NdAlSi: Magnetic Weyl Semimetal

• NdAlSi is a noncentrosymmetric rare-earth intermetallic that unites local 4f magnetism with a topological Weyl-band structure, making it a key magnetic semimetal.
• The material exhibits magnetically reconfigurable Weyl nodes whose number and position evolve with magnetic order, impacting collective magnetism and Fermi-surface reconstruction.
• NdAlSi displays unconventional quantum oscillations, anisotropic transport, and disorder-tunable surface states, offering insights into Weyl-mediated electrodynamics.

NdAlSi is a non-centrosymmetric rare-earth intermetallic in the $R$AlSi family that has emerged as a prototypical magnetic Weyl semimetal in which local-moment magnetism, Weyl-band topology, and small Fermi surfaces are strongly entangled. It crystallizes in the tetragonal space group $I4_1md$ (No. 109), thereby breaking inversion symmetry already in the paramagnetic state, while Nd $4f$ magnetism breaks time-reversal symmetry in the ordered phases (Wang et al., 2022, Li et al., 2023). Across the literature, NdAlSi is described as a platform for Weyl-mediated collective magnetism, ferrimagnetic regulation of Weyl fermions, disorder-tuned surface topology, unconventional quantum oscillations, anomalous thermal and thermoelectric responses, and domain-wall-driven emergent electrodynamics (Gaudet et al., 2020, Li et al., 2023, Li et al., 2024, Wang et al., 2022, Yamada et al., 15 Jan 2026).

1. Crystal structure and Weyl-semimetal electronic structure

NdAlSi adopts the body-centered tetragonal LaPtSi-type structure with space group $I4_1md$, a noncentrosymmetric setting with vertical mirror planes $m_x$ and $m_y$, vertical glide mirrors $m_{xy}$ and $m_{x\overline{y}}$, and no horizontal mirror plane (Wang et al., 2022, Li et al., 2023). Reported lattice parameters are $a=b\approx 4.20\ \text{Å}$ and $c\approx 14.52\ \text{Å}$, and single crystals were described as nearly stoichiometric in early characterization work (Wang et al., 2022). The absence of inversion symmetry is the structural prerequisite for Weyl nodes in the paramagnetic phase, while magnetic order further reconstructs and multiplies the Weyl-node manifold (Li et al., 2023, Kunze et al., 2024).

Density-functional calculations and spectroscopic studies consistently place NdAlSi in the Weyl-semimetal category. One ARPES study reported 40 Weyl nodes in the paramagnetic state and showed surface Fermi arcs together with bulk Weyl-fermion dispersions, establishing NdAlSi experimentally as a magnetic Weyl semimetal (Li et al., 2023). In the polarized ferromagnetic state, a separate study reported 56 Weyl nodes in DFT and found that the experimentally relevant chemical potential is shifted by $I4_1md$0 (Gaudet et al., 2020). Optical spectroscopy in the paramagnetic phase further identified linear-in-frequency interband conductivity consistent with Weyl nodes near the Fermi energy and extracted, for NdAlSi, $I4_1md$1, $I4_1md$2, $I4_1md$3, $I4_1md$4, and $I4_1md$5, supporting mainly type-II, overtilted Weyl states (Kunze et al., 2024).

The Weyl-node count depends on magnetic configuration in the literature. One transport-oriented study summarized prior calculations as giving 40 Weyl nodes in the paramagnetic state and 52, 56, and 56 in the ferrimagnetic, antiferromagnetic, and spin-polarized states, respectively (Zhang et al., 5 Feb 2025). Another ARPES/DFT study emphasized that ferrimagnetism does not merely shift pre-existing Weyl nodes, but folds the Brillouin zone and generates additional nodes in the low-temperature UUD state (Li et al., 2023). This suggests that in NdAlSi the Weyl sector is not a passive background to magnetism; it is itself magnetically reconfigurable.

2. Magnetic order, crystalline electric fields, and microscopic interactions

The low-temperature magnetic phase diagram of NdAlSi is rich and multi-stage. Heat capacity and transport measurements reported two magnetic transitions at $I4_1md$6 and $I4_1md$7, interpreted as entry into an antiferromagnetic-like or incommensurate SDW-like state followed by a ferrimagnetic state (Wang et al., 2022). Neutron diffraction established a higher-temperature transition at $I4_1md$8 into an incommensurate phase and a lower-temperature transition at $I4_1md$9 into a commensurate ferrimagnetic phase (Gaudet et al., 2020). Later neutron spectroscopy described the sequence as paramagnetic above $4f$0, incommensurate amplitude-modulated spiral below $4f$1, and commensurate ferrimagnetic $4f$2 order below $4f$3 (Lygouras et al., 2024).

Strong Ising anisotropy is a defining feature. Early susceptibility measurements found $4f$4 at $4f$5 (Gaudet et al., 2020), while another study reported an anisotropy ratio of about 45 at 2 K (Wang et al., 2022). For $4f$6, the low-temperature magnetization exhibits two step-like metamagnetic transitions and evolves from roughly $4f$7 of the full moment, consistent with an $4f$8 ferrimagnetic state, to a fully polarized $4f$9 state (Wang et al., 2022). Neutron diffraction refined the low-temperature commensurate structure as a one-dimensional down-up-up pattern with FM and AFM components $I4_1md$0 and $I4_1md$1, respectively, and a saturated high-field moment of $I4_1md$2 above $I4_1md$3 (Gaudet et al., 2020).

The crystalline-electric-field sector is unusually compressed. Inelastic neutron scattering on polycrystalline $I4_1md$4AlSi identified two NdAlSi CEF excitations at 2.5 and 4.2 meV and described the $I4_1md$5 multiplet as split into five Kramers doublets (Yang et al., 14 Aug 2025). The fitted Nd$I4_1md$6 ground doublet is

$I4_1md$7

with dominant $I4_1md$8 weight of 76.2% (Yang et al., 14 Aug 2025). This was interpreted as substantial but weaker single-ion anisotropy than in CeAlSi or PrAlSi, helping rationalize why NdAlSi supports competing magnetic orders rather than a simple robust ferromagnet (Yang et al., 14 Aug 2025).

Microscopic modeling based on high-precision neutron diffraction and spectroscopy found that the low-energy excitations are dispersive crystal-field excitons rather than conventional gapless magnons, with gapped modes near $I4_1md$9 and $m_x$0 in the commensurate state (Lygouras et al., 2024). The exchange network was found to be extended-ranged and sign-changing, with $m_x$1 antiferromagnetic and more distant couplings predominantly ferromagnetic or sign-changing within uncertainty (Lygouras et al., 2024). The same study concluded that low-symmetry anisotropic Dzyaloshinskii–Moriya interactions, rather than a simple high-symmetry Weyl-induced DM term, play an important role in stabilizing the canted spiral texture, with the observed canting requiring $m_x$2 (Lygouras et al., 2024).

3. Weyl-mediated magnetism and magnetically reconstructed Fermi surfaces

NdAlSi is widely regarded as a rare case in which Weyl electrons participate directly in collective magnetism. Neutron diffraction, quantum oscillations, and DFT together showed that the incommensurate propagation vector

$m_x$3

tracks nesting between topologically non-trivial Fermi pockets containing Weyl nodes, especially those associated with $m_x$4 features in the polarized electronic structure (Gaudet et al., 2020). At $m_x$5, the modulation length was reported as $m_x$6, and the growth of third-harmonic peaks at $m_x$7 was interpreted as squaring-up of the amplitude-modulated Ising SDW on cooling (Gaudet et al., 2020). This established the material as a “rare example of Weyl fermions driving collective magnetic order” (Gaudet et al., 2020).

The Fermi surface is unusually sensitive to magnetic configuration. Shubnikov–de Haas measurements resolved temperature-dependent frequencies in both the paramagnetic state and the low-temperature canted $m_x$8-$m_x$9-$m_y$0 state, while the fully polarized high-field state showed a dominant temperature-independent frequency $m_y$1 (Zhang et al., 2023). In the ordered low-field state, $m_y$2 changed from 40 T at 2 K to 46.5 T at 5 K and $m_y$3 from 77 T to 73.6 T, corresponding to an about 16% expansion of one Fermi-surface sheet and about 4.5% shrinkage of another (Zhang et al., 2023). The fully polarized orbit has cyclotron mass $m_y$4, and angle-dependent SdH measurements were described by an ellipsoidal pocket with long-to-short axis ratio 1.92 (Zhang et al., 2023).

A complementary study discovered temperature-dependent quantum oscillations in resistivity and specific heat at constant magnetic field, attributed to destructive interference between oscillations from spin-split Fermi surfaces under strong Weyl-fermion–$m_y$5 exchange combined with Rashba–Dresselhaus and Zeeman effects (Wang et al., 2022). The phenomenological form

$m_y$6

was used to capture the oscillation nodes and their temperature motion, with fitted values $m_y$7, $m_y$8 meV, and $m_y$9 (Wang et al., 2022). The estimated exchange interaction strength of about 0.16 eV was reported to agree with a DFT band splitting of about 0.15 eV in the polarized paramagnetic state (Wang et al., 2022). This suggests that in NdAlSi even nominally single-particle quantum oscillation observables are strongly renormalized by the evolving $m_{xy}$0-moment background.

4. Surface electronic structure, disorder, reconstruction, and low-symmetry boundaries

ARPES on the conventional surface established both topological and magnetically regulated surface physics. On fresh, ordered cleaved surfaces, surface-projected DFT for an Nd-terminated surface reproduced the measured constant-energy contours, while photon-energy-independent arc-like states satisfied chiral-mode criteria expected for topological surface Fermi arcs (Li et al., 2023, Li et al., 2024). In the ferrimagnetic state below $m_{xy}$1, new low-temperature bands appeared at locations expected from magnetic Brillouin-zone folding, providing direct evidence that ferrimagnetism regulates Weyl fermions by shifting and generating Weyl nodes (Li et al., 2023).

Surface disorder in NdAlSi has been used to study a non-Anderson disorder-driven transition. ARPES and STM showed that as the cleaved surface degrades, the SFAs first blur and then disappear completely, while bulk-like bands remain comparatively intact and may even appear sharper (Li et al., 2024). Time-dependent ARPES resolved a progression from sharp trivial surface states and SFAs immediately after cleavage, to blurred surface states after $m_{xy}$2 hours, and finally suppression of all surface states after $m_{xy}$3 hours (Li et al., 2024). This evolution was interpreted as a Weyl-semimetal to diffusive-metal transition in the disordered near-surface region rather than an Anderson localization transition (Li et al., 2024).

A distinct line of work identified a surface-selective spontaneous $m_{xy}$4 reconstruction on the Al-terminated surface. ARPES, surface-projected DFT, phonon calculations, and STM showed that one cleavage surface remains essentially unreconstructed and Nd-terminated, whereas the opposite Al-terminated surface reconstructs and hosts isolated non-topological surface Fermi arcs generated by Brillouin-zone folding (Li et al., 2024). These states exhibit substantially shorter quasiparticle lifetimes, with the unreconstructed-surface lifetime reported as at least 4 to 11 times longer than on the reconstructed surface (Li et al., 2024). The reconstructed boundary was interpreted as a non-Hermitian boundary, with effective surface term

$m_{xy}$5

so that the reconstructed surface acts as a lossy boundary for topological and bulk electrons (Li et al., 2024).

NdAlSi has also become a model system for low-symmetry-facet bulk–boundary correspondence. On the $m_{xy}$6 surface, the projected first bulk Brillouin zone is incommensurate with the surface Brillouin zone, apparently creating a paradox for Fermi-arc connectivity (Li et al., 12 Sep 2025). ARPES and semi-infinite Green’s-function calculations resolved this by showing that successive projected bulk Brillouin zones accumulate into a superlattice commensurate with the surface periodicity, with $m_{xy}$7 successive projected bulk zones required for closure on $m_{xy}$8 (Li et al., 12 Sep 2025). The same analysis suggested that overlapping arc replicas can hybridize into closed surface Fermi-arc loops on low-symmetry facets (Li et al., 12 Sep 2025).

5. Charge, thermal, and thermoelectric transport

NdAlSi displays a wide range of transport anomalies associated with Weyl carriers, magnetic order, and sample-specific scattering. Longitudinal magnetotransport studies reported significant negative magnetoresistance in the $m_{xy}$9 geometry and fitted the high-field magnetoconductivity with a $m_{x\overline{y}}$0 chiral-anomaly term, extracting a chiral coefficient $m_{x\overline{y}}$1 (Zhang et al., 5 Feb 2025). An earlier thermal-transport study described positive longitudinal magneto-electric conductivity and positive longitudinal magneto-thermal conductivity in the quasi-classical regime, with the anomaly-related charge and heat currents linked by the Wiedemann–Franz law (Tanwar et al., 2023). In that work, the semiclassical chiral contribution was written as

$m_{x\overline{y}}$2

and the thermal counterpart as $m_{x\overline{y}}$3 (Tanwar et al., 2023).

The Hall sector is more heterogeneous across studies. One comparison paper on NdAlGe emphasized that NdAlSi does not exhibit a clear anomalous Hall effect, describing $m_{x\overline{y}}$4 as smooth and featureless near the low-field transition, with no Hall plateaus observed despite a calculated intrinsic Hall conductivity $m_{x\overline{y}}$5 near $m_{x\overline{y}}$6 (Yang et al., 2023). A later comparison with NdGaSi likewise stated that NdAlSi does not exhibit any measurable anomalous Hall conductivity (Saraswati et al., 17 Apr 2025). By contrast, another transport study reported an exotic anomalous Hall effect with out-of-sync behavior relative to the magnetization, $m_{x\overline{y}}$7 nearly four orders of magnitude larger than $m_{x\overline{y}}$8, and $m_{x\overline{y}}$9 at 2 K and 9 T (Zhang et al., 5 Feb 2025). This divergence indicates that the Hall response of NdAlSi is an active point of experimental nonuniformity; a plausible implication is that geometry, surface condition, or disorder level may strongly affect the visibility and decomposition of Hall contributions.

Thermoelectric measurements revealed unusually high-mobility multiband transport and a correlation-enhanced Nernst signal. Two-carrier Hall fits yielded dominant hole-like carrier densities $a=b\approx 4.20\ \text{Å}$0 and $a=b\approx 4.20\ \text{Å}$1, with low-temperature mobilities $a=b\approx 4.20\ \text{Å}$2 and $a=b\approx 4.20\ \text{Å}$3 (Yamada et al., 2024). Quantum oscillations identified $a=b\approx 4.20\ \text{Å}$4, $a=b\approx 4.20\ \text{Å}$5, and $a=b\approx 4.20\ \text{Å}$6 pockets with frequencies 51 T, 67 T, and 128 T, respectively (Yamada et al., 2024). After subtracting a two-pocket background, an excess Nernst contribution $a=b\approx 4.20\ \text{Å}$7 appeared between about 10 and 30 K, strongest just above $a=b\approx 4.20\ \text{Å}$8, and was attributed not to anomalous or topological Nernst physics but to a correlation-driven $a=b\approx 4.20\ \text{Å}$9 effect on the $c\approx 14.52\ \text{Å}$0 pocket near a nesting hotspot (Yamada et al., 2024). The estimated maximum $c\approx 14.52\ \text{Å}$1 on the $c\approx 14.52\ \text{Å}$2 pocket was about $c\approx 14.52\ \text{Å}$3 (Yamada et al., 2024).

Thermal Hall measurements uncovered a further transport anomaly. The Hall Lorenz number

$c\approx 14.52\ \text{Å}$4

was reported to exceed $c\approx 14.52\ \text{Å}$5 over a broad temperature and field range, reaching about $c\approx 14.52\ \text{Å}$6 at 8 K and $c\approx 14.52\ \text{Å}$7 T in the main data set, while $c\approx 14.52\ \text{Å}$8 reached about $c\approx 14.52\ \text{Å}$9 at 20 K and 14 T (Zhang et al., 2024). Charge-neutral excitations such as phonon Hall and magnon Hall effects were argued against, and the enhancement was instead attributed to Kondo-type elastic scattering off localized $I4_1md$00 electrons that creates a peculiar energy dependence of the quasiparticle relaxation time (Zhang et al., 2024). This situates NdAlSi in a regime where RKKY-driven magnetic order and Kondo-type scattering effects may coexist in transport, even if the low carrier masses argue against heavy-fermion behavior in the usual sense (Zhang et al., 2023, Zhang et al., 2024).

6. Domain walls, emergent electrodynamics, comparative context, and controversies

NdAlSi is also notable for domain-wall physics. Mesoscopic devices imaged by magnetic force microscopy revealed stripe-like up/down magnetic domains whose population changes strongly with field, particularly near a depinning scale $I4_1md$01 (Yamada et al., 15 Jan 2026). Domain-wall scattering is exceptionally strong: the domain-wall contribution to the longitudinal resistivity reaches about $I4_1md$02, roughly 5% of the total resistivity, and can approach $I4_1md$03 under zero-field cooling (Yamada et al., 15 Jan 2026). Under oscillatory current drive in the pinned regime, domain-wall motion generates an emergent electric field directly visible in the out-of-phase component of the complex impedance, with the electrodynamic relation

$I4_1md$04

linking the wall’s sliding coordinate $I4_1md$05 and spin-tilting angle $I4_1md$06 to the measured response (Yamada et al., 15 Jan 2026). Spin-dynamics simulations found that sliding dominates over spin tilting, and the observed negative $I4_1md$07 was interpreted as a signature of dissipative, phase-lagged wall motion (Yamada et al., 15 Jan 2026).

Within the broader $I4_1md$08Al$I4_1md$09 family, NdAlSi often serves as the benchmark for Weyl-mediated helical magnetism. The NdAlGe comparison paper explicitly treated NdAlSi as the historical prototype of a helical incommensurate SDW stabilized by bond-oriented Dzyaloshinskii–Moriya interaction arising from Weyl-mediated RKKY coupling, with comparison values $I4_1md$10, $I4_1md$11, $I4_1md$12, $I4_1md$13, $I4_1md$14, and $I4_1md$15 (Yang et al., 2023). In that family context, magnetism was argued to be robust across NdAl$I4_1md$16, while transport—especially AHE—was much more sensitive to disorder, stoichiometry, and spin fluctuations (Yang et al., 2023).

Two interpretive controversies remain prominent. The first concerns the magnetic structure itself. A 2025 reanalysis argued that the original neutron diffraction evidence commonly taken to imply helical order is more naturally explained by a fan-type structure, because a true helix requires a single propagation vector for all spin components whereas the reported data used $I4_1md$17 for the in-plane part and $I4_1md$18 for the out-of-plane part (Kurumaji, 4 Jun 2025). Structure-factor calculations in that note yielded vanishing intensity at $I4_1md$19 for the helical model but finite intensities at both $I4_1md$20 and $I4_1md$21 for the fan model, and the author emphasized that the distinction matters because fan structures have no chirality or handedness (Kurumaji, 4 Jun 2025). By contrast, the 2024 neutron-spectroscopy work continued to model NdAlSi as a helical Weyl ferrimagnet with canted spiral order (Lygouras et al., 2024). The present status is therefore not one of universal agreement.

The second controversy concerns anomalous Hall transport. Some studies treat the lack of clear or measurable AHE as a defining feature of NdAlSi (Yang et al., 2023, Saraswati et al., 17 Apr 2025), whereas others report substantial anomalous Hall conductivity and unconventional field tracking relative to magnetization (Zhang et al., 5 Feb 2025). Taken together, these reports indicate that NdAlSi is not a simple “textbook” magnetic Weyl semimetal with a universally reproducible Hall fingerprint. Instead, it is a material in which topology, magnetism, domain structure, surface termination, and disorder appear to be comparably important control parameters.

In sum, NdAlSi occupies a distinctive position among magnetic topological semimetals: it is simultaneously a noncentrosymmetric Weyl semimetal, a rare-earth local-moment system with compressed CEF scales, a candidate example of Weyl-mediated collective magnetism, a platform for magnetically reconstructed Fermi surfaces, a disorder-tunable surface topological system, and a host of unusually strong domain-wall electrodynamics (Gaudet et al., 2020, Li et al., 2023, Li et al., 2024, Yamada et al., 15 Jan 2026). The literature does not present a fully closed narrative—especially regarding helical versus fan order and the magnitude or even visibility of AHE—but precisely this combination of robust core phenomenology and open microscopic questions has made NdAlSi a central material for research on the coupled physics of Weyl fermions and rare-earth magnetism.