3D bulk-resolved $g$-wave magnetic order parameter symmetry in the metallic altermagnet CrSb

Abstract

Electronic phases of matter, such as magnetism and superconductivity, are defined and distinguished by their order parameters that quantify the spontaneous symmetry breaking underlying each phase. The simplest cases are the uniform magnetisation of ferromagnets and isotropic gap function of conventional superconductors. Unconventional superconductors often have a nodal gap function, where the gap changes sign at nodes on the Fermi surface. This concept of unconventional or nodal order parameter symmetry has recently been extended to numerous magnetic systems, including altermagnets, in which up- and down-spin species are non-degenerate around the Fermi surface. Here we demonstrate that magnetic quantum oscillation measurements can provide a direct, bulk-sensitive, 3D mapping of the order parameter in an unconventional magnet. By rotating a magnetic field through high- and low-symmetry directions of the CrSb Brillouin zone, we show that this material's altermagetic band structure leads to the loss of mirror symmetry for each spin-split Fermi sheet away from highly symmetric nodal orientations. In momentum space, the difference between up and down spins follows the profile of the $\mathcal{Y}_{4}^{-3}=zy(3x^2-y^2)$ spherical harmonic - analogous to a $g$-orbital of the hydrogen atom. While notoriously difficult to resolve in unconventional superconductors, our work demonstrates that the order parameter symmetry of unconventional magnets can be conclusively determined through quantum-oscillatory quasiparticle spectroscopy. Our results empirically establish CrSb as a prototypical $g$-wave metallic altermagnet, which in pristine form possesses low residual resistivities down to $\sim$1 $\mu \Omega$cm, opening numerous avenues for next-generation spintronic device applications