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REVIEW 4 major objections 5 minor 45 references

Criticality and magnetic phases of Ising Shastry-Sutherland candidate holmium tetraboride

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

Pith's one-line read This paper reports the discovery of a previously unseen in-plane 1/7 magnetic order in HoB4 that exists only inside a narrow critical temperature window at 1.8 T.

desk verdict The new in-plane scattering signal in HoB4's critical phase is worth taking seriously, but the 1/7 claim is statistically shaky and the phase claim needs more data. read the letter →

arxiv 2504.15966 v1 pith:CECJKL2E submitted 2025-04-22 cond-mat.str-el cond-mat.mtrl-sci

classification cond-mat.str-elcond-mat.mtrl-sci
keywords holmiumtetraborideShastry-SutherlandlatticefrustratedmagnetismneutrondiffractionmagnetizationplateauincommensuratemagneticorderIsingmodelsimulatedannealing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that holmium tetraboride, a frustrated Shastry-Sutherland magnet, hosts a previously unseen magnetic phase at the edge of its antiferromagnetic order. In a narrow temperature window between $T_{N1}$ and $T_{N2}$ at $B = 1.8$ T, neutron scattering shows the out-of-plane incommensurate order acquiring an additional in-plane modulation, most clearly at a wave vector near $1/7$ of a reciprocal lattice unit. If the claim holds, the critical region between the two ordering temperatures contains a genuine ordered phase with in-plane components, distinct from the surrounding antiferromagnetic and paramagnetic phases. The paper also uses simulations of a three-dimensional longitudinal-field Ising model to show that out-of-plane couplings and lattice defects can split in-plane magnetic peaks and stabilize extra magnetization plateaus, offering a mechanism for sample-dependent features.

What carries the argument

The load-bearing mechanism is the three-dimensional Ising Shastry-Sutherland Hamiltonian extended with five in-plane couplings $J_1$--$J_5$, three out-of-plane couplings $J_6$--$J_8$, and a longitudinal Zeeman field $h$ (Eq. 2). Ground states are found by simulated annealing with parallel tempering on a $60 \times 60 \times 9$ spin lattice, and the resulting order is read from the Fourier transform of the two-spin correlation function (Eq. 4). The qualitative argument is that increasing the out-of-plane coupling $J_7$ splits a single in-plane ordering peak into pairs and quadruplets of peaklets, matching the neutron peak splitting in the critical phase, while single-site and 'chunk' defects generate narrow magnetization plateaus that are absent in the clean lattice.

What would settle it

Cool the same crystal through the lower transition at $B = 1.8$ T in fine temperature steps while tracking the $1/7$ satellite: if the order is intrinsic to the critical phase, the peak should vanish abruptly at the transition and reappear reversibly on warming, whereas hysteresis or a smeared onset would point to defect or domain-wall stabilization.

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Extended reading notes

Core claim

The central discovery is a new magnetic phase, the only one known in HoB4 with in-plane magnetic Bragg reflections, confined to the critical phase between $T_{N1} = 7.22$ K and $T_{N2} = 5.97$ K at $B = 1.8$ T. On warming from the antiferromagnetic phase, the incommensurate order at $L \approx 0.43$ r.l.u. develops satellite peaks $\vec{Q}_{\varepsilon} = (\pm\epsilon,0,\delta')$ and $\vec{Q}_{\gamma} = (0,\pm\gamma,\delta')$, with $\epsilon = 0.0245 \pm 0.004$ r.l.u. and $\gamma = 0.142 \pm 0.00025 \approx 1/7$ r.l.u. The authors describe the $1/7$ feature as a likely commensurate ordering that appears as an additional modulation of the out-of-plane incommensurate order; no other in-plane order is observed elsewhere in the phase diagram.

Load-bearing premise

The simulation-based explanation assumes that a classical Ising model with the field along the $c$ axis describes the critical phase, even though the magnetic moments in the adjacent antiferromagnetic phase are canted $23^\circ$ away from $c$, leaving a sizeable transverse field component.

Editorial extensions

If this is right

  • HoB4's critical temperature window should be treated as a distinct ordered phase, not a fluctuation-dominated crossover, and any future field-temperature phase diagram should include the in-plane-ordered $C$ phase at $B \approx 1.8$ T between $T_{N1}$ and $T_{N2}$.
  • The robust out-of-plane incommensurate order at $L \approx 0.43$ r.l.u. persists even as the $1/3$ plateau disappears, indicating it is set by leading Hamiltonian terms while the $1/3$ and $1/7$ orders are sub-leading.
  • Defect-induced plateaus can appear in narrow field ranges, so reported plateaus such as $1/2$, $4/9$, or $3/5$ may vary from sample to sample; the cleaner single crystal studied here shows only a trace near $5/9$.
  • Out-of-plane couplings alone can produce in-plane magnetic ordering in a Shastry-Sutherland magnet, so two-dimensional treatments are insufficient for HoB4 and a full three-dimensional model is required.
  • The absence of many small plateaus in this crystal suggests it has fewer defects than earlier samples, making it a useful reference for separating intrinsic from defect-driven physics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the $1/7$ wave vector is a commensurate lock-in selected by sub-leading couplings, fine field sweeps near $T = 5$ K should reveal neighboring commensurate modulations (for example $1/9$ or $1/5$) at slightly different fields; the current data do not test this.
  • The coexistence of the out-of-plane incommensurate order with an in-plane modulation points toward a multi-$\vec{Q}$ state; polarized neutron scattering could determine whether the combined order has a chiral or stripe character invisible in unpolarized Laue data.
  • The defect mechanism predicts a direct materials test: introducing controlled vacancies or stacking faults into HoB4 should create the same narrow magnetization plateaus at the fields where the simulations show them, while a deliberately defect-free crystal should lose the $5/9$ trace.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript reports a combined neutron diffraction, magnetization/susceptibility, and simulated-annealing study of the Shastry-Sutherland candidate HoB4, using a single crystal for all measurements. The central experimental claim is the discovery of a previously unreported in-plane ordered phase confined to a critical temperature window between T_N1 and T_N2 at B = 1.8 T. In this window, neutron data show magnetic Bragg reflections with in-plane modulation vectors Q_eps = (±eps, 0, delta') and Q_gamma = (0, ±gamma, delta'), with reported eps = 0.0245 ± 0.004 r.l.u., delta' = 0.43 r.l.u., and gamma = 0.142 ± 0.00025 r.l.u., interpreted as a likely commensurate 1/7 in-plane ordering. The authors also present a 3D classical Ising SSL model with out-of-plane interactions and defects, showing that out-of-plane couplings can split in-plane Bragg peaks into multiple features and that defects can stabilize additional magnetization plateaus, offering a qualitative explanation for sample-dependent behavior. The paper concludes that defects and out-of-plane interactions are important for understanding frustrated SSL magnets, while acknowledging that the model does not reproduce the observed L_inc = 0.43 or 1/3 orders and that a full quantum treatment is beyond the manuscript's scope.

Significance. If the central claim is correct, the manuscript reports a genuinely new magnetic phase in HoB4: the only in-plane ordered phase identified in this compound, occurring in the critical regime between two established transitions. This would be a useful contribution to the experimental phase diagram of rare-earth Shastry-Sutherland magnets and would motivate further study of sub-leading Hamiltonian terms near phase boundaries. The experimental strengths include the use of a single crystal for all measurements, which removes sample-shape and demagnetization ambiguities, and the clear observation of an in-plane peak-splitting phenomenon that is not present in earlier reports. The simulation part, while explicitly acknowledged as qualitative, demonstrates a plausible mechanism by which out-of-plane interactions can generate in-plane structure in a frustrated Ising system, and the defect study provides a concrete and falsifiable suggestion for sample-dependent plateau formation. The paper is honest about the model's failures, which is a positive feature.

major comments (4)
  1. [Section IV, Fig. 4f] The assignment gamma = 0.142 ± 0.00025 approx 1/7 is not supported by the quoted uncertainty. The difference between 0.142 and 1/7 = 0.142857 is approximately 0.000857, which is about 3.4 standard deviations of the reported fitted value. Either the uncertainty is underestimated, the fit should be re-evaluated, or the modulation should be described as incommensurate with gamma approx 0.142. Since the phrase 'likely commensurate 1/7th ordering' is central to the characterization of the new phase, this point must be addressed before publication.
  2. [Section IV, Fig. 4a-c] The existence of a distinct thermodynamic phase in the critical C window currently rests on neutron data at a single temperature (T = 5 K) and a single field (B = 1.8 T). No scans are shown above T_N1 or at other field values to establish that the gamma satellites appear only inside the C phase, and no resolution analysis (for example, comparing peak widths with nuclear Bragg peaks) is presented to exclude critical diffuse scattering or a multi-domain splitting of the L_inc = 0.43 order. A temperature sweep across both phase boundaries and a field sweep at fixed temperature, together with a resolution check, are needed to substantiate the claim that this is a true phase rather than a near-critical fluctuation effect.
  3. [Section V, Eq. (2) and Fig. 5] The simulation is offered as a qualitative explanation for the in-plane ordering, but it explicitly fails to reproduce the L_inc = 0.43 or 1/3 orders, and the coupling parameters are initialized from dipole-dipole estimates and then varied over ±60% without a fitting procedure tied to the experimentally observed Q-vectors. As presented, the connection between Fig. 5(d-f) and the measured eps and gamma splittings is only qualitative. The mechanistic claim that out-of-plane interactions 'trigger' the observed in-plane order would be considerably strengthened by a quantitative comparison between the simulated splitting in Fourier space and the measured modulation vectors, or by identifying parameter regimes where the model reproduces the 0.43 and 1/7 peaks simultaneously.
  4. [Section V, paragraph beginning 'Questions can arise'] The model used is a longitudinal-field Ising model, but the authors note that the AFM phase has spins canted 23 degrees away from the c axis, meaning the field along c has a sizeable transverse component. The manuscript acknowledges that a transverse-field Ising model or quantum treatment may be required, but this limitation is important because the proposed classical annealing mechanism for the in-plane peaks could be invalid if transverse components or quantum fluctuations are the actual origin of the observed order. The authors should either test whether a small transverse-field term changes the annealing results, or explicitly restrict their mechanistic claim to the longitudinal-field component of the phase diagram.
minor comments (5)
  1. [Fig. 4 caption and text] The caption reports gamma = 0.14 r.l.u. while the main text reports gamma = 0.142 ± 0.00025 r.l.u.; these values should be made consistent.
  2. [Eq. (2)] The sign convention for the Zeeman term -h sum S_m should be stated explicitly, since the direction of the applied field relative to the Ising axis and the sign of h determine the physical meaning of positive and negative magnetization plateaus.
  3. [Table 2] The interaction parameters in Table 2 are listed without units; it would be helpful to state explicitly that they are in units of J1 (or Kelvin/meV) in the table caption or in the text.
  4. [References] Reference [10] duplicates reference [4] (both are Shastry and Sutherland, Physica B+C 108, 1069 (1981)); please replace one with another relevant citation.
  5. [Abstract and Section I] The abstract contains a typo ('crystalize'); there are also minor grammatical issues in the introduction (for example, 'the spin s are arranged') that should be corrected in a careful proofreading pass.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the experimental discovery and the simulation explanation are independent of each other.

full rationale

The paper's central claim, the discovery of in-plane magnetic order in HoB4 in the critical temperature window (Section IV, Fig. 4), rests on neutron Laue diffraction data and is not derived from the simulations. The simulated-annealing model in Section V uses Eq. (2) with interaction parameters initialized from dipole-dipole distances in Table 2, and the paper explicitly states the model 'fails to reproduce the L_inc = 0.43 or the 1/3rd phase' and that 'more work is required to find either the 1/7th in-plane split peaks or the 1/3rd out-of-plane peaks observed in our data.' The in-plane peak splitting in the FFT is an emergent consequence of varying the out-of-plane coupling J7, not a fitted reproduction of the measured gamma = 0.142 or epsilon = 0.0245 wave vectors. The prior work cited as [39] supplies a baseline extended SSL model and a 5/9 plateau connection, but the new in-plane phase claim does not reduce to that citation. There is no self-definitional relation, no fitted input masquerading as a prediction, and no imported uniqueness theorem. The skeptical concerns about the new phase resting on a single temperature point or about resolution-limited scattering are correctness/evidence issues, not circularity.

Assumptions & free parameters 10 free parameters · 4 assumptions · 0 invented entities

The core experimental discovery does not rest on the Hamiltonian parameters, but the mechanistic explanation does. All coupling values and defect concentrations are chosen by hand from dipole-dipole distances and varied, not fitted to the target neutron peaks. No new physical entities are introduced.

free parameters (10)
  • J2 (in-plane exchange, relative to J1=1) = 1.03
    Set from dipole-dipole distance estimate in Table 2 and used in Fig. 5; not fit to HoB4 data.
  • J3 (in-plane exchange) = 0.19
    Chosen from dipole-dipole estimate; not fit to target peaks.
  • J4 (in-plane exchange) = 0.35
    Chosen from dipole-dipole estimate; not fit to target peaks.
  • J5 (in-plane exchange) = 0.14
    Chosen from dipole-dipole estimate; not fit to target peaks.
  • J6 (out-of-plane exchange) = 0.77
    Chosen from dipole-dipole estimate; not fit to target peaks.
  • J7 (out-of-plane exchange) = 0.12, 0.29, 0.5
    Varied to demonstrate peak splitting; not determined by experiment.
  • J8 (out-of-plane exchange) = 0.308
    Chosen from dipole-dipole estimate; not fit to target peaks.
  • h (Zeeman field) = 6
    Chosen in Fig. 5c-f to realize the |M|=0.5 plateau; not tied to a specific HoB4 field value.
  • Single-site defect count = 1000 spins removed
    Arbitrary choice to model vacancies; not measured.
  • Chunk defect count = 30 domains of 3x3x3 spins
    Arbitrary choice to model larger defects; not measured.
assumptions (4)
  • domain assumption Ising spin model with longitudinal field only (Eq. 2) approximates HoB4 in the IC, C, 1/3, and PFP phases.
    The authors justify this by citing figures in [32] and noting spins point along c in those phases, but the AFM phase has 23 degree canting, so the model is an approximation. Section V.
  • domain assumption Classical simulated annealing and parallel tempering find ground states of the frustrated 3D Ising Hamiltonian.
    Annealing on a 60x60x9 lattice is assumed to converge to representative low-energy states; no convergence checks or residual energy analysis are presented. Section V.
  • domain assumption Initial J_i values can be estimated from dipole-dipole interactions using U~S1S2/r^3.
    Exchange contributions and crystal field effects are neglected in the initial guess; authors vary parameters within 60% to compensate. Eq. 3, Table 2.
  • domain assumption Randomly removing spins models real defects in the crystal.
    Real defects could be stacking faults or exchange disorder; the paper uses only missing-spin vacancies, so the defect model is a simplified proxy. Section V.

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Pith. "Pith review of Criticality and magnetic phases of Ising Shastry-Sutherland candidate holmium tetraboride." pith.science (2026). https://pith.science/paper/CECJKL2E

@misc{pith2026250415966,
  author       = {Pith},
  title        = {Pith review of: Criticality and magnetic phases of Ising Shastry-Sutherland candidate holmium tetraboride},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CECJKL2E}},
  note         = {Machine review of arXiv:2504.15966}
}
read the original abstract

Frustrated magnetic systems arising in geometrically constrained lattices represent rich platforms for exploring unconventional phases of matter, including fractional magnetization plateaus, incommensurate orders, and complex domain dynamics. However, determining the microscopic spin configurations that stabilize such phases is a key challenge, especially when in-plane and out-of-plane spin components coexist and compete. Here, we combine neutron scattering and magnetic susceptibility experiments with simulations to investigate the emergence of field-induced fractional plateaus and the related criticality in a frustrated magnet holmium tetraboride (HoB4) that represents the family of rare earth tetraborides that crystalize in a Shastry-Sutherland lattice in the ab plane. We focus on the interplay between classical and quantum criticality near phase boundaries as well as the role of material defects in the stabilization of the ordered phases. We find that simulations using classical annealing can explain certain observed features in the experimental Laue diffraction and the origin of multiple magnetization plateaus. Our results show that defects and out of plane interactions play an important role and can guide the route towards resolving microscopic spin textures in highly frustrated magnets.

Figures

Figures reproduced from arXiv: 2504.15966 by the authors.

Figure 5
Figure 5. a. Phase diagram for variable 𝐽7 and ℎ in the absence of defects. The rest of parameter values: 𝐽1 = 1, 𝐽2 = 1.03, 𝐽3 = 0.19, 𝐽4 = 0.35, 𝐽5 = 0.14, 𝐽6 = 0.77, 𝐽8 = 0.308. b. The evolution of magnetization plateau |𝑀| = 0.5, as the function of 𝐽7 in the absence of defects. c. in-plane |𝑀| = 0.5 magnetic ordering for 𝐽1 = 1, 𝐽2 = 1.03, 𝐽3 = 0.19, 𝐽4 = 0.35, 𝐽5 = 0.14, 𝐽6 = 0.77, 𝐽7 = 0.12, 𝐽8 = 0.308, ℎ = 6, showing s… view at source ↗

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Works this paper leans on

45 extracted references · 41 canonical work pages

  1. [1]

    Introduction Frustrated magnetic materials exhibit some of the most exotic and poorly understood phases in condensed matter physics, driven by competing interactions that prevent conventional magnetic order [1- 3]. Lattices such as the Shastry-Sutherland lattice (SSL), Kagome, and triangular lattices host a variety of unconventional phases, including frac...

  2. [2]

    51.41 0.141.9 0.771.09

  3. [3]

    Seeking Quasiparticles from Low -Energy Spin Dynamics

    0 1.4 Table 2: Initial guess of interaction parameters according to dipole -dipole interactions. 𝑟𝑖 represents the distances between Holmium ions connected through 𝐽𝑖 interaction in 𝐻𝑜𝐵4 single crystal as measured using XRD in Section II. 11 Where 𝐶ሺ𝑥, 𝑦ሻ = 〈𝑆ሺ0,0ሻ, 𝑆ሺ𝑥, 𝑦ሻ〉 is two -spin correlation function. Since the observed in -plane spin structure co...

  4. [4]

    Balents, Nature 464, 199 (2010)

    L. Balents, Nature 464, 199 (2010)

  5. [5]

    Moessner and A

    R. Moessner and A. P. Ramirez, Physics Today 59, 24 (2006)

  6. [6]

    J. G. Rau, E. K.-H. Lee, H.-Y . Kee, Annual Rev. Condens. Matter Phys. 7, 195 (2016)

  7. [8]

    Miyahara and K

    S. Miyahara and K. Ueda, J. Phys.: Condens. Matter 15, R327 (2003)

  8. [9]

    H.P Hu et al., Scientific reports 5, 8433 (2015)

Show all 45 references
  1. [10]

    Lacroix, P

    C. Lacroix, P. Mendels, F. Mila, Introduction to Frustrated Magnetism, Springer (2011)

  2. [11]

    Kitaev, Annals of Physics 21, 2 (2006)

    A. Kitaev, Annals of Physics 21, 2 (2006)

  3. [12]

    Savary and L

    L. Savary and L. Balents, Rep. Prog. Phys. 80, 016502 (2017)

  4. [13]

    B. S. Shastry and B. Sutherland, Physica B+C 108, 1069 (1981)

  5. [14]

    Jensen and A

    J. Jensen and A. R. Mackintosh, Rare Earth Magnetism: Structures and Excitations, Oxford University Press (1991)

  6. [15]

    Yu. I. Dublenych, Phys. Rev. E. 88, 022111 (2013)

  7. [16]

    Huo et al., J

    L. Huo et al., J. Appl. Phys. 11 , 073908 (2013)

  8. [17]

    Brunt et al., Scientific Reports

    D. Brunt et al., Scientific Reports. 8, 232 (2018)

  9. [18]

    Siemensmeyer et al., Phys

    S. Siemensmeyer et al., Phys. Rev. Lett. 101, 177201 (2008)

  10. [19]

    Marshall et al., Nat

    M. Marshall et al., Nat. Com. 14, 3641 (2023)

  11. [20]

    Qureshi et al., Phys

    N. Qureshi et al., Phys. Rev. B. 106, 094427 (2022)

  12. [21]

    Sachdev, Quantum Phase Transitions, Cambridge University Press (1999)

    S. Sachdev, Quantum Phase Transitions, Cambridge University Press (1999)

  13. [22]

    H. v. Löhneysen et al., Rev. Mod. Phys. 79, 1015 (2007)

  14. [23]

    A. W. Sandvik, Phys. Rev. Lett. 104, 137204 (2010)

  15. [24]

    Heidrich-Meisner et al., Phys

    F. Heidrich-Meisner et al., Phys. Rev. B. 75, 064413 (2007)

  16. [25]

    A. M. Samarakoon et al., Phys. Rev. R 4, L022061 (2022)

  17. [26]

    A. M. Samarakoon et al., arXiv:2011.05685 (2020)

  18. [27]

    A.Brassington et al., Phys. Rev. Mat 8, 094001 (2024)

  19. [28]

    Yang et al., Phys

    J-W. Yang et al., Phys. Rev. B 109, 205111 (2024)

  20. [29]

    Corboz et al., arXiv: 2502.14091 (2025)

    P. Corboz et al., arXiv: 2502.14091 (2025)

  21. [30]

    Zhang et al., Phys

    X-T. Zhang et al., Phys. Rep 1070, 1-59 (2024)

  22. [31]

    Cui et al., ArXiv:2411.00302 (2024)

    Y . Cui et al., ArXiv:2411.00302 (2024)

  23. [32]

    Onizuka et al., Journal of the Physical Society of Japan 69, 1016-1018 (2000)

    K. Onizuka et al., Journal of the Physical Society of Japan 69, 1016-1018 (2000)

  24. [33]

    Shi et al., Nat

    Z. Shi et al., Nat. Com 1 , 2301 (2022). 15

  25. [34]

    Matsuda et al., Phys

    Y .H. Matsuda et al., Phys. Rev. Lett. 111, 137204 (2013)

  26. [35]

    Brunt et al., Phys

    D. Brunt et al., Phys. Rev. B. 95, 024410 (2017)

  27. [36]

    Yu. I. Dublenych, Phys. Rev. Lett. 109, 167202 (2012)

  28. [37]

    Farkašovský and L

    P. Farkašovský and L. Regeciová, The European Physical Journal B. 92, 33 (2019)

  29. [38]

    Haravifard et al., PNAS

    S. Haravifard et al., PNAS. 109 (7), 2286-2289 (2012)

  30. [39]

    Haravifard et al., PNAS

    S. Haravifard et al., PNAS. 111 (40), 14372-14377 (2014)

  31. [40]

    Haravifard et al., PNAS

    S. Haravifard et al., PNAS. 112 (5), E383-E384 (2015)

  32. [41]

    Kayris et al., Phys

    P. Kayris et al., Phys. Rev. X. Quantum. 1, 020320 (2020)

  33. [42]

    Jha et al., International Conference of Rebooting Computing (ICRC), 119-123 (2021)

    A.A. Jha et al., International Conference of Rebooting Computing (ICRC), 119-123 (2021)

  34. [43]

    Manovitz et al., Nature 638, 86-92 (2025)

    T. Manovitz et al., Nature 638, 86-92 (2025)

  35. [44]

    Salloum et al., Procedia Computer Science, 246, 3285 – 3293 (2024)

    H. Salloum et al., Procedia Computer Science, 246, 3285 – 3293 (2024)

  36. [45]

    castelvecchi, Nature (2024)

    D. castelvecchi, Nature (2024)

  37. [46]

    Beck et al., Sciencedirect 161, 11-25 (2024)

    T. Beck et al., Sciencedirect 161, 11-25 (2024)

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