Theory of Spiral Magnetism in Weyl semimetal SmAlSi

Recent neutron scattering and thermodynamic measurements suggest that Weyl electrons in the emergent Weyl semimetal SmAlSi mediate unconventional magnetic interactions and induce spiral magnetic order. In this work, we investigate the nature of these interactions by modelling long-range $f-f$ exchange mediated by itinerant $d$ electrons via the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism, employing a material-specific tight-binding Hamiltonian obtained from first-principles calculations. The magnetic susceptibility is derived from the spin-spin correlation function based on the random phase approximation. Our results demonstrate that Fermi-surface nesting alone cannot account for the experimentally observed magnetic modulation at the wave vector (1/3, 1/3, 0); however, incorporating appropriate antiferromagnetic exchange interactions among the $d$ electrons yields the correct propagation vector. The spin-texture analysis reveals a configuration that is close to a cycloidal spin structure, preserving combined glide and time-reversal symmetry, and reflecting an intricate competition between inter- and intra-sublattice interactions in SmAlSi.