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Multiple magnetic orders discovered in the superconducting state of EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$

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Pith's one-line read The paper claims that two previously unknown magnetic transitions occur inside the superconducting state of optimally doped EuFe2(As0.79P0.21)2, at about 0.9 K and 0.6 K, with one corresponding transition at about 0.9 K in the overdoped…

desk verdict Sub-Kelvin heat-capacity anomalies in P-doped EuFe2As2 look real and reproducible, but the 'magnetic orders' framing outruns the evidence until the overdoped crystal is cleaned up and a microscopic probe lands. read the letter →

arxiv 2412.16169 v1 pith:E257SGSE submitted 2024-12-06 cond-mat.supr-con cond-mat.str-el

Nan Zhou , Yue Sun , Ivan S. Veshchunov , S. Kittaka , X. L. Shen , H. M. Ma , W. Wei , Y. Q. Pan
show 8 more authors
M. Cheng Y. F. Zhang Y. Kono Yuping Sun T. Tamegai Xuan Luo Zhixiang Shi Toshiro Sakakibara
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords ironpnictideEuFe2As2phosphorusdopingsuperconductingstatemagneticphasetransitionspecificheatlow-temperaturemagnetismfield-angle-resolvedcapacity
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 is trying to establish that the iron-pnictide superconductor EuFe2(As0.79P0.21)2 hosts two new magnetic phase transitions at $T_1\simeq 0.9\,$K and $T_2\simeq 0.6\,$K, deep inside its superconducting state, and that only one of them survives in the overdoped, non-superconducting crystal EuFe2(As0.71P0.29)2. The evidence is thermodynamic: sharp specific-heat jumps confirmed by low-temperature magnetization anomalies measured down to 0.2 K. The authors propose that these sub-kelvin orders come from the localized Eu2+ moments, either a new spin order or a reorientation of the already ordered europium spins. If true, this gives a previously unseen setting to study how magnetism and superconductivity coexist, because the new magnetic order is not destroying superconductivity but living inside it.

What carries the argument

The central probe is the heat capacity $C(T)/T$ measured down to 0.4 K in a rotating $^3$He refrigerator, which reveals sharp jumps at $T_1$, $T_2$, and $T_3$ and lets the authors track how these transitions move in a magnetic field. The supporting measurements are the Capacitance-Faraday magnetization, which confirms that the specific-heat anomalies are accompanied by changes in the dc magnetization, and angle-resolved specific heat, whose evolving twofold-to-fourfold symmetry provides a fingerprint of the underlying spin order. The paper's phase diagram assembles these characteristic temperatures and fields, and its entropy analysis—$S_{\rm mag}$ reaching roughly 83%–95% of $R\ln 8$ at the 18.5 K Eu transition—is used to argue that the low-temperature jumps release too little entropy to be a full ordering of the $S = 7/2$ Eu moments.

What would settle it

Neutron diffraction on a large single crystal of EuFe2(As0.79P0.21)2 in zero field below 0.4 K would settle it: observation of new magnetic Bragg peaks entering at $T_1$ and $T_2$ confirms the bulk magnetic-order claim, while their absence in a crystal that still shows both heat-capacity jumps rules it out.

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Extended reading notes

Core claim

On the authors' own terms, the core discovery is that the specific heat of optimally doped EuFe2(As0.79P0.21)2 shows two distinct $\lambda$-anomalies at $T_1 \simeq 0.9\,\text{K}$ and $T_2 \simeq 0.6\,\text{K}$, below the superconducting transition, and that these anomalies are magnetic in origin: they have counterparts in dc magnetization measured by a Capacitance-Faraday method, they evolve strongly with applied field and orientation, and the magnetic entropy released at the low-temperature transitions is tiny, consistent with a spin reorientation rather than a full melting of the $S = 7/2$ Eu moments. In the overdoped, non-superconducting EuFe2(As0.71P0.29)2 crystal only one such transition survives, at $T_3 \simeq 0.9\,\text{K}$, and its field behavior matches $T_2$, suggesting a common microscopic origin. The paper argues that these new phases point to a localized Eu$^{2+}$ spin order or a spin reorientation.

Load-bearing premise

The sub-kelvin specific-heat jumps are intrinsic phase transitions of the doped EuFe2As2 crystals, not artifacts of impurity phases, element vacancies, or sample inhomogeneity.

Editorial extensions

If this is right

  • Below $T_c$, the superconducting state of optimally doped EuFe2(As,P)2 contains two further ordered phases, so transport, penetration-depth, and vortex-matter measurements below 1 K should show signatures of these orders.
  • The disappearance of one transition when going from $x = 0.21$ to $x = 0.29$ ties the new order to the same doping axis that suppresses superconductivity, giving a control parameter to separate the two transitions.
  • The strong field- and orientation-dependence of the heat capacity implies an anisotropic magnetic response of the low-temperature phase, so torque magnetometry and angular-resolved neutron scattering could map its symmetry directly.
  • The small entropy released at the jumps suggests a spin reorientation rather than a new long-range moment, in which case the transition is a rotation of the Eu$^{2+}$ moment direction that should appear as a change of the magnetic easy axis.

Reading between the lines

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

  • A testable extension would be to measure $C(\phi)$ in a detwinned single crystal at fixed field while sweeping through $T_1$ and $T_2$; if the twofold-to-fourfold evolution of the heat capacity is tied to the magnetic order rather than to the superconducting gap, the angular periodicity should follow the magnetic field direction, not the crystal axes.
  • The paper's reservations about impurity phases suggest a control experiment: growing overdoped crystals with different fluxes and lower vacancy concentrations, then checking whether the $T_3$ anomaly persists; if it disappears with improved stoichiometry, the vacancy scenario would win.
  • Because the proposed origin is a reorientation of the existing Eu$^{2+}$ order, a testable consequence is that the sub-kelvin transitions should shift or split in a magnetic field applied along different crystallographic directions; such a measurement would distinguish a simple spin flop from a more complex multi-axis reorientation.
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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 heat capacity, resistivity, and magnetization measurements on two single crystals of EuFe2(As1-xPx)2 with x = 0.21 and x = 0.29. Two anomalies in C/T at T1 ~ 0.9 K and T2 ~ 0.6 K are observed in the superconducting optimally doped crystal, and one anomaly at T3 ~ 0.9 K in the overdoped non-superconducting crystal. The anomalies move systematically with applied field and show angular dependence, leading the authors to propose new low-temperature magnetic orders from Eu2+ spins or spin reorientation and to construct a B-T phase diagram.

Significance. If the anomalies are intrinsic bulk transitions, this is a potentially valuable finding for the coexistence of superconductivity and magnetism in iron pnictides. The paper's strengths are the systematic field- and orientation-dependent specific heat measurements, the reproducible jumps at distinct temperatures that evolve with field, and the entropy analysis reaching ~83-95% of Rln8 for the Eu2+ moment at TN. However, the intrinsic origin of the sub-Kelvin anomalies is not yet established, and the systematic C(T)/M(T) temperature mismatch needs explanation before the discovery claim can be accepted.

major comments (4)
  1. [Final section and Fig. 1(d)] The assignment of the sub-Kelvin heat capacity anomalies to intrinsic magnetic orders of the main EuFe2(As1-xPx)2 phase is not secured. In the final section the authors explicitly leave 'some unconsidered situations' and the impurity scenario open, and the overdoped crystal is described as having 'a small amount of elements vacancies' and being non-superconducting (p. 2, Fig. 1(d)). Because the anomalies shown in Figs. 2(c)-(g) are small relative to the background, they could in principle arise from a minority impurity phase or from P-poor regions in the crystal. The authors should provide evidence that the anomalies scale with the main-phase volume fraction (e.g., measurements on a second batch, a different piece, or deliberately co-synthesized impurity-phase candidates) and ideally element-specific or local probes (muSR, neutron scattering) to confirm magnetic order.
  2. [Comparison of C(T) and M(T), Fig. 2 and Fig. S6] The systematic mismatch between the heat capacity transition temperatures and the magnetization anomalies is acknowledged but not resolved. For the optimally doped crystal under 0.3 T, the heat capacity gives T1 ~ 0.81 K and T2 ~ 0.65 K, while the magnetization shows Tm1* ~ 0.6 K and Tm2* ~ 0.43 K (inset of Fig. 2(a)); under 1 T, T2 ~ 0.76 K versus Tm2 ~ 0.66 K; for the overdoped crystal under 0.3 T, T3 ~ 0.84 K versus Tm3 ~ 0.72 K. A true bulk thermodynamic transition should appear at the same temperature in C(T) and M(T) measured on the same sample. The systematic lag of ~0.1-0.2 K must be addressed before the heat capacity jumps can be identified with magnetic ordering; it suggests thermometry offsets, broadened/inhomogeneous transitions, or distinct physical origins of the two signals.
  3. [Fig. 4 and Fig. 5] The determination of the transition temperatures in Fig. 4 by 'intersection of two extrapolated red lines' is not reproducible without error bars or a quantitative criterion. The anomalies are small and sit on a rapidly varying background (including the nuclear Schottky contribution at low T and the phonon background at higher T), and no standard deviation from repeated measurements or from different crystals is given. Please provide the raw analysis method (e.g., equal-area construction on C/T after subtracting a smooth background), state the uncertainty in each T1/T2/T3 point, and include the same for the B* values used in the phase diagram.
  4. [Doping evolution claim, x = 0.29 sample] The doping-evolution conclusion that 'one of the magnetic orders becomes absent' in the overdoped crystal is weakened by the imperfect nature of the overdoped reference: it is non-superconducting, has element vacancies, and is the only representative of x = 0.29. The absence of T1 in this single sample could be a consequence of sample quality rather than the P content. Measuring at least one additional composition (e.g., x = 0.25 or a second x = 0.29 crystal of better quality) would substantially strengthen the claim.
minor comments (5)
  1. [Reference [26]] Reference [26] is cited as 'self-flux method [26 ? ]' with a placeholder question mark; supply the complete reference.
  2. [Text after Fig. 2] The phrase 'see the inset of Figs. 1(a) and 1(b)' is incorrect; the Faraday magnetization data are shown in the insets of Figs. 2(a) and 2(b).
  3. [Fig. S1 caption] The SI caption of Fig. S1 uses overlapping labels: '(a)–(e)' for the first sample and '(e)–(j)' for the second; relabel the second set to avoid ambiguity.
  4. [Typos] There are several typos: 'capacitiy' in the Fig. S3 caption, 'anomalies heat capacity' in the main text, and 'The inset show' in the Fig. 1(b) caption.
  5. [Fig. S6] In Fig. S6 the normalization M/M(1.3 K) is used, but data extend only to 0.2 K; state the reference temperature and field consistently in the caption and text.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the claimed low-temperature orders are direct experimental observations, and the self-citations only cover measurement technique and prior sample-characterization context.

full rationale

The paper's central claims are experimental readouts: heat-capacity jumps at T1 ~ 0.9 K and T2 ~ 0.6 K in EuFe2(As0.79P0.21)2 and one at T3 ~ 0.9 K in EuFe2(As0.71P0.29)2, with magnetization anomalies measured independently by a Capacitance-Faraday method. The characteristic temperatures are stated to be 'determined from the intersection of two extrapolated red lines' (Fig. 4), i.e., from the data themselves, not from any fitted model. The only model-dependent step is the Debye-Einstein lattice subtraction used to estimate the magnetic entropy (Fig. S7); that subtraction cannot generate the positions of the observed C/T jumps and does not feed back into the identification of T1, T2, or T3. Self-citations are present but not load-bearing: references [25], [26], and [27-29] include current authors and support the crystal-growth method, the angle-resolved specific-heat apparatus, and prior characterization of overdoped EuFe2(As1-xPx)2 samples; none is invoked as a uniqueness theorem or as a premise from which the existence of new transitions is deduced. The paper itself flags the open impurity/inhomogeneity scenario for the overdoped crystal and notes the ~0.2 K lag between C/T and magnetization features; these are validity concerns about whether the anomalies are intrinsic, not evidence that a derivation reduces to its inputs. Because the discovery claim is not obtained by fitting or by a self-citation chain, no circular step can be exhibited.

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

The central claim rests on the measurement being intrinsic to the EuFe2(As,P)2 phase. The free parameters appear only in the background subtraction used to estimate magnetic entropy, not in the identification of the transitions. No new theoretical entities are introduced.

free parameters (4)
  • Debye temperature T_D = not reported
    Fitted parameter in Debye-Einstein lattice specific heat model (Fig. S7); affects C_mag and S_mag estimates but not the transition temperatures.
  • Einstein temperature T_E = not reported
    Fitted parameter in the same lattice model (Fig. S7); affects C_mag and S_mag estimates but not the transition temperatures.
  • gamma (low-T linear specific heat) = not reported
    Coefficient in C_p = gamma T + beta T^3 fit at 0.4-1.5 K (Fig. S7); used for background subtraction.
  • beta (low-T phonon coefficient) = not reported
    Coefficient in the low-T fit (Fig. S7); used for background subtraction.
assumptions (4)
  • standard math Debye-Einstein model for lattice heat capacity background
    Used in Fig. S7 to separate C_mag from C_lattice; relies on standard phonon heat capacity formulas.
  • domain assumption Cp anomalies at T1, T2, T3 are bulk thermodynamic phase transitions
    Central to the claim of new magnetic orders; if they were artifacts (e.g., from a small impurity phase), the paper's conclusion would not follow.
  • domain assumption The overdoped crystal's single transition is intrinsic to x=0.29
    The x=0.29 crystal has element vacancies and is non-superconducting; the authors still interpret the presence of T3 and absence of a second transition as a doping effect.
  • domain assumption Magnetization and specific heat anomalies at slightly different temperatures correspond to the same transitions
    The authors compare Tm1* (0.6 K), Tm2* (0.43 K) with T1 (0.81 K), T2 (0.65 K) and attribute the ~0.2 K difference to multi-phase interaction, an assumption needed to use magnetization as supporting evidence.

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Pith. "Pith review of Multiple magnetic orders discovered in the superconducting state of EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$." pith.science (2026). https://pith.science/paper/E257SGSE

@misc{pith2026241216169,
  author       = {Pith},
  title        = {Pith review of: Multiple magnetic orders discovered in the superconducting state of EuFe$_2$(As$_1-x$P$_x$)$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E257SGSE}},
  note         = {Machine review of arXiv:2412.16169}
}
abstract

The interplay between superconductivity and magnetism is an important subject in condensed matter physics. EuFe$_{2}$As$_{2}$-based iron pnictides could offer an interesting plateau to study their relationship that has attracted considerable attention. So far, two magnetic phase transitions were observed in EuFe$_{2}$As$_{2}$-based crystal, which were deemed to originate from the itinerant Fe moments ($\sim$ 190 K) and the localized Eu$^{2+}$ moments ($\sim$ 19 K), respectively. Here, we systematically studied the heat capacity for the EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ crystals with \textit{x} = 0.21 (optimally doped) and \textit{x} = 0.29 (overdoped). We have found two new magnetic orders in the superconducting state (ranging from 0.4 to 1.2 K) in the optimally doped crystal. As more P was introduced into the As site, one of the magnetic orders becomes absent in the overdoped crystal. Additionally, we observed strong field and orientation dependence in heat capacity. The present findings in EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ have detected the new low-temperature magnetic orders, which may originate from the localized Eu$^{2+}$ spins order or the spin reorientation.

Figures

Figures reproduced from arXiv: 2412.16169 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Room temperature XRD patterns for the two P-doped crystals studied in this paper. (b) Temperature dependence [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The magnetizations with ZFC (half solid circle) and FC (solid circle) modes for (a) EuFe [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Azimuthal angle dependence of the specific heat ∆ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Magnetic-temperature phase diagram determined from the field angle-resolved specific heat measurements for (a) [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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