Altermagnetic spin-split Fermi surfaces in CrSb revealed by quantum oscillation measurements

Abstract

Altermagnets, a class of collinear magnets defined by their spin-split electronic bands, are a focus of intense research, where a key challenge is to experimentally verify this unique band structure as a bulk property. Here, we report a comprehensive quantum oscillation study on the prototypical altermagnet CrSb. By combining high-field magnetotransport and torque measurements with DFT+$U$ calculations including spin-orbit coupling, we successfully identify a multitude of quantum-oscillation frequencies originating from four spin-non-degenerate bands. These results provide definitive, bulk-sensitive evidence for the altermagnetic spin-split Fermi surface of CrSb, which provides a firm foundation for exploring its novel electronic properties.

Figures (3)

• Figure 1: Quantum oscillations in CrSb. (a) Magnetic field dependence of resistivity for $B \parallel c$ in the CVT-grown sample, along with the oscillatory component (SdH oscillations) $\rho_{osc}$ obtained by subtracting a polynomial background $\rho_{bg}$. The upper-left inset shows the crystal and magnetic structures of CrSb drawn in VESTA software Momma11JAC. (b) Corresponding Fourier transform. (c) Magnetic field dependence of the resistivity for $B \parallel a^*$ in the flux-grown sample, and the SdH oscillations obtained by subtracting a polynomial background. (d) Corresponding Fourier transform and (inset) Fourier transform for $B \parallel c$ in the same flux-grown sample. (e) Fourier transform of SdH oscillations (inset) at field angle $\theta = -60^{\circ}$ in the flux-grown sample. $\theta$ is measured from the $c$ axis toward the $a^*$ axis. (f) Fourier transform of magnetic torque dHvA oscillations (inset) for $B \parallel a$. The $\alpha$, $\beta$, $\delta$, $\epsilon$, and $\zeta$ frequency peaks are labeled in (b), (d), (e), and (f). Harmonics of $\alpha$ and $\epsilon$ are also indicated. The lowest frequency peaks [marked with asterisks in (d), (e), and (f)] are neglected (see text for explanation).
• Figure 2: Fermi surface in CrSb. Magnetic-field-direction dependences of the quantum oscillation frequencies for field rotation in the (a) $ca^*$ and (b) $a^*a$ planes. The experimental frequency branches are labeled with Greek letters. Different symbols correspond to different samples and/or field windows of Fourier transforms as indicated in (b), and their sizes indicate the oscillation amplitudes. The solid curves plot the theoretical frequencies calculated from the Fermi surface in (c) for $-90 \leqslant \theta \leqslant 90^{\circ}$ (a) and $-30 \leqslant \phi \leqslant 30^{\circ}$ (b). The attached names of the underlying orbits include the band number, orbit center, and, if necessary, inner (i) or outer (o). gp denotes a general point. (c) Fermi surface obtained from our DFT+$U$ calculation (with SOC). The color indicates the spin polarization $s_z$. Extremal orbits relevant to experimental frequencies are indicated: $B \parallel c$ for bands-1 and 2, and $B \parallel a^*$ for bands-3 and 4.
• Figure 3: Temperature and magnetic-field dependences of quantum-oscillation amplitudes in CrSb. (a) Temperature dependences of the oscillation amplitudes of $\alpha$ for $B \parallel c$, $\beta$ and $\epsilon$ for $B \parallel a^*$, $\delta$ at $\theta = -60^{\circ}$, and $\zeta$ for $B \parallel a$. The solid curves are the Lifshitz--Kosevich fittings, from which the effective masses are determined. (b) Magnetic-field dependences of the oscillation amplitudes of $\alpha$ for $B \parallel c$ and $\beta$ and $\epsilon$ for $B \parallel a^*$. The solid lines are linear fittings, from which the electron scattering times are estimated.