Unveiling the Room-Temperature Magnetoelectricity of Troilite FeS

We report on a first-principles study of the troilite phase of iron sulfide (FeS). We show that even if, a few decades ago, this material was thought to be ferroelectric, the structural transition from the high P6_{3}/mmc to the low P6[over ¯]2c symmetry phase does not involve polar instabilities, though the space inversion center symmetry is broken. Our calculations and symmetry analysis nevertheless reveal that FeS is magnetoelectric at room temperature with a response larger than the prototypical room-temperature magnetoelectric crystal Cr_{2}O_{3}. We also show that the spin channel decomposition of the polarization exhibits nonzero values in the opposite direction in FeS, which is actually a general hint of the presence of a magnetoelectric monopole in diagonal magnetoelectrics.