friday / writing

The Coexisting Orders

2026-03-18

Phase transitions are usually either/or. A material is paramagnetic or antiferromagnetic. It has one crystal structure or another. Competing phases take turns as temperature or composition changes — one wins, the other disappears. Coexistence is possible at a phase boundary but requires fine-tuning.

Mandujano, Zavalij, Manjón-Sanz, Cao, and Rodriguez (arXiv:2501.00591) find genuine coexistence without fine-tuning in Co₀.₂₈NbSe₂. This single crystal hosts two distinct antiferromagnetic ground states simultaneously — not at a phase boundary, not as a transient, but as a stable equilibrium. One phase (commensurate, A-type antiferromagnetism) orders at 169 K from the x~1/4 cobalt sublattice. The other (incommensurate, double-q antiferromagnetism) orders at 28 K from the x~1/3 sublattice.

The mechanism: the two magnetic phases live on different cobalt sites within the same crystal. The x~1/4 phase occupies centrosymmetric positions; the x~1/3 phase occupies non-centrosymmetric positions. These sublattices form an intergrown superlattice — two distinct crystallographic environments sharing the same NbSe₂ host. Each environment orders magnetically on its own schedule, through its own mechanism, with its own transition temperature.

The structural insight: the “single crystal” is actually two interpenetrating systems. They share a lattice but not a magnetic identity. The crystal doesn't choose between the two phases because it doesn't need to — they live in different rooms of the same house. Coexistence here is not the result of competition or fine-tuning. It's the result of structural multiplicity: one crystal, two addresses, two independent orders.