Higher-order spin magnetic multipole moments in antiferromagnets

Antiferromagnets with vanishing net magnetization can host higher-order spin magnetic multipole moments that capture the spatial complexity of their microscopic spin arrangements. Understanding and quantifying these multipole degrees of freedom open new avenues for describing and manipulating antiferromagnetic order beyond conventional dipolar magnetism. In this work, we present a general formalism to extract spin multipole moments from response functions computed within density functional theory. The approach provides a practical route to evaluate multipole moments in crystalline solids and establishes connections to experimentally measurable quantities in representative antiferromagnetic materials.