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  Karpinsky, D.; Eliseev, E.; Xue, F.; Silibin, M.; Franz, A.; Glinchuk, M.; Troyanchuk, I.; Gavrilov, S.; Gopalan, V.; Chen, L.-Q.; Morozovska, A.: Thermodynamic potential and phase diagram for multiferroic bismuth ferrite (BiFeO₃). npj Computational Materials 3 (2017), p. 20/1-10

10.1038/s41524-017-0021-3
Open Access Version

Abstract:
We construct a Landau–Ginzburg thermodynamic potential, and the corresponding phase diagram for pristine and slightly doped bismuth ferrite, a ferroelectric antiferromagnet at room temperature. The potential is developed based on new X-ray and neutron diffraction experiments complementing available data. We demonstrate that a strong biquadratic antiferrodistortive-type coupling is the key to a quantitative description of Bi1−x LaxFeO3 multiferroic phase diagram including the temperature stability of the antiferromagnetic, ferroelectric, and antiferrodistortive phases, as well as for the prediction of novel intermediate structural phases. Furthermore, we show that “rotomagnetic” antiferrodistortive–antiferromagnetic coupling is very important to describe the ferroelectric polarization and antiferrodistortive tilt behavior in the R3c phase of BiFeO3. The Landau–Ginzburg thermodynamic potential is able to describe the sequence of serial and trigger-type phase transitions, the temperature-dependent behavior of the order parameters, and the corresponding susceptibilities to external stimuli. It can also be employed to predict the corresponding ferroelectric and antiferrodistortive properties of Bi1−x La x FeO3 thin films and nanoparticles by incorporating the gradient and surface energy terms that are strongly dependent on the shape, size, and preparation method.