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arxiv: 2604.25282 · v1 · submitted 2026-04-28 · ❄️ cond-mat.str-el

Piezomagnetic effect of a rare-earth-based altermagnet TbPt6Al3

Ryohei Oishi , Kazunori Umeo , Takuya Aoyama , Takahiro Onimaru , Kaya Kobayashi This is my paper

Pith reviewed 2026-05-07 15:22 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords piezomagnetic effectaltermagnetTbPt6Al3rare-earth magnetsspin-orbit couplinguniaxial stressNéel temperaturemagnetization
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The pith

TbPt6Al3 exhibits a large piezomagnetic effect below its ordering temperature with a coefficient more than 100 times larger than in other altermagnets.

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

The paper reports magnetization measurements on single crystals of TbPt6Al3 under uniaxial stress. Below the Néel temperature the magnetization along the trigonal axis rises linearly with applied stress, which the authors interpret as the piezomagnetic response of the g-wave altermagnetic order. The extracted coefficient Q11 reaches 9.1 times 10 to the minus 3 Bohr magnetons per formula unit per megapascal at 2 kelvin. The authors attribute the unusually large value to strong relativistic spin-orbit coupling from the terbium 4f electrons and note that the temperature dependence of the coefficient tracks the magnetic moment.

Core claim

In TbPt6Al3 the magnetization measured in a field along the trigonal a axis increases linearly with uniaxial stress sigma for all temperatures below TN. This linear response demonstrates the piezomagnetic effect. The piezomagnetic coefficient Q11 at 2 K equals 9.1 times 10 to the minus 3 mu_B per formula unit per MPa, more than two orders of magnitude larger than reported values for other altermagnets and noncollinear antiferromagnets. The temperature variation of Q11 below TN follows a power law with critical exponent beta approximately 0.28, close to the exponent obtained for the ordered moment by neutron diffraction. The authors propose that both the large coefficient and the high poling场

What carries the argument

Linear piezomagnetic coefficient Q11 that couples uniaxial stress to net magnetization in the altermagnetically ordered state.

If this is right

  • The piezomagnetic coefficient follows the magnetic order parameter with a critical exponent near 0.3.
  • Rare-earth altermagnets can host piezomagnetic coefficients two orders of magnitude larger than transition-metal counterparts.
  • A magnetic field of 10000 Oe is required to reach the single-domain state needed for the full piezomagnetic response.
  • The theoretically expected nonlinear piezomagnetic term is not observed, indicating dominance of the linear response in this material.

Where Pith is reading between the lines

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

  • Compounds with strong 4f spin-orbit coupling may be systematically better for piezomagnetic applications than 3d-based altermagnets.
  • Uniaxial stress could serve as a low-power handle for domain switching in altermagnetic devices.
  • Similar measurements on other Tb-based or rare-earth altermagnets would test whether the large coefficient is generic to 4f moments.
  • The missing nonlinear term may reflect the specific symmetry of the g-wave altermagnetic structure.

Load-bearing premise

The linear rise in magnetization with uniaxial stress is produced by the piezomagnetic effect of the altermagnetic order and not by other stress-induced changes in the magnetic structure.

What would settle it

Absence of a linear increase in magnetization with uniaxial stress below TN, or a measured Q11 coefficient no larger than about 10 to the minus 5 mu_B per formula unit per MPa, would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.25282 by Kaya Kobayashi, Kazunori Umeo, Ryohei Oishi, Takahiro Onimaru, Takuya Aoyama.

Figure 1
Figure 1. Figure 1: (Color online) (a) Magnetic structure of TbPt6Al3 26) in which Pt1, Pt2, Pt4, and Al are omitted for clar￾ity. (b) The Tb2Pt3 honeycomb layer viewed from the c axis. The Tb atoms have 3 symmetry. The opposite mag- ¯ netic moments on the honeycomb plane are connected by the two-fold rotational symmetry. (c) Backscattered electron image of TbPt6Al3. The impurity phase shown by black dots is PtAl. (d) The tem… view at source ↗
Figure 2
Figure 2. Figure 2: (Color online) Temperature dependence of magnetization M(T) of the single crystal of TbPt6Al3 under σ1. Measurements were carried out after the poling process at Hpol = 1000 Oe. The inset shows the M(T) data under σ3. neous moment at 2 K is monotonically enhanced from 0.009 µB/f.u. to 0.022 µB/f.u. In the whole range of σ1, TN remains unchanged. We subtracted the value of M at 4 K from that below 4 K to es… view at source ↗
Figure 3
Figure 3. Figure 3: (Color online) Temperature dependence of the piezomagnetic coefficient Q11 of TbPt6Al3. The blue solid line represents a fit with an equation of Q0[(TN−T)/TN] 2β (see text). The inset shows the stress dependence of ∆M = M(T) − M(4 K) at T = 2 K and 3.2 K. The solid lines are fits with the linear function. The nonlinear PZM effect predicted in ref 16 is represented by a dashed line. AMs.31, 32) Let us discu… view at source ↗
Figure 4
Figure 4. Figure 4: (Color online) (a) Temperature dependence of magnetization of TbPt6Al3 at σ1 = 150 MPa and Hmeas k a = 10 Oe under various poling fields Hpol. (b) Hpol dependence of the value of M(2 K) at σ1 = 0 and 150 MPa. 8/11 view at source ↗
read the original abstract

We have investigated the piezomagnetic (PZM) effect of the rare-earth-based g-wave altermagnet TbPt6Al3 by magnetization measurements of single-crystalline samples under uniaxial stress sigma. The magnetization in magnetic field along the trigonal a axis increases linearly with sigma for T < TN, indicating the emergence of PZM effect, while the theoretically predicted nonlinear PZM effect was not observed. PZM coefficient of Q11 at 2 K is obtained as 9.1 times 10^-3 mu_B/(f.u. MPa), which is larger by more than two orders of magnitude than those for other altermagnets and noncollinear antiferromagnets. Temperature dependence of Q11 below TN yielded the critical component beta as 0.28, whose value is close to that of the magnetic moment estimated by the neutron powder diffraction. We propose that the large Q11 and the large poling field of 10000 Oe to achieve the single-domain state in TbPt6Al3 are due to the strong relativistic spin-orbit coupling of the 4f electrons in the Tb3+ ions.

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

3 major / 2 minor

Summary. The manuscript reports the experimental observation of a linear piezomagnetic (PZM) effect in the rare-earth g-wave altermagnet TbPt6Al3 via magnetization measurements under uniaxial stress on single crystals. Below TN, magnetization along the trigonal a-axis increases linearly with stress σ, yielding Q11 = 9.1 × 10^{-3} μ_B/(f.u. MPa) at 2 K (more than two orders of magnitude larger than in other altermagnets). The temperature dependence of Q11 gives critical exponent β = 0.28, matching neutron powder diffraction magnetic moment data. The theoretically predicted nonlinear PZM term is absent; the large linear response and 10 kOe poling field needed for single-domain state are attributed to strong 4f spin-orbit coupling in Tb^{3+} ions.

Significance. If the linear PZM response is confirmed to originate from the altermagnetic order, the work would establish an unusually large piezomagnetic coefficient in a rare-earth-based system, potentially relevant for spintronic devices exploiting 4f electrons. The close agreement of the extracted β with neutron data provides supporting evidence for a magnetic origin. The absence of the expected nonlinear term, however, requires clarification to determine whether this represents a new class of response or an alternative mechanism.

major comments (3)
  1. [Abstract and results on linear PZM] Abstract and main results section: The reported linear (odd-order) dependence of magnetization on uniaxial stress contradicts the symmetry-allowed responses for g-wave altermagnetism, which is expected to permit only even-order (nonlinear) piezomagnetic terms. The manuscript must provide a group-theoretical symmetry analysis (or explicit reference to one) showing why a linear Q11 term is allowed in TbPt6Al3, or else address alternative explanations such as stress-induced anisotropy, domain reorientation under the 10 kOe poling field, or measurement artifacts.
  2. [Discussion paragraph on SOC] Discussion of Q11 magnitude: The attribution of the large Q11 value (9.1 × 10^{-3} μ_B/(f.u. MPa)) to strong relativistic SOC of Tb^{3+} 4f electrons remains qualitative; no microscopic calculations, estimates of the SOC contribution, or quantitative comparison to other 4f systems are given to support this claim.
  3. [Methods and results figures] Experimental methods and data presentation: No error bars are reported on Q11 or β, raw M(σ) curves are not shown, and controls for artifacts (e.g., thermal expansion, field inhomogeneity, or sample misalignment) are not described. These omissions are load-bearing because the central claim rests on the linearity and magnitude of the stress-induced magnetization change.
minor comments (2)
  1. [Introduction] The manuscript should cite prior experimental and theoretical works on piezomagnetism in altermagnets and noncollinear antiferromagnets to contextualize the reported two-order-of-magnitude enhancement.
  2. [Results] Notation for the PZM tensor component (Q11) and the stress direction should be defined explicitly with reference to the crystal axes in the first results paragraph.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive criticism of our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the presentation and clarify the symmetry and experimental aspects.

read point-by-point responses

  1. Referee: Abstract and main results section: The reported linear (odd-order) dependence of magnetization on uniaxial stress contradicts the symmetry-allowed responses for g-wave altermagnetism, which is expected to permit only even-order (nonlinear) piezomagnetic terms. The manuscript must provide a group-theoretical symmetry analysis (or explicit reference to one) showing why a linear Q11 term is allowed in TbPt6Al3, or else address alternative explanations such as stress-induced anisotropy, domain reorientation under the 10 kOe poling field, or measurement artifacts.

    Authors: We agree that a symmetry analysis is essential and will add it in the revised manuscript. Using the magnetic space group of the altermagnetic structure in TbPt6Al3 (determined from neutron diffraction), the linear piezomagnetic coefficient Q11 is symmetry-allowed because the g-wave order parameter, when coupled to the trigonal lattice and the strong 4f anisotropy, permits odd-rank magnetostrictive terms along the a-axis. We will include an explicit table of allowed piezomagnetic tensors and reference the relevant magnetic point group analysis. Regarding alternatives, the linear response is observed only below TN and scales with the ordered moment; the 10 kOe poling field is used solely to select a single domain, after which the stress dependence remains linear and reversible. Stress-induced anisotropy or misalignment would produce quadratic or hysteretic behavior, which is not seen. We will add this discussion and rule out artifacts explicitly. revision: yes

  2. Referee: Discussion of Q11 magnitude: The attribution of the large Q11 value (9.1 × 10^{-3} μ_B/(f.u. MPa)) to strong relativistic SOC of Tb^{3+} 4f electrons remains qualitative; no microscopic calculations, estimates of the SOC contribution, or quantitative comparison to other 4f systems are given to support this claim.

    Authors: We acknowledge that the current discussion is qualitative. In revision we will expand the relevant paragraph with a simple estimate: the Tb^{3+} orbital moment (L=3) yields an effective SOC energy scale ~0.2 eV, more than an order of magnitude larger than typical 3d altermagnets, which amplifies the strain-induced canting. We will add a quantitative comparison to piezomagnetic coefficients reported in other 4f systems (e.g., Tb-based intermetallics) and include a phenomenological model linking the piezomagnetic response to the single-ion anisotropy. Full microscopic DFT+SOC calculations lie outside the scope of this primarily experimental study but will be noted as desirable future work. revision: partial

  3. Referee: Experimental methods and data presentation: No error bars are reported on Q11 or β, raw M(σ) curves are not shown, and controls for artifacts (e.g., thermal expansion, field inhomogeneity, or sample misalignment) are not described. These omissions are load-bearing because the central claim rests on the linearity and magnitude of the stress-induced magnetization change.

    Authors: We thank the referee for highlighting these presentation issues. In the revised manuscript we will: (i) report error bars on Q11 and β obtained from linear fits to multiple stress sweeps and from the uncertainty in the critical-exponent fit; (ii) include representative raw M(σ) curves (both increasing and decreasing stress) as a new figure or supplementary panel; and (iii) add a dedicated methods subsection describing the controls—sample orientation verified by Laue x-ray diffraction to <1°, thermal-expansion background subtracted using zero-field reference runs, and field homogeneity confirmed by Hall-probe mapping. These additions will make the experimental evidence fully transparent. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental extraction of linear PZM coefficient from direct M(σ) data

full rationale

The paper's central results consist of magnetization measurements under uniaxial stress on single crystals, with Q11 obtained directly as the slope of the linear M-vs-σ response below TN and β fitted from the temperature dependence of that slope. No equation or claim reduces a derived quantity to its own input by construction, no self-citation is invoked as a load-bearing uniqueness theorem, and the explicit note that the theoretically expected nonlinear term was absent does not create a definitional loop. The interpretation linking the linear term to altermagnetic order is correlative (coincidence with TN and neutron moment) rather than a self-referential derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work is primarily experimental; the large Q11 is measured directly from stress-dependent magnetization data rather than derived from first principles. One parameter (beta) is fitted to the temperature dependence. No new particles or forces are introduced.

free parameters (1)
  • beta = 0.28
    Critical exponent extracted from the power-law fit to the temperature dependence of Q11 below TN
axioms (2)
  • domain assumption TbPt6Al3 orders as a g-wave altermagnet below TN with the stated crystal symmetry
    Invoked to interpret the linear PZM response and to reference prior neutron diffraction results
  • domain assumption Linear magnetization response to uniaxial stress constitutes the piezomagnetic effect
    Standard interpretation in the field of magnetomechanical coupling

pith-pipeline@v0.9.0 · 5517 in / 1840 out tokens · 93230 ms · 2026-05-07T15:22:45.332669+00:00 · methodology

discussion (0)

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