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arxiv: 2510.01075 · v2 · submitted 2025-10-01 · ❄️ cond-mat.str-el

Spontaneous lattice distortion and crystal field effects in HoB4

S. Goswami , D. I. Gorbunov , D. Kriegner , I. Ishii , C. A. Correa , T. Suzuki , D. Brunt , G. Balakrishnan
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S. Zherlitsyn J. Wosnitza O. A. Petrenko M. S. Henriques
This is my paper

Pith reviewed 2026-05-18 10:30 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords HoB4quadrupolar orderingstructural phase transitionShastry-Sutherland latticemagnetoelastic couplingcrystal electric fieldantiferromagnetic transitionelastic modulus softening
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The pith

Below TN2, HoB4 changes from tetragonal to monoclinic crystal structure as a direct sign of quadrupolar ordering on the Ho ions.

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

The paper tracks how the lattice of HoB4 responds when the material cools through its two antiferromagnetic transitions. Measurements show that the tetragonal structure distorts into a monoclinic one right at the lower transition temperature. This distortion appears as the visible result of ferroquadrupolar order that couples to the lattice and softens the C44 elastic modulus. The authors link the effect to a nearly degenerate ground state of the Ho3+ ions found from crystal-field calculations. Such magnetoelastic coupling offers a concrete way to understand the competing orders in Shastry-Sutherland magnets.

Core claim

Below TN2, the crystal structure of HoB4 changes to monoclinic (space group P21/b) as a macroscopic manifestation of the quadrupolar ordering. Between 300 and 3.5 K the total distortion amplitude reaches 0.46 Å with a relative volume change of 3.5 × 10^{-3}. The transition is consistent with the large softening of the C44 modulus around TN2 caused by ferroquadrupolar order, and a lattice instability already appears just below TN1. CEF analysis indicates a quasi-degenerate ground state for the Ho3+ ions.

What carries the argument

The monoclinic structural distortion (space group P21/b) that acts as the macroscopic signature of ferroquadrupolar ordering and produces the observed C44 softening.

If this is right

  • The distortion amplitude totals 0.46 Å and the volume change is 3.5 × 10^{-3} down to 3.5 K.
  • A lattice instability sets in immediately below the higher transition at TN1 and is visible in both diffraction and ultrasound data.
  • The huge softening of C44 around TN2 matches the ferroquadrupolar character of the ordering.
  • CEF calculations place the Ho3+ ions in a quasi-degenerate ground state that favors quadrupolar degrees of freedom.

Where Pith is reading between the lines

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

  • Similar monoclinic distortions may appear in other rare-earth tetraborides that share the Shastry-Sutherland geometry when quadrupolar order sets in.
  • Pressure or chemical substitution could shift the balance between magnetic and quadrupolar phases and move the structural transition temperature.
  • The same elastic softening mechanism might be detectable in ultrasound measurements on related compounds even when diffraction resolution is limited.

Load-bearing premise

The structural distortion is caused by ferroquadrupolar ordering of the Ho ions rather than by some other magnetic or lattice mechanism.

What would settle it

High-resolution x-ray diffraction that finds no symmetry lowering or a different space group below TN2 would show that the distortion is not tied to the quadrupolar order.

Figures

Figures reproduced from arXiv: 2510.01075 by C. A. Correa, D. Brunt, D. I. Gorbunov, D. Kriegner, G. Balakrishnan, I. Ishii, J. Wosnitza, M. S. Henriques, O. A. Petrenko, S. Goswami, S. Zherlitsyn, T. Suzuki.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Temperature evolution of PXRD patterns of HoB [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Le Bail fitting to the PXRD pattern at 3.5 K treated [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Rietveld-refined PXRD pattern of HoB [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Variation of the calculated crystal structure factor [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of lattice parameters, angle, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a)], detailed knowledge of the transitionary phases surrounding this main phase is still lacking. The ultra￾sound data are very useful in locating different states within the phase diagram, but potentially they could also be used to assess the nature of various magnetic phases. IV. SUMMARY From the above results, analysis, and discussion, it is noticeable that the Ho, Dy, and Nd tetraborides all share unu… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature variation of the elastic modules in HoB [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

The tetraboride HoB4 crystallizes in a tetragonal structure (space group P4/mbm), with the Ho atoms realizing a Shastry-Sutherland lattice. It orders antiferromagnetically at TN1 = 7.1 K and undergoes further magnetic transition at TN2 = 5.7 K. The complex magnetic structures are attributed to competing order parameters of magnetic and quadrupolar origin with significant magnetoelastic coupling. Here, we investigate the response of the lattice of HoB4 across the antiferromagnetic phase transitions by using low-temperature powder x-ray diffraction and ultrasound-velocity measurements, supported by crystal electric field (CEF) calculations. Below TN2, the crystal structure of HoB4 changes to monoclinic (space group P21/b) as a macroscopic manifestation of the quadrupolar ordering. Between 300 and 3.5 K, the total distortion amplitude is 0.46~\AA\ and the relative volume change is $3.5 \times 10^{-3}$. This structural phase transition is compatible with the huge softening of the modulus $C_{44}$ observed around TN2 due to ferroquadrupolar order. A lattice instability developing immediately below TN1 is seen consistently in x-ray and ultrasound data. CEF analysis suggests a quasi-degenerated ground state for the Ho$^{3+}$ ions in this system.

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 examines the lattice response of HoB4 across its antiferromagnetic transitions (TN1 = 7.1 K, TN2 = 5.7 K) in the Shastry-Sutherland lattice using low-temperature powder x-ray diffraction, ultrasound velocity measurements, and crystal electric field (CEF) calculations. The central claim is that the tetragonal P4/mbm structure undergoes a spontaneous distortion to monoclinic P21/b below TN2, with a total distortion amplitude of 0.46 Å and relative volume change of 3.5 × 10^{-3}, interpreted as a macroscopic manifestation of ferroquadrupolar ordering; this is supported by observed C44 softening and a quasi-degenerate Ho^{3+} ground state from CEF analysis.

Significance. If the structural transition holds, the work provides direct experimental evidence linking quadrupolar order to lattice distortion via magnetoelastic coupling in a frustrated rare-earth system. The use of independent probes—powder XRD for symmetry lowering and ultrasound for modulus softening—along with CEF interpretation is a methodological strength, as these observables are not derived from the same fitted parameters. The alignment of the lattice instability with the two magnetic transitions adds internal consistency to the competing-order picture.

major comments (2)
  1. [Powder x-ray diffraction results] Powder XRD section: The assignment of monoclinic P21/b symmetry below TN2 is load-bearing for the central claim of quadrupolar-driven distortion; the manuscript must include explicit Rietveld refinement statistics (R_wp, χ²), temperature-dependent lattice parameters, and a direct comparison to alternative space groups to confirm the symmetry lowering is not an artifact of peak broadening or incomplete modeling.
  2. [Ultrasound-velocity measurements] Ultrasound and interpretation section: The attribution of C44 softening to ferroquadrupolar order as the driver of the observed 0.46 Å distortion requires a quantitative link; without an estimate relating the elastic anomaly magnitude to the structural strain (e.g., via magnetoelastic coupling constants), the causal connection remains interpretive rather than demonstrated.
minor comments (2)
  1. [Abstract and CEF analysis] Abstract and methods: Full error bars on lattice parameters, data exclusion criteria for XRD patterns, and details of the CEF fitting procedure (including the specific Hamiltonian parameters and energy level diagram) are needed for reproducibility.
  2. [Figures] Figure clarity: Temperature-dependent XRD patterns and sound-velocity plots should include vertical markers for TN1 and TN2 and error bars on extracted quantities to allow readers to assess the sharpness of the transitions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Powder x-ray diffraction results] Powder XRD section: The assignment of monoclinic P21/b symmetry below TN2 is load-bearing for the central claim of quadrupolar-driven distortion; the manuscript must include explicit Rietveld refinement statistics (R_wp, χ²), temperature-dependent lattice parameters, and a direct comparison to alternative space groups to confirm the symmetry lowering is not an artifact of peak broadening or incomplete modeling.

    Authors: We agree that these details will improve the clarity and rigor of the structural analysis. In the revised manuscript we will add the Rietveld statistics (R_wp and χ²) for representative temperatures both above and below TN2. We will also include a figure displaying the temperature evolution of the lattice parameters (a, b, c, and β angle) across the transitions. For alternative space groups, we have tested several orthorhombic and monoclinic candidates; P21/b yields the lowest residuals and best accounts for the observed peak splitting and intensity changes. A brief summary of this comparison will be added to the main text, with full tables placed in the supplementary information. revision: yes

  2. Referee: [Ultrasound-velocity measurements] Ultrasound and interpretation section: The attribution of C44 softening to ferroquadrupolar order as the driver of the observed 0.46 Å distortion requires a quantitative link; without an estimate relating the elastic anomaly magnitude to the structural strain (e.g., via magnetoelastic coupling constants), the causal connection remains interpretive rather than demonstrated.

    Authors: We acknowledge that a direct quantitative estimate of the magnetoelastic coupling constants would make the causal link more explicit. However, obtaining such constants requires a microscopic model that incorporates the full strain dependence of the CEF levels and the quadrupolar susceptibility, which lies outside the present experimental scope. The manuscript instead relies on the precise coincidence of the C44 anomaly with the onset of the monoclinic distortion, together with the CEF evidence for a quasi-degenerate ground state that permits ferroquadrupolar order. We will revise the discussion section to state this interpretive character more explicitly while underscoring the consistency between the independent XRD and ultrasound data sets. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central claim rests on direct experimental observables: powder x-ray diffraction patterns establishing the monoclinic P21/b structure below TN2, and ultrasound data showing C44 softening. CEF calculations are invoked only for interpretive context regarding the Ho3+ ground state and are not used to derive or define the lattice distortion itself. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the temperature evolution of the distortion aligns with independent magnetic transitions without the result being forced by the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis relies on standard crystal-field theory for rare-earth ions and typical fitting of CEF parameters to match magnetic data; no new entities are postulated.

free parameters (1)
  • Crystal electric field parameters
    CEF parameters are adjusted to reproduce experimental magnetic properties and to infer the quasi-degenerate ground state.
axioms (1)
  • domain assumption Ho^{3+} ions experience a crystal electric field consistent with the high-temperature tetragonal symmetry that produces a quasi-degenerate ground state.
    Invoked to explain why quadrupolar effects are strong enough to drive the observed lattice distortion.

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Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    00730(2) ˚ A

    08576(4) ˚ A and c = 4. 00730(2) ˚ A. As the K α 1 and K α 2 wavelengths of the x-rays gen- erated by the Cu tube of the instrument are not fil- tered, all peaks are composed of both components (Kα 2 / Kα 1 = 0.48). All the numerical results presented refer to the Cu K α 1 component of the x-ray peaks, unless otherwise stated. Symmetry analysis for the cry...

    work page

  2. [2]

    The evolution of the FWHM with temper- ature for these reflections (and others) can be found in the Supplemental Material (Fig

    25◦ at 3.5 K. The evolution of the FWHM with temper- ature for these reflections (and others) can be found in the Supplemental Material (Fig. S1). The distortion cul- minates in the splitting of the peak (332) t at T ≈ 5 K. No further structural changes are noticed down to 3.5 K. All these observations are consistent with a reduction of the crystal tetrago...

    work page

  3. [3]

    Moreover, the re- flection conditions for both space groups (tetragonal and monoclinic) are very similar, and the Bragg peaks are generated at close positions, making it difficult to assign a priori a certain peak to a specific crystal symmetry. A few higher-order reflections differentiating the two sym- metries, such as (104) m and (304) m (allowed only for th...

    work page 2003

  4. [4]

    This means that the monoclinic model is correct, and that Brunt et al

    The trend found here repro- duces the one obtained in earlier work (see Supplemental Material of [ 30]). This means that the monoclinic model is correct, and that Brunt et al. were right in pointing out that a lattice distortion involving displacement of the Ho and B2 sublattices could explain the apparent ‘neg- ative’ nuclear intensity in their neutron e...

    work page

  5. [5]

    The structural transition is a lifting mecha- nism of the frustration in the Shastry-Sutherland lattice

    [ 11]. The structural transition is a lifting mecha- nism of the frustration in the Shastry-Sutherland lattice. The presence of quadrupolar order has also been sug- gested previously for NdB 4 [ 21], but no clear structural signature was found. Recently, Khalyavin et al. [22] ver- ified that the ground state magnetic structure of NdB 4 consists of two dist...

    work page

  6. [6]

    In both cases, sharp variations of the speed of sound mark the transitions between different magnetic phases

    by either measuring the speed of sound as a function of magnetic field at con- stant temperature or by varying temperature in a con- stant field. In both cases, sharp variations of the speed of sound mark the transitions between different magnetic phases. The low-temperature magnetic H − T phase di- agram for H ∥ c is rather complex; it contains four main (s...

    work page 2020

  7. [7]

    P. Link, A. Gukasov, J.-M. Mignot, T. Matsumura, and T. Suzuki, Neutron-diffraction study of quadrupolar or- der in tmte: First evidence for a field-induced magnetic superstructure, Phys. Rev. Lett. 80, 4779 (1998)

    work page 1998

  8. [8]

    Onimaru, T

    T. Onimaru, T. Sakakibara, N. Aso, H. Yoshizawa, H. S. Suzuki, and T. Takeuchi, Observation of modu- lated quadrupolar structures in PrPb 3, Phys. Rev. Lett. 94, 197201 (2005)

    work page 2005

  9. [9]

    J. A. Paix˜ ao, C. Detlefs, M. J. Longfield, R. Caciuffo, P. Santini, N. Bernhoeft, J. Rebizant, and G. H. Lander, Triple- → q octupolar ordering in NpO 2, Phys. Rev. Lett. 89, 187202 (2002)

    work page 2002

  10. [10]

    Okuyama, T

    D. Okuyama, T. Matsumura, H. Nakao, and Y. Mu- rakami, Quadrupolar frustration in Shastry-Sutherland lattice of DyB 4 studied by resonant x-ray scattering, J. Phys. Soc. Jpn. 74, 2434 (2005)

    work page 2005

  11. [11]

    S. Ji, C. Song, J. Koo, J. Park, Y. J. Park, K.-B. Lee, S. Lee, J.-G. Park, J. Y. Kim, B. K. Cho, K.-P. Hong, C.-H. Lee, and F. Iga, Resonant x-ray scattering study of quadrupole-strain coupling in DyB 4, Phys. Rev. Lett. 99, 076401 (2007)

    work page 2007

  12. [12]

    Yanagisawa, T

    T. Yanagisawa, T. Goto, Y. Nemoto, S. Miyata, R. Watanuki, and K. Suzuki, Ultrasonic investigation of quadrupole ordering in HoB 2C2, Phys. Rev. B 67, 115129 (2003)

    work page 2003

  13. [13]

    Yanagisawa, W

    T. Yanagisawa, W. M. Yuhasz, T. A. Sayles, P.-C. Ho, M. B. Maple, H. Watanabe, Y. Yasumoto, Y. Nemoto, T. Goto, Z. Henkie, and A. Pietraszko, Ultrasonic inves- tigation of field-dependent ordered phases in the filled skutterudite compound PrOs 4As12, Phys. Rev. B 77, 094435 (2008)

    work page 2008

  14. [14]

    Mitsumoto, S

    K. Mitsumoto, S. Goto, Y. Nemoto, M. Akatsu, T. Goto, N. D. Dung, T. D. Matsuda, Y. Haga, T. Takeuchi, K. Sugiyama, R. Settai, and Y. Onuki, Quadrupole ef- fects in tetragonal crystals PrCu 2Si2 and DyCu 2Si2, J. Phys.-Condens.Mat. 25, 296002 (2013)

    work page 2013

  15. [15]

    Ishii, T

    I. Ishii, T. Mizuno, K. Takezawa, S. Kumano, Y. Kawamoto, T. Suzuki, D. I. Gorbunov, M. S. Henriques, and A. V. Andreev, Magnetic-field-induced quadrupolar ordering and the crystal electric field ef- fect in the distorted kagome lattice antiferromagnet Dy3Ru4Al12, Phys. Rev. B 97, 235130 (2018)

    work page 2018

  16. [16]

    Watanuki, G

    R. Watanuki, G. Sato, K. Suzuki, M. Ishihara, T. Yanagi- sawa, Y. Nemoto, and T. Goto, Geometrical quadrupolar frustration in DyB 4, J. Phys. Soc. Jpn. 74, 2169 (2005)

    work page 2005

  17. [17]

    H. Sim, S. Lee, K.-P. Hong, J. Jeong, J. R. Zhang, T. Kamiyama, D. T. Adroja, C. A. Murray, S. P. Thomp- son, F. Iga, S. Ji, D. Khomskii, and J.-G. Park, Spon- taneous structural distortion of the metallic Shastry- Sutherland system DyB 4 by quadrupole-spin-lattice cou- pling, Phys. Rev. B 94, 195128 (2016)

    work page 2016

  18. [18]

    K. H. J. Buschow and J. H. N. Creyghton, Magnetic prop- erties of rare earth tetraborides, J. Chem. Phys. 57, 3910 (1972)

    work page 1972

  19. [19]

    Etourneau, J

    J. Etourneau, J. Mercurio, A. Berrada, P. Hagenmuller, R. Georges, R. Bourezg, and J. Gianduzzo, The magnetic and electrical properties of some rare earth tetraborides, J. Less Common Met. 67, 531 (1979)

    work page 1979

  20. [20]

    Z. Fisk, M. B. Maple, D. C. Johnston, and L. D. Woolf, Multiple phase transitions in rare earth tetraborides at low temperature, Solid State Commun. 39, 1189 (1981)

    work page 1981

  21. [21]

    S. B. Shastry and B. Sutherland, Exact ground state of a quantum mechanical antiferromagnet, Physica B+C 108, 1069 (1981)

    work page 1981

  22. [22]

    Michimura, A

    S. Michimura, A. Shigekawa, F. Iga, M. Sera, T. Taka- batake, K. Ohoyama, and Y. Okabe, Magnetic frustra- tions in the Shastry-Sutherland system ErB 4, Physica B 378-380, 596 (2006)

    work page 2006

  23. [23]

    F. Iga, A. Shigekawa, Y. Hasegawa, S. Michimura, T. Takabatake, S. Yoshii, T. Yamamoto, M. Hagiwara, and K. Kindo, Highly anisotropic magnetic phase dia- gram of a 2-dimensional orthogonal dimer system TmB 4, J. Magn. Magn. Mater. 310, e443 (2007)

    work page 2007

  24. [24]

    Siemensmeyer, E

    K. Siemensmeyer, E. Wulf, H.-J. Mikeska, K. Flachbart, S. Gab´ ani, S. Mat’aˇ s, P. Priputen, A. Efdokimova, and N. Shitsevalova, Fractional magnetization plateaus and magnetic order in the Shastry-Sutherland magnet TmB 4, 11 Phys. Rev. Lett. 101, 177201 (2008)

    work page 2008

  25. [25]

    L. Ye, T. Suzuki, and J. G. Checkelsky, Electronic trans- port on the Shastry-Sutherland lattice in Ising-type rare- earth tetraborides, Phys. Rev. B 95, 174405 (2017)

    work page 2017

  26. [26]

    Yoshii, T

    S. Yoshii, T. Yamamoto, M. Hagiwara, S. Michimura, A. Shigekawa, F. Iga, T. Takabatake, and K. Kindo, Mul- tistep magnetization plateaus in the Shastry-Sutherland system TbB 4, Phys. Rev. Lett. 101, 087202 (2008)

    work page 2008

  27. [27]

    Yamauchi, N

    H. Yamauchi, N. Metoki, R. Watanuki, K. Suzuki, H. Fukazawa, S. Chi, and J. A. Fernandez-Baca, Mag- netic structure and quadrupolar order parameter driven by geometrical frustration effect in NdB 4, J. Phys. Soc. Jpn 86, 044705 (2017)

    work page 2017

  28. [28]

    D. D. Khalyavin, D. Brunt, N. Qureshi, A. R. Wildes, B. Ouladdiaf, R. D. Johnson, G. Balakrishnan, and O. A. Petrenko, Magnetic ground state of NdB 4: Interplay be- tween anisotropic exchange interactions and hidden or- der on a Shastry-Sutherland lattice, Phys. Rev. B 109, L220411 (2024)

    work page 2024

  29. [29]

    Ohlendorf, S

    R. Ohlendorf, S. Spachmann, L. Fischer, K. Dey, D. Brunt, G. Balakrishnan, O. A. Petrenko, and R. Klin- geler, Magnetoelastic coupling and Gr¨ uneisen scaling in NdB4, Phys. Rev. B 103, 104424 (2021)

    work page 2021

  30. [30]

    Ohlendorf, S

    R. Ohlendorf, S. Spachmann, L. Fischer, F. L. Carstens, D. Brunt, G. Balakrishnan, O. A. Petrenko, and R. Klin- geler, Magnetic phase diagram and magnetoelastic cou- pling of NdB 4 studied by high-resolution capacitance dilatometry up to 35 T, Phys. Rev. B 108, 224411 (2023)

    work page 2023

  31. [31]

    Watanuki, T

    R. Watanuki, T. Kobayashi, R. Noguchi, and K. Suzuki, Possible multipolar transition in NdB 4, J. Phys.: Conf. Ser. 150, 042229 (2009)

    work page 2009

  32. [32]

    Metoki, H

    N. Metoki, H. Yamauchi, M. Hagihala, R. Watanuki, S. Kawamura, M. Kofu, K. Nakajima, and M. Matsuda, Magnetic and quadrupole coupling emerging in NdB 4 with geometrically frustrated orthogonal antiferromag- netic dimer, Phys. Rev. B 111, 104424 (2025)

    work page 2025

  33. [33]

    Yamauchi, N

    H. Yamauchi, N. Metoki, R. Watanuki, T. Hong, J. A. Fernandez-Baca, M. Hagihala, T. Masuda, H. Yoshizawa, and S. Itoh, Neutron spectroscopy study on crystalline electric field excitations in NdB 4, J. Phys. Soc. Jpn 94, 054705 (2025)

    work page 2025

  34. [34]

    Okuyama, T

    D. Okuyama, T. Matsumura, T. Mouri, N. Ishikawa, K. Ohoyama, H. Hiraka, H. Nakao, K. Iwasa, and Y. Mu- rakami, Competition of magnetic and quadrupolar or- der parameters in HoB 4, J. Phys. Soc. Jpn. 77, 044709 (2008)

    work page 2008

  35. [35]

    J. Y. Kim, B. K. Cho, and S. H. Han, Anisotropic mag- netic phase diagrams of HoB 4 single crystal, J. Appl. Phys. 105, 07E116 (2009)

    work page 2009

  36. [36]

    Brunt, G

    D. Brunt, G. Balakrishnan, A. R. Wildes, B. Ouladdiaf, N. Qureshi, and O. A. Petrenko, Field-induced magnetic states in holmium tetraboride, Phys. Rev. B 95, 024410 (2017)

    work page 2017

  37. [37]

    Brunt, M

    D. Brunt, M. C. Hatnean, O. A. Petrenko, M. R. Lees, and G. Balakrishnan, Single-crystal growth of metallic rare-earth tetraborides by the floating-zone technique, Crystals 9, 211 (2019)

    work page 2019

  38. [38]

    For details on MGML see https://mgml.eu

    work page

  39. [39]

    Kriegner, Z

    D. Kriegner, Z. Matˇ ej, R. Kuˇ zel, and V. Hol´ y, Powder diffraction in Bragg–Brentano geometry with straight lin- ear detectors, J. Appl. Crystallogr. 48, 613 (2015)

    work page 2015

  40. [40]

    Petricek, L

    V. Petricek, L. Palatinus, J. Plasil, and M. Dusek, Jana2020 – a new version of the crystallographic comput- ing system jana, Z. Krist-Cryst. Mater. 238, 271 (2023)

    work page 2023

  41. [41]

    B´ erar and G

    J.-F. B´ erar and G. Baldinozzi, Modeling of line-shape asymmetry in powder diffraction, J. Appl. Crystallogr. 26, 128 (1993)

    work page 1993

  42. [42]

    Stokes, D.M

    H.T. Stokes, D.M. Hatch, and B.J. Campbell, ISODIS- TORT, ISOTROPY Software Suite, iso.byu.edu

    work page

  43. [43]

    B. J. Campbell, H. T. Stokes, D. E. Tanner, and D. M. Hatch, ISODISPLACE: a web-based tool for explor- ing structural distortions, J. Appl. Crystallogr. 39, 607 (2006)

    work page 2006

  44. [44]

    Capillas, E

    C. Capillas, E. Kroumova, M. I. Aroyo, J. M. Perez-Mato, H. T. Stokes, and D. M. Hatch, SYMMODES: a software package for group-theoretical analysis of structural phase transitions, J. Appl. Crystallogr. 36, 953 (2003)

    work page 2003

  45. [45]

    J. M. Perez-Mato, D. Orobengoa, and M. I. Aroyo, Mode crystallography of distorted structures, Acta Crystallo- graphica Section A: Foundations of Crystallography 66, 558 (2010)

    work page 2010

  46. [46]

    Bilbao Crystallographic Server, http://www.cryst.ehu.es/

    work page

  47. [47]

    L¨ uthi, Physical Acoustics in the Solid State (Springer, Heidelberg, 2005)

    B. L¨ uthi, Physical Acoustics in the Solid State (Springer, Heidelberg, 2005)

    work page 2005

  48. [48]

    Zherlitsyn, S

    S. Zherlitsyn, S. Yasin, J. Wosnitza, A. A. Zvyagin, A. V. Andreev, and V. Tsurkan, Spin-lattice effects in selected antiferromagnetic materials (review article), Low Tem- perature Physics 40, 123 (2014)

    work page 2014

  49. [49]

    Mnyukh, Hysteresis of solid-state reactions: Its caus e and manifestations, Am

    Y. Mnyukh, Hysteresis of solid-state reactions: Its caus e and manifestations, Am. J. Condens. Mat. Phys. 3, 142 (2013)

    work page 2013

  50. [50]

    Le Bail, Whole powder pattern decomposition meth- ods and applications: A retrospection, Powder Diffrac- tion 20, 316–326 (2005)

    A. Le Bail, Whole powder pattern decomposition meth- ods and applications: A retrospection, Powder Diffrac- tion 20, 316–326 (2005)

    work page 2005

  51. [51]

    Ivantchev, E

    S. Ivantchev, E. Kroumova, G. Madariaga, J. M. P´ erez- Mato, and M. I. Aroyo, SUBGROUPGRAPH: a com- puter program for analysis of group–subgroup relations between space groups, J. Appl. Crystallogr. 33, 1190 (2000)

    work page 2000

  52. [52]

    H. M. Rietveld, Line profiles of neutron powder- diffraction peaks for structure refinement, Acta Crystal- logr. 22, 151 (1967)

    work page 1967

  53. [53]

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

    work page 1969

  54. [54]

    V. V. Novikov, N. V. Mitroshenkov, A. V. Matrovnikov, D. V. Avdashchenko, S. V. Trubnichov, and A. V. Mo- rozov, Peculiarities of the lattice thermal properties of rare-earth tetraborides, J. Therm. Anal. Calorim. 120, 1597 (2015)

    work page 2015

  55. [55]

    M. S. Henriques, V. Petˇ r ´ ıˇ cek, S. Goswami, and M. Duˇ sek, Analysis of magnetic structures in JANA2020, Acta Crystallogr. B 80, 409 (2024)

    work page 2024

  56. [56]

    A. P. Cracknell, B. L. Davies, S. C. Miller, and W. F. Love, Kronecker Product Tables, Vol. 1 (Plenum Press, New York, 1979)

    work page 1979

  57. [57]

    S. C. Miller and W. F. Love, Tables of Irreducible Representations of Space Groups and Co-Re presen (Pruett Press, Boulder, Colorado, 1967)

    work page 1967

  58. [58]

    Hutchings, Point-charge calculations of energy lev- els of magnetic ions in crystalline electric fields, in Solid State Physics , Vol

    M. Hutchings, Point-charge calculations of energy lev- els of magnetic ions in crystalline electric fields, in Solid State Physics , Vol. 16, edited by F. Seitz and D. Turnbull (Academic Press, 1964) pp. 227–273

    work page 1964

  59. [59]

    Y. P. Varshni, Temperature dependence of the elastic constants, Phys. Rev. B 2, 3952 (1970)

    work page 1970

  60. [60]

    Brunt, G

    D. Brunt, G. Balakrishnan, D. Mayoh, M. R. Lees, D. I. Gorbunov, N. Qureshi, and O. A. Petrenko, Magnetisa- 12 tion process in the rare earth tetraborides, NdB 4 and HoB4, Sci. Rep. 8, 232 (2018)

    work page 2018

  61. [61]

    Petrenko, G

    O. Petrenko, G. Balakrishnan, D. Brunt, and B. F ˚ ak, Detailed measurements of the crystalline electric field of Shastry-Sutherland magnets rare earth tetraborides. In- stitut Laue-Langevin (ILL) (2015)

    work page 2015

  62. [62]

    Spontaneous lattice distortion and crystal field effects in HoB 4

    D. Brunt, Magnetic Properties of Frustrated Shastry-Sutherland Magnets; Ph.D. thesis , The University of Warwick (2017). Supplemental Material to “Spontaneous lattice distortion and crystal field effects in HoB 4” S. Goswami, 1 D. I. Gorbunov, 2 D. Kriegner, 1, 3 I. Ishii, 4 C. A. Corr ˆea,1 T. Suzuki,4 D. Brunt, 5, 6 G. Balakrishnan, 5 S. Zherlitsyn, 7 J....

    work page 2017