Emergent magnetic nonanalyticity in Dirac altermagnets

Symmetry has long provided the organizing principle for understanding how materials respond to external perturbations. Here we show that what is permitted by symmetry need not be what actually emerges from the underlying system, and this distinction becomes particularly consequential for symmetry-related gapless Dirac fermions such as in altermagnets. A perturbation that shifts the Dirac points drives a Lifshitz reconstruction and generates an intrinsically nonanalytic effective potential, giving rise to undiscovered singular responses. In Dirac altermagnets, this nonanalyticity acquires a magnetic manifestation through C-paired spin-polarized Dirac cones: breaking the pairing symmetry C lifts their degeneracy and converts the associated Lifshitz reconstruction into an itinerant magnetization. As a consequence, piezomagnetism, the induction of a net magnetization by a mechanical strain, becomes nonlinear and nonanalytic, with Mproptosgn(varepsilon)varepsilon^2, whereas the linear response is absent despite being allowed by symmetry. Accordingly, the leading response cannot be inferred from the conventional symmetry-based paradigm of material response built upon the cornerstones of Neumann's principle and analytic Landau expansion. First-principles calculations identify the monolayer Fe_2S as a candidate material realization for such singular magnetic responses. These results suggest quantum singularities as a new degree of freedom for engineering material responses.