statistical averages, averaging over various samples.\n9. The statement that “the magnetic origin is further validated by the resonant behaviors in their energy dependence” on page 5 is not fully correct. A structural Bragg peak may also show resonance (if needed, this can be measured). Resonant enhancement alone is not sufficient evidence of magnetic origin. Please revise or remove this statement. The real evidence of magnetic scattering is discussed in the paper (polarization/azimuthal most notably, also temperature).\n10. Could the proposed model still explain the data if there is a slight preference for the different TM ions to align along different directions (e.g., due to local distortions or partial ordering)? In other words, the authors assume that all TM ions are aligned perfectly with each other, and that still they have a different single ion anisotropy. This may not be the case. The ions may indeed have orbitals pointing along different directions, but only due to some structural distortion. A discussion of model sensitivity to such perturbations would be helpful.\n11. The discussion is compelling but remains qualitative. The schematic in Fig. 1i invokes a heuristic “J vs. Δ” phase diagram. While illustrative, this oversimplifies the physics in a multicomponent, anisotropic, exchange-frustrated system. A more realistic modeling attempt—beyond a cartoon—would strengthen the interpretation of their findings. The paper would benefit from:\na. Citations to prior work on single-ion anisotropy in the TMPX₃ family. What is known about the anisotropy of Fe²⁺ vs. Co²⁺ in similar environments? Why would it be different in this case? Are the valencies different? How do their d-orbtital occupations modify the single-ion anisotropy.\nb. Even a minimal model (Landau theory, classical spin simulations, or ab initio-derived anisotropy/exchange estimates) would help to contextualize the competition that gives rise to the observed non-periodic but ordered state.\nIn conclusion, this is an interesting and well-executed study with potentially broad relevance. However, the key claims require further support, particularly regarding the characterization of diffuse scattering and the theoretical understanding of the proposed magnetic state. Once the above issues are addressed, I would support publication.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "Yao Shen et al. used combined neutron and resonant soft x-ray scattering (RSXS) techniques to study the high-entropy (HE) honeycomb-lattice van der Waals material (Mn Fe Co Ni )PS . Surprisingly, the neutron diffraction data reveal a single propagation vector k = (0, 1, 0); while the azimuthal dependent RSXS study indicates coexisting short range magnetic orders and the spin moment directions vary with all four transition-metal elements. Overall, the experimental data quality is high; the modelling and data analysis seems solid. This is a very interesting piece of work. Because of the four different species of magnetic ions occupying the same site, short range magnetic orders are typically expected. Also, figuring out the magnetic interactions in high-entropy magnets is not straightforward. Therefore, this work, by combining neutron and resonant x-ray scattering, is quite illustrating and can be applied to investigate other HE magnets. All being said, there are some concerns need to be addressed before accepting this manuscript for publication.\n1) From the neutron diffraction data, a single propagation vector k = (0, 1, 0) is revealed. Whether the spin structure is long-range or short-range ordered, there should be some forms of periodic spin arrangement. However, the authors propose a non-periodic magnetic order, such as the picture in Fig 1h, this seems a bit confusing. The authors need to present a better and clear picture.\n2) The authors should be a bit more rigorous about the differentiation about the long-range and short-range magnetic order. For instance, in the results part on page 3, the authors claim that long-range order is indicated from the magnetic susceptibility data. However, the bulk magnetization data is not enough to support this point. This is further supported by the specific heat measurement in ref. [11], which shows a broad thermodynamic transition. More importantly, the neutron diffraction data in Fig 2 can in principle directly reveal the magnetic correlation length and the nature of the magnetic order. However, the data analysis is not strong enough the support the major points in this manuscript. I suggest more detailed analysis should be presented.\nIn order to reveal whether the magnetic ground state is 3D or 2D, the author should present the scans and fits of some typical magnetic peaks, along both the in-plane and out-of-plane directions. In addition, the experimental resolution should be specified or some comparative scans and fits of the nearby structural Bragg peaks are needed. At this point, in Fig 2e, the authors simply claim 3D and 2D signals, which seems a bit casual. For example, it is not clear whether the magnetic peaks can be fitted by simple Lorentzian peaks or not. Also, the two peaks in shaded regions, presenting 3D signals, clearly have different peak widths. In fig 2f, what is the critical exponent from the fit? All being said, the data analysis should be performed in more details. By revealing the peak widths and correlation lengths, the nature of the spin state will be more convincing.\nSome other minor comments:\n1) I don’t think the discussion about the T transition will impact much about the data and conclusions of this manuscript.\n2) In Fig 2e, using empty circles for the 250K will be better.\n3) Fig 2f, is the temperature dependent data also collected at CORELLI? Does the peak intensity represents the integrated signals? What is the sample mass and what is the counting time at each temperature? The authors may consider include some more details of the neutron experiments.\n4) In fig 3h, what is the reason that there are more than 3 peaks of the energy profile of the magnetic peak near the Fe L edge? In Fig 3j, the legend is missing.\n5) Fig 4, the authors may consider showing the experimental data first in the legend. Also, the dash lines presenting the fits of the π-pol data are not that great. The authors may consider using solid lines with different transparency or thickness or some other forms to present the data in a better way.\n6) The manuscript reports the magnetic moment of (Mn Fe Co Ni )PS is 1.5 μ /site, as determined by neutron diffraction. Since the data analysis is based on an average spin structure, if the spin moment directions are different among the different magnetic ions, which is also supported by the resonant x-ray scattering study, the net spin moment size might be reduced as well. This might be the major reason why the spin moment size is much reduced, in comparison with the effects from the 2D magnetic order and the disorders.\n7) The authors should use the symbols, like the angle , consistently in this manuscript, including the supplementary file. Also, a scale factor K is used to calculate the magnetic signals of the resonant x-ray scattering data. This might be confused with the HKL notations of momenta.\n8) In the main text, it seems the discussion about the mechanism in Fig 1i is very limited. If this panel is included in the main text, more discussion is needed.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Reviewer 1:\n1. Reviewer:\nThis paper reports neutron diffraction and RSXS measurements on the high-entropy magnetic\ncompound (Mn1/4Fe1/4Co1/4Ni1/4)PS3. The authors find that despite strong chemical\ndisorder, this material develops long-range zigzag antiferromagnetic order below 72 K. RSXS\nreveals element-specific spin orientations, showing that different transition-metal\nions settle into distinct magnetic configurations. They speculate that this could be due to a\ncompetition between exchange interactions and single-ion anisotropy. The main finding is that this magnetic\norder lacks a periodic spin pattern but remains long-range and collective. This is potentially\nimportant for understanding magnetism in disordered or high-entropy systems.\nThe manuscript is very well written, clear and interesting. The data is of very high quality, and\nthe topic is relevant in the context of understanding complex magnetic orders in high-entropy\nmaterials. I am inclined to recommend this for publication in Nature Communications, but there\nare certain aspects that require more rigor, in order to meet the standards of a high-impact\npublication.\n1. Our answer:\nWe appreciate your support of recognizing the significance of our work and recommending\npublication in Nature Communications.\n2. Reviewer:\nFrom a high level, I have an issue with the title of the paper, which is misleading. If sharp\nmagnetic Bragg peaks are observed, there is a periodicity. It may well be the case that spins of\ndifferent sublattices are pointing in different directions, but they are still ordered in the same\nway. They all have a well-defined propagation vector. A similar situation could be found in a\nmaterial with domains that have different orientation, in which case it would not be labeled as\n“non-periodic”. Please change the title to something more straightforward.\n2. Our answer:\nThank you for the comments. The magnetic order observed here is highly unusual. As you\npointed out, it features well-defined magnetic Bragg peaks and propagation vector, indicating\na periodicity, while spin orientations are distinct for different elements. The situation is slightly\ndifferent from domains in conventional materials characterized by microscopic repeating\npattern but discontinuous macroscopic periodicity. Here, as the element distribution is\natomically disordered, as evidenced by neutron and X-ray diffraction, as well as STEM, even\nthe microscopic repeating pattern is missing.\nTo avoid misleading, we have changed the title from\n“Non-periodic magnetic order in a high-entropy antiferromagnet”\nto\n“Long-range magnetic order with disordered spin orientations in a high-entropy\nantiferromagnet”\n3. Reviewer:\nIn regards to the temperature dependence of diffuse scattering via neutrons, the diffuse\ncomponent observed along L in Fig. 2e should be plotted as a function of temperature. It is\nunclear whether the 2D correlations persist above T_N, and whether they evolve gradually or\nabruptly. A temperature series of (0,1,L) cuts would help clarify this. Present it on a log scale\nto expose the faint tails.\n3. Our answer:\nThank you for the suggestions. We have added the 90 K L cut into the revised Fig. 2g, which\nexhibits weak but finite intensity, indicating that 2D correlations persist above T . This can be\nN\nseen more clearly in the detailed temperature dependence of Q=(1/2, 1/2, 0) intensity added\ninto the revised Fig. 2h, which also reveals that the 2D correlations evolve gradually with\ntemperature:\n“g, Q cuts along L direction across the magnetic signals. The shaded area denotes the 3D\nmagnetic signals, which exhibit different peak widths due to different contributions of\nsample mosaicity. The 250 K data can be treated as a background reference. Note that the\nintensities are presented on a log scale. h, Temperature dependence of the integrated\nintensities of 3D magnetic signals at Q = (0, 1, 1) and 2D magnetic signals at Q = (0.5,\n0.5, 0), which corresponds to Q = (0,−1, 1/6) in another domain [31]. The solid line is a\nfit to I − BG (T − T)2β (BG: background), and the dashed line is a guide for the eye.”\nN\n∝\nCorrespondingly, we have added the following sentences to the revised manuscript:\n“Regarding the temperature dependence, the intensity of the 3D magnetic signals\ndecreases with increasing temperature, and a phase transition takes place at T ≈ 72 K (Fig.\nN\n2h), consistent with the susceptibility measurements. The temperature dependence was\nfitted using I − BG (T − T)2β (BG: background), yielding a critical exponent β = 0.40(5).\nN\nMeanwhile, the 2D magnetic signals remain detectable above T , persisting weakly at 90\nN\n∝\nK (Fig. 2g) before vanishing around that temperature (Fig. 2h).”\n4. Reviewer:\nAlong similar lines, neutron cuts should be plotted along other directions. All presented diffuse\nscattering is along L. Cuts along H or K, in log scale for comparison with the cut along L, would\nclarify if the diffuse component is genuinely 2D or anisotropic.\n4. Our answer:\nThank you for your suggestions. As per your instruction, we have added the Q cuts along H and\nK directions in log scale in the revised Fig. 2, indicating the absence of diffuse scattering in HK\nplane:\nIn addition, we include the H and K cuts for different L in the revised Supplementary:\n“\n“FIG. S10. Magnetic peak widths obtained from neutron diffraction and RSXS. a,\nOne-dimensional Q cuts along H direction across Q = (0, 1, L) with various L. The dots\nrepresent neutron diffraction data, and the solid lines are fits with Gaussian profiles. b, Q\ncuts along K direction.”\n”\n5. Reviewer:\nPlease show a plot that compares the widths of magnetic and structural Bragg peaks in the\nneutron data. Are magnetic peaks resolution-limited? If not, this would suggest a finite\ncorrelation length and should be discussed.\n5. Our answer:\nThank you for your considerate suggestions. In the revised Fig. 2, we have added the 1D Q cuts\nalong H and K directions for both the magnetic and structural Bragg peaks, which,\nsupplemented by Gaussian fitting, exhibit comparable peak widths, indicating long-range\nmagnetic order:\n“e, f, One-dimensional Q cuts along H and K directions, respectively, across the nuclear\n[Q = (0, 2, 0)] and magnetic reflections [Q = (0, 1, 0)] at the indicated temperatures. The\nsolid lines are fits with Gaussian profiles, yielding FWHM (in unit of r.l.u.) of 0.0539(6)\n(nuclear) and 0.0496(5) (magnetic) along H, and 0.070(1) (nuclear) and 0.068(1)\n(magnetic) along K.”\nWe have also added the following sentences to the revised manuscript:\n“Detailed examination of the H and K dependence reveals that the in-plane magnetic peak\nwidths are comparable to those of the nuclear reflections, confirming the establishment of\nlong-range magnetic order (Fig. 2e, f).”\nThe comparison along L direction is available as Fig. S5c in the newly added section on stacking\nfaults, which also shows comparable peak width for the magnetic and structural signals:\n“c, One-dimensional Q cuts along the L direction. The blue, red, and green vertical ticks\ndenote nuclear reflections originating from three distinct crystallographic domains.”\n6. Reviewer:\nIs there any signature of structural disorder or local distortions in diffuse x-ray diffraction? A\ncomparison of diffuse intensity around Bragg peaks in x-ray diffraction would support the\nstructural homogeneity assumption.\n6. Our answer:\nThank you for your reminding. Since the nuclear peaks along H and K directions can be well\ndescribed by Gaussian profiles, we expect negligible in-plane distortion. However, disorder is\nexpected to exist considering the high-entropy nature of this material, which goes beyond the\nresolution of our techniques. Regarding the out-of-plane direction, we have rechecked the\nneutron diffraction data and performed additional x-ray diffraction measurements on the single\ncrystals and saw clear indications of stacking faults. The results are presented as a whole new\nsection in the revised Supplementary:\n“3. STRUCTURAL DISORDER\nHere we examine structural disorder in HEPS , particularly stacking faults within its\n3\nlayered architecture. In an ideal TMPX structure, honeycomb layers exhibit perfect A-B-\nB-A-B stacking can occur, leading to stacking fault disorder that manifests as diffuse\nscattering along the L direction in diffraction patterns. Figure S5a&b present the neutron\ndiffraction and x-ray diffraction (XRD) patterns in the 0KL plane. While structural\nreflections satisfying H + K = 6n, where n is an integer, exhibit no indication of diffuse\nscattering, diffusive signals appear along L for Q = (0, −4, L) and Q = (0, −2, L), a hallmark\nof stacking faults. This can be seen more clearly in the L cuts presented in Fig. S5c&d.\nNote that stacking fault effects cancel out for H + K = 6n reflections [1]. Additionally, the\nhoneycomb lattice symmetry naturally gives rise to three equivalent structural domains\n[2]. In our neutron diffraction data collected from a large single crystal (several millimeters\nin size), this multidomain configuration produces nuclear signals at non-integer L positions\n(Fig. S5c). Conversely, XRD measurements performed on a smaller crystal (≈ 100 μm)\nusing a laboratory diffractometer revealed single-domain characteristics, as indicated by\nthe absence of non-integer L signals (Fig. S5d). Notably, the magnetic diffuse scattering\nexhibits slightly broader features compared to the stacking-fault induced nuclear diffuse\nsignals (Fig. S5c), suggesting contributions from other sources for the two-dimensional\n(2D) magnetic signals, such as reduced out-of-plane magnetic correlations.\nFIG. S5. Stacking fault characterization in HEPS . a, b, Neutron diffraction and XRD\n3\npatterns in the 0KL plane, respectively. Magnetic signals appear at Q = (0, ±1, L), while\nall other reflections correspond to nuclear (structural) contributions. c, d, One-dimensional\nQ cuts along the L direction. The blue, red, and green vertical ticks denote nuclear\nreflections originating from three distinct crystallographic domains.”\n7. Reviewer:\nThe neutron refinement yields a moment of 1.51 µB, but this is an average quantity. A more\nnuanced discussion of how much spectral weight is in the diffuse versus 3D component, and\nwhether the long-range order is homogeneous across the sample, is needed. This moment size\nshould be compared to the ones obtained in magnetization curves, since these are both averaged\nmeasurements.\n7. Our answer:\nThis is a good point. Taking Q=(0, 1, 0) as an example, we have compared the spectral weights\nof different components and estimate that the 3D magnetic signals occupy 67% of the total\nspectral weigh, indicating a total static moment of 1.85 µ , which is slightly smaller than the\nB\none obtained from the susceptibility measurements (2.19 µ ). These discussions are added to\nB\nthe revised manuscript:\n“Above 80 K, the susceptibility follows Curie-Weiss behavior with a Curie-Weiss\ntemperature of -43 K and an effective moment of 3.03 μ /site, corresponding to a saturated\nB\nmoment of 2.19 μ /site assuming a g-factor of 2 (Supplementary Note 2).”\nB\n“The reduced moment is partially attributed to the presence of 2D magnetic signals, which\naccount for a substantial portion of the spectral weight. To make a quantitative estimation\nof the total static moment, we integrated the intensity of Q = (0, 1, 0) over L between -0.5\nand 0.5, capturing both the 2D and 3D contributions (Fig. 2g). We find that the 3D signal\nspectral weight, obtained by fitting with a Gaussian profile, accounts for 67% of the total\nspectral weight. Since neutron diffraction intensity is proportional to the squared static\nmoment, we estimate the total static moment to be around 1.85 μ /site, slightly smaller\nB\nthan that derived from the magnetic susceptibility (2.19 μ /site). The discrepancy may\nB\narise from fluctuating moments or element-specific spin orientations, which will be\ndiscussed subsequently. Overall, these analyses suggest that the long-range order is mostly\nhomogeneous across the sample.”\nAdditionally, the Curie-Weiss fitting is available in the revised Supplementary:\n“Above 80 K, the magnetic susceptibility follows Curie-Weiss behavior (Fig. S4), with a\nCurie-Weiss temperature of -43 K and a Curie constant of 1.147 emu·K/mol. This\ncorresponds to an effective moment of 3.03 μ /site, implying a saturated moment of 2.19\nB\nμ /site assuming a g-factor of 2. This value is slightly higher than that derived from neutron\nB\ndiffraction measurements.\nFIG. S4. Curie-Weiss fit of the magnetic susceptibility above 80 K.”\nFurthermore, as pointed out by Reviewer 3, the element-specific spin orientations may also\ncontribute to the reduced net spin moment derived from neutron diffraction, an analysis that is\nbased on an average spin structure. We have added this point to the revised version:\n“Furthermore, the element-specific spin orientation may contribute to the reduced net spin\nmoment derived from neutron diffraction refinement, an analysis that is based on an\naverage spin structure.”\n8. Reviewer:\nA comparison of the magnetic Bragg peak widths between the resonant x-ray and neutron data\nwould be very beneficial. Are the x-ray peaks broader, as one would expect because they only\nprobe the specific element’s domains? Can this give a sense of the domain sizes of each\nelemental composition?\n8. Our answer:\nThank you for the questions. We have added the x-ray peak widths in the revised Supplementary,\nwhich show that different elements exhibit various peak widths:\n“FIG. S10. … c, L dependent peak widths obtained from fitting. In the neutron diffraction\ndata, the 2D magnetic peak width decreases when approaching the 3D signals at L = 0 and\nL = 1. This behavior is not observed in RSXS data since RSXS probes element-specific\nmagnetic correlations. Furthermore, the Q resolution in RSXS varies across different\nelements due to differences in incident energy, penetration depth, and beam footprint,\ncomplicating direct comparisons of peak widths between elements and with neutron\ndiffraction results.”\n”\nThis observation potentially indicates that domain size might vary with elements. However, it\nshould be noted that the Q resolution in RSXS varies across different elements due to\ndifferences in incident energy, penetration depth, and beam footprint, complicating direct\ncomparisons of peak widths between elements and with neutron diffraction results. We have\nadded the following sentences to the revised manuscript:\n“The magnetic signals of Ni exhibit sharper peak profiles (Fig. 3e, see also Supplementary\nFig. 10). However, it should be noted that Q resolution varies for different elements due\nto the various incident energy, penetration depth, and beam footprint.”\n9. Reviewer:\nSince this may be a highly variable system, data on more samples needs to be obtained and\nshown. For example, only one susceptibility curve is shown per composition. Please show\nmagnetization data for multiple crystals to demonstrate sample reproducibility. Are T1 and T2\nalways present and the same? Are the anomalies consistent across several crystals? If needed,\nthe quantities in Table 1 should be stated as statistical averages, averaging over various samples.\n9. Our answer:\nFollowing your suggestions, we have measured multiple samples, the results of which are\npresented in the revised Supplementary:\n“To confirm the reproducibility of the phase transitions, we repeat the magnetic\nsusceptibility measurements on several HEPS single crystals, obtaining consistent results\n3\n(Fig. S3).\nFIG. S3. Magnetic susceptibility measurements of multiple different HEPS single\n3\ncrystals.”\nAs shown in this figure, T , T and anomalies are qualitatively consistent across different\n1 2\ncrystals while minor deviations exist, which, however, do not affect the main conclusions of\nour paper.\nRegarding the quantities in Table 1, for the non-high-entropy TMPX parameters, they are\n3\nobtained from earlier reports. For the HEPS parameters, we display the results obtained from\n3\nthe single crystal we used for neutron diffraction measurements, which is expected to represent\nthe intrinsic properties of this material considering the consistent behaviors in magnetization.\n10. Reviewer:\nThe statement that “the magnetic origin is further validated by the resonant behaviors in their\nenergy dependence” on page 5 is not fully correct. A structural Bragg peak may also show\nresonance (if needed, this can be measured). Resonant enhancement alone is not sufficient\nevidence of magnetic origin. Please revise or remove this statement. The real evidence of\nmagnetic scattering is discussed in the paper (polarization/azimuthal most notably, also\ntemperature).\n10. Our answer:\nThank you for pointing this out. Indeed, structural Bragg peaks may show resonance due to\nanisotropic tensor of susceptibility (ATS). We have removed these sentences as suggested:\n“The magnetic origin of these signals is further validated by the resonant behaviors in their\nenergy dependence (Fig. 3g–j).”\n11. Reviewer:\nCould the proposed model still explain the data if there is a slight preference for the different\nTM ions to align along different directions (e.g., due to local distortions or partial ordering)? In\nother words, the authors assume that all TM ions are aligned perfectly with each other, and that\nstill they have a different single ion anisotropy. This may not be the case. The ions may indeed\nhave orbitals pointing along different directions, but only due to some structural distortion. A\ndiscussion of model sensitivity to such perturbations would be helpful.\n11. Our answer:\nThank you for the thoughtful suggestions. For HEPS , the single-ion anisotropy is determined\n3\nby high-energy parameters such as cubic crystal electric field (CEF) splitting (10Dq), spin-orbit\ncoupling (SOC), and trigonal distortion, as well as low-energy parameters such as lattice\ndistortion beyond trigonal fields. For the high-energy parameters, the resulting single-ion\nanisotropy can be analyzed using exact diagonalization (ED) approach. By doing so, we find\nthat for the same trigonal field, Mn2+ and Ni2+ are almost isotropic, while Fe2+ exhibits easy-\naxis anisotropy and Co2+ exhibits easy-plane anisotropy due to their different electronic counts.\nRegarding the low-energy parameters, while it is difficult to model such lattice distortion,\nqualitative discussions can be made to demonstrate that even for the same type of elements, the\nsingle-ion anisotropy can vary from site to site. Nevertheless, the variation is subtle, much less\npronounced than the effect of high-energy parameters. To demonstrate these points, we have\nadded a new note in the Supplementary Information:\n“5. SINGLE-ION ANISOTROPY\nSingle-ion anisotropy arises from the combined effects of electronic filling, crystal electric\nfield (CEF) splitting, and spin-orbit coupling (SOC). Here, supplemented with exact\ndiagonalization (ED) calculations of atomic models, we demonstrate how these parameters,\nparticularly electronic filling and trigonal distortion, influence the single-ion anisotropy.\nFor a TMO octahedron, the cubic CEF splits the ten 3d orbitals into a high-energy e\n6 g\nmanifold and a low-energy t manifold, separated by an energy difference of 10D .\n2g q\nTrigonal distortion, which is relevant for HEPS , further splits the t states while leaving\n3 2g\nthe e manifold unaffected. Since the TMO octahedra in HEPS are elongated, the\ng 6 3\ncorresponding trigonal field is positive (δ > 0), splitting the t manifold into a low-energy\n2g\nsinglet and a high-energy doublet. In contrast, the neighboring magnetic cations induce a\nnegative trigonal field (δ < 0) [4]. Based on the single-ion anisotropy observed in TMPX ,\n3\nwe conclude that in HEPS , the overall trigonal field is negative. Here, only the orbital\n3\ndegree of freedom is considered. Incorporating SOC, which is weak but finite for 3d\nelements, further reduces the symmetry.\nWe now focus on the ED calculations, performed using an atomic model that includes all\nten spin-resolved 3d orbitals. The Hund’s coupling is set to 1 eV, and the cubic CEF\nsplitting is fixed at 10D = 1 eV. The SOC strength is varied according to the atomic values\nq\nof the respective ions. For the Mn2+ ion (3d5) in the high-spin state, the half-filled 3d shell\nleads to a ground state with S = 5/2 (n = 6, n is the degeneracy degree) and quenched\norbital momentum, rendering it insensitive to trigonal distortion (Fig. S7a). The ground\nstate exhibits isotropic Zeeman splitting under magnetic fields applied along different\ndirections, indicating negligible single-ion anisotropy. For the Fe2+ ion (3d6), in the\nabsence of trigonal distortion, the combination of cubic CEF and SOC yields a triplet\nground state (n = 3) and a nearly degenerate quintuplet excited state (n = 5). Note that\nfinite SOC breaks down the S = 2 state here. Applying trigonal distortion, the triplet ground\nstate splits into a singlet and a doublet (Fig. S7b). If exchange interactions are sufficiently\nstrong, these states recombine into a triplet, and the intrinsic energy gap can be mapped\ninto the single-ion anisotropy. Upon applying a magnetic field, the energy change is more\npronounced along the c direction, indicating easy-axis anisotropy, consistent with the spin\norientation observed in∗ FePS .\nwell-defined doublet, which remains robust with trigonal distortion but develops distinct\nanisotropy (Fig. S7c). The Zeeman splitting is less pronounced when the magnetic field is\napplied along the c direction, indicating easy-plane anisotropy, in line with the spin\norientation observed∗ in CoPS .\neasy-axis anisotropy, whereas Co2+ prefers easy-plane anisotropy due to their distinct\nelectronic filling.\nSimilar to Mn2+, the Ni2+ ion (3d8) with a half-filled e manifold exhibits quenched orbital\ng\ndegrees of freedom, leading to a triplet ground state, which is inert to trigonal distortion\nand shows isotropic Zeeman splitting (Fig. S7d).\nIt is worth noting that thus far, we have only considered high-energy parameters, such as\ncubic CEF, SOC, and the trigonal field. These parameters cause Fe2+ and Co2+ ions to\nexhibit robust single-ion anisotropy, whereas Mn2+ and Ni2+ ions behave nearly isotropic.\nOther low-energy parameters, such as lattice distortion beyond the trigonal field, can\nintroduce further anisotropy and determine the spin orientation for Mn2+ and Ni2+. Order-\nby-disorder and anisotropic exchange interactions, such as Kitaev terms, may also play a\nrole [5]. Nevertheless, we can conclude that the spin orientations for Fe2+ and Co2+ ions\nare more resistant to competition with exchange interactions due to their substantial single-\nion anisotropy.\nFurthermore, we would like to emphasize that the determined spin orientation for each\nelement is an average effect. For ions of the same element, local distortion varies from site\nto site due to atomic disorder intrinsic to high-entropy materials. As an example, the\ndetailed CEF for Mn2+ ions depends on whether neighboring ions are Mn2+, Fe2+, Co2+, or\nNi2+. Consequently, single-ion anisotropies may vary across the lattice for each element.\nNonetheless, the variation is subtle, and our data unambiguously demonstrate that the\naverage spin orientations for different elements are distinct.\nFIG. S7. Exact diagonalization calculations of atomic models. a, Left panel: energy\nlevel diagram for a Mn2+ (d5) ion as a function of trigonal distortion δ. Here, the cubic\ncrystal field splitting 10D is fixed to 1 eV, and the spin-orbit coupling is fixed to the\nq\natomic value. Note that n is the degree of degeneracy. Right panel: Zeeman splitting as a\nfunction of external magnetic fields applied parallel and perpendicular to the c direction,\nrespectively, with trigonal distortion δ = −20 meV. b-d, Same as a but for Fe2+∗ (d6), Co2+\n(d7), and Ni2+ (d8), respectively.”\n12. Reviewer:\nThe discussion is compelling but remains qualitative. The schematic in Fig. 1i invokes a\nheuristic “J vs. Δ” phase diagram. While illustrative, this oversimplifies the physics in a\nmulticomponent, anisotropic, exchange-frustrated system. A more realistic modeling attempt—\nbeyond a cartoon—would strengthen the interpretation of their findings. The paper would\nbenefit from:\n12. Our answer:\nThank you for the suggestions. In the following, we provide more modeling attempts to\ndemonstrate the origin of single-ion anisotropy for each element and their competition with\nexchange interactions.\n13. Reviewer:\nCitations to prior work on single-ion anisotropy in the TMPX3 family. What is known about\nthe anisotropy of Fe2+ vs. Co2+ in similar environments? Why would it be different in this\ncase? Are the valencies different? How do their d-orbtital occupations modify the single-ion\nanisotropy.\n13. Our answer:\nBased on the spin structure determined for TMPX (illustrated in Fig. 1a-d and Table I), Mn2+\n3\nand Fe2+ tend to exhibit easy-axis anisotropy while Co2+ and Ni2+ favor easy-plane anisotropy.\nFurthermore, the analysis of their spin dynamics measured by inelastic neutron scattering\ndemonstrates that the anisotropy of Mn2+ and Ni2+ is negligible while Fe2+ and Co2+ show robust\nsingle-ion anisotropy. Through ED calculations mentioned earlier, we prove that this is indeed\ndue to the difference in d-orbital occupations which respond distinctly to the same trigonal\ndistortion. In addition to the newly added Supplementary Note on ED calculations, we have\nchanged these sentences in the main text from:\n“At the local level, each TM element in HEPS adopts a preferential spin orientation\n3\ngoverned by single-ion anisotropy, which is shaped by the ionic environment, electronic\nhoppings, and potentially spin-orbit coupling.\n…\nNote that the single-ion anisotropy is least profound for Mn2+ and Ni2+, which have half-\nfilled 3d and e shells, respectively, making their spin orientations less resistant to\ng\ncompetition with exchange interactions.”\nto\n“At the local level, each TM element in HEPS adopts a preferential spin orientation\n3\ngoverned by single-ion anisotropy, which is shaped by the ionic environment, electronic\nhoppings, and potentially spin-orbit coupling. Based on the magnetic structure and spin\ndynamics of TMPX probed by neutron scattering, it is concluded that Fe2+ and Co2+ ions\n3\nexhibit robust easy-axis and easy-plane anisotropy, respectively, while Mn2+ and Ni2+ ions\nare mostly isotropic [28, 31, 36, 37, 39, 41–43]. This is due to their different d-orbital\noccupations. For Mn2+ and Ni2+ ions, which have half-filled 3d and e shells, respectively,\ng\norbital degrees of freedom are mostly quenched, leading to negligible anisotropy, whereas\nFe2+ and Co2+ ions tend to exhibit robust but distinct anisotropy due to combined spin-\norbit coupling and trigonal distortion (Supplementary Note 5).\n…\nNote that the single-ion anisotropy is least profound for Mn2+ and Ni2+, making their spin\norientations less resistant to competition with exchange interactions.”\n14. Reviewer:\nEven a minimal model (Landau theory, classical spin simulations, or ab initio-derived\nanisotropy/exchange estimates) would help to contextualize the competition that gives rise to\nthe observed non-periodic but ordered state.\n14. Our answer:\nDue to the extreme complexity of high-entropy materials arising from their intrinsic atomic\ndisorder, so far there is no effective modeling approach that can well describe their physical\nproperties, including electronic behaviors, magnetism or mechanical performance.\nNevertheless, we agree that appropriate modeling is critical to contextualize the competition\nand strengthen the interpretation of our conclusions. Thus, we adopted a simplified toy model\nto explore the competition between single-ion anisotropy and exchange interactions, which is\navailable as a newly added Supplementary Note:\n“6. COMPETITION BETWEEN SINGLE-ION ANISOTROPY AND EXCHANGE\nINTERACTIONS\nTo demonstrate the competition between single-ion anisotropy and exchange interactions,\nwe construct a toy model: an antiferromagnetic spin chain composed of two types of atoms\narranged alternatively, labeled as Spin 1 and Spin 2. We adopt the Hamiltonian:\nwhere J is the intra-chain exchange interaction, ij denotes bond sums along the chain,\nand Δ and Δ are single-ion anisotropies for Spin 1 and Spin 2, respectively. To reflect the\n1 2\n⟨ ⟩\nco-existence and competition of easy-plane and easy-axis anisotropies in HEPS , here,\n3\nspin 1 is set to present strong easy-axis anisotropy (Δ = −1) and Spin 2 intermediate easy-\n1\nplane anisotropy (Δ = 1/2). The Hamiltonian is solved within the mean-field framework.\ntheir single-ion anisotropy (Fig. S8). We define Θ as the angle between the spin and the x\ndirection, following the definition in the main text. Thus, Θ = 90◦ for Spin 1 and Θ = 0◦\n1 2\nfor Spin 2.\nWhen J is non-zero, it favors antiparallel alignment for the Spin 1 and Spin 2 sublattices,\nwhich competes with the single-ion anisotropy. Consequently, Spin 1 starts to rotate\ntoward the x axis (Θ < 90◦) and Spin 2 rotates toward the z axis (Θ > 0◦). As Δ is larger\n1 2 1\nthan Δ , Θ is more robust than Θ .\n2 1 2\nWhen J is sufficiently large, it enforces an antiparallel alignment for both Spin 1 and Spin\n2, making them aligned along the z direction due to the stronger single-ion anisotropy of\nSpin 1.\nThe situation is much more complex in real materials. There are multiple types of\nexchange interactions and single-ion anisotropies, making effective modeling difficult.\nNevertheless, our toy model here qualitatively demonstrates that the competition between\nsingle-ion anisotropy and exchange interactions can indeed trigger the element-specific\nspin orientations illustrated in the main text.\nFIG. S8. Calculated exchange interaction dependent spin orientations. We adopt an\nantiferromagnetic spin chain composed of two types of atoms arranged alternatively, with\ndistinct single-ion anisotropies. The spin orientations are then determined by tuning the\nintra-chain exchange interaction J.”\nThrough these simulations, we can see that indeed the competition between single-ion\nanisotropy and exchange interactions can modify the spin orientations and that Fe2+ and Co2+\nions, with more robust anisotropy, show spin orientations more resistance to such competition.\nWe have added these sentences to the main text:\n“This competition can be illustrated by a toy model, which demonstrates how spin\norientations are tuned by the anisotropy-to-interaction ratio (Supplementary Note 6).”\n15. Reviewer:\nIn conclusion, this is an interesting and well-executed study with potentially broad relevance.\nHowever, the key claims require further support, particularly regarding the characterization of\ndiffuse scattering and the theoretical understanding of the proposed magnetic state. Once the\nabove issues are addressed, I would support publication.\n15. Our answer:\nThank you again for your positive comments. Following your suggestions, we have provided\nfurther analysis for the diffuse scattering and theoretical understanding of the proposed magnetic order\nin this high-entropy material. We hope you find the revision satisfactory, and all the issues\naddressed appropriately.\nResponse to Reviewer 2:\n1. Reviewer:\nIn this manuscript, the authors characterize the magnetism of a high-entroy (HE)\nantiferromagnet HEPS3. This material consists of two-dimensional layers of transition metal\nions arranged in a honeycomb, with equal compositions of each transition metal distributed\nrandomly throughout (hence “high entropy”). While the four parent compounds each display\nlong-range antiferromagnetic order, it is unexpected to see long-range order in a chemically\ndisordered compound. However, using a combination of neutron diffraction and RSXS, the\nauthors were able to resolve long-range magnetic order, with each magnetic atom ordering with\na different configuration.\nThere are aspects of the paper that are convincing, but there are some points that need to be\nclarified:\n1. Our answer:\nWe thank the Referee for the thoughtful review.\n2. Reviewer:\nIt is not emphasized enough why both neutron diffraction and RSXS are used, instead of RSXS\nalone. It would be helpful to emphasize that neutron diffraction provides greater access to\nreciprocal space. Recommend inclusion of an Ewald sphere diagram for RSXS in the SI.\n2. Our answer:\nThank you for the suggestions. To emphasize the importance of combining neutron diffraction\nand RSXS, we have changed the sentences from\n“Neutron diffraction is a powerful tool for detecting various forms of magnetic order,\nwhile resonant soft x-ray scattering (RSXS) achieves element-specific resolution by tuning\nthe incident photon energy to the resonant edge of the target element.”\nto\n“Neutron diffraction is a powerful tool for detecting various forms of magnetic order,\nincluding long-range and short-range types, with greater access to reciprocal space. In\ncontrast, resonant soft x-ray scattering (RSXS), despite its limited reciprocal space\ncoverage, achieves element-specific resolution by tuning the incident photon energy to the\nresonant edge of the target element.”\nas suggested.\nIn addition, we have added the reciprocal space coverage of Ni L3-edge RSXS to Fig. S2b:\n“b, Reciprocal space projected onto the ab plane. The dashed lines outline the Brillouin\nzones for the hexagonal and monoclinic notations. The diamond marker denotes a 3D\nmagnetic peak. The green circle illustrates the reciprocal space that can be accessed by Ni\nL -edge RSXS. TM, transition metal.”\n3\n3. Reviewer:\nIn susceptibility measurements, we see two phase transitions at 72K and 40K. However, in both\nthe neutron diffraction and RSXS, ordering is only seen at 72K. What could be happening at\n40K? Why doesn’t the neutron/RSXS data reflect this transition as well?\n3. Our answer:\nThis is an interesting question. Our neutron diffraction and resonant soft x‑ray scattering (RSXS)\nmeasurements unambiguously demonstrate that the transition at 72 K originates from the\nlong‑range magnetic order. By contrast, the nature of the 40 K transition remains uncertain,\nalthough we can formulate some tentative expectations. Below 40 K, the zero‑field‑cooling\n(ZFC) and field‑cooling (FC) curves split, indicating spin‑glass behaviors or spin reorientations.\nHowever, magnetic susceptibility and neutron diffraction (as well RSXS) probe the magnetic\nresponses on different length and time scales. Thus, it is possible that the process corresponding\nto the 40 K transition happens on scales beyond the momentum and temporal resolution of\nconventional neutron and x‑ray scattering techniques, making the investigation on this\ntransition fall beyond the scope of the present work. We have added these sentences to the\nrevised Supplementary:\n“Our neutron diffraction and resonant soft x-ray scattering (RSXS) measurements\nunambiguously demonstrate that the transition at 72 K originates from the long-range\nmagnetic order. By contrast, the nature of the 40 K transition remains uncertain, but we\ncan formulate some tentative expectations. Below 40 K, the zero-field-cooling (ZFC) and\nfield-cooling (FC) curves split, indicating spin-glass behaviors or spin reorientations.\nHowever, magnetic susceptibility and neutron diffraction (as well RSXS) probe the\nmagnetic responses on different length and time scales. Thus, it is possible that the process\ncorresponding to the 40 K transition happens on scales beyond the momentum and\ntemporal resolution of conventional neutron and x‑ray scattering techniques, making the\ninvestigation of this transition fall beyond the scope of the present work.”\n4. Reviewer:\nThe distinction between the “2D” and “3D” magnetic orders is unclear to me in the final\nmagnetic order diagram.\n4. Our answer:\nThank you for bringing this to attention. The primary distinction between the 3D and 2D\nmagnetic order is the inter-layer correlations. For the 3D magnetic order, adjacent layers are\ncoupled such that moments on neighboring planes are parallel, leading to sharp magnetic Bragg\npeaks along both the in-plane (H, K) and out-of-plane (L) directions. By contrast, for the 2D\nmagnetic order, the inter-layer coupling is reduced; the spin pattern in one layer weakly\ninfluences the arrangement in adjacent layers. Correspondingly, the magnetic signals are\ndiffusive along the out-of-plane (L) direction. The van‑der‑Waals crystals under current study\nare proximately two‑dimensional. Thus, our discussion is restricted to the spin configuration\nand orientation within a single honeycomb layer, while the inter-layer coupling is omitted, as\nwe note in the main text: “the in-plane k vector is identical for both 3D and 2D magnetic signals,\nimplying that the 2D signals share the same in-plane spin arrangement and correlation\ncharacteristics as the 3D ones”. To avoid misleading, we have added these sentences to the\nrevised manuscript:\n“The primary distinction between the 2D and 3D magnetic order is the reduced interlayer\ncorrelations. For the 3D magnetic order, adjacent layers are strongly coupled with parallel\nalignment of magnetic moments between neighboring planes. In contrast, the 2D magnetic\norder exhibits reduced or essentially decoupled layers, where the spin arrangement in one\nlayer weakly affects neighboring layers. While stacking faults may play a role here, they\ncannot completely explain the observed 2D signals (Supplementary Note 3).”\n5. Reviewer:\nThe azimuthal data is unconvincing with only 40° of azimuth. I am convinced that there is long-\nrange ordering in this HE material, but the differences in orientations of the moments in each\nelement are less convincing.\n5. Our answer:\nThe azimuthal range of 40 degrees is imposed by the experimental hardware. We acknowledge\nthat, when only a single x-ray polarization channel is recorded, such limited angular coverage\nis insufficient to uniquely determine the spin orientation. To overcome this limitation, we\nmeasured the azimuthal dependence in both the σ and π polarization channels and performed a\nsimultaneous fit to the two datasets. In the fitting routine we not only model the variation of the\nmagnetic intensity against azimuthal angle for each channel but also consider the relative\nintensity ratio between the channels. The combined information from the azimuthal dependence\nand the channel-dependent intensity ratio provides a robust, unambiguous determination of the\nspin directions. This analysis is illustrated in Supplementary Fig. S14, which has been expanded\nin the revised version, showing how the spin orientation governs the azimuthal profiles in the\ntwo polarization channels:\n6. Reviewer:\nSpeculation is made as to the mechanisms behind this long-range order, but there is no strong\nconclusion.\n6. Our answer:\nThank you for your comments. We would like to emphasize that high-entropy materials are\nintrinsically disordered at the atomic scale, making their electronic structure and magnetic\ninteractions exceptionally complex. Consequently, a quantitative theoretical framework is\npresently lacking. Because of this, most studies in literature rely on experimental exploration\nwithout the benefit of a robust theoretical underpinning. Nevertheless, developing tractable\nmodels—even highly simplified toy models—is essential for gaining insight into the\nfundamental driving forces behind the unconventional magnetic order in these systems.\nAccordingly, we have constructed several such models to explore possible mechanisms:\n1. We consider an atomic model involving Hund’s coupling, cubic crystal electric field splitting\n(CEF), spin-orbit coupling (SOC) and trigonal distortion and solve it using exact\ndiagonalization (ED) approach to understand the single-ion anisotropy of each element in\nHEPS3. This leads to a newly added Supplementary Note:\n“5. SINGLE-ION ANISOTROPY\nSingle-ion anisotropy arises from the combined effects of electronic filling, crystal electric\nfield (CEF) splitting, and spin-orbit coupling (SOC). Here, supplemented with exact\ndiagonalization (ED) calculations of atomic models, we demonstrate how these parameters,\nparticularly electronic filling and trigonal distortion, influence the single-ion anisotropy.\nFor a TMO octahedron, the cubic CEF splits the ten 3d orbitals into a high-energy e\n6 g\nmanifold and a low-energy t manifold, separated by an energy difference of 10D .\n2g q\nTrigonal distortion, which is relevant for HEPS , further splits the t states while leaving\n3 2g\nthe e manifold unaffected. Since the TMO octahedra in HEPS are elongated, the\ng 6 3\ncorresponding trigonal field is positive (δ > 0), splitting the t manifold into a low-energy\n2g\nsinglet and a high-energy doublet. In contrast, the neighboring magnetic cations induce a\nnegative trigonal field (δ < 0) [4]. Based on the single-ion anisotropy observed in TMPX ,\n3\nwe conclude that in HEPS , the overall trigonal field is negative. Here, only the orbital\n3\ndegree of freedom is considered. Incorporating SOC, which is weak but finite for 3d\nelements, further reduces the symmetry.\nWe now focus on the ED calculations, performed using an atomic model that includes all\nten spin-resolved 3d orbitals. The Hund’s coupling is set to 1 eV, and the cubic CEF\nsplitting is fixed at 10D = 1 eV. The SOC strength is varied according to the atomic values\nq\nof the respective ions. For the Mn2+ ion (3d5) in the high-spin state, the half-filled 3d shell\nleads to a ground state with S = 5/2 (n = 6, n is the degeneracy degree) and quenched\norbital momentum, rendering it insensitive to trigonal distortion (Fig. S7a). The ground\nstate exhibits isotropic Zeeman splitting under magnetic fields applied along different\ndirections, indicating negligible single-ion anisotropy. For the Fe2+ ion (3d6), in the\nabsence of trigonal distortion, the combination of cubic CEF and SOC yields a triplet\nground state (n = 3) and a nearly degenerate quintuplet excited state (n = 5). Note that\nfinite SOC breaks down the S = 2 state here. Applying trigonal distortion, the triplet ground\nstate splits into a singlet and a doublet (Fig. S7b). If exchange interactions are sufficiently\nstrong, these states recombine into a triplet, and the intrinsic energy gap can be mapped\ninto the single-ion anisotropy. Upon applying a magnetic field, the energy change is more\npronounced along the c direction, indicating easy-axis anisotropy, consistent with the spin\norientation observed in∗ FePS .\nwell-defined doublet, which remains robust with trigonal distortion but develops distinct\nanisotropy (Fig. S7c). The Zeeman splitting is less pronounced when the magnetic field is\napplied along the c direction, indicating easy-plane anisotropy, in line with the spin\norientation observed∗ in CoPS .\neasy-axis anisotropy, whereas Co2+ prefers easy-plane anisotropy due to their distinct\nelectronic filling.\nSimilar to Mn2+, the Ni2+ ion (3d8) with a half-filled e manifold exhibits quenched orbital\ng\ndegrees of freedom, leading to a triplet ground state, which is inert to trigonal distortion\nand shows isotropic Zeeman splitting (Fig. S7d).\nIt is worth noting that thus far, we have only considered high-energy parameters, such as\ncubic CEF, SOC, and the trigonal field. These parameters cause Fe2+ and Co2+ ions to\nexhibit robust single-ion anisotropy, whereas Mn2+ and Ni2+ ions behave nearly isotropic.\nOther low-energy parameters, such as lattice distortion beyond the trigonal field, can\nintroduce further anisotropy and determine the spin orientation for Mn2+ and Ni2+. Order-\nby-disorder and anisotropic exchange interactions, such as Kitaev terms, may also play a\nrole [5]. Nevertheless, we can conclude that the spin orientations for Fe2+ and Co2+ ions\nare more resistant to competition with exchange interactions due to their substantial single-\nion anisotropy.\nFurthermore, we would like to emphasize that the determined spin orientation for each\nelement is an average effect. For ions of the same element, local distortion varies from site\nto site due to atomic disorder intrinsic to high-entropy materials. As an example, the\ndetailed CEF for Mn2+ ions depends on whether neighboring ions are Mn2+, Fe2+, Co2+, or\nNi2+. Consequently, single-ion anisotropies may vary across the lattice for each element.\nNonetheless, the variation is subtle, and our data unambiguously demonstrate that the\naverage spin orientations for different elements are distinct.\nFIG. S7. Exact diagonalization calculations of atomic models. a, Left panel: energy\nlevel diagram for a Mn2+ (d5) ion as a function of trigonal distortion δ. Here, the cubic\ncrystal field splitting 10D is fixed to 1 eV, and the spin-orbit coupling is fixed to the\nq\natomic value. Note that n is the degree of degeneracy. Right panel: Zeeman splitting as a\nfunction of external magnetic fields applied parallel and perpendicular to the c direction,\nrespectively, with trigonal distortion δ = −20 meV. b-d, Same as a but for Fe2+∗ (d6), Co2+\n(d7), and Ni2+ (d8), respectively.”\n2. We establish a one-dimensional spin chain with two different kinds of atoms with distinct\nanisotropy to explore whether the competition between single-ion anisotropy and exchange\ninteractions can modify the spin orientations. This leads to another newly added Supplementary\nNote:\n“6. COMPETITION BETWEEN SINGLE-ION ANISOTROPY AND EXCHANGE\nINTERACTIONS\nTo demonstrate the competition between single-ion anisotropy and exchange interactions,\nwe construct a toy model: an antiferromagnetic spin chain composed of two types of atoms\narranged alternatively, labeled as Spin 1 and Spin 2. We adopt the Hamiltonian:\nwhere J is the intra-chain exchange interaction, ij denotes bond sums along the chain,\nand Δ and Δ are single-ion anisotropies for Spin 1 and Spin 2, respectively. To reflect the\n1 2\n⟨ ⟩\nco-existence and competition of easy-plane and easy-axis anisotropies in HEPS , here,\n3\nspin 1 is set to present strong easy-axis anisotropy (Δ = −1) and Spin 2 intermediate easy-\n1\nplane anisotropy (Δ = 1/2). The Hamiltonian is solved within the mean-field framework.\ntheir single-ion anisotropy (Fig. S8). We define Θ as the angle between the spin and the x\ndirection, following the definition in the main text. Thus, Θ = 90◦ for Spin 1 and Θ = 0◦\n1 2\nfor Spin 2.\nWhen J is non-zero, it favors antiparallel alignment for the Spin 1 and Spin 2 sublattices,\nwhich competes with the single-ion anisotropy. Consequently, Spin 1 starts to rotate\ntoward the x axis (Θ < 90◦) and Spin 2 rotates toward the z axis (Θ > 0◦). As Δ is larger\n1 2 1\nthan Δ , Θ is more robust than Θ .\n2 1 2\nWhen J is sufficiently large, it enforces an antiparallel alignment for both Spin 1 and Spin\n2, making them aligned along the z direction due to the stronger single-ion anisotropy of\nSpin 1.\nThe situation is much more complex in real materials. There are multiple types of\nexchange interactions and single-ion anisotropies, making effective modeling difficult.\nNevertheless, our toy model here qualitatively demonstrates that the competition between\nsingle-ion anisotropy and exchange interactions can indeed trigger the element-specific\nspin orientations illustrated in the main text.\nFIG. S8. Calculated exchange interaction dependent spin orientations. We adopt an\nantiferromagnetic spin chain composed of two types of atoms arranged alternatively, with\ndistinct single-ion anisotropies. The spin orientations are then determined by tuning the\nintra-chain exchange interaction J.”\n3. We consider a honeycomb lattice with well-defined magnetic order and by calculating the\nstructure factor we show that RSXS can probe such magnetic order even if only a quarter of the\nsites are occupied. This is available in the Supplementary Note of the original version of the\nmanuscript.\nWe also wish to emphasize that, as discussed in the main text, the high‑entropy character\nof HEPS appears to be essential for stabilizing its unconventional magnetic order. A\n3\ncomprehensive theoretical description lies beyond the scope of the present study. Nevertheless,\nwe hope that our experimental findings will motivate future theoretical investigations into the\nentropy‑driven mechanisms underlying this magnetic state.\n7. Reviewer:\nThe mechanisms in figure 1i are not discussed sufficiently.\n7. Our answer:\nThank you for pointing this out. We have added a new Supplementary Note to help interpret\nFig. 1i, which is Supplementary Note 6 presented in Question 6. Meanwhile, we cite it in the\nmain text:\n“This competition can be illustrated by a toy model, which demonstrates how spin\norientations are tuned by the anisotropy-to-interaction ratio (Supplementary Note 6).”\nAdditionally, we add more sentences to the caption of Fig. 1i to help discuss its mechanism:\n“i, Schematic diagram showing the evolution of spin orientations with different exchange\ninteraction (J) to single-ion anisotropy (Δ) ratio. When J is negligible, the spin moments\ntend to preserve their anisotropy as in the non-HE materials, e.g., Mn2+/Fe2+ and Co2+/Ni2+\nbeing almost perpendicular and parallel to the ab plane, respectively (left panel). In another\naspect, dominant J would enforce a universal parallel alignment (right panel). A\ncompromised case is realized in HEPS (middle panel, see also Supplementary Note 6).”\n3\n8. Reviewer:\nMore minor comments:\nIn the main text of the paper, please mention the energies tuned to for RSXS experiments.\n8. Our answer:\nThank you for the suggestion. We have added the energies tuned to for RSXS experiments in\nthe revised version. For the REIXS experiment:\n“The x-ray energies were chosen to be 639.3 eV, 706.9 eV, 777.7 eV, and 851.9 eV for the\nMn, Fe, Co, and Ni L edges, respectively.”\n“To be more specific, the x-ray energies are 638.4 eV, 707 eV, 779 eV, and 853.9 eV for\nthe Mn, Fe, Co, and Ni L edges, respectively.”\n3\n9. Reviewer:\nA crystal structure diagram showing where the PS3 is located would be helpful.\n9. Our answer:\nThank you for the suggestion. We have added the following figure to the supplementary:\n“FIG. S1. Lattice structure of HEPS .”\n3\n10. Reviewer:\nIt is mentioned that the FC/ZFC splitting is due to a potential spin glass. Why, then, is long\nrange order seen at 6K?\n10. Our answer:\nThis question is related to Question 3, in our answer of which we demonstrate that the FC/ZFC\nsplitting is related to spin-glass behaviors or spin reorientations, the length and time scales of\nwhich could go beyond the momentum and temporal resolution of conventional neutron and\nx‑ray scattering techniques. For example, if the change in domain size is subtle, neutron\ndiffraction may not catch the transition due to its limited momentum resolution. To avoid\nmisleading and as the third Reviewer pointed out: “I don’t think the discussion about the T2\ntransition will impact much about the data and conclusions of this manuscript”, we have\nchanged the sentences from\n“This second transition likely originates from glassy behaviors or spin reorientations. Note\nthat T observed in HEPS is very close to that of non-HE MnPS (T ≈ 78 K, see Table\nN 3 3 N\nI). Interestingly, in binary or ternary TMPX compounds, where disorder is expected to be\n3\nless significant than in HEPS , the anomaly related to T is more rounded, suggesting\n3 1\nshort-range transitions rather than long-range ones, and the overlap region (ΔT = T − T )\n1 2\nis diminished (Fig. 1g).”\nto\n“This second transition likely originates from glassy behaviors or spin reorientations\n(Supplementary Note 2). Note that T observed in HEPS is very close to that of non-HE\nN 3\nMnPS (T ≈ 78 K, see Table I). Interestingly, in binary or ternary TMPX compounds,\nwhere disorder is expected to be less significant than in HEPS , the anomaly related to T\n3 1\nis more rounded, suggesting reduced correlation length (Fig. 1g).”\nIn parallel, we have added the related discussions to the revised Supplementary Information as\nmentioned in our answer to Question 3.\n11. Reviewer:\nThere are some grammatical errors that make reading the text of the paper more difficult.\nRecommend running through a grammatical editing software.\n11. Our answer:\nThank you for your suggestions. We have revised the manuscript accordingly and hope you\nfind the current satisfactory and meet the standards of Nature Communications.\nResponse to Reviewer 3:\n1. Reviewer:\nYao Shen et al. used combined neutron and resonant soft x-ray scattering (RSXS) techniques\nto study the high-entropy (HE) honeycomb-lattice van der Waals material\n(Mn1/4Fe1/4Co1/4Ni1/4)PS3. Surprisingly, the neutron diffraction data reveal a single\npropagation vector k = (0, 1, 0); while the azimuthal dependent RSXS study indicates coexisting\nshort range magnetic orders and the spin moment directions vary with all four transition-metal\nelements. Overall, the experimental data quality is high; the modelling and data analysis seems\nsolid. This is a very interesting piece of work. Because of the four different species of magnetic\nions occupying the same site, short range magnetic orders are typically expected. Also, figuring\nout the magnetic interactions in high-entropy magnets is not straightforward. Therefore, this\nwork, by combining neutron and resonant x-ray scattering, is quite illustrating and can be\napplied to investigate other HE magnets. All being said, there are some concerns need to be\naddressed before accepting this manuscript for publication.\n1. Our answer:\nWe thank the Referee for the thoughtful review and support of our work.\n2. Reviewer:\nFrom the neutron diffraction data, a single propagation vector k = (0, 1, 0) is revealed. Whether\nthe spin structure is long-range or short-range ordered, there should be some forms of periodic\nspin arrangement. However, the authors propose a non-periodic magnetic order, such as the\npicture in Fig 1h, this seems a bit confusing. The authors need to present a better and clear\npicture.\n2. Our answer:\nThank you for pointing this out. The confusion stems from the novel magnetic order observed\nin HEPS itself: the material exhibits well-defined magnetic Bragg peaks and propagation\n3\nvector, which reveal “some forms of periodic spin arrangement”, while spin orientations are\ndistinct for different elements. To avoid misleading, we have changed the title from\n“Non-periodic magnetic order in a high-entropy antiferromagnet”\nto\n“Long-range magnetic order with disordered spin orientations in a high-entropy\nantiferromagnet”\n3. Reviewer:\nThe authors should be a bit more rigorous about the differentiation about the long-range and\nshort-range magnetic order. For instance, in the results part on page 3, the authors claim that\nlong-range order is indicated from the magnetic susceptibility data. However, the bulk\nmagnetization data is not enough to support this point. This is further supported by the specific\nheat measurement in ref. [11], which shows a broad thermodynamic transition.\n3. Our answer:\nThank you for the comments. We agree that the bulk magnetization data is not enough to\nsupport the presence of long-range magnetic order. Thus, we have changed the sentences from\n“While a high-entropy scenario is well established, an anomaly indicative of long-range\nmagnetic ordering is observed in the magnetic susceptibility measurements of HEPS at\nN 1\nto\n“While a high-entropy scenario is well established, an anomaly indicative of magnetic\nphase transition is observed in the magnetic susceptibility measurements of HEPS at\nN 1\n4. Reviewer:\nMore importantly, the neutron diffraction data in Fig 2 can in principle directly reveal the\nmagnetic correlation length and the nature of the magnetic order. However, the data analysis is\nnot strong enough to support the major points in this manuscript. I suggest more detailed\nanalysis should be presented.\nIn order to reveal whether the magnetic ground state is 3D or 2D, the author should present the\nscans and fits of some typical magnetic peaks, along both the in-plane and out-of-plane\ndirections. In addition, the experimental resolution should be specified or some comparative\nscans and fits of the nearby structural Bragg peaks are needed. At this point, in Fig 2e, the\nauthors simply claim 3D and 2D signals, which seems a bit casual. For example, it is not clear\nwhether the magnetic peaks can be fitted by simple Lorentzian peaks or not. Also, the two peaks\nin shaded regions, presenting 3D signals, clearly have different peak widths. In fig 2f, what is\nthe critical exponent from the fit? All being said, the data analysis should be performed in more\ndetails. By revealing the peak widths and correlation lengths, the nature of the spin state will\nbe more convincing.\n4. Our answer:\nThank you for pointing these out. In the revised manuscript, we have added the Q cuts along H\nand K directions for both the structural and magnetic peaks in Fig. 2, which, supplemented with\nGaussian fitting, show comparable peak widths, indicating in-plane long-range\ncorrelation/ordering:\n“e, f, One-dimensional Q cuts along H and K directions, respectively, across the nuclear\n[Q = (0, 2, 0)] and magnetic reflections [Q = (0, 1, 0)] at the indicated temperatures. The\nsolid lines are fits with Gaussian profiles, yielding FWHM (in unit of r.l.u.) of 0.0539(6)\n(nuclear) and 0.0496(5) (magnetic) along H, and 0.070(1) (nuclear) and 0.068(1)\n(magnetic) along K.”\nHere, the structural peaks can be regarded as references for the experimental resolution. We\nhave also added the following sentences to the revised version:\n“Detailed examination of the H and K dependence reveals that the in-plane magnetic peak\nwidths are comparable to those of the nuclear reflections, confirming the establishment of\nlong-range magnetic order (Fig. 2e, f).”\nThe different peak widths for Q=(0, 1, 0) and Q=(0, 1, 1) in Fig. 2g are potentially caused by\nvariation in Q resolution convoluted with sample mosaicity. Note that Q=(0, 1, 1) is affected\nby out-of-plane sample mosaicity while Q=(0, 1, 0) is not. We have added this point to the\nrevised manuscript:\n“The shaded area denotes the 3D magnetic signals, which exhibit different peak widths\ndue to different contributions of sample mosaicity.”\nRegarding the critical exponent, fit in Fig. 2f with formula of I-BG (T -T)2β gives β=0.40(5)\nN\nwhich is within the error of theoretical values of either 3D XY (~0.35) or 3D Heisenberg (~0.37)\n∝\nantiferromagnet. Note that atomic disorder may play a role here. We have added the following\nsentences to the revised manuscript:\n“Regarding the temperature dependence, the intensity of the 3D magnetic signals\ndecreases with increasing temperature, and a phase transition takes place at T ≈ 72 K (Fig.\nN\n2h), consistent with the susceptibility measurements. The temperature dependence was\nfitted using I − BG (T − T)2β (BG: background), yielding a critical exponent β = 0.40(5).\nN\nMeanwhile, the 2D magnetic signals remain detectable above T , persisting weakly at 90\nN\n∝\nK (Fig. 2g) before vanishing around that temperature (Fig. 2h).”\nAnd the caption of Fig. 2 is changed from\n“The solid and dashed lines are guides for the eye.”\nto\n“The solid line is a fit to I − BG (T − T)2β (BG: background), and the dashed line is a\nN\nguide for the eye.”\n∝\n5. Reviewer:\nSome other minor comments:\nI don’t think the discussion about the T2 transition will impact much about the data and\nconclusions of this manuscript.\n5. Our answer:\nThank you for the comments. We have removed part of the discussion about the T transition\n2\nand changed the sentences from\n“This second transition likely originates from glassy behaviors or spin reorientations. Note\nthat T observed in HEPS is very close to that of non-HE MnPS (T ≈ 78 K, see Table\nN 3 3 N\nI). Interestingly, in binary or ternary TMPX compounds, where disorder is expected to be\n3\nless significant than in HEPS , the anomaly related to T is more rounded, suggesting\n3 1\nshort-range transitions rather than long-range ones, and the overlap region (ΔT = T − T )\n1 2\nis diminished (Fig. 1g).”\nto\n“This second transition likely originates from glassy behaviors or spin reorientations\n(Supplementary Note 2). Note that T observed in HEPS is very close to that of non-HE\nN 3\nMnPS (T ≈ 78 K, see Table I). Interestingly, in binary or ternary TMPX compounds,\nwhere disorder is expected to be less significant than in HEPS , the anomaly related to T\n3 1\nis more rounded, suggesting reduced correlation length (Fig. 1g).”\n6. Reviewer:\nIn Fig 2e, using empty circles for the 250K will be better.\n6. Our answer:\nThank you for the suggestions. We have changed the figure as suggested. It now goes as follows:\n7. Reviewer:\nFig 2f, is the temperature dependent data also collected at CORELLI? Does the peak intensity\nrepresents the integrated signals? What is the sample mass and what is the counting time at each\ntemperature? The authors may consider include some more details of the neutron experiments.\n7. Our answer:\nYes, the temperature dependent data was also collected at CORELLI, and the intensity\nrepresents the integrated signals of the corresponding magnetic peak. The sample measures 27\nmg in weight and 6mm*3mm in size. For the temperature dependent measurement, the counting\ntime was 5 min with a step of 2K. We have changed the caption of Fig. 2h from\n“Temperature dependence of the 3D magnetic signals.”\nto\n“Temperature dependence of the integrated intensities of 3D magnetic signals at Q = (0,\n1, 1) and 2D magnetic signals at Q = (0.5, 0.5, 0), which corresponds to Q = (0, 1, 1/6) in\nanother domain [31].”\n-\nMeanwhile, we have changed the neutron diffraction experiment section in the Methods from\n“The neutron diffraction measurements were conducted using the CORELLI instrument\nat Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL) [42, 43].\nOne piece of single crystal was aligned first in the H0L scattering plane and subsequently\nin the 0KL scattering plane, utilizing monoclinic notation. Diffraction patterns were\ncollected at 6 K, 90 K, and 250 K by rotating the sample with a fixed tilting angle.\nTemperature dependence measurements were conducted with the sample position and\norientations held constant.”\nto\n“All neutron diffraction measurements were conducted using the CORELLI instrument at\nSpallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL) [45, 46]. One\npiece of single crystal (27 mg in weight; 6×3 mm in size) was aligned first in the H0L\nscattering plane and subsequently in the 0KL scattering plane, utilizing monoclinic\nnotation. Diffraction patterns were collected at 6 K, 90 K, and 250 K by rotating the sample\nwith a fixed tilting angle. For the temperature dependence measurements, the sample\nposition and orientations were unchanged; data were acquired with a 5 min counting time\nper temperature point with a step of 2 K.”\n8. Reviewer:\nIn fig 3h, what is the reason that there are more than 3 peaks of the energy profile of the\nmagnetic peak near the Fe L edge? In Fig 3j, the legend is missing.\n8. Our answer:\nThank you for pointing this out. Now Fig. 3j looks like this:\nRegarding the energy profile of magnetic peak near Fe L edge in Fig. 3h, it is related to the\nnumber of intermediate states. For Fe2+ ions, the L edge intermediate states have the d7c1\n3\nconfiguration where c stands for core hole. Thus, there are 480 intermediate states in total, some\nof which are degenerated and some of which are not, leading to multiple peaks in energy profile\nfor both the magnetic signals and x-ray absorption spectroscopy (XAS). In fact, this applies to\nother transition-metal ions as well, such as Mn2+ (d6c1, 840 intermediate states). For example,\nin MnP, due to intertwined spin and orbital order, the energy dependence at Mn L edge exhibits\ncomplex profiles [B. Y. Pan et al., Phys. Rev. X 9, 021055 (2019)]:\nNote that in Fig. 3g, there are multiple peaks as well.\n9. Reviewer:\nFig 4, the authors may consider showing the experimental data first in the legend. Also, the\ndash lines presenting the fits of the π-pol data are not that great. The authors may consider using\nsolid lines with different transparency or thickness or some other forms to present the data in a\nbetter way.\n9. Our answer:\nThank you for the suggestions. We have changed the figure as suggested. It now goes as follows:\n10. Reviewer:\nThe manuscript reports the magnetic moment of (Mn1/4Fe1/4Co1/4Ni1/4)PS3 is 1.5 μB/site,\nas determined by neutron diffraction. Since the data analysis is based on an average spin\nstructure, if the spin moment directions are different among the different magnetic ions, which\nis also supported by the resonant x-ray scattering study, the net spin moment size might be\nreduced as well. This might be the major reason why the spin moment size is much reduced, in\ncomparison with the effects from the 2D magnetic order and the disorders.\n10. Our answer:\nThank you for the inspiring comments, which have never come to our mind before. We have\nadded these discussions to the revised manuscript in this regard:\n“Furthermore, the element-specific spin orientation may contribute to the reduced net spin\nmoment derived from neutron diffraction refinement, an analysis that is based on an\naverage spin structure.”\n11. Reviewer:\nThe authors should use the symbols, like the angle Θ, consistently in this manuscript, including\nthe supplementary file. Also, a scale factor K is used to calculate the magnetic signals of the\nresonant x-ray scattering data. This might be confused with the HKL notations of momenta.\n11. Our answer:\nThank you for your thoughtful suggestions. We have revised the manuscript accordingly and\nnow the symbols are used consistently: Θ is the angle between the spin moment and lattice a\ndirection defined in Fig. 1e; θ is the sample angle defined in Fig. 3a; φ is the azimuthal angle;\nΔ is the single-ion anisotropy; δ is the trigonal field parameter; J is the exchange interaction;\nH, K, and L are reciprocal lattice indices; κ is the scale factor for magnetic signal calculations.\n12. Reviewer:\nIn the main text, it seems the discussion about the mechanism in Fig 1i is very limited. If this\npanel is included in the main text, more discussion is needed.\n12. Our answer:\nThank you for pointing this out. We have changed the caption of Fig. 1i from\n“Schematic diagram showing the evolution of spin orientations with different exchange\ninteraction (J) to single-ion anisotropy (Δ) ratio. When J is negligible, the spin moments\ntend to preserve their anisotropy as in the non-HE materials, while dominating J would\nenforce a universal parallel alignment. A compromised case is realized in HEPS .”\n3\nto\n“Schematic diagram showing the evolution of spin orientations with different exchange\ninteraction (J) to single-ion anisotropy (Δ) ratio. When J is negligible, the spin moments\ntend to preserve their anisotropy as in the non-HE materials, e.g., Mn2+/Fe2+ and Co2+/Ni2+\nbeing almost perpendicular and parallel to the ab plane, respectively (left panel). In another\naspect, dominant J would enforce a universal parallel alignment (right panel). A\ncompromised case is realized in HEPS (middle panel, see also Supplementary Note 6).”\n“6. COMPETITION BETWEEN SINGLE-ION ANISOTROPY AND EXCHANGE\nINTERACTIONS\nTo demonstrate the competition between single-ion anisotropy and exchange interactions,\nwe construct a toy model: an antiferromagnetic spin chain composed of two types of atoms\narranged alternatively, labeled as Spin 1 and Spin 2. We adopt the Hamiltonian:\nwhere J is the intra-chain exchange interaction, ij denotes bond sums along the chain,\nand Δ and Δ are single-ion anisotropies for Spin 1 and Spin 2, respectively. To reflect the\n1 2\n⟨ ⟩\nco-existence and competition of easy-plane and easy-axis anisotropies in HEPS , here,\n3\nspin 1 is set to present strong easy-axis anisotropy (Δ = −1) and Spin 2 intermediate easy-\n1\nplane anisotropy (Δ = 1/2). The Hamiltonian is solved within the mean-field framework.\ntheir single-ion anisotropy (Fig. S8). We define Θ as the angle between the spin and the x\ndirection, following the definition in the main text. Thus, Θ = 90◦ for Spin 1 and Θ = 0◦\n1 2\nfor Spin 2.\nWhen J is non-zero, it favors antiparallel alignment for the Spin 1 and Spin 2 sublattices,\nwhich competes with the single-ion anisotropy. Consequently, Spin 1 starts to rotate\ntoward the x axis (Θ < 90◦) and Spin 2 rotates toward the z axis (Θ > 0◦). As Δ is larger\n1 2 1\nthan Δ , Θ is more robust than Θ .\n2 1 2\nWhen J is sufficiently large, it enforces an antiparallel alignment for both Spin 1 and Spin\n2, making them aligned along the z direction due to the stronger single-ion anisotropy of\nSpin 1.\nThe situation is much more complex in real materials. There are multiple types of\nexchange interactions and single-ion anisotropies, making effective modeling difficult.\nNevertheless, our toy model here qualitatively demonstrates that the competition between\nsingle-ion anisotropy and exchange interactions can indeed trigger the element-specific\nspin orientations illustrated in the main text.\nFIG. S8. Calculated exchange interaction dependent spin orientations. We adopt an\nantiferromagnetic spin chain composed of two types of atoms arranged alternatively, with\ndistinct single-ion anisotropies. The spin orientations are then determined by tuning the\nintra-chain exchange interaction J.”\nAnd cite it in the main text:\n“This competition can be illustrated by a toy model, which demonstrates how spin\norientations are tuned by the anisotropy-to-interaction ratio (Supplementary Note 6).”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made substantial improvements to the manuscript and supplemental information. They have addressed every one of my questions in a satisfactory way, and they have also addressed the other referees' questions. As a result, I endorse this paper for publication in Nature Communications.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The authors have clarified my concerns, updated the manuscript and responded well to other referees' questions. I can recommend the publication of this manuscript at Nature Communications now.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

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