Fig. 1: Complex structure of BiFeO3.
From: Switching the spin cycloid in BiFeO3 with an electric field
a Schematic unit cell of BFO with P along \([111]\). In thin films, an electric field applied in-plane, (b) switches the polarization by 71\({{^\circ }}\) to \([\bar{1}11]\). In contrast, a field applied in the out-of-plane direction, (c) will drive successive 71° and 109° switches, resulting in a 180° final polarization along \([\bar{1}\bar{1}\bar{1}]\). d Iron moments in BFO are antiferromagnetically aligned along the \([111]\), modulated by the cycloid propagation along \({{{{{\boldsymbol{k}}}}}}\), \([\bar{1}10]\). Other allowed directions of \({{{{{\boldsymbol{k}}}}}}\) also lie within this \((111)\). The canting of the AFM alignment gives rise to an uncompensated magnetization, \(M({{{{{\boldsymbol{r}}}}}})\), which rotates primarily in the \({{{{{\boldsymbol{k}}}}}}\)-\({{{{{\boldsymbol{P}}}}}}\) plane with the same period as the antiferromagnetic moments, ~65 nm. e \(M\) is further frustrated by DMI associated with the octahedral rotations, giving rise to a modulation \({M}_{{SDW}}({{{{{\boldsymbol{r}}}}}})\) out of the \({{{{{\boldsymbol{k}}}}}}\)-\({{{{{\boldsymbol{P}}}}}}\), \((11\bar{2})\) plane. The \((11\bar{2})\) plane is shown by the shaded plane and \({M}_{{SDW}}\) points along the \([11\bar{2}]\) direction.
