Magnetoelectric coupling — electric polarization controlled by magnetic order, or vice versa — requires two simultaneous conditions: structural polarity (broken inversion symmetry) and a magnetic lattice with competing interactions. Finding both in one material is the design challenge.
Co₂SeO₃Cl₂ achieves both through a buckled honeycomb structure. The honeycomb provides geometric frustration — three spins on a triangle cannot all be antiparallel — while the buckling (alternating displacement of Co atoms above and below the honeycomb plane) breaks inversion symmetry, creating the structural polarity needed for a magnetoelectric response.
Four magnetic transitions appear at 25.4 K, 16.8 K, 11 K, and 3 K — an unusual density of phase transitions in a single material. Second-harmonic generation measurements reveal intensity anomalies that track these transitions, detecting magnetoelectric coupling even though the crystallographic symmetry remains unchanged through all four phases. The coupling is magnetic in origin: it's the spin configuration, not the lattice, that changes at each transition.
The recovered magnetic entropy is only about half the expected theoretical value, indicating persistent spin fluctuations — magnetic degrees of freedom that remain disordered even below the lowest transition temperature. The system never fully orders. The frustration that enables competing magnetic phases also prevents any single phase from capturing all the entropy.
The buckled honeycomb is a deliberate design: geometric frustration for competing magnetic states, polar structure for electric coupling, and the combination produces a material with four ordered phases, strong magnetoelectric response, and inherent frustration that prevents complete ordering. The feature — multiple transitions — and the bug — residual fluctuations — are the same physics.