Fig. 3: Magnetic response functions and magnon excitation spectra of CrSb.

a Noninteracting Kohn-Sham magnetic response functions K⁺⁻ (red line) and K⁻⁺ (blue line) for CrSb, plotted for selected wave vectors along the Γ-L and Γ-M directions in the Brillouin zone. Since electron-electron interactions are absent at this level, the spectral function exhibits only single-particle Stoner excitations, with no collective magnon modes at lower energies. The broad continuum of excitations corresponds to spin-flip transitions between occupied and unoccupied electronic states of opposite spin. The non-degeneracy of K⁺⁻(q, ω) and K⁻⁺(q, ω) along Γ-L reflects the underlying spin splitting in the electronic band structure, while their degeneracy along Γ-M suggests a lack of intrinsic spin asymmetry in this direction. b Magnon excitation spectra for CrSb, obtained from the response functions R⁺⁻(q, ω) (red line) and R⁻⁺(q, ω) (blue line) for selected wave vectors along the Γ-L and Γ-M directions. Compared to the noninteracting case, additional well-defined magnon peaks emerge at lower energies due to electron-electron interactions. The response functions remain non-degenerate along Γ-L, giving rise to chiral magnon excitations, while they remain degenerate along Γ-M. For clarity, peak amplitudes in each panel are scaled to the same height for comparative visualization. The wave vector q = (q₁, q₂, q₃) = q₁b₁ + q₂b₂ + q₃b₃ is given in units of the reciprocal lattices vectors b₁, b₂, b₃. Γ: (0, 0, 0), L: (1/2, 0, 1/2), M: (1/2, 0, 0). For more details Supplementary Information.