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We propose a way to use electric-field to control the magnetic ordering ofthe tetragonal BiFeO3. Based on systematic first-principles studies of theepitaxial strain effect on the ferroelectric and magnetic properties of thetetragonal BiFeO3, we find that there exists a transition from C-type to G-typeantiferromagnetic (AFM) phase at in-plane constant a ~ 3.905 {\AA} when theferroelectric polarization is along [001] direction. Such magnetic phasetransition can be explained by the competition between the Heisenberg exchangeconstant J1c and J2c under the influence of biaxial strain. Interestingly, whenthe in-plane lattice constant enlarges, the preferred ferroelectricpolarization tends to be canted and eventually lies in the plane (along [110]direction). It is found that the orientation change of ferroelectricpolarization, which can be realized by applying external electric-field, hassignificant impact on the Heisenberg exchange parameters and therefore themagnetic orderings of tetragonal BiFeO3. For example, at a ~ 3.79 {\AA}, anelectric field along [111] direction with magnitude of 2 MV/cm could change themagnetic ordering from C-AFM to G-AFM. As the magnetic ordering affects manyphysical properties of the magnetic material, e.g. magnetoresistance, we expectsuch strategy would provide a new avenue to the application of multiferroicmaterials.

Electric-field control of magnetic ordering in the tetragonal BiFeO3