Prediction of Room-Temperature Electric Field Reversal of Magnetization in the Family of $A_4B_3$O$_9$ Layered Oxides

The promise of a strong magnetoelectric (ME) coupling in a multiferroic (MF) material is not only of fundamental interest, but also forms the basis of next generation memory devices where the direction of magnetization can be reversed by an external electric field. Using group-theory led first-principles calculations, we determine the ME properties of a relatively understudied family of layered oxides with the general formula $A_4B_3$O$_9$. We show how the tetrahedral rotations in these oxides can lead to a variety of hitherto unknown structural phases with different symmetries. In particular, a polar phase in the $Cmc2_1$ space group has been identified where a weak ferromagnetic mode arises spontaneously via a canting of the antiferromagnetically ordered $B$-site spins. In this polar phase, the polar mode couples to the magnetic modes through a rare $\Gamma$-point ME-MF coupling scheme such that the net magnetization can be directly reversed by an electric field switching of the polar mode. Moreover, in agreement with previous experimental observations, we predict room-temperature magnetism in $A_4B_3$O$_9$ layered oxides which is supported by our calculations of the magnetic exchange interaction parameters, further indicating the potential of these compounds in practical technological applications.