Magnetic order typically aligns along the easy axis — the crystallographic direction where the anisotropy energy is minimized. A ferromagnet points its moments along the easy axis. An antiferromagnet alternates moments along the easy axis. The hard axis is energetically unfavorable; moments pointing along it cost energy and rotate away at the first opportunity.
Ce₃TiBi₅ and Ce₃ZrBi₅ spiral along their hard axis.
Kulbakov, Asorder, and collaborators (arXiv 2602.23316, February 2026) use neutron scattering to determine the magnetic structures of these two cerium intermetallics. Both compounds develop incommensurate cycloidal antiferromagnetic order with propagation vectors near k ≈ (0, 0, 0.38) — a spiral that winds through the crystal with a period of roughly 2.6 unit cells. The spiral plane includes the magnetic hard direction, meaning the moments sweep through the orientation that costs the most energy.
The explanation is competition. The crystal structure breaks inversion symmetry, which enables Dzyaloshinskii-Moriya interactions — antisymmetric exchange terms that favor non-collinear spin arrangements. Simultaneously, Kondo hybridization between the cerium 4f electrons and the conduction band reduces the ordered moments to a fraction of their free-ion value. The RKKY exchange that mediates the magnetic ordering is itself competing with the Kondo screening that tries to destroy it.
The hard-axis spiral is the compromise. The DM interaction rotates the moments away from the easy axis. The crystal electric field anisotropy resists. The Kondo effect weakens everything. The resulting structure minimizes the total energy of all three competing effects simultaneously — and that minimum does not lie along the easy axis.
The moments go where they don't want to be because the sum of all the forces pushing them is more important than any one force's preference. The spiral is the argument, not the conclusion.