CeAlSi: Magnetic Weyl Semimetal

• The material is a noncentrosymmetric semimetal that exhibits magnetic Weyl physics with 40 Weyl nodes and spectroscopically-identified Fermi arcs.
• It features a tetragonal LaPtSi-type structure with alternating Ce layers that foster pronounced magnetic anisotropy and complex domain-wall topology.
• Comprehensive studies reveal tunable anomalous Hall, Nernst, and optical effects that link topology, magnetism, and 4f-electron correlations.

CeAlSi is a rare-earth intermetallic semimetal in the $R$AlSi family that crystallizes in the noncentrosymmetric tetragonal space group $I4_1md$ and is now established as a magnetic Weyl semimetal. Angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations identified surface Fermi arcs and bulk Weyl cones in its paramagnetic state, while ordered Ce moments, Ce $4f$ spectral weight near the Fermi level, and pronounced magnetic anisotropy make it a model system for studying the coupled evolution of topology, magnetism, and electronic correlations (Sakhya et al., 2022).

1. Crystal structure and symmetry setting

CeAlSi is a semimetallic member of the rare-earth $R$AlSi family. It adopts the tetragonal LaPtSi-type structure with space group $I4_1md$ (No. 109), and reported lattice parameters include $a=4.25\ \text{\AA}$, $c=14.58\ \text{\AA}$, as well as refined values $a=4.2550\ \text{\AA}$ and $c=14.5919\ \text{\AA}$ from powder diffraction and Rietveld refinement (Sakhya et al., 2022, Cao et al., 2021). The structure is built from stacked $R$, Al, and Si layers along the $I4_1md$0-axis, with each layer containing only one element, and later magnetic modeling further emphasized that the unit cell contains two alternating Ce layers (Cao et al., 2021, Sun et al., 2021).

Its symmetry content is central to its topological classification. The crystal hosts two vertical mirror planes and two vertical glide mirror planes, but it lacks a horizontal mirror plane and, more importantly, lacks inversion symmetry (Sakhya et al., 2022). This broken inversion symmetry is sufficient to permit Weyl nodes already in the paramagnetic phase. In later crystalline-electric-field analysis, the Ce site was treated as having $I4_1md$1 local symmetry, a point that becomes important for single-ion anisotropy and the low-energy magnetic manifold (Yang et al., 14 Aug 2025).

This structural setting distinguishes CeAlSi from centrosymmetric magnetic semimetals. In CeAlSi, inversion breaking is not an emergent low-temperature effect but a built-in crystallographic property, so magnetic ordering acts on a pre-existing noncentrosymmetric Weyl background rather than creating that background from scratch. A common misconception is therefore that CeAlSi becomes topological only when it orders magnetically; the spectroscopic evidence instead shows that inversion symmetry breaking already produces Weyl physics in the paramagnetic state (Sakhya et al., 2022).

2. Weyl topology and spectroscopic verification

The most direct evidence for the Weyl-semimetal state in CeAlSi comes from the combined ARPES and DFT study that established the material as a non-centrosymmetric magnetic Weyl semimetal (Sakhya et al., 2022). In calculations using experimental lattice parameters, GGA, self-consistent SOC, and GGA$I4_1md$2 for Ce $I4_1md$3-electrons with $I4_1md$4, the paramagnetic phase contains a rich Weyl-node structure: $I4_1md$5 pairs each of $I4_1md$6, $I4_1md$7, and $I4_1md$8, plus $I4_1md$9 pairs of $4f$0, for a total of $4f$1 Weyl nodes. The $4f$2 nodes lie on the $4f$3 plane, the $4f$4 nodes lie away from that plane, and the spinless $4f$5 node splits into two spinful nodes, $4f$6 and $4f$7, with the same chirality. The Weyl nodes in the $4f$8 plane are pinned by $4f$9 symmetry, while nodal lines on mirror-invariant planes are stabilized by $R$0 and $R$1.

Surface-sensitive vacuum-ultraviolet ARPES on the $R$2 surface at $R$3 resolved a circular pocket at $R$4, mustache-like pockets at $R$5 and $R$6, and, crucially, non-dispersing features along $R$7 identified as Fermi arcs (Sakhya et al., 2022). Their photon-energy independence distinguishes them from the strongly photon-energy-dispersing bulk pockets at $R$8, $R$9, and $I4_1md$0. The identification is reinforced by second-derivative and curvature analysis and by agreement with the calculated surface spectral function.

The topological assignment was strengthened through loop measurements in surface momentum space. One loop around an arc termination showed a single left-moving chiral mode corresponding to Chern number $I4_1md$1, while another showed a single right-moving chiral mode corresponding to $I4_1md$2 (Sakhya et al., 2022). These measurements directly implement bulk-boundary correspondence: the observed open surface states terminate at projected Weyl nodes and inherit their chiral charge.

Bulk-sensitive soft-X-ray ARPES then resolved the corresponding bulk Weyl dispersion. At $I4_1md$3, measurements on the $I4_1md$4 plane showed a Fermi surface consistent with the bulk Brillouin zone and a linearly dispersing Weyl cone assigned to $I4_1md$5, with the Weyl fermion located at $I4_1md$6 within experimental resolution (Sakhya et al., 2022). In the same spectroscopic study, Ce $I4_1md$7 weight was observed near the Fermi level, including a sharp dispersionless peak at about $I4_1md$8 identified as the $I4_1md$9 Kondo resonance peak, while the $a=4.25\ \text{\AA}$0 peak near $a=4.25\ \text{\AA}$1 was not observed. This places CeAlSi outside the category of a purely weakly correlated Weyl semimetal.

3. Magnetic order, anisotropy, and domain-wall topology

CeAlSi is ferromagnetic, but the reported ordering temperature depends on probe and sample. Domain and thermodynamic studies place the magnetic transition near $a=4.25\ \text{\AA}$2–$a=4.25\ \text{\AA}$3, magnetization in one transport study gave $a=4.25\ \text{\AA}$4, and another transport study reported $a=4.25\ \text{\AA}$5 (Sun et al., 2021, Cao et al., 2021, Cheng et al., 2023). Across these studies, the consistent picture is that Ce moments order in a noncollinear ferromagnetic phase with magnetization lying primarily in the $a=4.25\ \text{\AA}$6 plane, while the $a=4.25\ \text{\AA}$7-axis is magnetically hard (Sun et al., 2021, Piva et al., 2021).

The real-space magnetic texture is unusually rich. Full vector magnetization mapping by vector magneto-optical Kerr effect microscopy revealed large domains, roughly $a=4.25\ \text{\AA}$8 across, and two topologically distinct classes of domain walls: walls aligned along tetragonal axes such as $a=4.25\ \text{\AA}$9, and diagonal walls along $c=14.58\ \text{\AA}$0 (Sun et al., 2021). The $c=14.58\ \text{\AA}$1-type walls are chiral and charge-neutral: the magnetization rotates through the wall with nonzero $c=14.58\ \text{\AA}$2, and the sense of rotation is the same for corresponding walls. The $c=14.58\ \text{\AA}$3-type walls are non-chiral and charged: $c=14.58\ \text{\AA}$4 passes continuously through zero, and the wall carries finite magnetic charge density,

$c=14.58\ \text{\AA}$5

The emergent chirality of the vertical walls was traced to a local Lifshitz invariant,

$c=14.58\ \text{\AA}$6

which is forbidden by the bulk mirror symmetry in a naive uniform description but allowed locally because the noncollinear magnetic bilayers break that symmetry at the wall (Sun et al., 2021).

The same study revised the low-temperature anisotropy landscape. What had previously been described as four in-plane easy axes along the diagonals splits into an octet below about $c=14.58\ \text{\AA}$7; at $c=14.58\ \text{\AA}$8, histogram peaks appear near approximately $c=14.58\ \text{\AA}$9, $a=4.2550\ \text{\AA}$0, $a=4.2550\ \text{\AA}$1, and $a=4.2550\ \text{\AA}$2 (Sun et al., 2021). A Landau model written in terms of the two Ce-layer moments $a=4.2550\ \text{\AA}$3 and $a=4.2550\ \text{\AA}$4 attributes this octet to interlayer coupling in a noncollinear state. In that interpretation, the same microscopic noncollinearity explains easy-axis splitting, chiral vertical walls, and nonchiral diagonal walls.

Scanning SQUID microscopy independently showed that CeAlSi contains both stable ferromagnetic domains and metastable domains with larger susceptibility, dissipation, and slow fluctuations, likely reflecting frustrated or glassy magnetic behavior (Xu et al., 2020). The coexistence of these phases was attributed to magnetoelastic and magnetostriction effects. The measured strain response is of order $a=4.2550\ \text{\AA}$5 under weak fields of a few tens of Gauss, and the inferred internal distortions correspond to picometer-scale unit-cell deformations (Xu et al., 2020). Field-cooling experiments further showed that very small in-plane fields of only a few Gauss can reorganize the domain pattern, with strong dependence on field orientation relative to $a=4.2550\ \text{\AA}$6, $a=4.2550\ \text{\AA}$7, and $a=4.2550\ \text{\AA}$8; stable domain areas can exceed roughly $a=4.2550\ \text{\AA}$9, and directional control changes domain-wall lengths by a median of $c=14.5919\ \text{\AA}$0 with a maximum increase of $c=14.5919\ \text{\AA}$1 in the field of view (Xu et al., 2021). These observations are significant because, in a Weyl semimetal, such magnetic textures act as real-space perturbations to the Weyl electrons rather than as passive micromagnetic details.

4. Magnetotransport, anomalous responses, and external tuning

Early transport work characterized CeAlSi as a metallic, electron-dominated ferromagnet with nonsaturating magnetoresistance of about $c=14.5919\ \text{\AA}$2 at $c=14.5919\ \text{\AA}$3 and $c=14.5919\ \text{\AA}$4 for $c=14.5919\ \text{\AA}$5 (Cao et al., 2021). In that study, the Hall resistivity was approximately linear below $c=14.5919\ \text{\AA}$6, the high-field fit gave a negative $c=14.5919\ \text{\AA}$7, and the extracted electron carrier density displayed a kink around $c=14.5919\ \text{\AA}$8, indicating sensitivity of the electronic structure to Ce-moment ordering. Pressure up to $c=14.5919\ \text{\AA}$9 did not destroy the magnetic transition and no superconductivity was observed down to $R$0 (Cao et al., 2021).

More detailed transport and thermoelectric work established that CeAlSi hosts strong anomalous Hall and anomalous Nernst responses and that these are tunable by magnetism and pressure (Cheng et al., 2023). At ambient pressure, the anomalous Hall effect appears already in the paramagnetic regime and is enhanced as temperature approaches the ferromagnetic ordering temperature, while the anomalous Nernst effect emerges below about $R$1, saturates below about $R$2, and reaches an anomalous Nernst angle of about $R$3 at $R$4. In this framework, ferromagnetism acts as a Zeeman-like perturbation that does not change the Weyl-node classification or quantity but shifts the Weyl-node positions in momentum and energy space, thereby modulating Berry curvature and transverse transport.

The anomalous Hall response is strongly anisotropic. Measurements of $R$5 for $R$6 and $R$7 for $R$8 showed opposite signs and large magnitudes, with $R$9 at $I4_1md$00 and $I4_1md$01 at $I4_1md$02 (Alam et al., 2022). Above $I4_1md$03, $I4_1md$04 increases further and peaks near $I4_1md$05, whereas $I4_1md$06 decreases with increasing temperature. That study attributed the sign reversal to magnetization-direction-induced band-structure reconstruction that shifts Weyl points along $I4_1md$07-X, and argued explicitly that $I4_1md$08-space topology, not scalar spin chirality, governs the anomalous transport when the scalar spin chirality is zero (Alam et al., 2022).

Pressure studies reveal two distinct regimes. At relatively low pressure, up to about $I4_1md$09–$I4_1md$10, the Curie temperature rises with slope $I4_1md$11, from $I4_1md$12 at ambient pressure to $I4_1md$13 at $I4_1md$14, yet the in-plane noncollinear ferromagnetic structure and the calculated band structure change only weakly (Piva et al., 2021). In the same regime, both the anomalous Hall effect and the loop Hall effect are suppressed, as is the anomalous quantum-oscillation amplitude. This led to the proposal that the decisive pressure-sensitive variable is the magnetic domain-wall landscape rather than bulk order or bulk bands (Piva et al., 2021, Piva et al., 2023). A simplified model of Weyl fermions scattering off ferromagnetic domain walls reproduced Hall-response scales of order $I4_1md$15 and provided a concrete mechanism for extrinsic AHE/LHE contributions mediated by walls with a local out-of-plane component $I4_1md$16 (Piva et al., 2023).

At higher pressure, transport and XRD extended the tuning landscape substantially. One study reported an enhancement and eventual sign change of the anomalous Hall effect at $I4_1md$17, identified a Lifshitz transition near $I4_1md$18, loss of ferromagnetism above about $I4_1md$19, and a structural phase transition around $I4_1md$20, with the ambient $I4_1md$21 structure persisting to about $I4_1md$22 (Cheng et al., 2023). In the accompanying DFT, Weyl nodes along $I4_1md$23-X shift from about $I4_1md$24 above $I4_1md$25 at $I4_1md$26 to $I4_1md$27 below $I4_1md$28 at $I4_1md$29 and $I4_1md$30 below $I4_1md$31 at $I4_1md$32.

Magnetic field provides another axis of control. Lower-field quantum-oscillation work found a single dominant frequency near $I4_1md$33 and an anomalous reduction of oscillation amplitude on cooling below $I4_1md$34, with Landau-fan intercepts changing from about $I4_1md$35 at $I4_1md$36 to about $I4_1md$37 at $I4_1md$38, consistent with a ferromagnetism-driven change in Fermi-surface topology (Piva et al., 2021, Piva et al., 2023). A later high-field study up to $I4_1md$39 reported an abrupt frequency change near $I4_1md$40, from a low-field $I4_1md$41 orbit to high-field $I4_1md$42 and $I4_1md$43 orbits, which was interpreted as a field-induced Lifshitz transition (Piva et al., 15 Oct 2025). In that work, the magnetoresistance reached about $I4_1md$44 at $I4_1md$45 and $I4_1md$46 for $I4_1md$47, and the results were taken as consistent with ferromagnetism bringing the Weyl nodes closer to the Fermi level.

5. Optical, nonlinear optical, and photogalvanic phenomena

Room-temperature infrared spectroscopy showed that CeAlSi already exhibits a Weyl-like optical response in the paramagnetic phase (Kunze et al., 2024). After subtraction of the Drude term, the interband optical conductivity displays a linear-in-frequency dependence over a broad low-energy range, with two quasi-linear regimes of different slope. Within the analysis used in that study, CeAlSi is assigned mainly type-II Weyl character with overtilted cones: the fitted tilting parameter is $I4_1md$48, the average Fermi velocity is $I4_1md$49, and the upper linear regime extrapolates to finite conductivity at $I4_1md$50, which was taken as characteristic of tilted Weyl cones (Kunze et al., 2024). The significance of these measurements is that the optical Weyl signature does not rely on long-range magnetic order at room temperature; inversion-symmetry breaking alone already organizes the low-energy electrodynamics.

Low-temperature nonlinear optics revealed a much stronger coupling between magnetism and topology. In second-harmonic generation, CeAlSi shows a nonlinear optical diode effect in which reversing the light-propagation direction changes the SHG intensity by more than six-fold across the entire $I4_1md$51–$I4_1md$52 range, with a maximum directional contrast of $I4_1md$53 around $I4_1md$54, corresponding to more than a $I4_1md$55-fold change in SHG intensity (Tzschaschel et al., 2023). The effect persists over a bandwidth exceeding $I4_1md$56. The mechanism was formulated as interference between lattice and magnetic tensor components, particularly $I4_1md$57 and $I4_1md$58, so that magnetization reversal switches which propagation direction is brighter. DFT associated the broadband nature of the effect with linearly dispersive bands emerging from Weyl nodes rather than with narrow flat-band resonances. The same study also demonstrated nonvolatile current-induced magnetization switching: in bulk crystals, $I4_1md$59 switched $I4_1md$60 and $I4_1md$61, while a focused-ion-beam microdevice switched at $I4_1md$62, corresponding to about $I4_1md$63 (Tzschaschel et al., 2023).

First-principles calculations further predicted a large circular photogalvanic effect in CeAlSi (Karmakar et al., 2023). In that work, the dominant injection-current component $I4_1md$64 reaches $I4_1md$65, or about $I4_1md$66, with pronounced peaks at $I4_1md$67 and $I4_1md$68 and a broad near-infrared response over $I4_1md$69–$I4_1md$70. The unstrained ground state was reported to host $I4_1md$71 pairs of Weyl nodes with opposite chirality. Uniaxial compressive strain along $I4_1md$72 was found to be the most effective tuning parameter: $I4_1md$73 strain raises the injection current by $I4_1md$74, to $I4_1md$75, and broadens the Weyl-node landscape to $I4_1md$76 nodes total at $I4_1md$77 (Karmakar et al., 2023). These optical results establish CeAlSi as a rare case in which Weyl topology, magnetization, and nonlinear response can all be manipulated in one material platform.

6. Local-moment physics, correlations, and relation to the broader family

CeAlSi is not only a topological semimetal but also a $I4_1md$78-electron magnet with a well-defined local-moment hierarchy. Inelastic neutron scattering on polycrystalline CeAlSi resolved two crystalline-electric-field excitations at $I4_1md$79 and $I4_1md$80, plus an extra low-energy feature near $I4_1md$81 at $I4_1md$82, attributed to either spin-wave excitations or Zeeman splitting of the ground-state doublet in the molecular field (Yang et al., 14 Aug 2025). Heat capacity showed a broad Schottky anomaly together with a sharp ferromagnetic peak at $I4_1md$83; the magnetic entropy reaches about $I4_1md$84 at $I4_1md$85, close to $I4_1md$86, and reaches $I4_1md$87 by $I4_1md$88, slightly below $I4_1md$89 (Yang et al., 14 Aug 2025). Joint fits to neutron and thermodynamic data yielded a Ce$I4_1md$90 Kramers-doublet ground state

$I4_1md$91

dominated by $I4_1md$92 with $I4_1md$93 weight (Yang et al., 14 Aug 2025). This supports the description of CeAlSi as a strongly anisotropic effective spin-$I4_1md$94 Weyl magnet.

The local-moment picture is compatible with spectroscopic indications of moderate correlation effects rather than heavy-fermion behavior. ARPES identified a $I4_1md$95 resonance near $I4_1md$96, and pressure-dependent transport reported $I4_1md$97-like behavior at higher pressure, suggesting possible Kondo-like physics (Sakhya et al., 2022, Cheng et al., 2023). At the same time, high-field quantum-oscillation work argued that CeAlSi does not resemble a canonical heavy-fermion system, citing weak $I4_1md$98-electron hybridization and a relatively small Sommerfeld coefficient in support of a different mechanism for its field-induced Fermi-surface reconstruction (Piva et al., 15 Oct 2025). A plausible implication is that CeAlSi occupies an intermediate regime: correlated enough for $I4_1md$99 states and CEF physics to matter, but still sufficiently itinerant for Weyl-band electrodynamics and relatively light quantum-oscillation masses to remain visible.

Within the wider $4f$00Al$4f$01 family, CeAlSi often serves as the commensurate magnetic reference compound. A 2025 comparison with CeAlGe concluded that CeAlSi is fully commensurate, with $4f$02, shows only $4f$03 magnetic scattering in SANS, and exhibits neither multi-$4f$04 order nor singular angular magnetoresistance (SAMR) (Yao et al., 22 Sep 2025). In $4f$05, both incommensurate order and SAMR appear only above a critical concentration $4f$06. In that interpretation, CeAlSi lies on the side of stronger single-ion in-plane anisotropy and weaker Weyl-mediated chiral multi-spin coupling, whereas CeAlGe enters a multi-$4f$07 regime. This comparison is important because it shows that neither noncentrosymmetric Weyl bands nor ferromagnetism alone guarantees the more exotic transport responses found elsewhere in the family.

Taken together, the literature defines CeAlSi as a noncentrosymmetric magnetic Weyl semimetal whose essential physics is set by three concurrent ingredients: inversion-breaking crystal symmetry, noncollinear ferromagnetism with complex domain-wall topology, and a strongly anisotropic Ce$4f$08 local-moment sector with $4f$09 spectral weight near the Fermi level. That combination has made it a benchmark system for investigating how Weyl nodes, Berry-curvature-driven transport, magnetic textures, strain, pressure, and nonlinear optical phenomena can be tuned within a single rare-earth material platform.