---
title: 'RAlSi: Rare-Earth Aluminosilicides'
url: https://www.emergentmind.com/topics/ralsi
type: topic
---

# RAlSi: Rare-Earth Aluminosilicides

Searching arXiv for recent and foundational papers on RAlSi and closely related usages.
RAlSi commonly denotes the rare-earth aluminosilicide family \(R\)AlSi, where \(R\) is a rare-earth element such as Ce, Nd, Sm, or Pr. In the recent arXiv literature, these compounds are treated primarily as noncentrosymmetric or closely related rare-earth intermetallics within the broader \(R\)Al\(X\) platform, notable for magnetic order, Weyl-semimetal candidacy, and strong coupling between itinerant topology and localized \(4f\) degrees of freedom [2405.04077], [2111.05235], [2508.10675]. The same letter sequence can appear in broader Al–Si materials contexts, but the exact designation “RAlSi” is used most concretely for this rare-earth intermetallic family; related Al–Si eutectics, Si–Al composites, and silica–alumina systems are relevant only by compositional analogy rather than exact nomenclature [2304.03740], [2204.08111], [1604.04839].

## 1. Chemical identity and crystallographic setting

In its principal usage, RAlSi denotes compounds of formula \(R\mathrm{AlSi}\) with a rare-earth element on the \(R\) site. CeAlSi and NdAlSi are described as belonging to the \(R\)Al\(X\) family (\(R=\) rare earth, \(X=\) Si or Ge), which has attracted attention as a platform for magnetic Weyl semimetals [2405.04077]. SmAlSi and CeAlSi were likewise investigated as members of the noncentrosymmetric rare-earth aluminum silicide family and placed within the broader \(RAX\) or \(R\)Al\(X\) context [2111.05235].

For CeAlSi and NdAlSi, the crystal structure is reported as noncentrosymmetric, with space group \(I4_{1}md\), and also nonsymmorphic [2405.04077]. The same space group \(I4_1md\) (No. 109) is reported for SmAlSi and CeAlSi, where the structure is described as tetragonal LaPtSi-type and explicitly noncentrosymmetric [2111.05235]. In the soft-x-ray ARPES study of CeAlSi and NdAlSi, the rare-earth ions form two interpenetrating body-centered tetragonal sublattices offset by \((0,a/2,c/4)\), a structural feature central to the observed zone-selection effect [2405.04077].

Concrete lattice parameters are reported for several members. For the ARPES study, the experimental lattice constants were \(a=b=4.25~\text{\AA}\) and \(c=14.5~\text{\AA}\) for CeAlSi and NdAlSi [2405.04077]. For single-crystal SmAlSi and CeAlSi, Rietveld refinement yielded \(a = 4.1583\ \text{\AA}\), \(c = 14.4562\ \text{\AA}\) for SmAlSi and \(a = 4.2550\ \text{\AA}\), \(c = 14.5919\ \text{\AA}\) for CeAlSi, with \(Z=4\) in both cases [2111.05235]. CeAlSi and NdAlSi are explicitly stated to crystallize in \(I4_1md\) with the rare-earth ion at Wyckoff \(4a\), site symmetry \(2mm\), i.e. point symmetry \(C_{2v}\), in the crystalline-electric-field analysis [2508.10675]. PrAlSi is treated separately there as centrosymmetric, space group \(I4_1/amd\) (No. 141), with Pr\(^{3+}\) in point symmetry \(D_{2d}\) [2508.10675].

## 2. Electronic structure and Weyl-semimetal context

The modern interest in RAlSi is driven by its role as a magnetic Weyl-semimetal platform. Because inversion symmetry is broken, the paramagnetic phase can host Weyl nodes; in CeAlSi and NdAlSi, first-principles calculations predict three types of 32 Weyl nodes near the Fermi level, specifically 8 W1, 16 W2, and 8 W3 [2405.04077]. These compounds are therefore treated not simply as magnetic intermetallics, but as systems in which rare-earth magnetism and Weyl electronic structure coexist on the same crystallographic backbone.

The soft-x-ray ARPES measurements establish that the observed states are bulk three-dimensional bands. In CeAlSi, a \(k_z\)-\(k_x\) constant-energy map at \(E-E_{\rm F}=-1.18~\mathrm{eV}\) shows elliptical contours around \(\Sigma\) points and clear \(k_z\) dispersion, with a band-folding periodicity \(\Delta k_z \sim 0.86~\mathrm{\AA^{-1}}\), matching \(2\pi/c\) [2405.04077]. NdAlSi shows the same essential behavior at \(E-E_{\rm F}=-0.41~\mathrm{eV}\), again with \(\Delta k_z \sim 0.86~\mathrm{\AA^{-1}} \approx 2\pi/c\) [2405.04077]. This establishes that the ARPES spectra probe bulk 3D electronic structure rather than a surface-limited band manifold.

A central result is the “zone-selection effect,” defined operationally as the strong sensitivity of photoelectron intensity distributions to the covered Brillouin zone in the nonsymmorphic structure [2405.04077]. The paper does not provide an explicit analytical selection rule, but attributes the effect conceptually to interference among photoelectron amplitudes from sublattice-related orbitals displaced by fractional lattice translations, analogous to graphite [2405.04077]. As a consequence, the same intrinsic band can appear bright in one Brillouin zone and weak or nearly absent in another equivalent zone.

This effect has direct implications for Weyl-cone detection. By combining data from multiple equivalent zones and summing intensity maps with a weighting ratio of \(1:0.8\), the reconstructed spectra agree well with DFT after an overall 80 meV energy shift [2405.04077]. That reconstruction permits experimental tracing of W1 on \(\Sigma-\Gamma-\Sigma\), W3 on \(X-\Gamma-X\), and W2 on a plane at \(k_z=0.3~\mathrm{\AA^{-1}}\) [2405.04077]. A plausible implication is that single-zone ARPES can systematically under-represent topological features in nonsymmorphic RAlSi compounds.

## 3. Magnetic order and transport phenomenology

Magnetism in RAlSi depends strongly on the rare-earth ion. CeAlSi is reported as ferromagnetic below \(T_{\rm C}=8.5\) K in the ARPES study and below \(T_C \approx 9.4\) K in the transport study [2405.04077], [2111.05235]. NdAlSi is antiferromagnetic below \(T_{\rm N}=7.2\) K in the ARPES study, while the crystalline-electric-field work resolves a more specific sequence: incommensurate ferrimagnetic order below \(7.2\) K and a commensurate ferrimagnetic phase below about \(3.2\)–\(3.3\) K [2405.04077], [2508.10675]. SmAlSi is reported as antiferromagnetic with \(T_N \approx 10.7\) K [2111.05235]. PrAlSi is described as ferromagnetic with multiple transitions at \(T_C \approx 17.8\) K, \(T_{M1} \approx 16.5\) K, and \(T_{M2} \approx 9\) K [2508.10675].

Transport measurements place SmAlSi and CeAlSi in the semimetallic regime with nonsaturating magnetoresistance. At \(1.8\) K and \(9\) T, SmAlSi exhibits magnetoresistance of about \(900\%\), whereas CeAlSi exhibits about \(80\%\) under the same conditions [2111.05235]. In SmAlSi, the Hall resistivity is nonlinear and changes slope sign between low and high field at 2 K, indicating coexisting electrons and holes and motivating a two-band analysis [2111.05235]. For CeAlSi, Hall resistivity is nearly linear below 100 K, with a small anomalous Hall effect in the ferromagnetic state, and fitting in the \(6\)–\(9\) T range gives \(R_0<0\), implying dominant electron-type carriers [2111.05235].

The two-band transport equations used for SmAlSi are reported explicitly as
\[
\rho_{xx} = \frac{1}{e} \frac{(n_e \mu_e + n_h \mu_h) + (n_e \mu_e \mu_h^2 + n_h \mu_h \mu_e^2)B^2} {(n_e\mu_e+n_h\mu_h)^2 + \mu_e^2\mu_h^2(n_h-n_e)^2 B^2},
\]
and
\[
\rho_{yx} = \frac{B}{e} \frac{(n_h\mu_h^2-n_e\mu_e^2) + \mu_e^2\mu_h^2(n_h-n_e)B^2} {(n_e\mu_e+n_h\mu_h)^2 + \mu_e^2\mu_h^2(n_h-n_e)^2 B^2},
\]
with the magnetoresistance defined as
\[
\mathrm{MR} = \frac{\rho_{xx}(B)-\rho_{xx}(0)}{\rho_{xx}(0)} \times 100\%.
\]
At 1.8 K, the fitted carrier densities for SmAlSi are \(n_e = 10.88 \times 10^{25}\ \mathrm{m}^{-3}\) and \(n_h = 8.3 \times 10^{25}\ \mathrm{m}^{-3}\) [2111.05235].

An important family-level feature is the sensitivity of carrier density to magnetic ordering. In SmAlSi, both \(n_e\) and \(n_h\) show a kink around \(T_N\), while in CeAlSi the electron carrier density shows a kink around \(T_C\) [2111.05235]. This suggests direct coupling between rare-earth magnetic order and the low-energy electronic structure.

## 4. Quantum oscillations and topological transport signatures

Among the RAlSi compounds examined by transport, SmAlSi provides the clearest quantum-oscillation evidence for nontrivial topology. With \(B \parallel c\), clear Shubnikov–de Haas oscillations are observed in \(\rho_{xx}(B)\) up to 14 T over the temperature range \(2\)–\(50\) K [2111.05235]. The FFT spectra show two principal frequencies, \(F_\alpha = 11.8\ \mathrm{T}\) and \(F_\beta = 35.3\ \mathrm{T}\), together with a harmonic near \(2F_\beta\) [2111.05235].

Using the Onsager relation,
\[
F = \frac{\hbar}{2\pi e}A_F,
\]
the extremal cross-sectional areas are reported as \(A_{F,\alpha} = 1.1 \times 10^{-3}\ \text{\AA}^{-2}\) and \(A_{F,\beta} = 3.4 \times 10^{-3}\ \text{\AA}^{-2}\), with corresponding Fermi wavevectors \(k_{F,\alpha} = 1.9 \times 10^{-2}\ \text{\AA}^{-1}\) and \(k_{F,\beta} = 3.3 \times 10^{-2}\ \text{\AA}^{-1}\) [2111.05235]. These small frequencies and cross-sections indicate small Fermi pockets.

The oscillations are analyzed with the Lifshitz–Kosevich expression
\[
\Delta \rho_{xx} \propto \sqrt{\frac{B}{2F}\, R_T R_D R_S \cos\!\left[2\pi\left(\frac{F}{B}+\gamma-\delta+\varphi\right)\right],
\]
with
\[
R_T = \frac{\lambda \mu T/B}{\sinh(\lambda \mu T/B)}, \qquad
R_D = \exp\!\left(-\lambda \mu T_D/B\right), \qquad
R_S = \cos\!\left(\pi S g \frac{m_0}{m^*}\right),
\]
\[
\mu = \frac{m^*}{m_0}, \qquad
\lambda = \frac{2\pi^2 k_B m_0}{e\hbar} \approx 14.7\ \mathrm{T/K},
\]
and
\[
\gamma = \frac12 - \frac{\phi_B}{2\pi}.
\]
The effective masses are \(m_\alpha^*=0.10\,m_0\) and \(m_\beta^*=0.09\,m_0\) [2111.05235]. Table II further gives \(T_{D,\alpha}=7.9\ \mathrm{K}\), \(T_{D,\beta}=19.2\ \mathrm{K}\), \(\tau_{D,\alpha}=1.03\times10^{-13}\ \mathrm{s}\), \(\tau_{D,\beta}=0.34\times10^{-13}\ \mathrm{s}\), \(\mu_{q,\alpha}=0.18\ \mathrm{m^2\,V^{-1}\,s^{-1}}\), \(\mu_{q,\beta}=0.07\ \mathrm{m^2\,V^{-1}\,s^{-1}}\), \(v_{F,\alpha}=2.2\times10^{5}\ \mathrm{m/s}\), \(v_{F,\beta}=4.2\times10^{5}\ \mathrm{m/s}\), \(E_{F,\alpha}=27.5\ \mathrm{meV}\), and \(E_{F,\beta}=90.2\ \mathrm{meV}\) [2111.05235].

Berry phases extracted by LK phase fitting are \(\phi_{B,\alpha}=(1.07\pm0.25)\pi\) and \(\phi_{B,\beta}=(1.32\pm0.25)\pi\), and Landau-fan analysis yields intercepts near \(0.965\) and \(0.946\) for the \(\alpha\) and \(\beta\) pockets [2111.05235]. The paper interprets these results as consistent with nontrivial Berry phase. For CeAlSi, by contrast, low-field MR shows no quantum oscillations in that study, so no comparable SdH analysis is reported there [2111.05235].

## 5. Crystalline electric fields and single-ion anisotropy

The crystalline-electric-field structure of RAlSi provides a quantitative account of how different rare-earth ions select different magnetic ground states. Polycrystalline CeAlSi, PrAlSi, and NdAlSi were studied by inelastic neutron scattering, heat capacity, and magnetic susceptibility, with LaAlSi serving as a nonmagnetic reference for phonon background and lattice heat capacity [2508.10675].

For CeAlSi and NdAlSi, the CEF Hamiltonian used at the \(C_{2v}\) rare-earth site is
\[
\begin{aligned}
\hat H^{C}_{2v,\mathrm{CEF}} =\;& B_2^0 \hat O_2^0 + B_2^2 \hat O_2^2 \\
&+ B_4^0 \hat O_4^0 + B_4^2 \hat O_4^2 + B_4^4 \hat O_4^4 \\
&+ B_6^0 \hat O_6^0 + B_6^2 \hat O_6^2 + B_6^4 \hat O_6^4 + B_6^6 \hat O_6^6 ,
\end{aligned}
\]
whereas PrAlSi in point symmetry \(D_{2d}\) is modeled by
\[
\hat H^{D}_{2d,\mathrm{CEF}} = B_2^0 \hat O_2^0 + B_4^0 \hat O_4^0 + B_4^4 \hat O_4^4 + B_6^0 \hat O_6^0 + B_6^4 \hat O_6^4 .
\]
The neutron cross section is written as
\[
\frac{\mathrm{d}^2 \sigma}{\mathrm{d}\Omega\, \mathrm{d}\omega}
= A\sum_{m,n} p_n \left| \langle \Gamma_m | \hat J_\perp | \Gamma_n \rangle \right|^2 \delta(\hbar\omega + E_n - E_m),
\]
and magnetic entropy is obtained from
\[
S_m(T)=\int \frac{C_m(T)}{T}\, dT.
\]
These formulas structure the family-wide CEF analysis [2508.10675].

CeAlSi shows well-resolved CEF excitations at 19.2 and 24.9 meV, with a Kramers-doublet ground state dominated by \(|\pm3/2\rangle\) at 94.5% weight [2508.10675]. The fitted CEF parameters are \(B_2^0 = 1.928\times 10^{-1}\ \mathrm{meV}\), \(B_2^2 = 1.107\times 10^{0}\ \mathrm{meV}\), \(B_4^0 = 7.281\times 10^{-2}\ \mathrm{meV}\), \(B_4^2 = -2.335\times 10^{-2}\ \mathrm{meV}\), and \(B_4^4 = 0.000\ \mathrm{meV}\), with \(B_6^n=0\) because Ce\(^{3+}\) has \(J=5/2\) [2508.10675]. The first excited doublet lies at \(19.160\) meV and the second at \(25.066\) meV, implying a well-isolated low-energy doublet [2508.10675].

PrAlSi shows a single clear INS excitation at 5.4 meV, but the fitted level scheme contains multiple nearby levels at \(4.743\), \(5.303\), \(5.576\), \(6.638\), \(9.018\), and \(9.707\) meV [2508.10675]. Its ground-state doublet is almost pure \(|\pm3\rangle\), with 99.2% weight, making it the most anisotropic of the three magnetic members analyzed [2508.10675].

NdAlSi has much lower-lying CEF excitations, observed at 2.5 and 4.2 meV, with fitted levels at \(2.463\), \(4.092\), \(4.445\), and \(6.213\) meV [2508.10675]. Its ground-state doublet is only 76.2% \(|\pm9/2\rangle\), with substantial admixture of other \(m_J\) states [2508.10675]. The paper interprets this as weaker single-ion anisotropy than in CeAlSi or PrAlSi.

A key comparative conclusion follows. CeAlSi and PrAlSi are described as having robust CEF levels in the magnetic state, whereas NdAlSi exhibits broadening, shifting, and eventually splitting of CEF excitations below 15 K, especially in the commensurate ferrimagnetic phase [2508.10675]. McPhase estimates molecular fields of about 1.5 T in-plane and 3.7 T out-of-plane for NdAlSi, and the authors connect the resulting CEF renormalization to competing magnetic couplings and possible Dzyaloshinskii–Moriya interactions [2508.10675]. This suggests that RAlSi spans both rigid-doublet ferromagnets and exchange-competing ferrimagnets within the same broad chemical family.

## 6. Related usages, boundary cases, and nomenclature

The exact string “RAlSi” does not uniformly identify every Al–Si material discussed in adjacent literatures. One recurrent ambiguity concerns whether the term is being used as a chemical family name, a shorthand for rapidly solidified Al–Si, or a loose label for silicon–aluminum materials more generally. The available papers distinguish these usages sharply.

In materials processing, laser rapid solidification of a hyper-eutectic Al–20 wt% Si alloy produces an ultrafine, bicontinuous, highly connected, isotropically branched Si network with average equivalent radius \(r_{eq}=0.0225~\mu\mathrm{m}\), spacing \(\lambda=0.091~\mu\mathrm{m}\), and specific surface density \(s_S = 58.0307~\mu\mathrm{m}^{-1}\) [2304.03740]. That paper explicitly frames the subject as rapidly solidified Al–Si eutectics, not as the rare-earth intermetallic RAlSi family. Its “bottom line for rapidly solidified Al–Si / ‘RAlSi’” indicates broad relevance by abbreviation or context rather than exact stoichiometric naming [2304.03740]. This suggests a secondary usage in which “RAlSi” functions informally as a contraction for rapidly solidified Al–Si, but not as a crystallographic family label.

In cryogenic instrumentation, the silicon–aluminum composite Japan Fine Ceramics SA001 is a 75 vol% Si / 25 vol% Al material with \(T_c = 1.18 \pm 0.01~\mathrm{K}\), residual resistivity \(0.065 \pm 0.001~\mu\Omega\mathrm{m}\) at 1.5 K, and measured thermal contraction \(0.120 \pm 0.013\%\) from 293 K to 77 K [2204.08111]. That paper explicitly states that it does not identify SA001 as “RAlSi” and treats the match only as a closely related Si–Al composite material family match by composition, cryogenic function, and application [2204.08111].

Likewise, amorphous silica–alumina nanoparticles containing homogeneously dispersed pentacoordinated Al(V) species on Si–O–Al surface motifs are highly relevant to Al–Si connectivity, but the system is chemically and structurally distinct from intermetallic \(R\)AlSi [1604.04839]. The ASA work concerns Al coordination in an amorphous oxide network, not rare-earth aluminosilicide intermetallics.

A practical nomenclature distinction therefore emerges. In the exact and best-established sense, RAlSi refers to the rare-earth aluminosilicides \(R\mathrm{AlSi}\), especially CeAlSi, NdAlSi, SmAlSi, and PrAlSi [2405.04077], [2111.05235], [2508.10675]. Other Al–Si materials may be compositionally related or occasionally associated with the same letter sequence, but they are separate materials classes.

## 7. Scientific significance and current picture

The current arXiv literature presents RAlSi as a rare-earth-tunable platform where topology, nonsymmorphic photoemission selection effects, magnetic order, and crystalline-electric-field anisotropy can all be studied within closely related compounds. CeAlSi and NdAlSi show that soft-x-ray ARPES can resolve bulk 3D bands and Weyl-cone dispersions, but only if zone-selection effects are handled through deliberate multi-zone reconstruction [2405.04077]. SmAlSi shows that at least some members possess small Fermi pockets and transport signatures consistent with a nontrivial Berry phase [2111.05235]. CeAlSi, PrAlSi, and NdAlSi further show that the local \(4f\) physics is not incidental: the CEF level scheme and ground-state wavefunction purity govern whether the material behaves as a robust anisotropic ferromagnet or as a more weakly anisotropic system with competing ferrimagnetic orders and low-temperature CEF renormalization [2508.10675].

This body of work supports a compact comparative picture. CeAlSi combines noncentrosymmetric Weyl-semimetal band topology, ferromagnetism, a nearly pure \(|\pm3/2\rangle\) CEF doublet, and ARPES-visible Weyl cones after multi-zone reconstruction [2405.04077], [2508.10675]. PrAlSi exhibits an even purer anisotropic ground state, but with a denser manifold of low-lying excited levels that plausibly enrichs its magnetic phase behavior [2508.10675]. NdAlSi retains the same broader family identity yet differs qualitatively through weaker single-ion anisotropy, incommensurate-to-commensurate ferrimagnetism, and exchange-driven CEF reshaping [2405.04077], [2508.10675]. SmAlSi broadens the family further by providing strong quantum-oscillation evidence for small pockets with \(\pi\)-like Berry phases and by showing that magnetic order remains robust under pressure up to 46.2 GPa [2111.05235].

Taken together, the literature establishes RAlSi as a rare-earth intermetallic family in which fixed structural motifs coexist with sharply variable magnetic ground states and experimentally accessible topological electronic structure. A plausible implication is that rare-earth substitution in \(R\mathrm{AlSi}\) offers an unusually direct route for tuning the balance among nonsymmorphic band interference, Weyl-node phenomenology, \(4f\)-derived anisotropy, and exchange-driven magnetic complexity.

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