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arxiv: 2603.09525 · v1 · submitted 2026-03-10 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

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Bulk magnetic properties of distorted square lattice compounds M'-LnTaO4 (Ln = Tb, Dy, Ho, Er)

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Pith reviewed 2026-05-15 13:29 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords antiferromagnetic orderneutron diffractionlanthanide tantalatesdistorted square latticeKramers doubletmagnetic susceptibilityspecific heat
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The pith

M'-TbTaO4 develops long-range antiferromagnetic order below 2.1 K with Tb moments aligned primarily along the c-axis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures bulk magnetic properties of the monoclinic compounds M'-LnTaO4 for Ln = Tb, Dy, Ho, and Er, in which the magnetic ions form a distorted two-dimensional square lattice. Powder neutron diffraction confirms the crystal structures and establishes that M'-TbTaO4 orders antiferromagnetically at 2.1 K with moments lying mainly along the c direction and antiferromagnetic nearest-neighbor couplings. Susceptibility and heat-capacity data indicate antiferromagnetic correlations in all four compounds, with possible short-range order near 2.7 K in the Dy case and no long-range order detected above 1.8 K for Ho and Er; the Er compound additionally shows a Kramers-doublet ground state. A reader would care because the series lets one track how the lanthanide ion's electronic configuration and the lattice distortion together control the appearance of magnetic order.

Core claim

Powder neutron diffraction confirms the crystal structure for Ln = Tb, Ho, Er and determines that M'-TbTaO4 displays long-range antiferromagnetic order below T_N = 2.1 K, with the Tb3+ moments aligned primarily along the c-axis and antiferromagnetic nearest-neighbour interactions. Susceptibility data suggest M'-DyTaO4 may display short-range ordering around 2.7 K, while M'-HoTaO4 and M'-ErTaO4 show antiferromagnetic correlations but do not order above 1.8 K. Magnetic specific-heat measurements provide evidence for a Kramers doublet ground state in M'-ErTaO4.

What carries the argument

Powder neutron diffraction used to determine both the nuclear crystal structure and the magnetic structure of the distorted square lattice.

If this is right

  • Magnetic ordering temperature and character change with the lanthanide ion's Kramers or non-Kramers character and crystal-electric-field scheme.
  • M'-DyTaO4 is the only member likely to exhibit short-range order near 2.7 K.
  • M'-HoTaO4 and M'-ErTaO4 remain without long-range order down to at least 1.8 K despite antiferromagnetic correlations.
  • M'-ErTaO4 shares a Kramers-doublet ground state with the heavier Yb analogue.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Lower-temperature neutron diffraction or specific-heat runs could test whether Ho and Er compounds order below the present 1.8 K limit.
  • The series supplies a controlled platform for examining how lattice distortion modulates frustration on a square lattice of rare-earth moments.
  • Systematic comparison across the lanthanide row may reveal trends driven by changing spin-orbit coupling and crystal-field parameters.

Load-bearing premise

Powder neutron diffraction patterns uniquely fix the magnetic structure and the absence of thermodynamic anomalies above 1.8 K rules out long-range order at any lower temperature.

What would settle it

Appearance of a magnetic Bragg peak or a specific-heat lambda anomaly below 1.8 K in M'-HoTaO4 or M'-ErTaO4 would demonstrate that long-range order occurs at lower temperature than currently reported.

Figures

Figures reproduced from arXiv: 2603.09525 by Ivan da Silva, Nicola D. Kelly, Si\^an E. Dutton.

Figure 1
Figure 1. Figure 1: FIG. 1. Crystal structure of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Rietveld refinement against room-temperature TOF PND data for [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Unit cell volume of [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: shows the Curie-Weiss fits as black solid lines with extrapolation below 50 K as dashed lines. The negative Curie-Weiss temperatures indicate antiferromagnetic interactions and the effective magnetic moments µef f agree quite well with the expected moments for free ions, µ = gJ p J(J + 1). Magnetic isotherms were measured for all samples at T = 2, 4, 6, 8, 10 and 100 K and are shown in [PITH_FULL_IMAGE:fi… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Magnetic isotherms for [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Magnetic specific heat data at various applied fields for the four [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Magnetic structure model for one magnetic unit cell of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
read the original abstract

We report bulk magnetic properties of the monoclinic lanthanide tantalates, M'-LnTaO4 (Ln = Tb, Dy, Ho, Er), where the magnetic Ln3+ ions are arranged on a distorted 2D square lattice. The heavier analogue M'-YbTaO4 has been investigated as a spin-orbit-coupled, quasi-two-dimensional frustrated magnet, and the properties of the other M'-LnTaO4 are expected to vary depending on the electronic configuration of the Ln ion, namely Kramers vs non-Kramers behaviour and different crystal electric field parameters. In this work, powder neutron diffraction is used to confirm the crystal structure for Ln = Tb, Ho, Er, and to determine the magnetic structure of M'-TbTaO4, which displays long-range antiferromagnetic (AFM) order below T_N = 2.1 K. The Tb3+ moments are aligned primarily along the c-axis with AFM nearest-neighbour interactions. Susceptibility data suggest that M'-DyTaO4 may display short-range ordering around 2.7 K, while M'-HoTaO4 and M'-ErTaO4 show AFM correlations but do not order above 1.8 K. Measurements of the magnetic specific heat provide evidence for a Kramers doublet ground state in M'-ErTaO4, similar to its heavier analogue M'-YbTaO4.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports bulk magnetic properties of monoclinic M'-LnTaO4 (Ln = Tb, Dy, Ho, Er) compounds in which Ln3+ ions form a distorted 2D square lattice. Powder neutron diffraction confirms the crystal structures for Tb, Ho, and Er analogues and determines the magnetic structure of M'-TbTaO4 as long-range antiferromagnetic order below T_N = 2.1 K, with Tb3+ moments aligned primarily along the c-axis and antiferromagnetic nearest-neighbor interactions. Susceptibility data suggest short-range ordering near 2.7 K in M'-DyTaO4, while M'-HoTaO4 and M'-ErTaO4 exhibit antiferromagnetic correlations but no long-range order above 1.8 K; magnetic specific-heat measurements support a Kramers doublet ground state in M'-ErTaO4, analogous to the Yb compound.

Significance. If the magnetic structure assignment is robust, the work supplies systematic experimental data on how magnetic behavior varies across the Ln series in these distorted square-lattice tantalates, particularly the contrast between Kramers and non-Kramers ions and the role of crystal-electric-field effects relative to the previously studied Yb analogue. The results are obtained with standard powder neutron diffraction, susceptibility, and specific-heat techniques and therefore add directly comparable observations to the literature on quasi-two-dimensional frustrated lanthanide magnets.

major comments (2)
  1. [Magnetic structure determination for M'-TbTaO4] In the section presenting the magnetic structure of M'-TbTaO4, the assignment of Tb3+ moments as primarily c-axis aligned with AFM nearest-neighbor interactions is based on fitting observed magnetic Bragg peaks from powder neutron diffraction. Powder averaging inherently limits the ability to distinguish moment directions and propagation vectors; the manuscript does not report explicit R-factor or goodness-of-fit comparisons against alternative models (e.g., a-axis moments or different k-vectors), leaving open the possibility that other symmetry-allowed structures produce statistically indistinguishable fits.
  2. [Specific-heat measurements] The specific-heat analysis for M'-ErTaO4 is used to infer a Kramers doublet ground state. The temperature range and subtraction procedure for the lattice contribution should be stated explicitly, together with the quantitative criterion (e.g., entropy release or Schottky anomaly fit) that distinguishes this ground state from a possible singlet or higher degeneracy.
minor comments (2)
  1. [Figures] Figure captions for the neutron diffraction patterns should include the wavelength, temperature, and any subtracted background details to allow direct assessment of the magnetic peak intensities.
  2. [Magnetic susceptibility] The susceptibility data for M'-DyTaO4 are described as suggesting short-range order around 2.7 K; the precise criterion (e.g., deviation from Curie-Weiss behavior or a broad maximum) used to identify this temperature should be stated in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to improve clarity and rigor where appropriate.

read point-by-point responses
  1. Referee: In the section presenting the magnetic structure of M'-TbTaO4, the assignment of Tb3+ moments as primarily c-axis aligned with AFM nearest-neighbor interactions is based on fitting observed magnetic Bragg peaks from powder neutron diffraction. Powder averaging inherently limits the ability to distinguish moment directions and propagation vectors; the manuscript does not report explicit R-factor or goodness-of-fit comparisons against alternative models (e.g., a-axis moments or different k-vectors), leaving open the possibility that other symmetry-allowed structures produce statistically indistinguishable fits.

    Authors: We agree that powder neutron diffraction data inherently limits unique determination of moment directions due to orientational averaging. Our analysis of the observed magnetic Bragg peaks shows that the proposed c-axis aligned AFM structure with nearest-neighbor interactions provides a consistent fit, while alternative models (such as a-axis moments) yield poorer agreement with the peak intensities and positions. To address this point explicitly, we will include R-factor and goodness-of-fit comparisons against symmetry-allowed alternatives in the revised manuscript. revision: yes

  2. Referee: The specific-heat analysis for M'-ErTaO4 is used to infer a Kramers doublet ground state. The temperature range and subtraction procedure for the lattice contribution should be stated explicitly, together with the quantitative criterion (e.g., entropy release or Schottky anomaly fit) that distinguishes this ground state from a possible singlet or higher degeneracy.

    Authors: We will revise the manuscript to state the temperature range (1.8–20 K) and lattice subtraction procedure (using a Debye model fitted to high-temperature data or a non-magnetic reference) explicitly. The quantitative criterion is the magnetic entropy release approaching R ln(2) above ~5 K, which we will report with the associated Schottky anomaly fit to confirm the Kramers doublet ground state and rule out higher degeneracy or singlet scenarios. revision: yes

Circularity Check

0 steps flagged

No significant circularity: purely experimental claims with no derivation chain

full rationale

The manuscript reports direct measurements (powder neutron diffraction for crystal and magnetic structures of TbTaO4, susceptibility, and specific heat) without any theoretical model, ansatz, fitted parameter renamed as prediction, or self-citation load-bearing step. The magnetic structure assignment follows from observed Bragg peaks and is presented as an experimental determination, not a derived result that reduces to its own inputs by construction. Prior work on the Yb analogue is cited only for context and does not underpin the current data interpretation. No equations or uniqueness theorems are invoked that would create circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is an experimental characterization paper. No free parameters, axioms, or invented entities are invoked in the abstract.

pith-pipeline@v0.9.0 · 5575 in / 1083 out tokens · 33535 ms · 2026-05-15T13:29:54.988280+00:00 · methodology

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Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    The background was fitted with a Chebyshev polynomial with 12 coefficients and the peakshape was a Voigt function with axial divergence asymmetry

    was carried out using the program TOPAS v5 [18]. The background was fitted with a Chebyshev polynomial with 12 coefficients and the peakshape was a Voigt function with axial divergence asymmetry. During refinement, thexandzcoordinates of theLnand Ta atoms were fixed at these values representing special positions in the cell:x Ln = 0,z Ln = 0.25; xTa = 0.5...

  2. [2]

    was carried out using the program TOPAS v5 [18] against banks 3–6 simultaneously, each with equal weighting. D. Magnetometry Magnetic measurements were made using a Quantum Design Materials Properties Mea- surement System (MPMS-3). Approximately 10 mg of each sample (weighed accurately in each case) was contained in clingfilm and the standard plastic samp...

  3. [4]

    P. W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science 235, 1196 (1987)

  4. [5]

    J. E. Greedan, Geometrically frustrated magnetic materials, J. Mater. Chem.11, 37 (2001)

  5. [6]

    J. R. Chamorro, T. M. McQueen, and T. T. Tran, Chemistry of Quantum Spin Liquids, Chem. Rev.121, 2898 (2021)

  6. [7]

    P. Park, G. Sala, T. Proffen, M. B. Stone, A. D. Christianson, and A. F. May, Quantum magnetism in the frustrated square lattice oxyhalides YbBi 2IO4 and YbBi2ClO4, Phys. Rev. B109, 014426 (2024)

  7. [8]

    Watanabe, N

    M. Watanabe, N. Kurita, H. Tanaka, W. Ueno, K. Matsui, T. Goto, and M. Hagihala, Con- trasting magnetic structures in SrLaCuSbO 6 and SrLaCuNbO 6: Spin- 1 2 quasi-square-lattice J1 −J 2 Heisenberg antiferromagnets, Phys. Rev. B105, 054414 (2022)

  8. [9]

    A. H. Abdeldaim, T. Li, L. Farrar, A. A. Tsirlin, W. Yao, A. S. Gibbs, P. Manuel, P. Lightfoot, G. J. Nilsen, and L. Clark, Realising square and diamond lattice S=1/2 Heisenberg antifer- romagnet models in theαandβphases of the coordination framework, KTi(C 2O4)2 ·xH 2O, Phys. Rev. Mater.4, 104414 (2020)

  9. [10]

    Mustonen, S

    O. Mustonen, S. Vasala, E. Sadrollahi, K. P. Schmidt, C. Baines, H. C. Walker, I. Terasaki, 22 F. J. Litterst, E. M. Baggio-Saitovitch, and M. Karppinen, Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by d 10-d0 cation mixing, Nat. Commun.9, 1085 (2018)

  10. [11]

    Mustonen, S

    O. Mustonen, S. Vasala, K. P. Schmidt, E. Sadrollahi, H. C. Walker, I. Terasaki, F. J. Litterst, E. Baggio-Saitovitch, and M. Karppinen, Tuning the S=1/2 square-lattice antiferromagnet Sr2Cu(Te1–xWx)O6 from N´ eel order to quantum disorder to columnar order, Phys. Rev. B98, 064411 (2018)

  11. [12]

    Guchhait, A

    S. Guchhait, A. Painganoor, S. S. Islam, J. Sichelschmidt, M. D. Le, N. B. Christensen, and R. Nath, Magnetic and crystal electric field studies of the rare earth based square lattice antiferromagnet NdKNaNbO5, Phys. Rev. B110, 144434 (2024)

  12. [13]

    L. H. Brixner and H. Y. Chen, On the Structural and Luminescent Properties of the M’ LnTaO4 Rare Earth Tantalates, J. Electrochem. Soc.130, 2435 (1983)

  13. [14]

    N. D. Kelly, L. Yuan, R. L. Pearson, E. Suard, I. Puente Orench, and S. E. Dutton, Magnetism on the stretched diamond lattice in lanthanide orthotantalates, Phys. Rev. Mater.6, 044410 (2022)

  14. [15]

    Zhang, N

    X. Zhang, N. D. Kelly, D. Sheptyakov, C. Liu, S. Deng, S. S. Saxena, and S. E. Dutton, Magnetoelastic coupling in the stretched diamond lattice of TbTaO 4, Mater. Adv.6, 2570 (2025)

  15. [16]

    Ramanathan, M

    A. Ramanathan, M. Mourigal, and H. S. La Pierre, Frustrated Magnetism and Spin Anisotropy in a Buckled Square Net YbTaO 4, Inorg. Chem.64, 158 (2024)

  16. [17]

    A. P. Ramirez, Strongly geometrically frustrated magnets, Annu. Rev. Mater. Sci.24, 453 (1994)

  17. [18]

    Kumar, R

    J. Kumar, R. Roy, D. Ranaut, J. G. Nakamura, S. Kanungo, and K. Mukherjee, YbTaO 4: A quasi-two-dimensional frustrated magnet possessing spin orbit entangled Kramers doublet ground state, Phys. Rev. B110, 174420 (2024)

  18. [19]

    S. P. Thompson, J. E. Parker, J. Potter, T. P. Hill, A. Birt, T. M. Cobb, F. Yuan, and C. C. Tang, Beamline I11 at Diamond: A new instrument for high resolution powder diffraction, Rev. Sci. Instrum.80, 075107 (2009)

  19. [20]

    H. M. Rietveld, A profile refinement method for nuclear and magnetic structures, J. Appl. Crystallogr.2, 65 (1969)

  20. [21]

    A. A. Coelho, TOPAS and TOPAS-Academic: An optimization program integrating computer 23 algebra and crystallographic objects written in C++, J. Appl. Crystallogr.51, 210 (2018)

  21. [22]

    Hartenbach, F

    I. Hartenbach, F. Lissner, T. Nikelski, S. F. Meier, H. M¨ uller-Bunz, and T. Schleid, ¨Uber oxotantalate der lanthanide des formeltyps MTaO 4 (M = La - Nd, Sm - Lu), Zeitschrift f¨ ur Anorg. und Allg. Chemie631, 2377 (2005)

  22. [23]

    A. C. Hannon, Results on disordered materials from the GEneral Materials diffractometer, GEM, at ISIS, Nucl. Instruments Methods Phys. Res. A551, 88 (2005)

  23. [24]

    N. D. Kelly, J. Lee, J. M. A. Steele, S. E. Dutton, and I. da Silva,M ′-LnTaO4: a model for the 2D square lattice of magnetic ions, STFC ISIS Neutron and Muon Source 10.5286/ISIS.E.RB2520021 (2025)

  24. [25]

    V. F. Sears, Neutron scattering lengths and cross sections, Neutron News3, 26 (1992)

  25. [26]

    Brochier, Cryostat ` a temp´ erature variable pour mesures neutroniques ou optiques, ILL Technical Report 77/74 (1977)

    D. Brochier, Cryostat ` a temp´ erature variable pour mesures neutroniques ou optiques, ILL Technical Report 77/74 (1977)

  26. [27]

    Smith and F

    D. Smith and F. Fickett, Low-Temperature Properties of Silver, J. Res. Natl. Inst. Stand. Technol.100, 119 (1995)

  27. [28]

    E. S. R. Gopal,Specific Heats at Low Temperatures(Springer US, Boston, MA, 1966)

  28. [29]

    S. A. Mather and P. K. Davies, Nonequilibrium Phase Formation in Oxides Prepared at Low Temperature: Fergusonite-Related Phases, J. Am. Ceram. Soc.78, 2737 (1995)

  29. [30]

    B. G. Mullens, M. Saura-M´ uzquiz, F. P. Marlton, M. Avdeev, H. E. A. Brand, S. Mondal, G. Vaitheeswaran, and B. J. Kennedy, Beyond the ionic radii: A multifaceted approach to understand differences between the structures of LnNbO 4 and LnTaO4 fergusonites, J. Alloys Compd.930, 167399 (2023)

  30. [31]

    B. G. Mullens, M. Saura-M´ uzquiz, G. Cordaro, F. P. Marlton, H. E. Maynard-Casely, Z. Zhang, G. Baldinozzi, and B. J. Kennedy, Variable Temperature In Situ Neutron Pow- der Diffraction and Conductivity Studies of Undoped HoNbO 4 and HoTaO4, Chem. Mater. 36, 5002 (2024)

  31. [32]

    Wakeshima, H

    M. Wakeshima, H. Nishimine, and Y. Hinatsu, Crystal structures and magnetic properties of rare earth tantalates RE3TaO7 (RE = rare earths), J. Phys. Condens. Matter16, 4103 (2004)

  32. [33]

    See Supplemental Material at [URL] for additional Rietveld refinements, tables of structural data, and further magnetic susceptibility analysis

  33. [34]

    R. D. Shannon, Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides, Acta Crystallogr.A32, 751 (1976). 24

  34. [35]

    J. Wang, X. Y. Chong, R. Zhou, and J. Feng, Microstructure and thermal properties of RETaO4 (RE = Nd, Eu, Gd, Dy, Er, Yb, Lu) as promising thermal barrier coating materials, Scr. Mater.126, 24 (2017)

  35. [36]

    V. Y. Markiv, N. M. Belyavina, M. V. Markiv, Y. Titov, A. M. Sych, A. N. Sokolov, A. A. Kapshuk, and M. S. Slobodyanyk, Peculiarities of polymorphic transformations in YbTaO 4 and crystal structure of its modifications, J. Alloys Compd.346, 263 (2002)

  36. [37]

    M. E. Fisher, Relation between the specific heat and susceptibility of an antiferromagnet, Philos. Mag.7, 1731 (1962)

  37. [38]

    G. A. Bain and J. F. Berry, Diamagnetic corrections and Pascal’s constants, J. Chem. Educ. 85, 532 (2008)

  38. [39]

    Mugiraneza and A

    S. Mugiraneza and A. M. Hallas, Tutorial: a beginner’s guide to interpreting magnetic sus- ceptibility data with the Curie-Weiss law, Commun. Phys.5, 95 (2022)

  39. [40]

    S. T. Bramwell, M. N. Field, M. J. Harris, and I. P. Parkin, Bulk magnetization of the heavy rare earth titanate pyrochlores - A series of model frustrated magnets, J. Phys. Condens. Matter12, 483 (2000)

  40. [41]

    Mukherjee, Y

    P. Mukherjee, Y. Wu, G. I. Lampronti, and S. E. Dutton, Magnetic properties of monoclinic lanthanide orthoborates,LnBO 3,Ln= Gd, Tb, Dy, Ho, Er, Yb, Mater. Res. Bull.98, 173 (2018)

  41. [42]

    Rodr´ ıguez-Carvajal, Recent advances in magnetic structure determination by neutron pow- der diffraction, Phys

    J. Rodr´ ıguez-Carvajal, Recent advances in magnetic structure determination by neutron pow- der diffraction, Phys. B192, 55 (1993)

  42. [43]

    N. D. Kelly, X. Liang, S. E. Dutton, K. Yamaura, and Y. Tsujimoto, High-pressure synthesis of the quantum magnetM-YbTaO 4 with a stretched diamond lattice (2025), under revision at Phys. Rev. Mater

  43. [44]

    Solana-Madruga, C

    E. Solana-Madruga, C. Ritter, C. Aguilar-Maldonado, O. Mentr´ e, J. P. Attfield, and A. M. Ar´ evalo-L´ opez, Mn3MnNb2O9: high-pressure triple perovskite with 1:2 B-site order and mod- ulated spins, Chem. Commun.57, 8441 (2021)

  44. [45]

    T. R. Cao, H. Zhao, X. Huai, A. Quane, T. T. Tran, F. Ye, and G. Cao, Field-tailoring quantum materials via magneto-synthesis: metastable metallic and magnetically suppressed phases in a trimer iridate, npj Quantum Mater. 10.1038/s41535-026-00852-0 (2026)

  45. [46]

    25 Appendix A: PXRD Rietveld refinements FIG

    Research data supporting this work will be made available at DOI:10.17863/CAM.125160. 25 Appendix A: PXRD Rietveld refinements FIG. S1. Rietveld refinement against room-temperature synchrotron PXRD data (λ= 0.82869 ˚A) forM ′-TbTaO4. Red circles: observed data, black line: calculated pattern, blue line: difference pattern, purple tick marks: Bragg reflect...