Breakdown of Universal Whirling Order in a Heisenberg Tsai-Type Approximant

Noncoplanar whirling magnetic order has recently been proposed as a universal magnetic state in non-Heisenberg Tsai-type quasicrystal approximants. Here, X-ray resonant magnetic scattering measurements on Heisenberg and non-Heisenberg Au-Al-R (R = Gd, Tb) 1/1 approximants reveal a clear breakdown of this universality in the Heisenberg limit. While the non-Heisenberg Au-Al-Tb system is well described by the previously identified whirling magnetic structure, the Heisenberg Au-Al-Gd counterpart exhibits qualitatively different azimuthal-angle dependences that are incompatible with the universal whirling-order model. Despite nearly identical crystal structures and comparable magnetic energy scales, the two systems stabilize distinct antiferromagnetic ground states with the same propagation vector k = (1, 0, 0), demonstrating that the apparent universality of whirling order is not a consequence of Tsai-cluster geometry alone but requires spin anisotropy. These results further reveal the emergence of a competing manifold of nearly degenerate magnetic states in the Heisenberg limit.