Nonsaturating magnetoresistance, anomalous Hall effect, and magnetic quantum oscillations in ferromagnetic semimetal PrAlSi

Abstract: We report a comprehensive investigation of the structural, magnetic, transport and thermodynamic properties of a single crystal PrAlSi, in comparison to its nonmagnetic analogue LaAlSi. PrAlSi exhibits a ferromagnetic transition at $T_C$ = 17.8 K which, however, is followed by two weak phase transitions at lower temperatures. Based on the combined dc and ac magnetic susceptibility measurements, we propose the two reentrant magnetic phases below $T_C$ to be spin glasses or ferromagnetic cluster glasses. When the magnetic glassy states are suppressed by small field, several remarkable features appear. These include a linear, nonsaturating magnetoresistance as a function of field that is reminiscent of a topological or charge-compensated semimetal, and a large anomalous Hall conductivity amounting to $\sim$2000 $Ω^{-1}$cm$^{-1}$. Specific-heat measurements indicate a non-Kramers doublet ground state and a relatively low crystal electric field splitting of the Pr$^{3+}$ multiplets of less than 100 K. Shubnikov-de Hass oscillations are absent in LaAlSi, whereas they are clearly observed below about 25 K in PrAlSi, with an unusual temperature dependence of the dominating oscillation frequency $F$. It increases from $F$ = 18 T at 25 K to $F$ = 33 T at 2 K, hinting at an emerging Fermi pocket upon cooling into the ordered phase. These results suggest that PrAlSi is a new system where a small Fermi pocket of likely relativistic fermions is strongly coupled to magnetism. Whether hybridization between $f$ and conduction band is also involved remains an intriguing open problem.

• The paper demonstrates that PrAlSi undergoes a ferromagnetic transition with reentrant glassy phases and pronounced Ising anisotropy.
• It employs magnetotransport measurements to reveal a nearly linear, nonsaturating positive magnetoresistance and a giant anomalous Hall conductivity exceeding 2000 Ω⁻¹cm⁻¹.
• Quantum oscillations uncover a magnetically-induced Fermi surface reconstruction, indicating a light cyclotron mass and a small emerging Fermi pocket intimately tied to magnetic order.

Nonsaturating Magnetoresistance, Anomalous Hall Effect, and Quantum Oscillations in Ferromagnetic Semimetal PrAlSi

Structural and Electronic Ground State

The study provides a comprehensive characterization of single-crystalline PrAlSi, revealing a centrosymmetric $\alpha$-ThSi$_2$ crystal structure (space group I4$_1$/amd) with site disorder between Al and Si on the 8$e$ Wyckoff position. The refined stoichiometry, PrAl$_{1.13}$Si$_{0.87}$, is typical of flux-grown samples and results in structural disorder, which, in combination with the low carrier density, is determinant for the observed physical properties. The presence of inversion symmetry precludes the natural emergence of Weyl nodes unless time-reversal symmetry is broken, as through intrinsic ferromagnetism.

Magnetic Phase Transitions and Anisotropy

PrAlSi undergoes a ferromagnetic (FM) transition at $T_C$ = 17.8 K with pronounced Ising anisotropy ($\chi_{\parallel c}/\chi_{\perp c} \sim 150$ at $T_C$), confirmed by both dc/ac magnetic susceptibility and isothermal magnetization measurements. Distinct from canonical ferromagnets, two additional reentrant transitions below $T_C$—at $T_{M1} \approx 16.5$ K and $T_{M2} \approx 9$ K—are identified. These are characterized as spin-glass or cluster-glass phases, supported by frequency- and field-dependent ac susceptibility and the bifurcation of zero-field-cooled and field-cooled dc susceptibility. The FM phase is easily suppressed by modest fields ($B_c \approx 0.4$ T), above which a conventional FM state is restored with saturation moment $M_{sat} \approx 3.4\ \mu_B$/Pr, consistent with the free-ion value and indicating weak Kondo screening and limited crystal electric field (CEF) splitting.

Magnetotransport: Nonsaturating Magnetoresistance and Quantum Oscillations

Below the critical field $B_c$, the spin-glass phases dominate, leading to weakly negative magnetoresistance due to spin-disorder scattering. Once these are suppressed (for $B>B_c$), PrAlSi exhibits a strong, nonsaturating, and nearly linear positive magnetoresistance (MR) up to the highest measured fields ($B=9$ T and $T=300$ K, MR ratio $\sim 40\%$), reminiscent of compensated or topological semimetals. Most notably, clear Shubnikov-de Haas (SdH) oscillations are present for $T<25$ K, with an unusual and strongly temperature-dependent frequency evolving from $F=33$ T at 2 K to $F=18$ T near 25 K. This behavior is absent in the isostructural, nonmagnetic reference compound LaAlSi, indicating that magnetic ordering in PrAlSi induces a small, emerging Fermi pocket strongly coupled to internal magnetism.

The observed frequency shift, amounting to a $\sim$40% change in extremal area, is nontrivial and unlikely due to thermal broadening alone; it thus points to a reconstructed Fermi surface driven by FM order. The deduced cyclotron mass $m^* \approx 0.0765\ m_0$ corroborates the presence of light, quasi-relativistic carriers. The Fermi energy is estimated at $\sim$127 meV from the SdH analysis.

Anomalous Hall Effect and Charge Compensation

Hall effect measurements reveal a sizable and nonlinear Hall resistivity both above and below $T_C$, due to the multiband character of transport. In the FM state, PrAlSi displays a giant anomalous Hall conductivity (AHE), $$\sigma^{A}_{xy} \sim 2000\ \Omega^{-1}\mathrm{cm}^{-1}$$ at $T<T_C$—a value notably larger than observed in prototypical magnetic Weyl semimetals like Co$_3$Sn$_2$S$_2$. The magnitude of AHE emerges in fields above $B_c$, as the glassy states are quenched, and is unaccompanied by hysteresis, consistent with the absence of spontaneous Hall conductivity in the spin-glass regime.

A compensated two-band model, critical for correctly capturing the nonlinear Hall response, yields low carrier densities ($n \sim 10^{19}$ cm$^{-3}$), typical of semimetals, with hole-dominated transport at low fields and higher mobility for the minority (electron-like) carriers.

Thermodynamics and Crystal Electric Field Effects

The specific heat displays a $\lambda$-type anomaly at $T_C$, confirming the bulk nature of the FM transition, with an additional Schottky contribution at $\sim$30 K attributed to low-lying CEF excitations. The entropy recovered at $T_C$ supports a non-Kramers doublet ground state for Pr$^{3+}$, consistent with the $D_{2d}$ point symmetry.

CEF splitting is estimated to be less than 100 K, resulting in enhanced low-temperature entropy and reinforcing the coexistence of local moment and itinerant electronic phenomena.

Theoretical and Practical Implications

The findings demonstrate that PrAlSi is a low-carrier, strongly compensated semimetal whose Fermiology and transport are intimately tied to magnetic ordering. The emergence of a small Fermi pocket coupled to FM order, together with a colossal AHE, situates PrAlSi as a candidate system for studying interplay between magnetism and relativistic fermions in the centrosymmetric limit. The structural disorder intrinsic to the (Al,Si) site mixing appears to further stabilize complex reentrant glassy states below the main FM phase.

From a practical perspective, the materials’ large, nonsaturating MR and strong AHE are potentially germane for spintronic applications requiring robust field-tunable transport properties at low temperatures. Theoretically, the possibility of inducing Weyl fermions via FM order in a centrosymmetric host, while maintaining site disorder, underscores the importance of symmetry and local-moment/conduction-electron coupling in engineering topologically nontrivial ground states.

The absence of Kondo or substantial heavy-fermion effects, combined with the modest CEF splitting and light carrier mass, offers a relatively clean platform for exploring intrinsic anomalous transport, Fermi surface evolution with magnetism, and the microscopic mechanism of reentrant glassy phases.

Prospects for Future Research

Critical outstanding questions include whether Weyl nodes are explicitly realized in the FM phase of PrAlSi and to what extent $f$-electron hybridization or RKKY-mediated correlations affect its electronic structure. Clarifying these issues may require ARPES, quantum oscillation studies under pressure or chemical substitution, and ab-initio band structure calculations incorporating spin-orbit coupling and correlation effects.

The proximity of the FM and CEF energy scales, alongside the tunability of glassy magnetic phases via field, highlights the system's utility for broader inquiries into disorder-driven quantum phase transitions and the rich phenomenology of rare earth-based magnetic semimetals.

Conclusion

PrAlSi manifests a complex interrelationship between structural disorder, magnetism, electronic structure, and topological transport phenomena. The emergence of a highly field-tunable, compensated semimetallic state with pronounced nonsaturating MR and giant AHE, together with strong evidence for magnetically-induced Fermi surface reconstruction, identifies PrAlSi as an important system for the study of topological and correlated electron effects in rare-earth intermetallics. Future investigations targeting the microscopic origins of its magnetic phases and their coupling to relativistic carriers will be pivotal in advancing both fundamental and applied aspects of quantum materials science.