Incommensurate magnetic order in Topological Antiferromagnet ErMn₆Sn₆

RMn₆Sn₆ (R166) compounds (R = Gd-Lu, Y) with kagome Mn bilayers separated by triangular R layers have the possibility to tune topological states within the kagome layer via the magnetism of the R layers. In particular, competition between uniaxial R and easy-plane Mn anisotropies leads to a temperature-dependent spin-reorientation transition which can switch topological electronic phases. Here we present detailed single-crystal neutron diffraction data for Er166 as a function of temperature, showing complex incommensurate antiferromagnetic (AFM) order between temperatures of T_ER ≈ 88 and T_N ≈ 350 K. The easy-plane ferrimagnetic order involving both Mn and Er sublattices below T_ER is in agreement with previous reports. Above T_ER, the Er and Mn lattices potentially decouple, and we find the Bragg peaks corresponding to incommensurate spiral-like magnetic order. Unlike Y166, we report even and odd higher-order harmonics of the AFM propagation vector. The second-order peaks, if magnetic, could indicate a zero-field fan-type order. On the other hand, second-order peaks could indicate a structural transition induced by magnetoelastic coupling.