Using the theory of symmetry and the microscopic model we predict the possibility of a linear antiferrodistortive-antiferromagnetic effect in the perovskites with structural antiferrodistortive and antiferromagnetic long-range ordering and find the necessary conditions of its occurrence. The main physical manifestations of this effect are the smearing of the antiferromagnetic transition and the jump of the specific heat near it. In the absence of external fields, linear antiferrodistortive-antiferromagnetic coupling can induce a weak antiferromagnetic ordering above the Neel temperature, but below the temperature of antiferrodistortive transition. Therefore, there is the possibility of observing weak improper antiferromagnetism in multiferroics such as bismuth ferrite ($\mathrm{BiFe}{\mathrm{O}}_3$) at temperatures $T>T_N$, for which the Neel temperature $T_N$ is about 645 K, and the antiferrodistortive transition temperature is about 1200 K. The improper mechanism may explain the antiferromagnetic order existence well above $T_N$ in ${\mathrm{BiFeO}}_3$ revealed by optical second harmonic generation. By quantitative comparison to the experiment we made estimations of the linear antiferrodistortive-antiferromagnetic effect in the solid solutions of multiferroic $\mathrm{B}{\mathrm{i}}_{1-\mathrm{x}}{\mathrm{R}}_{\mathrm{x}}\mathrm{Fe}{\mathrm{O}}_3$ ($\mathrm{R}=\mathrm{La},\mathrm{Nd}$).

• Received 15 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.054421