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We put forward double perovskites of the R$_2$NiMnO$_6$ family (with $R$ arare-earth atom) as a new class of multiferroics on the basis of {\it abinitio} density functional calculations. We show that changing $R$ from La to Ydrives the ground-state from ferromagnetic to antiferromagnetic with$\uparrow\uparrow\downarrow\downarrow$ spin patterns. This E$^*$-type orderingbreaks inversion symmetry and generates a ferroelectric polarization of few$\mu C/cm^2$. By analyzing a model Hamiltonian we understand the microscopicorigin of this transition and show that an external electric field can be usedto tune the transition, thus allowing electrical control of the magnetization.

Theoretical prediction of multiferroicity in double perovskite Y$_2$NiMnO$_6$