Ferromagnetic polar metals via epitaxial strain: a case study of SrCoO$_3$

While polar metals are a metallic analogue of ferroelectrics, magnetic polar metals can be considered as a metallic analogue of multiferroics. There have been a number of attempts to integrate magnetism into a polar metal by synthesizing new materials or heterostructures. Here we use a simple yet widely used approach--epitaxial strain in the search for intrinsic magnetic polar metals. Via first-principles calculations, we study strain engineering of a ferromagnetic metallic oxide SrCoO$_3$, whose bulk form crystallizes in a cubic structure. We find that under an experimentally feasible biaxial strain on the $ab$ plane, collective Co polar displacements are stabilized in SrCoO$_3$. Specifically, a compressive strain stabilizes Co polar displacements along the $c$ axis, while a tensile strain stabilizes Co polar displacements along the diagonal line in the $ab$ plane. In both cases, we find an intrinsic ferromagnetic polar metallic state in SrCoO$_3$. In addition, we also find that a sufficiently large biaxial strain ($> 4\%$) can yield a ferromagnetic-to-antiferromagnetic transition in SrCoO$_3$. Our work demonstrates that in addition to yielding emergent multiferroics, epitaxial strain is also a viable approach to inducing magnetic polar metallic states in quantum materials.