  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.
