EuAuBi: Polar Magnetic Topological Semimetal

• EuAuBi is a layered, noncentrosymmetric Eu–Au–Bi compound with a hexagonal structure and pronounced anisotropic electronic and transport properties.
• It exhibits intertwined magnetic order and metamagnetism, with field-induced spin textures and an orientation-dependent topological Hall effect.
• The material also shows signatures of ferroelectric metallicity and asymmetric multiband transport, hinting at potential bulk photovoltaic and superconducting phenomena.

EuAuBi is a layered, noncentrosymmetric Eu–Au–Bi compound that crystallizes in the hexagonal space group $P6_3mc$ (No. 186) and has been described across recent literature as a polar semimetal, a magnetic topological semimetal, and a Dirac semimetal with a notable band crossing near $E_F$ along $\Gamma$–A (Lipika et al., 28 Apr 2026, Lipika et al., 24 Jan 2026). Its Au and Bi atoms form a honeycomb-like network in the $ab$ plane, while Eu layers stack along the crystallographic $c$ axis between these planes, producing pronounced structural and transport anisotropy. Current work has established EuAuBi as a system in which crystal orientation, magnetic reconstruction, Rashba-type spin splitting, asymmetric multiband transport, and, in theory, switchable ferroelectric metallicity can all become experimentally consequential (Tan et al., 10 Jul 2025, Quan et al., 15 Jun 2026, Takahashi et al., 2022).

1. Crystal structure, polarity, and electronic classification

EuAuBi adopts a hexagonal LiGaGe-type derivative structure with broken inversion symmetry. In neutron diffraction at 10 K, the lattice parameters were reported as $a=b=4.772(7)\,\text{\AA}$ and $c=8.243(4)\,\text{\AA}$, whereas first-principles ferroelectric calculations used $a=4.799\,\text{\AA}$ and $c=8.295\,\text{\AA}$ (Lipika et al., 24 Jan 2026, Tan et al., 10 Jul 2025). The structural motif is consistent across reports: Au and Bi form buckled honeycomb-like layers in the $ab$ plane, and Eu occupies interstitial layers along $E_F$0. This buckling is central to both the polar symmetry and the anisotropic electronic response.

In the ferroelectric analysis, the paraelectric reference phase is the centrosymmetric $E_F$1 structure, whereas the polar ground state is $E_F$2. The inversion-breaking distortion is described by upward displacement of two Au atoms by $E_F$3 and downward displacement of two Bi atoms by $E_F$4, generating a polar axis along $E_F$5 and two inversion-related domain states FE1 and FE2 with opposite polarization (Tan et al., 10 Jul 2025). Charge-density redistribution $E_F$6 is strongest around Au, indicating that Au buckling is the dominant microscopic driver of the polar state.

Electronically, EuAuBi has been variously classified according to the focus of the measurement or calculation. One study identifies it as a Dirac semimetal with a symmetry-protected band crossing near $E_F$7 along $E_F$8–A (Lipika et al., 24 Jan 2026). Another describes it as a magnetic topological semimetal for which DFT suggests tunability to a triple-degenerate nodal point semimetal under magnetic field (Lipika et al., 28 Apr 2026). A multiband transport study emphasizes strong spin–orbit coupling from heavy Au and Bi and reports band inversion near the Brillouin-zone A point (Quan et al., 15 Jun 2026). These descriptions are not mutually exclusive; they indicate that EuAuBi lies in a polar, SOC-rich, low-carrier semimetallic regime in which both band topology and symmetry breaking are relevant.

2. Crystal growth, orientation control, and sample quality

The recent EuAuBi literature distinguishes sharply between Bi-flux and Pb-flux growth. Bi-flux growth yields plate-like crystals with the $E_F$9 plane parallel to the crystal surface and $\Gamma$0 reflections in XRD, but it also consistently produces $\Gamma$1 impurity, visible as $\Gamma$2 (111) peaks and known to superconduct near 2 K (Lipika et al., 28 Apr 2026). Pb-flux growth suppresses $\Gamma$3, stabilizes rod-shaped crystals elongated along $\Gamma$4, and enables magnetotransport in geometries inaccessible in the plate-like Bi-flux morphology.

Growth route	Morphology and orientation	Reported consequence
Bi flux	Plate-like, $\Gamma$5-oriented, $\Gamma$6 reflections	$\Gamma$7 impurity and extrinsic resistive drop near 2 K
Pb flux	Rod-shaped, $\Gamma$8-axis oriented, $\Gamma$9 reflections	Suppressed $ab$0 and access to $ab$1 Hall geometry

Pb-flux crystals are reported as $ab$2–$ab$3 mm long with hexagonal cross section. Laue diffraction on the side face shows sharp, domain-free spots indexed to the $ab$4 plane, and $ab$5–$ab$6 XRD shows $ab$7 reflections, together confirming $ab$8-axis orientation and high crystalline quality (Lipika et al., 28 Apr 2026). EDX mapping verifies stoichiometry. Growth in both Bi and Pb fluxes used sealed-quartz, glovebox-loaded methods, with detailed ratios and temperatures placed in supplementary material.

Sample quality directly affects the interpretation of low-temperature anomalies. In Bi-flux crystals, the apparent superconducting resistive drop was attributed to extrinsic $ab$9, and magnetization showed no Meissner response from EuAuBi itself (Lipika et al., 28 Apr 2026). In Pb-flux crystals, a residual Pb surface layer produces a small resistivity and magnetization feature near 7 K, but the bulk EuAuBi crystal shows no superconductivity down to 0.3 K. A plausible implication is that orientation control and impurity suppression were prerequisites for isolating intrinsic magnetotransport, especially the orientation-dependent Hall response.

3. Magnetic order, metamagnetism, and field-induced textures

Eu in EuAuBi is consistently treated as divalent $c$0 with localized $c$1 moments and $c$2. In Curie–Weiss analysis, the effective moment was reported as $c$3 per Eu and the Weiss temperature as $c$4, consistent with predominant antiferromagnetic interactions (Lipika et al., 24 Jan 2026). A separate superconductivity study reported $c$5 for $c$6 and $c$7 for $c$8, again near the Eu$c$9 value (Takahashi et al., 2022).

The zero-field magnetic transition temperature depends on sample set and probe. In Bi-flux crystals, magnetization and specific heat revealed three features at $a=b=4.772(7)\,\text{\AA}$0, $a=b=4.772(7)\,\text{\AA}$1, and $a=b=4.772(7)\,\text{\AA}$2, although zero-field powder neutron diffraction resolved only two magnetic phases: a commensurate antiferromagnetic phase and a low-temperature canted antiferromagnetic phase (Lipika et al., 24 Jan 2026). The propagation vector is $a=b=4.772(7)\,\text{\AA}$3, with Eu moments lying predominantly in the $a=b=4.772(7)\,\text{\AA}$4-plane and slight out-of-plane canting; refined envelope moments at 1.5 K were $a=b=4.772(7)\,\text{\AA}$5 and $a=b=4.772(7)\,\text{\AA}$6. By contrast, Pb-flux $a=b=4.772(7)\,\text{\AA}$7-axis crystals show a single Néel temperature $a=b=4.772(7)\,\text{\AA}$8, slightly higher than the $a=b=4.772(7)\,\text{\AA}$9 value in Bi-flux crystals, which was attributed to better crystallinity and reduced disorder (Lipika et al., 28 Apr 2026).

The field response is strongly anisotropic. Metamagnetic transitions occur for $c=8.243(4)\,\text{\AA}$0, whereas no metamagnetic transitions were observed for $c=8.243(4)\,\text{\AA}$1, establishing easy-plane anisotropy (Lipika et al., 24 Jan 2026). At low temperature, two hysteretic regimes appear around $c=8.243(4)\,\text{\AA}$2 and $c=8.243(4)\,\text{\AA}$3, bounding an intermediate field-induced phase with a tilted magnetization plateau. In ac susceptibility, two peaks in $c=8.243(4)\,\text{\AA}$4 define this plateau and shift to lower fields with increasing temperature; under $c=8.243(4)\,\text{\AA}$5–$c=8.243(4)\,\text{\AA}$6, frequency-dependent $c=8.243(4)\,\text{\AA}$7 yields a critical slowing-down time $c=8.243(4)\,\text{\AA}$8, interpreted as evidence for correlated spin textures (Lipika et al., 24 Jan 2026).

Thermodynamic signatures reinforce the first-order character of these field-induced reconstructions. In $c=8.243(4)\,\text{\AA}$9, a $a=4.799\,\text{\AA}$0 anomaly marks the antiferromagnetic transition, while under field an additional peak emerges in the same field–temperature window as the metamagnetic transitions and Hall anomalies (Lipika et al., 28 Apr 2026). Earlier work on Bi-flux crystals similarly reported a $a=4.799\,\text{\AA}$1-like peak around $a=4.799\,\text{\AA}$2 at $a=4.799\,\text{\AA}$3, overlapping the $a=4.799\,\text{\AA}$4-peak and signaling a first-order boundary of a field-induced correlated texture (Lipika et al., 24 Jan 2026). These results make EuAuBi a rare Eu-based semimetal in which commensurate and canted antiferromagnetism coexist with a narrow metamagnetic texture regime.

4. Magnetotransport and the orientation-dependent topological Hall effect

The transport response of EuAuBi is strongly geometry dependent. In Pb-flux $a=4.799\,\text{\AA}$5-axis crystals, the resistivity along $a=4.799\,\text{\AA}$6, $a=4.799\,\text{\AA}$7, is metallic and was fitted from 100–300 K by the Bloch–Grüneisen form

$a=4.799\,\text{\AA}$8

$a=4.799\,\text{\AA}$9

with $c=8.295\,\text{\AA}$0, $c=8.295\,\text{\AA}$1, and $c=8.295\,\text{\AA}$2 (Lipika et al., 28 Apr 2026). The residual resistivity ratio is $c=8.295\,\text{\AA}$3, and a kink near 5 K signals critical spin scattering near antiferromagnetic ordering. Field-dependent longitudinal transport follows the magnetic reconstruction: for $c=8.295\,\text{\AA}$4, $c=8.295\,\text{\AA}$5 shows step-like changes and hysteresis at $c=8.295\,\text{\AA}$6 and $c=8.295\,\text{\AA}$7, while at higher fields the magnetoresistance

$c=8.295\,\text{\AA}$8

becomes negative as spin-dependent scattering is reduced by moment polarization (Lipika et al., 28 Apr 2026).

The central magnetotransport development is the observation of an orientation-dependent topological Hall effect (THE) in the previously unexplored geometry $c=8.295\,\text{\AA}$9, $ab$0, with the Hall voltage in-plane. The measured Hall resistivity is antisymmetrized as

$ab$1

and decomposed according to

$ab$2

$ab$3

$ab$4

Because THE is expected to vanish at sufficiently high fields, the region above 5 T was fitted using $ab$5, which provided the best description, and the residual topological contribution was extracted as

$ab$6

At $ab$7, $ab$8 exhibits two distinct peaks coincident with the metamagnetic critical fields, persists up to $ab$9, and disappears above $E_F$00 (Lipika et al., 28 Apr 2026).

This behavior differs qualitatively from earlier Hall measurements on Bi-flux plates. In the geometry $E_F$01, $E_F$02, and $E_F$03, the Hall resistivity $E_F$04 had a positive slope, indicating hole-dominant carriers, with $E_F$05 and $E_F$06 at 2 K; no THE was observed in that configuration (Lipika et al., 24 Jan 2026). The later orientation-resolved work argues that prior geometries did not align with the first-order metamagnetic transitions, and therefore likely suppressed THE signatures.

The interpretation of the residual Hall signal is explicitly real-space rather than multiband. The two-peak structure, rather than a broad plateau, is attributed to real-space Berry curvature from non-collinear, possibly noncoplanar spin textures stabilized only within a narrow $E_F$07 field window (Lipika et al., 28 Apr 2026). The coincidence of THE peaks with hysteretic metamagnetic steps in $E_F$08 and $E_F$09, and with the extra peak in $E_F$10, argues for abrupt magnetic reconstructions rather than a single skyrmion phase extending over a broad field range. A common misconception is that any THE-like signal implies a wide skyrmion pocket; in EuAuBi, the reported signal is instead sharply tied to first-order metamagnetic boundaries.

5. Ferroelectric metallicity and bulk photovoltaic response

First-principles calculations identify EuAuBi as a candidate intrinsic ferroelectric metal in which metallicity, low carrier density, and switchable polarization coexist (Tan et al., 10 Jul 2025). The spontaneous polarization $E_F$11 lies along $E_F$12 and was estimated by two methods: $E_F$13 from the Berry-phase approach and $E_F$14 from Born effective charges. The reported $E_F$15 values are $E_F$16 for Eu, $E_F$17 for Au, and $E_F$18 for Bi. Relative to the paraelectric $E_F$19 phase, the ferroelectric transition is driven by a $E_F$20-point $E_F$21 soft mode with frequency $E_F$22, with a secondary $E_F$23 instability at $E_F$24. The dominant $E_F$25 eigenvector consists of antiparallel displacements of Au and Bi along $E_F$26, and in the FE phase its descendant mode is $E_F$27.

The switching pathway FE1 $E_F$28 PE $E_F$29 FE2, computed by climbing-image NEB, yields a double-well barrier of $E_F$30, smaller than canonical ferroelectric insulators such as $E_F$31 and $E_F$32 (Tan et al., 10 Jul 2025). The semimetallic carriers are dilute: the GGA+$E_F$33 calculation with $E_F$34 on Eu-$E_F$35 and SOC included gives $E_F$36, while experiment reports $E_F$37 at 2.5 K. Carriers derive mainly from Eu-$E_F$38 and Bi-$E_F$39 states, whereas polarization is dominated by Au buckling. This orbital and spatial separation is presented as an instance of the decoupled electron mechanism.

Electron–phonon coupling data support that interpretation. The total EPC constant is $E_F$40, and the FE $E_F$41 mode contributes only $E_F$42 to the total EPC strength (Tan et al., 10 Jul 2025). The weak coupling between metallic carriers and the polar phonon implies that screening does not fully suppress the ferroelectric instability. The calculation does, however, rely on a valence-manifold approximation in which the fully occupied valence bands are treated as insulating and the small semimetal pockets are neglected to first approximation.

The same study predicts a pronounced bulk photovoltaic effect. The second-order current is written as

$E_F$43

and for point group $E_F$44 only three independent nonzero tensor components remain: $E_F$45, $E_F$46, and $E_F$47 (Tan et al., 10 Jul 2025). The z-polarized shift current conductivity under x-polarized light, $E_F$48, reaches a peak magnitude of $E_F$49. Because the response is odd under inversion, polarization reversal changes the sign according to $E_F$50. On that basis, an experimental verification scheme was proposed in which a EuAuBi thin film is gated along $E_F$51, illuminated with linearly x-polarized light, and read out via hysteretic sign reversal of $E_F$52.

6. Asymmetric multiband transport and the large Nernst effect

A later transport study treats EuAuBi as an asymmetric multiband semimetal in which a very dilute electron pocket coexists with a dense hole pocket (Quan et al., 15 Jun 2026). In this analysis, the longitudinal resistivity is metallic, approximately $E_F$53 at 300 K, decreasing quasi-linearly to $E_F$54, with an upturn below $E_F$55 near the onset of antiferromagnetism. The two-band Hall fit resolves, at $E_F$56, $E_F$57, $E_F$58, $E_F$59, and $E_F$60. The hierarchy $E_F$61 and $E_F$62 persists to room temperature, so $E_F$63.

The electrical conductivity tensor is modeled as

$E_F$64

with $E_F$65 and $E_F$66 (Quan et al., 15 Jun 2026). In this framework, $E_F$67 and therefore $E_F$68 are overwhelmingly hole dominated, the Hall effect crosses from electron to hole dominance with increasing field, and the Seebeck coefficient changes from electron-dominant at low temperature to mixed at higher temperature. Experimentally, $E_F$69 has a broad negative minimum near $E_F$70, changes sign around $E_F$71, and remains positive at high $E_F$72.

The most striking thermoelectric signal is the adiabatic Nernst response $E_F$73. At $E_F$74, $E_F$75 reaches $E_F$76 near $E_F$77, a magnitude explicitly noted to be comparable to anomalous Nernst signals in magnetic Weyl semimetals, while nevertheless arising here from semiclassical multicarrier transport (Quan et al., 15 Jun 2026). The low-field profile is captured by

$E_F$78

with $E_F$79 fixed from Hall fits and $E_F$80 at 11.1 K. The peak occurs near $E_F$81, consistent with $E_F$82 for $E_F$83.

The Nernst scaling is the conceptual result of the study. Starting from the Mott relation

$E_F$84

and

$E_F$85

the low-field two-band limit gives

$E_F$86

with $E_F$87 in the degenerate limit (Quan et al., 15 Jun 2026). In EuAuBi’s extreme asymmetry, this reduces empirically to

$E_F$88

where $E_F$89 is derived from the electronic specific-heat coefficient $E_F$90, while $E_F$91–$E_F$92. The authors interpret the large Nernst effect as a semiclassical multiband phenomenon rather than a topological Berry-curvature contribution. This conclusion is supported by the absence of a sizable zero-field Nernst offset and by the mobility-controlled peak at $E_F$93.

7. Superconductivity, Rashba physics, and unresolved questions

Superconductivity in EuAuBi remains the most unsettled part of its phenomenology. A 2022 report on Bi-flux-grown crystals described EuAuBi as a magnetic Rashba semimetal with antiferromagnetic order at $E_F$94 and a superconducting transition at $E_F$95 (Takahashi et al., 2022). In that work, the Meissner fraction was estimated as $E_F$96 at 1.8 K in very low fields, the lower critical field was inferred to be extremely small because the Meissner signal vanished in fields of only $E_F$97, and the upper critical fields at the lowest temperature were highly anisotropic: $E_F$98 and $E_F$99. Using the Ginzburg–Landau relations

$\Gamma$00

the coherence lengths were estimated as $\Gamma$01 and $\Gamma$02.

That superconductivity study tied the inverted $\Gamma$03 anisotropy to Rashba-type spin splitting from the polar structure together with Zeeman splitting from Eu moments. The minimal Rashba term was written as

$\Gamma$04

and the Zeeman energy as

$\Gamma$05

with $\Gamma$06 including both external and exchange contributions (Takahashi et al., 2022). First-principles calculations showed that an in-plane Eu moment produces asymmetric in-plane dispersion along $\Gamma$07–$\Gamma$08–$\Gamma$09, whereas an out-of-plane moment preserves symmetry. On this basis, $\Gamma$10 was argued to enhance paramagnetic depairing by forcing finite-momentum pairing, while $\Gamma$11 yields weaker depairing and allows $\Gamma$12 to exceed both the Pauli limit and the orbital estimate.

Subsequent work has complicated that picture. Bi-flux crystals were later shown to contain $\Gamma$13 impurity that superconducts near 2 K, producing an extrinsic resistive drop without a Meissner response attributable to EuAuBi (Lipika et al., 28 Apr 2026). Another study reported a low-field resistivity decrease below $\Gamma$14 but found neither Meissner signature nor zero resistivity in its crystals, again suggesting extrinsic origins such as flux inclusions (Lipika et al., 24 Jan 2026). In high-quality Pb-flux $\Gamma$15-axis crystals, EuAuBi itself showed no superconductivity down to 0.3 K (Lipika et al., 28 Apr 2026). At the same time, the ferroelectric-metal calculation continues to cite prior reports of superconductivity below $\Gamma$16 as part of EuAuBi’s broader materials context (Tan et al., 10 Jul 2025). The present literature therefore does not yet provide a unified account of whether bulk superconductivity is intrinsic to stoichiometric EuAuBi or contingent on surface conditions, polar domains, or secondary phases.

Several broader questions remain open. The interplay of antiferromagnetism, putative superconductivity, and ferroelectric metallicity has not been resolved; the ferroelectric study explicitly notes that possible magnetoelectric or magneto-photogalvanic couplings were not analyzed (Tan et al., 10 Jul 2025). Proposed follow-up measurements across the literature include SHG to confirm broken inversion, ARPES to refine semimetal topology, domain imaging under bias, and surface-sensitive probes such as STM/STS, $\Gamma$17SR, and NMR (Tan et al., 10 Jul 2025, Takahashi et al., 2022). A plausible implication is that EuAuBi’s importance lies not in a single settled phase label, but in the unusually dense overlap of polarity, SOC, localized Eu magnetism, field-induced spin textures, and highly anisotropic transport signatures within one crystallographically simple platform.