Symmetry-breaking pathways to the broken helix

EuIn₂As₂ initially attracted attention when ab initio calculations predicted that it hosts an axion insulator state, assuming a simple collinear antiferromagnetic structure. Recent neutron scattering measurements have revealed a much more intricate magnetic ground state with two coexisting magnetic wavevectors reached by successive thermal phase transitions. The proposed high and low temperature phases were, respectively, a spin helix and a state with interpenetrating helical and antiferromagnetic order, termed a 'broken helix.' The broken helix protects the axion state by preserving the product of time-reversal and a C₂ rotational symmetry. Here, we uniquely identify the magnetic structure associated with each of these phases using a multimodal approach that combines symmetry-sensitive optical probes and scattering with group theoretical analysis. We find that the higher temperature phase hosts a 'nodal amplitude-modulated' structure rather than a helix, characterized by a variation in magnetic moment amplitude from layer to layer, with the moment vanishing in every third Eu layer. The lower temperature structure is similar to the 'broken helix,' with one important difference: the relative orientation of the magnetic structure and the lattice is not fixed, resulting in an 'unpinned broken helix.' As a result of this breaking of rotational symmetry, the axion phase is not generically protected in EuIn₂As₂; however, we demonstrate that it can be restored by tuning the magnetic structure with externally-applied uniaxial strain. Finally, we present a spin Hamiltonian that identifies the necessary spin interactions to explain the complex magnetic order in EuIn₂As₂. Our work highlights the importance of the multimodal approach in determining order-parameter symmetry and has implications for active research fields, including altermagnetism, multipolar order, and 'order-by-disorder' transitions.