GoKawiilCrystal growth
Single-crystal CrSb specimens were grown by the chemical vapour transport technique. Stoichiometric amounts of Cr (chunks, 99.995%) and Sb (Shots, 99.9999%) were used as source material. Iodine was added as a transport agent, calculated to have a pressure of 1 bar at growth conditions. The starting materials were sealed under vacuum in a quartz ampoule and placed in a horizontal two-zone furnace. The temperature was slowly ramped up to T 1 = 925 °C and T 2 = 900 °C, left for 2 weeks, and subsequently cooled at the furnace cooling rate to room temperature. The resulting crystals were hexagonal platelets up to 1.5 mm in diameter, along with larger areas possessing intergrown crystals of CrSb, several mm in size. Only single-crystal specimens were used in this study.
Sample characterization
Several crystals were picked from a batch of single crystals and crushed into a fine powder. This powdered sample was then distributed on a microscope slide, which had a thin layer of vacuum grease. Powder X-ray diffraction was measured in the Bragg–Brentano geometry on a Bruker D8, using a Cu source, with the results plotted in Extended Data Fig. 1. The measurement was performed in a 2θ range of 10°–90°, with no peaks observed below 20°.
The obtained data display sharp, well-defined peaks, indicating a high level of crystallinity. The data were analysed using the Rietveld method, yielding an excellent fit (R Bragg = 3.39), which describes all observed peaks, thereby indicating that the samples are phase pure. The measured crystal structure is in good agreement with previous studies40.
We also performed electrical transport, magnetization and Laue diffractometry measurements (Extended Data Fig. 1). Samples were predominantly screened by temperature-dependent resistivity measurements, used to extract their residual resistivity ratios (RRRs). To do this, we fitted the low-temperature data to the square of the temperature and extrapolated to absolute zero to determine the residual resistivity. The 300 K resistivity was then divided by this value to yield the RRR. Higher RRR values indicate longer mean free paths and hence higher crystalline quality. Typical RRR values were in the approximate range of 10–28. High-quality specimens were then oriented by Laue diffractometry, in preparation for high magnetic field de Haas–van Alphen (dHvA) effect measurements.
dHvA effect torque magnetometry measurements
High-quality samples were selected following characterization screening and brought to the National High Magnetic Field Laboratory, Tallahassee, Florida. For torque magnetometry measurements, we largely followed the methodology outlined in ref. 48. Samples were mounted on flexible BeCu cantilevers and affixed using multiple layers of General Electric low-temperature varnish, giving good thermal contact and strong adhesion between sample and cantilever. Cantilevers were soldered in place, such that the cantilever head was suspended above a copper baseplate by a short separation distance. As the magnetic field was swept, the change in capacitance between the cantilever and baseplate, due to the magnetic torque exerted on the sample, was measured by a General Radio analogue capacitance bridge using phase-sensitive detection. The change in torque was calibrated to units of farads using an Andeen-Hagerling digital capacitance bridge.
All dHvA measurements were performed in the 41.5 T all-resistive magnet in Tallahassee. A 3He sample environment was used, along with a probe mounting of our custom design. Rotations of the sample orientation with respect to the magnetic field were performed in situ using a brushless linear motor. Angles were calibrated by the change in sign of the torque background—identifying high-symmetry directions of the crystal—and verified using a Hall sensor.
The oscillatory component Δτ was isolated from the background magnetic torque τ by performing a locally estimated scatterplot smoothing (LOESS)49 subtraction. In general, owing to the intricate web sheet of the CrSb Fermi surface, the dHvA waveform at a given angle could be quite complicated because of the presence of numerous frequency components. To simplify our analysis and concentrate on the dogbone Fermi sheet, we often performed combined high-pass filtering with short LOESS windows in our analysis. The dogbone frequencies are most prominent above 3 kT, and so we performed Butterworth high-pass filtering of frequencies in inverse field in this range. This was combined with a short sliding LOESS window over τ, which effectively fits any slow oscillations within the background (assumed to be quadratic in H), therefore producing a Δτ waveform dominated by higher-frequency components. For the Δτ traces presented in Fig. 1, this involved using a LOESS window of 0.7 T. In Fig. 2, we used a window of length 1.2 T to show the strong spectral weight at lower frequencies due to the web. By contrast, in Fig. 4, we used a window of only 0.6 T to focus on the >3 kT components in our temperature-dependence study.
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