Figure 4: Representative cases of symmetry breaking and onset of improper polarization.
From: Improper electric polarization in simple perovskite oxides with two magnetic sublattices
Sketches illustrating the symmetry-breaking caused by having G-AFM spin configurations in both the rare-earth (Gd) and transition-metal (Fe) sublattices. In a only magnetic order within the Fe sublattice is assumed, while in the other panels both sublattices are ordered. c illustrates the symmetry breaking associated to the η6 shear strain, and in d we sketch X-point modulated anti-polar motions of the Gd cations. To better visualize the symmetry breaking, in c,d we use dashed lines connecting the Fe–Gd pairs that get closer because of the distortions, and arrows on the Fe cations indicate the induced forces. In addition, note that in c,d we show two elemental perovskite cells, so that the spatial modulation of the induced forces can be easily appreciated.
