---
title: 'NdAlSi: Magnetic Weyl Semimetal'
url: https://www.emergentmind.com/topics/ndalsi
type: topic
---

# NdAlSi: Magnetic Weyl Semimetal

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 [2201.07430][2303.17302]. 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 [2012.12970][2303.17302][2402.14447][2201.06412][2601.10638].

## 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 [2201.07430][2303.17302]. 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 [2201.07430]. 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 [2303.17302][2404.16002].

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 [2303.17302]. 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 \(E_F-E_F^{\mathrm{DFT}}\approx +30(3)\ \text{meV}\) [2012.12970]. 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, \(\Omega_1 = 230\ \mathrm{cm^{-1}}\), \(\Omega_2 = 2072\ \mathrm{cm^{-1}}\), \(\mu = 259\ \mathrm{cm^{-1}}\), \(\hat{w} = 1.45\), and \(v_F = 46\times 10^4\ \mathrm{m\,s^{-1}}\), supporting mainly type-II, overtilted Weyl states [2404.16002].

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 [2502.03015]. 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 [2303.17302]. 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 \(T_{m1}=7.3\ \text{K}\) and \(T_{m2}=3.5\ \text{K}\), interpreted as entry into an antiferromagnetic-like or incommensurate SDW-like state followed by a ferrimagnetic state [2201.07430]. Neutron diffraction established a higher-temperature transition at \(T_{\mathrm{inc}}=7.2(1)\ \text{K}\) into an incommensurate phase and a lower-temperature transition at \(T_{\mathrm{com}}=3.3(1)\ \text{K}\) into a commensurate ferrimagnetic phase [2012.12970]. Later neutron spectroscopy described the sequence as paramagnetic above \(T_\mathrm{inc}\approx 7.2\ \text{K}\), incommensurate amplitude-modulated spiral below \(T_\mathrm{inc}\), and commensurate ferrimagnetic \(udd\) order below \(T_\mathrm{com}\approx 3.5\ \text{K}\) [2412.20743].

Strong Ising anisotropy is a defining feature. Early susceptibility measurements found \(\chi_c/\chi_a > 80\) at \(1.8\ \text{K}\) [2012.12970], while another study reported an anisotropy ratio of about 45 at 2 K [2201.07430]. For \(B\parallel c\), the low-temperature magnetization exhibits two step-like metamagnetic transitions and evolves from roughly \(1/3\) of the full moment, consistent with an \((\uparrow\uparrow\downarrow)\) ferrimagnetic state, to a fully polarized \((\uparrow\uparrow\uparrow)\) state [2201.07430]. Neutron diffraction refined the low-temperature commensurate structure as a one-dimensional down-up-up pattern with FM and AFM components \(1.1(2)\,\mu_B/\mathrm{Nd}\) and \(3.8(4)\,\mu_B/\mathrm{Nd}\), respectively, and a saturated high-field moment of \(2.9(1)\,\mu_B/\mathrm{Nd}\) above \(\mu_0H_c=5.8\ \text{T}\) [2012.12970].

The crystalline-electric-field sector is unusually compressed. Inelastic neutron scattering on polycrystalline \(R\)AlSi identified two NdAlSi CEF excitations at 2.5 and 4.2 meV and described the \(J=9/2\) multiplet as split into five Kramers doublets [2508.10675]. The fitted Nd\(^{3+}\) ground doublet is
\[
\psi^{\pm} = \mp 0.010|\mp 7/2\rangle \mp 0.190|\mp 3/2\rangle \pm 0.217|\pm 1/2\rangle \mp 0.394|\pm 5/2\rangle \mp 0.873|\pm 9/2\rangle ,
\]
with dominant \( |\pm 9/2\rangle \) weight of 76.2% [2508.10675]. 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 [2508.10675].

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 \(\omega_1 \approx 0.8\ \text{meV}\) and \(\omega_2 \approx 2.3\ \text{meV}\) in the commensurate state [2412.20743]. The exchange network was found to be extended-ranged and sign-changing, with \(\mathcal{J}_1^z,\mathcal{J}_2^z\) antiferromagnetic and more distant couplings predominantly ferromagnetic or sign-changing within uncertainty [2412.20743]. 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 \(\det \mathcal D < 0\) [2412.20743].

## 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
\[
\mathbf{k}_{\mathrm{inc}}=\left(\frac{2}{3}+\delta,\frac{2}{3}+\delta,0\right)
\]
tracks nesting between topologically non-trivial Fermi pockets containing Weyl nodes, especially those associated with \(W_3\) features in the polarized electronic structure [2012.12970]. At \(T \approx 3.5\ \text{K}\), the modulation length was reported as \(\lambda_m = 145(8)\ \text{nm}\), and the growth of third-harmonic peaks at \(\mathbf{k}=(3\delta,3\delta,0)\) was interpreted as squaring-up of the amplitude-modulated Ising SDW on cooling [2012.12970]. This established the material as a “rare example of Weyl fermions driving collective magnetic order” [2012.12970].

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 \(u\)-\(d\)-\(d\) state, while the fully polarized high-field state showed a dominant temperature-independent frequency \(F_\delta \simeq 100\ \text{T}\) [2305.00437]. In the ordered low-field state, \(F_\alpha\) changed from 40 T at 2 K to 46.5 T at 5 K and \(F_\beta\) 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 [2305.00437]. The fully polarized orbit has cyclotron mass \(m^* \approx 0.3\,m_0\), and angle-dependent SdH measurements were described by an ellipsoidal pocket with long-to-short axis ratio 1.92 [2305.00437].

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–\(4f\) exchange combined with Rashba–Dresselhaus and Zeeman effects [2201.06412]. The phenomenological form
\[
\Delta \rho = 2A(B,T)\cos\left[2\pi\left(\frac{F}{B}+\phi'\right)\right] \cos\left[\pi\left(\frac{\alpha M(B,T)+\Delta_0+\mathcal{G}}{B}\right)\right]
\]
was used to capture the oscillation nodes and their temperature motion, with fitted values \(\alpha = 0.025 \pm 0.001\), \(\Delta_0 = 24 \pm 2\) meV, and \(m^* = 0.098\,m_e\) [2201.06412]. 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 [2201.06412]. This suggests that in NdAlSi even nominally single-particle quantum oscillation observables are strongly renormalized by the evolving \(4f\)-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 [2303.17302][2402.14447]. In the ferrimagnetic state below \(T_{\mathrm{com}}\sim 3.4\ \text{K}\), 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 [2303.17302].

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 [2402.14447]. Time-dependent ARPES resolved a progression from sharp trivial surface states and SFAs immediately after cleavage, to blurred surface states after \(\sim 3\) hours, and finally suppression of all surface states after \(\sim 10\) hours [2402.14447]. This evolution was interpreted as a Weyl-semimetal to diffusive-metal transition in the disordered near-surface region rather than an Anderson localization transition [2402.14447].

A distinct line of work identified a surface-selective spontaneous \(2\times 1\) 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 [2402.14518]. 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 [2402.14518]. The reconstructed boundary was interpreted as a non-Hermitian boundary, with effective surface term
\[
H_{NH} = i\Gamma(x) + \delta H,
\]
so that the reconstructed surface acts as a lossy boundary for topological and bulk electrons [2402.14518].

NdAlSi has also become a model system for low-symmetry-facet bulk–boundary correspondence. On the \((103)\) surface, the projected first bulk Brillouin zone is incommensurate with the surface Brillouin zone, apparently creating a paradox for Fermi-arc connectivity [2509.10106]. 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 \(N_{\min}=3\) successive projected bulk zones required for closure on \((103)\) [2509.10106]. The same analysis suggested that overlapping arc replicas can hybridize into closed surface Fermi-arc loops on low-symmetry facets [2509.10106].

## 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 \( \mathbf{E}\parallel\mathbf{B} \) geometry and fitted the high-field magnetoconductivity with a \(B^2\) chiral-anomaly term, extracting a chiral coefficient \(C_{\rm W} \approx 52\ \mathrm{m\Omega^{-1}\ m^{-1}\ T^{-2}}\) [2502.03015]. 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 [2305.04650]. In that work, the semiclassical chiral contribution was written as
\[
\sigma_{\text{ch}} = N_w \frac{e^2 v_F^3}{4 \pi^2 \hbar} \frac{(eB)^2 \tau_{wp}}{E_F^2},
\]
and the thermal counterpart as \(K_{\text{ch}} = L_0 \sigma_{\text{ch}} T\) [2305.04650].

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 \(\rho_{yx}(H)\) as smooth and featureless near the low-field transition, with no Hall plateaus observed despite a calculated intrinsic Hall conductivity \(\sigma_{xy}\sim 500\ \Omega^{-1}\text{cm}^{-1}\) near \(E_F\) [2301.04893]. A later comparison with NdGaSi likewise stated that NdAlSi does not exhibit any measurable anomalous Hall conductivity [2504.12784]. By contrast, another transport study reported an exotic anomalous Hall effect with out-of-sync behavior relative to the magnetization, \(R_A\) nearly four orders of magnitude larger than \(R_0\), and \(\sigma_{xy}^{A} = 947\ \Omega^{-1}\,\mathrm{cm}^{-1}\) at 2 K and 9 T [2502.03015]. 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 \(n_1 \approx 6.5 \times 10^{19}\,\text{cm}^{-3}\) and \(n_2 \approx 2.5 \times 10^{19}\,\text{cm}^{-3}\), with low-temperature mobilities \(\mu_1 \sim 2000\,\text{cm}^2/\text{Vs}\) and \(\mu_2 \sim 6000\,\text{cm}^2/\text{Vs}\) [2404.03762]. Quantum oscillations identified \(\Sigma\), \(\beta\), and \(\gamma\) pockets with frequencies 51 T, 67 T, and 128 T, respectively [2404.03762]. After subtracting a two-pocket background, an excess Nernst contribution \(\Delta S_{xy}\) appeared between about 10 and 30 K, strongest just above \(T_N=7\ \text{K}\), and was attributed not to anomalous or topological Nernst physics but to a correlation-driven \(d\tau/dE\) effect on the \(\Sigma\) pocket near a nesting hotspot [2404.03762]. The estimated maximum \(|d\tau/dE|\) on the \(\Sigma\) pocket was about \(33\ \mathrm{eV}^{-1}\) [2404.03762].

Thermal Hall measurements uncovered a further transport anomaly. The Hall Lorenz number
\[
L_{xy}\equiv \frac{\kappa_{xy}}{\sigma_{xy}T}
\]
was reported to exceed \(L_0\) over a broad temperature and field range, reaching about \(2L_0\) at 8 K and \(\mu_0H=5.5\) T in the main data set, while \(L_{xz}\) reached about \(2.2L_0\) at 20 K and 14 T [2411.17156]. 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 \(4f\) electrons that creates a peculiar energy dependence of the quasiparticle relaxation time [2411.17156]. 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 [2305.00437][2411.17156].

## 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 \(B_d \sim 0.13\ \text{T}\) [2601.10638]. Domain-wall scattering is exceptionally strong: the domain-wall contribution to the longitudinal resistivity reaches about \(1.6\,\mu\Omega\text{ cm}\), roughly 5% of the total resistivity, and can approach \(\sim 10\%\) under zero-field cooling [2601.10638]. 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
\[
V(t) = -\frac{\hbar P}{2e}\left(\frac{d\phi(t)}{dt} - \beta\frac{dX(t)}{dt}\right)
\]
linking the wall’s sliding coordinate \(X\) and spin-tilting angle \(\phi\) to the measured response [2601.10638]. Spin-dynamics simulations found that sliding dominates over spin tilting, and the observed negative \(\Im\rho_{xx}\) was interpreted as a signature of dissipative, phase-lagged wall motion [2601.10638].

Within the broader \(R\)Al\(X\) 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 \(T_{\text{inc}}=7.2\ \text{K}\), \(T_{\text{com}}=3.3\ \text{K}\), \(M_{\text{sat}}\approx 2.9\ \mu_B\), \(RRR=6.0\), \(n_h=6.66\times 10^{19}\ \text{cm}^{-3}\), and \(\mu_h=11008\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}\) [2301.04893]. In that family context, magnetism was argued to be robust across NdAl\(X\), while transport—especially AHE—was much more sensitive to disorder, stoichiometry, and spin fluctuations [2301.04893].

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 \(\vec{k}_{in}=(1/3,1/3,0)\) for the in-plane part and \(\vec{k}_{out}=(2/3,2/3,0)\) for the out-of-plane part [2506.04000]. Structure-factor calculations in that note yielded vanishing intensity at \(\vec{Q}_{1/3}\) for the helical model but finite intensities at both \(\vec{Q}_{1/3}\) and \(\vec{Q}_{2/3}\) for the fan model, and the author emphasized that the distinction matters because fan structures have no chirality or handedness [2506.04000]. By contrast, the 2024 neutron-spectroscopy work continued to model NdAlSi as a helical Weyl ferrimagnet with canted spiral order [2412.20743]. 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 [2301.04893][2504.12784], whereas others report substantial anomalous Hall conductivity and unconventional field tracking relative to magnetization [2502.03015]. 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 [2012.12970][2303.17302][2402.14447][2601.10638]. 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.

Source: https://www.emergentmind.com/topics/ndalsi