Weak ferromagnetism has been widely found in antiferromagnetic systems, including the technically important orthorhombic perovskites $R\mathrm{Fe}{\mathrm{O}}_3$ ($R=\mathrm{rare}\mathrm{earth}$) 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.

中文翻译：

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钙钛矿氧化物中的弱铁磁性

在反铁磁系统中已广泛发现弱铁磁性，包括技术上重要的正交晶系钙钛矿 $\mathrm{[R}铁{\mathrm{Ø}}_3$ （$\mathrm{[R}=\mathrm{罕见}\mathrm{地球}$）是由于与晶体对称性相关的自旋倾斜。反对称交换相互作用（AEI）和单离子各向异性（SIA）是负责反铁磁系统中非共线结构发展的基本机制。AEI和SIA具有相同的结构限制，以促进旋转倾斜。尽管AEI和SIA都源自自旋轨道耦合效应，但它们对局部结构的依赖性却截然不同。对倾斜自旋的结构依赖性的考虑促使我们重新审视正铁素体族。沿着$C$ 在精确定向的晶体上测量的轴从 $啦铁{\mathrm{Ø}}_3$ 至 $鲁铁{\mathrm{Ø}}_3$。基于Moriya的模型，AEI对钙钛矿结构中八面体位点的变形敏感。但是，用稀土取代，位点畸变不会表现出单调变化。相反，在八面体旋转和自旋倾斜角与稀土离子半径之间都发现了线性关系，这表明SIA在正铁氧体中起自旋倾斜的重要作用。