Weak ferromagnetism in perovskite oxides

Weak ferromagnetism has been widely found in antiferromagnetic systems, including the technically important orthorhombic perovskites $R\mathrm{Fe}{\mathrm{O}}_{3}$ ($R=\mathrm{rare}\phantom{\rule{0.16em}{0ex}}\mathrm{earth}$) owing to spin canting associated with crystal symmetry. Antisymmetric exchange interaction (AEI) and single-ion anisotropy (SIA) are the essential mechanisms responsible for the development of noncollinear structures in antiferromagnetic systems. AEI and SIA share the same structural restriction to facilitate the spin canting. While both AEI and SIA originate from the spin-orbit coupling effect, they have sharply different dependences on the local structure. Consideration of the structural dependence of a canted spin motivates us to revisit the orthoferrite family. The spin canting along the $c$ axis measured on precisely oriented crystals increases monotonically from $\mathrm{La}\mathrm{Fe}{\mathrm{O}}_{3}$ to $\mathrm{Lu}\mathrm{Fe}{\mathrm{O}}_{3}$. Based on Moriya's model, AEI is sensitive to the octahedral-site distortion in the perovskite structure. However, the site distortion does not exhibit a monotonic change with the rare-earth substitution. Instead, a linear relationship has been found in both the octahedral rotation and the spin canting angle versus the rare-earth ionic radius, which indicates that SIA plays a significant role leading the spin canting in orthoferrites.