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Magnetism and Antiferroelectricity in MgB$_6$

We report on a density functional theory study demonstrating the coexistence of weak ferromagnetism and antiferroelectricity in boron-deficient MgB6. A boron vacancy produces an almost one dimensional extended molecular orbital, which is responsible for the magnetic moment formation. Then, long-range magnetic order can emerge from the overlap of such orbitals above percolation threshold. Although there is a finite density of states at the Fermi level, the localized nature of the charge density causes an inefficient electron screening. We find that the Mg ions can displace from the center of their cubic cage, thus generating electrical dipoles. In the ground state these order in an antiferroelectric configuration. If proved experimentally, this will be the first material without d or f electrons displaying the coexistence of magnetic and electric order.