Magnetic Order from First-Principles Linear Response

Abstract: The magnetic order of a material is usually predicted by comparing the energies of trial spin configurations, a strategy that cannot reach orders outside the chosen set and rapidly becomes intractable as the number of magnetic sites grows. We show that the order can instead be identified directly from the paramagnetic state: the leading eigenmodes of its self-consistent magnetization response, obtained with spin--orbit coupling at arbitrary wavevector within the primitive cell, determine both the ordering wavevector and the pattern of moments, with no candidate configurations. With no prior assumption about the order, the method correctly reproduces the G-type stacking with out-of-plane moments in the altermagnet candidate KV$_2$Se$_2$O, the $3{:}1$ ferrimagnetic tetrahedra of Cu$_2$OSeO$_3$, and the incommensurate spiral instability of monolayer NiI$_2$. Our results establish the response of the paramagnetic state as a predictive and unbiased route to assessing magnetic order, enabling systematic searches for complex magnets.