Ferroelectric materials switch their polarization in an applied electric field. Ferromagnets switch their magnetization. Ferroelastics switch their strain state under stress. These are the classical ferroic orders — each defined by a macroscopic property that can be toggled between two or more stable orientations by a conjugate field.
Chirality — the handedness of a crystal structure, whether it's a left-handed or right-handed screw — seems like it should fit. A crystal with two mirror-image configurations, switchable by some perturbation, would be “ferrochiral.” The analogy is clean. But the analogy is wrong.
Gómez-Ortiz, Mamoudou Taganga, McCabe, Romero, and Bousquet (arXiv:2603.22501) prove that structural chirality in periodic crystals cannot be a primary ferroic order parameter. The proof is group-theoretical. Ferroic transitions are driven by zone-center instabilities — uniform, long-wavelength distortions where the unit cell deforms but the periodicity doesn't change. Chirality-producing transitions, the ones that create enantiomorphic space-group pairs (structures related by a mirror but not by any proper rotation), cannot originate from zone-center modes. The instabilities that break mirror symmetry to produce chirality necessarily involve finite wavevectors — they modulate the structure over multiple unit cells.
The prohibition isn't accidental. It follows from the representation theory of space groups. The achiral parent must contain the two chiral daughters as subgroups, and the researchers show that in every case, the irreducible representation connecting them doesn't transform at the Brillouin zone center. Systematically — not a single exception across all 230 space groups.
The consequence: you can't switch chirality the way you switch polarization. A ferrochiral material would require a field that couples to a finite-wavevector mode, but ferroic fields are uniform by definition. You would need a field that varies on the scale of the lattice itself. No macroscopic field does this.
Chirality is a structural property. It can exist. It can even emerge through phase transitions. But it cannot be controlled by the mechanisms that control every other ferroic order. The symmetry that makes it interesting — the absence of mirrors — is exactly the symmetry whose breaking requires the wrong kind of instability.