Symmetry-Breaking Pathway towards The Unpinned Broken Helix

The search for materials exhibiting novel emergent properties relies on identification of their characteristic symmetries. A prominent example are materials in which magnetic symmetries promote topological phases, and consequently quantized responses to external stimuli.<br/><br/>EuIn₂As₂ attracted attention when ab-initio calculations predicted that it hosts the elusive axion insulator state, based on the assumption of a simple collinear antiferromagnetic structure. Recently, scattering measurements revealed a much more intricate magnetic ground state, characterized by two coexisting magnetic wavevectors, reached by successive thermal phase transitions. The proposed magnetic phases were a spin helix and a state with interpenetrating helical and antiferromagnetic order, termed a `broken helix.' The symmetries of both deduced phases protected the axion state.<br/><br/>In this talk I will show results of magneto-optical experiments which are not compatible with the magnetic structures deduced by scattering. I will further demonstrate how combining the experimental information from scattering and symmetry-sensitive optics with an analysis based on group theory allowed us to uniquely identify the magnetic structure associated with each of the two phases. We find that the higher temperature phase hosts a ‘nodal amplitude-modulated’ structure rather than a helix, characterized by a variation of magnetic moment amplitude from layer to layer, with the moment vanishing entirely 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 the consequent breaking of rotational symmetry, the axion phase is not generically protected in EuIn₂As₂but we show that it can be restored if the magnetic structure is tuned with externally applied uniaxial strain. Finally, I will present a spin Hamiltonian that identifies the interactions needed to account for the complex magnetic order in EuIn₂As₂, and how they arise from coupling to itinerant degrees of freedom.<br/><br/>Taken together, our results emphasize the power of a multimodal approach combining scattering and symmetry-sensitive optical probes in identifying complex magnetic structures, as well identifying EuIn₂As₂as a remarkably tunable platform for exploration of magnetic symmetries.