Motivated by the ongoing interest in understanding the actual magnetic ground state of the promising axion insulator candidate ${\mathrm{EuIn}}_2{\mathrm{As}}_2$, we present here a spin symmetry analysis and ab initio calculations, aiming to identify specific exchange-dominated physics that could offer insights into the current debate. We investigate two noncollinear coplanar magnetic orders reported in this compound: the helical and broken-helical phases. Our symmetry analysis shows that magnetic-exchange alone results in the formation of an out-of-plane odd-parity wave order in momentum space with a single unpolarized nodal plane in both phases. Additionally, we identify an in-plane $g$-wave order that emerges exclusively in the broken-helical phase, providing a distinguishing feature for this phase. Furthermore, we report a nonrelativistic Edelstein effect with a distinct out-of-plane polarized spin density that dominates over spin-orbit coupling effects. Our ab initio calculations reveal a significant contrast in the magnitude of this effect between both phases, which could serve as a means to identify the magnetic transition and distinguish them from other magnetic ground states proposed for this compound.

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• Electronic structure
• Spin accumulation
• Topological insulators
• Ab initio calculations
• Linear response theory