A 20% substitution of Bi with La in the perovskite ${\mathrm{Bi}}_{1-x}{\mathrm{La}}_x{\mathrm{Fe}}_{0.5}{\mathrm{Sc}}_{0.5}{\mathrm{O}}_3$ system obtained under high-pressure and high-temperature conditions has been found to induce an incommensurately modulated structural phase. The room-temperature x-ray and neutron powder diffraction patterns of this phase were successfully refined using the $Imma(0,0,\gamma )s00$ superspace group ($\gamma =0.534\left(3\right)$) with the modulation applied to Bi/La and oxygen displacements. The modulated structure is closely related to the prototype antiferroelectric structure of ${\mathrm{PbZrO}}_3$ which can be considered as the lock-in variant of the latter with $\gamma =0.5$. Below $T_{\mathrm{N}}\sim 220$ K, the neutron diffraction data provide evidence for a long-range $G$-type antiferromagnetic ordering commensurate with the average $Imma$ structure. Based on a general symmetry consideration, we show that the direction of the spins is controlled by the antisymmetric exchange imposed by the two primary structural distortions, namely oxygen octahedral tilting and incommensurate atomic displacements. The tilting is responsible for the onset of a weak ferromagnetism, observed in magnetization measurements, whereas the incommensurate displacive mode is dictated by the symmetry to couple a spin-density wave. The obtained results demonstrate that antisymmetric exchange is the dominant anisotropic interaction in $\mathrm{Fe}^{3+}$-based distorted perovskites with a nearly quenched orbital degree of freedom.

• Received 8 April 2015
• Revised 14 October 2015

DOI:https://doi.org/10.1103/PhysRevB.92.224428