Observation of Weyl fermions in a magnetic non-centrosymmetric crystal

The study explores how breaking inversion symmetry and time-reversal symmetry in solids shapes Berry curvature and drives topological phenomena. Non-centrosymmetric crystals can host effects such as gyrotropy, nonlinear Hall and photogalvanic responses, and Weyl fermions with quantized chiral charge. Magnetic order further breaks time-reversal symmetry, enabling intrinsic anomalous Hall effects via Berry curvature. The authors target PrAlGe, a non-centrosymmetric ferromagnet predicted to host Weyl nodes near the Fermi level, making it a promising platform to directly correlate ARPES-resolved band topology with transport. They aim to spectroscopically observe surface Fermi arcs and bulk Weyl cones and to connect these with an intrinsic anomalous Hall response, establishing PrAlGe as a magnetic, non-centrosymmetric Weyl semimetal.

Prior works established the role of symmetry in generating Berry curvature and topological states, including Weyl semimetals with Fermi arcs and associated transport phenomena. Experimental Weyl candidates such as Mn3Sn and Co3Sn2S2 are centrosymmetric, whereas PrAlGe lacks both inversion and time-reversal symmetry, uniquely enabling spin currents without net charge. A body of theory predicts nonlocal gyrotropy, quantum nonlinear Hall effects, photogalvanic effects, and chiral Weyl fermions in non-centrosymmetric or magnetic systems. Within the RAlGe family, PrAlGe was predicted to host Weyl nodes close to EF, improving experimental access. The paper positions itself to provide direct spectroscopic evidence of Fermi arcs and bulk Weyl cones in PrAlGe and to link them to anomalous Hall transport dominated by Berry curvature.

- Crystal growth: Single crystals of PrAlGe grown by self-flux from Pr (99.9%), Al (99.99%), Ge (99.99%). Stoichiometry Pr1Al18Ge1 loaded in alumina crucibles, sealed in silica ampoules under partial Ar; held at 1150 °C then slowly cooled to 750 °C at 0.1 °C/min. - Structure and magnetism: Single-crystal X-ray diffraction confirmed space group I41/amd (No. 109) and lack of inversion symmetry. Magnetic susceptibility fitted by inverse Curie–Weiss law; ferromagnetic interactions inferred; Curie temperature TC ≈ 16 K; magnetization with MPMS-3 revealed soft ferromagnet with easy c-axis. - ARPES (VUV): Conducted at SSRL BL 5-2 with Scienta R4000. Angular resolution <0.2°, energy resolution <20 meV; beam spot ~20×40 µm^2; in-situ cleave; vacuum <5×10^-11 Torr; temperature ~11 K (<TC). Photon energies around 50 eV used to map (001) surface states. - ARPES (Soft X-ray): Performed at ADRESS beamline, Swiss Light Source. Combined energy resolution 40–80 meV, angular resolution <0.2°. In-situ cleave; vacuum <5×10^-11 Torr; temperature below TC. Photon energies (e.g., 478 eV) used to access bulk kz and map kz=0 Fermi surface and dispersions intersecting calculated Weyl nodes. - Transport: Four-probe resistance and Hall measurements in PPMS with silver paste contacts cured at room temperature. Magnetization M(μ0H) measured for H||c and H||a; Hall resistivity ρxy measured vs field and temperature to separate ordinary (RH) and anomalous (ρA) contributions. - First-principles calculations: DFT (VASP) with PAW, GGA (PBE) exchange-correlation, Hubbard U=4 eV on Pr, SOC included self-consistently; Γ-centered 14×14×14 k-mesh. Surface states for (001) computed via Wannier functions (Pr d,f; Al/Ge s,p) and iterative Green’s function for a semi-infinite slab, optimized to match experiment. Berry curvature and intrinsic anomalous Hall conductivity computed vs carrier density; comparison with ARPES-derived Weyl separation and transport.

- Crystal and magnetism: PrAlGe crystallizes in non-centrosymmetric I41/amd; exhibits soft ferromagnetism with TC ≈ 16 K and easy axis along c. - Surface Fermi arcs: VUV-ARPES on (001) at T≈11 K reveals an asymmetric Fermi surface across Γ–M consistent with broken inversion and time-reversal symmetries. A distinct, photon-energy–independent “U”-shaped surface band is observed, consistent with a topological Fermi arc connecting W3 and W4 projections. - Chiral charges from surface modes: Along straight and loop cuts, ARPES resolves chiral edge modes: loop P shows a single left-moving mode (enclosed Chern number n = −1), loop M shows a right-moving mode (n = +1). Momentum cut at ky ≈ −0.25(2π/a) shows mirror-related left/right-moving modes. These directly evidence projected chiral charges ±1 associated with bulk Weyl nodes. - Bulk Weyl cones: SX-ARPES maps the kz=0 bulk Fermi surface and dispersions with linear energy-momentum behavior intersecting calculated Weyl nodes. Within experimental resolution, W3 and W4 are located at (kx, ky) ≈ (0.15, −0.32) and (0.13, −0.22) in units of 2π/a on kz=0. W1 also shows linear dispersion. Experimental maps (cuts 1–3) qualitatively agree with calculations. - Anomalous Hall effect: ρxy shows a strong anomalous component emerging below TC; ρA saturates ≈1.5 μΩ·cm·T−1 at 2 K and total ρxy ≈1.4 μΩ·cm. Calculated intrinsic anomalous Hall conductivity σxy^A ≈ 600 Ω−1·cm−1 is weakly dependent on carrier concentration (p ≈ 0.9–1.7×10^21 cm−3), corresponding to an intrinsic ρA ≈ 0.6 μΩ·cm, in good agreement with experiment. A simple estimate using Weyl separation kWeyl ≈ 0.15 Å−1 gives σxy^Weyl ≈ 738 Ω−1·cm−1, consistent with ab initio. - Berry curvature hotspots: Calculated |Ω(k)| on kz=0 concentrates near W3/W4, coinciding with Fermi arc termination points and Weyl cone projections seen by ARPES, linking surface, bulk, and transport.

The work directly addresses whether magnetic, non-centrosymmetric PrAlGe hosts Weyl fermions whose Berry curvature governs transport. Surface-sensitive ARPES detects topological Fermi arcs with asymmetric connectivity across Γ–M, and closed-loop analyses reveal chiral edge modes indicating projected chiral charges ±1. Bulk-sensitive SX-ARPES demonstrates linear Weyl cone dispersions near EF at momenta consistent with theory. Transport shows a sizable anomalous Hall effect whose magnitude and carrier-density dependence match the calculated intrinsic Berry-curvature contribution. The spatial correlation between ARPES-observed Fermi arc endpoints and Berry-curvature hotspots in calculations substantiates a surface–bulk–transport correspondence. Collectively, the findings confirm a Weyl semimetal phase in PrAlGe where broken inversion and time-reversal symmetries yield strong Berry curvature effects, establishing PrAlGe as a platform to explore topological responses including anomalous Hall and potentially unconventional photocurrents.

The study establishes PrAlGe as a magnetic, non-centrosymmetric Weyl semimetal. Using ARPES, it observes topological Fermi arcs and bulk Weyl cones near the Fermi level with projected chiral charges ±1, and transport reveals a large intrinsic anomalous Hall effect consistent with Berry curvature from the Weyl band structure. The demonstrated surface–bulk–transport correspondence links spectroscopic topology to macroscopic response. Future directions include exploring photogalvanic and nonlinear Hall effects enabled by simultaneous breaking of inversion and time-reversal symmetry, leveraging spin-polarized topological currents for all-electrical spin generation without entropy production, and using soft ferromagnetism to magnetically control topological currents. Further high-resolution, low-temperature bulk probes may resolve Zeeman splittings and refine the Weyl node characterization.

Soft X-ray ARPES measurements were performed at temperatures comparable to TC and with 40–80 meV energy resolution, which, together with spectral linewidths, prevented a clear resolution of Zeeman splitting of bands. Some features (e.g., precise Weyl node energies and separations) are inferred within experimental resolution and guided by calculations; improved resolution and temperature conditions could provide more quantitative detail.