Rotomagnetic couplings influence on the magnetic properties of antiferrodistortive antiferromagnets

We consider the possibility to control multiferroic properties of paraelectric antiferromagnets via biquadratic rotomagnetic (RM) coupling. Using Landau-Ginzburg-Devonshire theory for EuTiO₃ as a prototype, we reveal a surprisingly strong influence of the RM coupling in the temperature region of antiferromagnetic and antiferrodistotive phases coexistence. In particular, the observed Neel temperature (T_N = 5.5 K) was shown to be defined by RM coupling, while without the RM coupling, T_N appeared to be much higher (T_N ≈ 25.2 K). For weak RM coupling, the antiferromagnetic phase transition appeared to be of the second order, while it becomes of the first order for the high enough RM coupling values. RM coupling significantly complicates the phase diagrams governed by external magnetic or electric fields. The critical value of the electric field required to induce the transition from antiferromagnetic to ferromagnetic phase appeared essentially smaller than the one calculated without RM coupling that can be important for applications.