EuAl2Si2: Magnetic Topology & Domain-Wall Effects

• EuAl2Si2 is a stoichiometric layered intermetallic compound characterized by A-type antiferromagnetism, field-tunable domain-wall stripes, and Weyl points near the Fermi level.
• It is synthesized as high-quality single crystals using a self-flux method, and exhibits anisotropic magnetotransport with a giant extrinsic domain-wall Hall effect dominating its response.
• The material’s coupled magnetic and topological properties, including pronounced Berry curvature contributions and orbital magnetoresistance, highlight its potential for spintronic and quantum device applications.

EuAl$_2$Si$_2$ is a stoichiometric layered intermetallic compound that crystallizes in the CaAl$_2$Si$_2$-type trigonal structure and exhibits coupled magnetic, topological, and magnetotransport phenomena. In the ordered state below $T_{\mathrm{N}} \approx 33.6$ K, it is an in-plane A-type antiferromagnet with Eu$^{2+}$ moments ferromagnetically aligned within each Eu layer and antiferromagnetically stacked along $c$. Under magnetic field it undergoes anisotropic field-driven phase evolution, including a spin-polarized ferromagnetic state with Weyl points near the Fermi level. A defining feature is a periodic, field-tunable domain-wall stripe lattice on the cleaved $ab$ surface, whose skew scattering generates a giant anomalous Hall effect that greatly exceeds the intrinsic Berry-curvature contribution; the same material also shows a large planar Hall effect and pronounced anisotropic magnetoresistance with mechanistic decomposition that distinguishes orbital, spin-fluctuation, and Berry-curvature contributions (Xia et al., 2023, Liu et al., 27 Aug 2025).

1. Crystal chemistry and materials characteristics

EuAl$_2$Si$_2$ crystallizes in the trigonal space group $_2$0 (No. 164). Single-crystal X-ray diffraction gives $_2$1 \AA, $_2$2 \AA, with $_2$3 and $_2$4. The unit cell consists of two interlaced Al-Si zigzag chains stacked along the $_2$5 axis between Eu layers, producing a strongly layered crystal architecture. On cleaved surfaces, only $_2$6 reflections are observed in powder XRD, consistent with high crystalline quality (Xia et al., 2023).

The Eu ions are divalent, Eu$_2$7 $_2$8, with a spin-only moment close to $_2$9 per Eu ion. Magnetization measurements approach $_2$0Eu at saturation, and the saturation magnetization reaches $_2$1 per formula unit, consistent with Eu$_2$2 $_2$3 (Xia et al., 2023, Liu et al., 27 Aug 2025).

Single crystals were grown by a self-flux method from Eu:Al:Si $_2$4, sealed in quartz, heated to $_2$5 for 20 h, slow-cooled to $_2$6 at $_2$7, and centrifuged to remove excess flux. EDS confirms stoichiometric Eu:Al:Si $_2$8, while PXRD and SXRD demonstrate high crystallinity. The resistivity is metallic, with residual resistivity ratio $_2$9 in one report and $_2$0 in another, reflecting the same high-quality single-crystal platform used for magnetotransport, magnetic imaging, ARPES, and quantum oscillation studies (Xia et al., 2023, Liu et al., 27 Aug 2025).

The layered architecture has direct physical consequences. The separation of magnetically active Eu planes by covalently bonded Al-Si sheets favors extended, low-curvature domain walls within the $_2$1 plane and periodic stripe textures on the cleaved surface. This structural aspect is central to the unusual domain-wall-mediated transport observed in the material (Xia et al., 2023).

2. Magnetic order, anisotropy, and field-driven phases

Below $_2$2 K, EuAl$_2$3Si$_2$4 adopts an A-type antiferromagnetic ground state. Eu moments are ferromagnetically aligned within each Eu layer and antiferromagnetically coupled between adjacent Eu layers along $_2$5. The easy axis lies in-plane, with spins aligned along the crystallographic $_2$6 axis. First-principles energetics and prior neutron data are reported to agree with this magnetic structure (Xia et al., 2023).

The magnetic susceptibility is nearly isotropic in the paramagnetic state but becomes anisotropic below $_2$7. The field scale for full polarization depends strongly on field orientation. At 2 K, the saturation fields are $_2$8 T for $_2$9 and $T_{\mathrm{N}} \approx 33.6$0 T for $T_{\mathrm{N}} \approx 33.6$1. For $T_{\mathrm{N}} \approx 33.6$2, the antiferromagnet transforms to a $T_{\mathrm{N}} \approx 33.6$3-axis-polarized ferromagnetic state at $T_{\mathrm{N}} \approx 33.6$4 T, with corresponding features in $T_{\mathrm{N}} \approx 33.6$5 and $T_{\mathrm{N}} \approx 33.6$6. For $T_{\mathrm{N}} \approx 33.6$7, two spin-flop transitions occur around $T_{\mathrm{N}} \approx 33.6$8-$T_{\mathrm{N}} \approx 33.6$9 T at low temperature; magnetoresistance also shows inflection points consistent with spin-flop transitions at low temperatures and low fields near $^{2+}$0 kOe $^{2+}$1 T) (Xia et al., 2023, Liu et al., 27 Aug 2025).

The paramagnetic regime above $^{2+}$2 is characterized by unsaturated magnetization and enhanced thermal spin fluctuations. In this regime, magnetoresistance becomes negative because magnetic field suppresses spin-fluctuation scattering. In the ordered state, $^{2+}$3 peaks at $^{2+}$4 and drops below it, described as indicative of reduced scattering and reconstruction of the electronic structure; in a separate formulation, the drop is associated with opening of a gap in the antiferromagnetic state (Liu et al., 27 Aug 2025).

An important consequence of this magnetic phase diagram is that EuAl$^{2+}$5Si$^{2+}$6 combines near-zero net magnetization in zero field with strong field tunability. This makes it possible to study both antiferromagnetic transport channels and the ferromagnetic, Weyl-point-bearing state within the same material system.

3. Domain-wall stripe lattice and magnetic microstructure

Low-temperature magnetic force microscopy on the $^{2+}$7 surface reveals a striking periodic stripe domain structure in zero and finite fields. In the A-type antiferromagnetic phase, bright stripes correspond to in-plane magnetized domains, whereas dark straight lines are antiferromagnetic domain walls carrying net magnetization along $^{2+}$8, which gives detectable MFM contrast and implies a local out-of-plane component at the domain wall (Xia et al., 2023).

Fast-Fourier-transform analysis quantifies the tunable periodicity of this stripe lattice. The average domain-wall spacing $^{2+}$9 decreases nearly monotonically from $c$0 nm at 0 T to $c$1 nm at 4 T for $c$2, while preserving periodic order. Equivalently, the domain-wall density per unit length $c$3 increases with field and is symmetric for positive and negative fields. Above $c$4 T, or by $c$5 T in perpendicular-field imaging, the domain-wall contrast vanishes because the Eu spins are fully polarized. The pattern is reversible upon reducing the field, and no pronounced hysteresis in the domain-wall texture is observed (Xia et al., 2023, Liu et al., 27 Aug 2025).

The proposed formation mechanism is a competition between domain-wall energy and magnetostatic stray-field energy at the surface. The large Eu$c$6 moments and relatively weak anisotropy favor subdivision into many domains to reduce stray-field energy, while the layered structure stabilizes straight domain walls. Adjacent domain walls along $c$7 are antiferromagnetically coupled in the ground state and contribute opposite signs to skew scattering. Accordingly, the net domain-wall Hall effect scales with the net magnetization of all domain walls rather than simply with their absolute number (Xia et al., 2023).

This domain-wall lattice is not merely a magnetic texture. It is an electronically active, field-reconfigurable superstructure whose periodicity controls an extrinsic Hall channel and therefore directly couples mesoscopic magnetic order to transport.

4. Hall transport and the giant domain-wall anomalous Hall effect

The transverse Hall resistivity is decomposed as

$c$8

where $c$9 is the ordinary Hall term, $ab$0 is the conventional anomalous Hall term that scales with magnetization, and $ab$1 is the extrinsic domain-wall skew-scattering term. Two-band fits to the ordinary Hall response were used where necessary to capture electron and hole contributions. Hall and longitudinal conductivities were obtained from the resistivities through

$ab$2

Within this framework, EuAl$ab$3Si$ab$4 exhibits an exceptionally large domain-wall contribution to the Hall response (Xia et al., 2023).

At 2 K and $ab$5 T for $ab$6, the intrinsic anomalous Hall conductivity peaks at $ab$7 S cm$ab$8, whereas the domain-wall Hall conductivity reaches $ab$9 S cm$_2$0. This is two orders of magnitude larger than the intrinsic anomalous Hall conductivity and is described as, among bulk materials, the largest anomalous-Hall-related conductivity reported. The domain-wall Hall angle,

$_2$1

attains $_2$2 at 4 K. The domain-wall Hall fraction,

$_2$3

reaches $_2$4 at 2 K near the peak, showing that the Hall response is dominated by domain-wall skew scattering (Xia et al., 2023).

The field dependence of the extrinsic Hall term is consistent with this interpretation. At 6 K, the extracted extra Hall resistivity reaches $_2$5 cm at $_2$6 T, and the evolution $_2$7 tracks $_2$8. This is consistent with a domain-wall skew-scattering mechanism in which asymmetric transmission at domain walls produces transverse deflection. The domain-wall contribution and $_2$9 both decrease with increasing temperature; the $_2$0 peak shifts with field and vanishes once the system is fully polarized at $_2$1 T (Xia et al., 2023).

The longitudinal transport is also notable. Six-probe magnetotransport with $_2$2 and current within $_2$3 gives metallic $_2$4 with $_2$5, a pronounced peak at $_2$6, and magnetoresistance at 2 K reaching $_2$7 at 31 T without saturation. High-field measurements extend to 31 T, and Hall data were symmetrized or antisymmetrized to remove longitudinal admixture (Xia et al., 2023).

In comparative context, noncollinear antiferromagnets such as Mn$_2$8 $_2$9 Sn, Ge, Ga, Pt$_2$00 show intrinsic anomalous Hall conductivities of $_2$01-450 S cm$_2$02 at low temperature and up to $_2$03 S cm$_2$04 at room temperature. EuAl$_2$05Si$_2$06 instead combines a collinear A-type antiferromagnetic order, near-zero net magnetization at zero field, a field-tunable periodic domain-wall stripe lattice, and Weyl points near $_2$07, thereby producing a domain-wall anomalous Hall effect that overwhelms the intrinsic Berry-curvature anomalous Hall effect by two orders of magnitude (Xia et al., 2023).

5. Electronic structure, topology, and microscopic mechanism

The antiferromagnetic ground state belongs to magnetic space group type-IV $_2$08 (BNS setting), preserving inversion symmetry while breaking $_2$09 and time-reversal symmetry. Parity analysis of occupied bands yields a $_2$10 index of 2, consistent with an axion-insulator-like topology, as in antiferromagnetic EuCd$_2$11As$_2$12. The nontrivial band inversion is sensitive to the Eu $_2$13 correlation parameter $_2$14, appearing for $_2$15-5 eV; mBJ increases gaps and suppresses inversion for higher $_2$16 (Xia et al., 2023).

In the spin-polarized ferromagnetic state induced by $_2$17, the magnetic space group becomes type-III $_2$18, with time-reversal symmetry broken and inversion preserved. Calculations and mBJ predict a pair of symmetry-protected linear crossings, identified as Weyl points, along $_2$19-A at $_2$20 meV below $_2$21. A complementary description places the Weyl points along high-symmetry directions near $_2$22, for example K-T-A, in the ferromagnetic phase. ARPES on the (001) surface reveals two linear, two-dimensional hole-like surface states $_2$23 and small electron-like pockets at $_2$24, consistent with semimetallic character (Xia et al., 2023, Liu et al., 27 Aug 2025).

Quantum oscillation measurements support this topological picture. Shubnikov-de Haas oscillations resolve two bulk frequencies, $_2$25 T and $_2$26 T. One report gives effective masses $_2$27 and $_2$28, and a Berry phase near $_2$29 for $_2$30, namely $_2$31, indicating nontrivial topology for the hole-1 band that forms the Weyl point. Another report gives corresponding extremal Fermi-surface areas $_2$32 nm$_2$33 and $_2$34 nm$_2$35, with Berry phases $_2$36 for the nontrivial hole pocket and $_2$37 for a trivial band. The $_2$38 pocket is described as three-dimensional and angle-insensitive across rotation from $_2$39 to $_2$40, whereas $_2$41 shows mild angular variation (Xia et al., 2023, Liu et al., 27 Aug 2025).

The intrinsic anomalous Hall effect is attributed to Berry curvature $_2$42 of occupied bands: $_2$43 with semiclassical anomalous velocity

$_2$44

First-principles calculations yield $_2$45 S cm$_2$46, close to the measured intrinsic value of about $_2$47 S cm$_2$48, but much smaller than the domain-wall contribution (Xia et al., 2023).

The microscopic picture of the giant extrinsic Hall response invokes topological bound states and asymmetric transmission at domain walls. For a domain wall lying in the $_2$49 plane, incident Bloch waves with opposite group velocities along $_2$50 have reflection and transmission coefficients that differ for $_2$51 because of the domain wall’s internal topological structure. If $_2$52 lies near Weyl points, the domain wall hosts chiral bound states that strongly bias transmission, generating a net transverse current and Hall voltage. The effect is additive over the domain-wall lattice and therefore scales with the domain-wall density $_2$53; opposite-polarity domain walls contribute opposite signs, so the net response tracks the domain-wall magnetization $_2$54 and $_2$55. The measured mean free path $_2$56-31.9 nm, inferred from quantum lifetimes $_2$57 s and $_2$58 s together with Fermi velocities $_2$59 and $_2$60 m s$_2$61, satisfies $_2$62 across the field range, placing transport in the regime where the Sorn-Paramekanti domain-wall skew-scattering theory applies (Xia et al., 2023).

6. Planar Hall effect, anisotropic magnetoresistance, and interpretation

EuAl$_2$63Si$_2$64 also exhibits a large planar Hall effect and pronounced anisotropic magnetoresistance. Magnetotransport for these measurements was performed in standard four-probe geometry with the magnetic field rotated within the $_2$65 plane; $_2$66 denotes the in-plane angle between current and magnetic field. The planar Hall effect amplitude is $_2$67 cm at 2 K and 8 T. Its angular dependence follows $_2$68, with $_2$69 periodicity and a $_2$70 phase shift relative to AMR, while the AMR follows $_2$71 and grows with field (Liu et al., 27 Aug 2025).

The extraction protocol explicitly separates planar Hall and normal Hall components and corrects for probe misalignment. The symmetrized transverse signal is

$_2$72

and the planar Hall resistivity is then obtained by angular antisymmetrization,

$_2$73

For AMR, the corresponding relations are

$_2$74

$_2$75

with

$_2$76

The fitted angular forms are

$_2$77

$_2$78

These relations provide the basis for the mechanistic decomposition of the PHE and AMR (Liu et al., 27 Aug 2025).

The dominant mechanisms depend on magnetic regime. In the field-induced ferromagnetic state, classical orbital magnetoresistance dominates the PHE and AMR. At 2 K, $_2$79 scales as $_2$80 over 1-9 T without saturation; $_2$81 remains nearly field independent, while $_2$82 increases quadratically with $_2$83, giving $_2$84. Parametric plots of $_2$85 versus $_2$86 show “shock-wave” trajectories attributed to asymmetric enhancement of $_2$87, which is presented as a hallmark of orbital magnetoresistance rather than chiral anomaly. In the paramagnetic regime, field-suppressed thermal spin fluctuations reduce spin-dependent scattering, yielding negative magnetoresistance at low fields and a circular expansion in parametric $_2$88-$_2$89 plots. Although $_2$90 also in this regime, the origin is assigned to the reduction of spin-disorder scattering rather than Berry curvature or chiral anomaly (Liu et al., 27 Aug 2025).

This interpretation is explicitly contrasted with a common reading of planar Hall data in topological materials. Despite the presence of Weyl points near $_2$91 and nontrivial Berry phases in quantum oscillations, EuAl$_2$92Si$_2$93 does not show a dominant chiral-anomaly transport signature in the ferromagnetic phase, most notably because a robust negative longitudinal magnetoresistance is absent. Berry curvature therefore plays only a minor role in the PHE and AMR, even though it underpins intrinsic anomalous Hall conductivity. This distinction addresses a recurrent misconception that planar Hall signals are by themselves definitive signatures of the Adler-Bell-Jackiw chiral anomaly; in EuAl$_2$94Si$_2$95, the data instead support a multi-origin transport response in which orbital magnetoresistance in the ferromagnetic state and field-suppressed spin fluctuations in the paramagnetic regime are dominant (Liu et al., 27 Aug 2025).

The broader significance of EuAl$_2$96Si$_2$97 lies in the coexistence of several experimentally separable ingredients: A-type antiferromagnetic order with negligible zero-field net magnetization, a field-driven transition into a ferromagnetic Weyl semimetal, a periodic and reversible domain-wall superstructure, a giant extrinsic anomalous Hall effect dominated by domain-wall skew scattering, and a large planar Hall response whose origin can be decomposed without conflating all anisotropic transport with topology. This suggests a materials platform for domain-wall-based spintronic devices, high-density memory and logic based on stable periodic domain-wall arrays, quantum sensing through tunable in-plane PHE, and micro- or nanoscale devices if the layered CaAl$_2$98Si$_2$99-type structure can indeed be exploited as a thin-lamella platform (Xia et al., 2023, Liu et al., 27 Aug 2025).