3D bulk-resolved g-wave altermagnetic order parameter in CrSb.

Abstract

Electronic phases of matter, such as magnetism and superconductivity, are defined and distinguished by their order parameters quantifying the spontaneous symmetry breaking underlying each phase. Simple cases include the uniform magnetization of ferromagnets^1,2 and the isotropic gap function of conventional superconductors³. Unconventional superconductors⁴ often have a nodal gap function, in which 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^5-8, including altermagnets^9-13, in which up- and down-spin species have non-degenerate Fermi surfaces. Here we demonstrate that magnetic quantum oscillation¹⁴ measurements can provide a high-resolution, bulk-sensitive, three-dimensional (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 the altermagnetic band structure of this material leads to a reduction of symmetry for each spin-split Fermi sheet away from nodal orientations. In momentum space, the exchange splitting between up and down spins follows the profile of the <math xmlns="http://www.w3.org/1998/Math/MathML"> <msubsup> <mrow> <mrow><mrow><mi>Y</mi></mrow> </mrow> </mrow> <mrow><mn>4</mn></mrow> <mrow><mo>-</mo> <mn>3</mn></mrow> </msubsup> <mo>=</mo> <mi>y</mi> <mi>z</mi> <mspace></mspace> <mo>(</mo> <mn>3</mn> <msup><mrow><mi>x</mi></mrow> <mrow><mn>2</mn></mrow> </msup> <mo>-</mo> <msup><mrow><mi>y</mi></mrow> <mrow><mn>2</mn></mrow> </msup> <mo>)</mo></math> real spherical harmonic-analogous to a g-orbital of the hydrogen atom. Although notoriously difficult to resolve in unconventional superconductors, our work demonstrates that the order parameter symmetry of unconventional magnets can be precisely mapped by quantum oscillatory quasiparticle spectroscopy, establishing CrSb as a prototypical g-wave metallic altermagnet.