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Magneto-electric coupling in type-I multiferroic ScFeO$_3$

We investigate the electronic structure and the ferroelectric properties of the recently discovered multiferroic ScFeO$_3$ by means of ab-initio calculations. The $3d$ manifold of Fe in the half-filled configuration naturally favors an antiferromagnetic ordering, with a theoretical estimate of the antiferromagnetic Néel temperature in good agreement with the experimental values. We find that the inversion symmetry-breaking is driven by the off-centering of Sc atoms, which results in a large ferroelectric polarization of $\sim$105\,$μ$C/cm$^{2}$. Surprisingly the ferroelectric polarization is sensitive to the local magnetization of the Fe atoms resulting in a large negative magnetoelectric interaction. This behavior is unexpected in type-I multiferroic materials because the magnetic and ferroelectric orders are of different origins.