  Using the theory of symmetry and the microscopic model we predicted the
possibility of a linear roto-antiferromagnetic effect in the perovskites with
structural antiferrodistortive and antiferromagnetic long-range ordering and
found 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 roto-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 antiferromagnetism in multiferroics such as
bismuth ferrite (BiFeO3) at temperatures T>TN, for which the Neel temperature
TN is about 645 K, and the antiferrodistortive transition temperature is about
1200 K. By quantitative comparison with experiment we made estimations of the
linear roto-antiferromagnetic effect in the solid solutions of multiferroic
Bi1-xRxFeO3 (R=La, Nd).
