PrAlSi: Magnetic Topological Semimetal

• PrAlSi is a rare-earth member of the RAlX family characterized by ferromagnetic order near 17.8 K, strong Ising anisotropy, and low carrier density.
• It showcases an intricate interplay between localized 4f electrons and itinerant conduction electrons, leading to competing interpretations of Weyl physics and magnetic band reconstruction.
• Transport and optical studies reveal anomalous Hall conductivity, linear magnetoresistance, quantum oscillations, and field-induced Lifshitz transitions that underscore its tunable electronic behavior.

to=arxiv_search 彩神争霸电脑版:json {"query":"PrAlSi", "max_results": 10} PrAlSi is a rare-earth member of the $R$Al$X$ ($R=$ light rare earth, $X=$ Si or Ge) family that has been studied as a ferromagnetic semimetal, a magnetic Weyl semimetal candidate, and a topological semimetal. Across this literature, PrAlSi is characterized by a Curie temperature near $17.8$ K, a low carrier density, strong Ising-like anisotropy, unusual quantum oscillations, and a recurrent emphasis on the interplay among localized $4f$ electrons, itinerant conduction electrons, and topological band structure. The central questions concern whether its Weyl-like features are set primarily by crystal symmetry, how strongly ferromagnetism reconstructs the bands, and to what extent the Pr $4f$ sector remains decoupled from low-energy conduction states (Lou et al., 2023, Lyu et al., 2020).

1. Structural assignment and family context

PrAlSi is routinely discussed together with LaAlSi, CeAlSi, NdAlSi, SmAlSi, and the Ge analogues as part of the $R$AlSi or broader $R$Al$X$ platform for studying topology and rare-earth magnetism. Published work, however, does not present a single structural description. One set of studies treats PrAlSi as non-centrosymmetric, either in a LaPtSi-type structure or more specifically in body-centered tetragonal $X$0, and uses inversion-symmetry breaking as the key ingredient enabling Weyl physics (Lou et al., 2023, Wang et al., 17 Mar 2025). Another set reports the tetragonal $X$1-ThSi$X$2-type structure with space group $X$3, together with Al/Si disorder on the same $X$4 Wyckoff site (Lyu et al., 2020).

Reported structural description	Reported details	Citation
Non-centrosymmetric	LaPtSi-type; $X$5; $X$6 Å	(Lou et al., 2023)
Non-centrosymmetric	Body-centered tetragonal $X$7; all atoms on $X$8 sites	(Wang et al., 17 Mar 2025)
Centrosymmetric	$X$9-ThSi$R=$0-type; $R=$1; Al and Si randomly occupy the same $R=$2 site	(Lyu et al., 2020)

The centrosymmetric report gives refined composition $R=$3 and lattice constants $R=$4 Å and $R=$5 Å for flux-grown material (Lyu et al., 2020). In the inelastic-neutron-scattering treatment, Pr$R=$6 is analyzed at $R=$7 point symmetry within $R=$8 (Yang et al., 14 Aug 2025). Because several Weyl-semimetal interpretations explicitly rely on inversion symmetry breaking, the coexistence of these structural assignments is not a minor detail; it directly affects how the electronic topology is rationalized. A plausible implication is that sample dependence, site disorder, or differing structural refinements remain important to the interpretation of PrAlSi.

2. Magnetic ordering, crystal electric fields, and anisotropy

PrAlSi exhibits a ferromagnetic transition at $R=$9 K and very strong Ising anisotropy, with $X=$0 at $X=$1 (Lyu et al., 2020). The effective moment is reported as $X=$2–$X=$3, consistent with free Pr$X=$4, while the Weiss temperatures are strongly anisotropic, $X=$5 K for $X=$6 and $X=$7 K for $X=$8, indicating competing FM and AFM interactions (Lyu et al., 2020). Below $X=$9, two additional weak transitions occur at $17.8$0 K and $17.8$1 K; combined dc and ac susceptibility led to the proposal that these are reentrant spin-glass or ferromagnetic cluster-glass phases rather than canted antiferromagnetism. Small fields of about $17.8$2 T suppress these glassy phases and stabilize the FM state, recovering a moment of $17.8$3 per Pr (Lyu et al., 2020).

Specific-heat work identified a non-Kramers doublet ground state and a relatively low crystal electric field splitting of the Pr$17.8$4 multiplets of less than $17.8$5 K, with a broad Schottky-like maximum near $17.8$6 K and full magnetic entropy $17.8$7 released by $17.8$8 K (Lyu et al., 2020). Later inelastic neutron scattering on polycrystalline PrAlSi resolved a sharp magnetic excitation at $17.8$9 meV and concluded that all nine $4f$0 crystal-field levels lie below $4f$1 meV (Yang et al., 14 Aug 2025). In that analysis, the magnetic entropy crosses $4f$2 near $4f$3 K, but without an extended plateau, suggesting that low-lying excited crystal-field states contribute to the ordered state (Yang et al., 14 Aug 2025).

The $4f$4 crystal-field Hamiltonian used for PrAlSi is

$4f$5

with fitted parameters $4f$6 meV, $4f$7 meV, $4f$8 meV, $4f$9 meV, and $4f$0 meV (Yang et al., 14 Aug 2025). The ground-state doublet is

$4f$1

so the ground state is dominated by $4f$2 at $4f$3, implying very strong uniaxial single-ion anisotropy (Yang et al., 14 Aug 2025).

First-principles modeling of the magnetic interactions places this anisotropy within a broader exchange framework. For PrAlSi, the relevant spin Hamiltonian is

$4f$4

and the dominant exchange is described as antiferromagnetic superexchange mediated by $4f$5-hybridization,

$4f$6

For PrAlSi, the maximum of $4f$7 occurs at $4f$8, consistent with collinear ferromagnetism within the rare-earth layers, while the single-ion anisotropy is quantified as $4f$9 meV (Bouaziz et al., 2023). That work explicitly rules out Fermi-surface nesting, Weyl-node nesting, and Dzyaloshinskii–Moriya interaction as the origin of the magnetic ground state in PrAlSi (Bouaziz et al., 2023).

3. Semimetallic band structure and the localized $R$0 sector

Angle-resolved photoemission spectroscopy and first-principles calculations with spin-orbit coupling, treating Pr $R$1 electrons as semi-core, identify PrAlSi as a semimetal with conduction and valence bands crossing near the Fermi level (Lou et al., 2023). The measured Fermi surface contains square-like pockets around $R$2, dumbbell-like sheets around $R$3, and ripple-shaped contours near the Brillouin-zone boundaries, together with an additional “arc”-like feature at the corners of the outer $R$4 pocket (Lou et al., 2023). Paramagnetic calculations reproduce these features, including the “arc”-like sheet, and most spectra are well matched by $R$5-integrated bulk calculations, indicating an essentially three-dimensional semimetallic structure (Lou et al., 2023). The intense $R$6 band at $R$7 is not captured by the bulk calculation and is assigned as a likely surface state (Lou et al., 2023).

A central conclusion of that ARPES study is that the low-energy band structure shows almost no change across the magnetic transition. Measurements through the FM transition found no evident evolution of the bands, and the spectra in both PrAlSi and SmAlSi were well reproduced by nonmagnetic calculations despite their distinct magnetic ground states and different $R$8-shell fillings (Lou et al., 2023). Resonant photoemission across the Pr $R$9 edge showed no resonant enhancement of the conduction states near $R$0, and the intensities under on-resonant and off-resonant photons were reported as comparable, supporting negligible $R$1–conduction electron hybridization (Lou et al., 2023).

Within that picture, the Weyl-related crossings are primarily associated with inversion symmetry breaking rather than with time-reversal breaking, and magnetism acts, if at all, only as a Zeeman-like shift of Weyl nodes without reconstructing the bulk bands (Lou et al., 2023). This weak-coupling interpretation also aligns with the high-field Lifshitz-transition study, which states that the Pr $R$2 bands lie well below the Fermi energy and that there is no significant $R$3–$R$4 hybridization, distinguishing PrAlSi from heavy-fermion systems in which Lifshitz transitions are tied to Zeeman–Kondo competition (Wu et al., 2022).

4. Magnetotransport, anomalous Hall response, and Lifshitz physics

Transport measurements establish PrAlSi as a low-carrier-density semimetal with pronounced field sensitivity. In the ferromagnetic phase above the small critical field $R$5, the magnetoresistance is large, positive, linear, and nonsaturating up to $R$6 T, reaching $R$7 at $R$8 T and $R$9 K (Lyu et al., 2020). Below $X$0, it is weakly field dependent and slightly negative, consistent with spin-disorder scattering in the glassy low-temperature states (Lyu et al., 2020). The Hall resistivity is highly nonlinear, and a large anomalous Hall conductivity of $X$1 develops below $X$2 once the glassy phases are suppressed (Lyu et al., 2020). Two-band analysis gives carrier concentrations of order $X$3, with holes more numerous than electrons but electrons more mobile, accounting for Hall-sign reversal at high field (Lyu et al., 2020).

The anomalous Hall effect has also been analyzed from the alloy series $X$4. In that framework, PrAlSi corresponds to the $X$5 end member, where $X$6 changes sharply and becomes negative, $X$7, and the scaling analysis does not yield a universal intrinsic intercept $X$8, implying that extrinsic scattering mechanisms dominate the anomalous Hall conductivity in PrAlSi even though the Weyl-node structure remains similar to that of PrAlGe (Yang et al., 2019). The calculated intrinsic anomalous Hall conductivity for PrAlSi is reported as $X$9–$X$00 when the Fermi energy is shifted by $X$01 meV to match experiment (Yang et al., 2019). This directly complicates a simple identification of the large observed AHE with intrinsic Berry curvature alone.

Quantum oscillations provide a complementary view of the Fermi surface. Shubnikov–de Haas oscillations are absent in LaAlSi but clear in PrAlSi below about $X$02 K (Lyu et al., 2020). In the low-field study, the dominant frequency increases from $X$03 T at $X$04 K to $X$05 T at $X$06 K, with a small cyclotron mass $X$07, suggesting the emergence or growth of a small Fermi pocket as the ordered state develops (Lyu et al., 2020). In the high-field study up to $X$08 T, a field-induced Lifshitz transition occurs at $X$09 T, well below the quantum limit estimated at $X$10–$X$11 T (Wu et al., 2022). Below $X$12, the oscillation spectrum is characterized by $X$13 T; above $X$14, this is replaced by $X$15 T and $X$16 T (Wu et al., 2022). The cyclotron mass for $X$17 is $X$18, roughly doubling as the field approaches $X$19, while the higher-field pockets have $X$20 and $X$21 (Wu et al., 2022).

The high-field analysis interprets the Lifshitz transition as a reconstruction in which a small hole pocket along $X$22–X disappears and transforms into a larger hole pocket and an emergent electron pocket, indicating a van Hove singularity in the underlying band structure (Wu et al., 2022). The Landau-fan intercept for the $X$23 pocket is near $X$24, indicating a nontrivial $X$25 Berry phase (Wu et al., 2022). The Onsager relation used in this analysis is

$X$26

Distinct quantum-oscillation studies therefore report different dominant frequencies and different tuning parameters. This suggests that the accessible extremal pockets in PrAlSi are highly sensitive to temperature, field range, and the underlying electronic state.

5. Infrared response and Weyl electrodynamics

Broad-frequency infrared spectroscopy on the $X$27AlSi series at room temperature, i.e. in the paramagnetic phase, finds that PrAlSi is metallic with a pronounced Drude peak, a plasma edge around $X$28, a Drude spectral weight of $X$29, and a screened plasma frequency of about $X$30 (Kunze et al., 2024). After subtraction of the Drude term, the interband optical conductivity of PrAlSi shows two linear-in-frequency regions, from about $X$31 to $X$32 and then above about $X$33, separated by a kink (Kunze et al., 2024). The higher-frequency linear regime extrapolates to a finite intercept rather than to zero, which is identified as the hallmark of a type-II Weyl semimetal (Kunze et al., 2024).

The optical analysis uses the standard Weyl-semimetal form

$X$34

and, for overtilted cones,

$X$35

From the limiting frequencies

$X$36

the room-temperature parameters extracted for PrAlSi are $X$37, $X$38, $X$39, $X$40, $X$41, and $X$42 Weyl nodes (Kunze et al., 2024). In this interpretation, the Weyl states are induced primarily by inversion symmetry breaking in the noncentrosymmetric structure, and the room-temperature optical response reflects weak electronic correlations compared with the Ge analogues (Kunze et al., 2024).

A later infrared study focused on the FM transition itself and reported a more strongly magnetically reconstructed optical spectrum (Gao et al., 2024). Above $X$43 K, the interband conductivity $X$44 has two linear segments connected by a kink at about $X$45; below $X$46, an additional linear segment appears between the original ones, with new kinks at $X$47 and $X$48 (Gao et al., 2024). The plasma edge undergoes a sudden blue shift below $X$49, corresponding to a carrier-density increase from $X$50 at $X$51 K to $X$52 at $X$53 K (Gao et al., 2024). Using Hall densities of order $X$54, that work estimates an effective mass $X$55, two orders of magnitude smaller than the free-electron mass, and extracts $X$56 from the low-energy linear slope by taking $X$57 (Gao et al., 2024).

The optical interpretation advanced there is that ferromagnetic order breaks time-reversal symmetry and splits Dirac/Weyl nodes into multiple Weyl nodes of lower degeneracy, thereby producing additional van Hove singularities and an extra linear segment in $X$58 (Gao et al., 2024). This is a substantially stronger magnetism–band-coupling scenario than the weak-coupling ARPES interpretation.

6. Competing interpretations and broader significance

The literature on PrAlSi contains two distinct interpretive tendencies. One emphasizes decoupling: the low-energy band structure changes little across the magnetic transition, nonmagnetic calculations reproduce the spectra, Pr $X$59 states are well localized, and the electronic topology is governed mainly by inversion-symmetry breaking rather than by magnetic reconstruction (Lou et al., 2023). The other emphasizes magnetic reconstruction: ferromagnetic order splits bands, shifts Weyl points in momentum and energy, increases the number of Weyl points, changes the symmetry of surface states from $X$60 to $X$61, and generates new optical features (Wang et al., 17 Mar 2025).

The temperature-dependent ARPES and ab-initio study in the second category reports $X$62 Weyl points in the paramagnetic phase and $X$63 in the ferromagnetic phase due to band splitting (Wang et al., 17 Mar 2025). It further reports that Weyl points of opposite chirality move to different energies in the FM state, yielding a net chirality charge below $X$64, and that the band shifts can reach about $X$65 meV with a momentum splitting of about $X$66 for one Weyl-point family (Wang et al., 17 Mar 2025). Calculations based on this picture predict phase-dependent optical conductivity and a Kerr angle up to $X$67 at low photon energies (Wang et al., 17 Mar 2025). These claims stand in clear tension with the earlier conclusion that magnetism has a negligible effect on the observed low-energy electronic structure (Lou et al., 2023).

At the level of magnetism itself, first-principles modeling offers a relatively consistent message: in PrAlSi, the magnetic ground state is not determined by nesting of topological Fermi-surface features, not by Weyl nodes, and not by Dzyaloshinskii–Moriya interaction, but mainly by short-range superexchange combined with large single-ion anisotropy (Bouaziz et al., 2023). Field-tuned transport adds a further layer by showing that even without strong $X$68–$X$69 hybridization, the Fermi surface can still undergo a field-induced Lifshitz transition well below the quantum limit (Wu et al., 2022). This suggests that weak hybridization does not preclude strong field or symmetry sensitivity of the low-energy carriers.

Taken together, PrAlSi occupies a distinctive position within the $X$70Al$X$71 family. It combines a ferromagnetic transition at $X$72 K, reentrant glassy phases in some samples, very strong uniaxial anisotropy, a low-lying crystal-field manifold, large anomalous Hall conductivity, nonsaturating linear magnetoresistance, temperature- and field-dependent quantum oscillations, and optical signatures that have been interpreted in both weak-coupling and strong reconstruction frameworks (Lyu et al., 2020, Yang et al., 14 Aug 2025, Wu et al., 2022). The main open issues are therefore not whether PrAlSi is electronically unusual, but how its structural symmetry should be assigned, how large the magnetic reconstruction of its bands actually is, and whether its Weyl-like responses are primarily symmetry-enforced, magnetically tunable, or sample-dependent in practice.