DOI:https://doi.org/10.1103/PhysRevB.99.184444

We report a description and comprehensive study on four successive magnetic transitions in ferromagnetic $T{b}_2\mathrm{MnNi}{O}_6$ double perovskite. In the ground state ($P{2}_1^{\prime }$), the moments of magnetic $A$and $B$ sites order according to different nonpolar magnetic modes, but the coupling between them generates an overall polar symmetry which makes this oxide potentially multiferroic due to magnetic trilinear coupling, and therefore ferromagnetic and ferroelectric in its ground state. Its macroscopic magnetization is large ($5{\mu }_B/f.u$) and not related to a weak ferromagnetic component induced by Dzyaloshinskii-Moriya interaction. However, a sharp and severe spin reorientation of the ferromagnetic transition-metal moments has been observed which opens the door to the magnetic switching of the ferroelectric state in this perovskite, and conversely to the control of the magnetization direction by electrical fields applied parallel to $b$. We also anticipate that in this material the direction of the magnetization (towards $c/a$) could be used as the key to switch the polar/nonpolar (ferroelectric/antiferroelectric) transformation.