Interplay of trimerization, chirality and ferroelecticity in multiferroic BaCoSiO4

Multiferroic materials combine multiple ferroic orders that may enable cross-functionalities, e.g. control of one ferroic order by the field conjugate to the other one. BaCoSiO${}_4$, a recently proposed multiferroic combines multiple unit cell-tripling modes, structural chirality and ferroelectric polarization, whose interactions result in a peculiar ground state. We derive the Landau free energy for interacting trimerization, electric polarization and structural chiral modes and find the corresponding coefficients from first-principles calculations. This results in a quantitative model for the description of domain walls and vortices, observed in recent experiments.