Tunable non-Abelian magnon topology in altermagnetic CrSb under field, anisotropy, and strain

Altermagnets host collinear, net-zero-moment order with momentum-dependent spin splitting protected by crystal symmetries. We study the magnon bands of CrSb and show that external magnetic field, lattice anisotropy, and elastic strain cooperatively tune a non-Abelian multiband topology. Starting from a fitted spin model with exchange and easy-axis anisotropy, we compute linear spin-wave spectra (Holstein–Primakoff + paraunitary/Colpa diagonalization) and evaluate non-Abelian Wilson loops over selected magnon subspaces. We find (i) field-induced gap openings at symmetry-protected crossings that convert trivial loops into winding loops with quantized Berry phases; (ii) anisotropy- and strain-controlled k-path-specific shifts of the topological "hot" region, Wilson-loop winding; and (iii) strain-field phase boundaries where Wilson-loop spectra undergo reconnections. Our results establish CrSb as a platform where symmetry, mechanics, and Zeeman control realize a reconfigurable, non-Abelian magnon band topology and expose a practical route to k-resolved topological engineering in altermagnets.