Symmetry-based prediction of the type-II multiferroics with pyrochlore structure

Based on the symmetry related concept of the group theory we predict two structures with enantiomorphic space groups $P_I4_3$ and $P_I4_1$. These phases arise as a result of spin ordering on $16d$ Wyckoff position in crystals with space group $Fd\bar3m$. It is shown that $P_I4_3$ and $P_I4_1$ hypothetical magnetic structures are multiferroics of type II. The ferroelectric polarization emerges through a mechanism of the hybrid improper ferroelectricity allowing trilinear coupling of polarization and two other antiferromagnetic order parameters. In addition to improper ferroelectricity, the symmetry analysis proves the possible coexistence of other improper ferroic orders including orbital, ferroelastic, ferroelastoelectric, ferrobielastic, optical, ferroaxial, ferrotoroidic, gyrotropic and other crystal freedom degrees.