Spin-polarized electronic states and atomic reconstructions at antiperovskite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>Sn</mml:mi><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>001</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> polar surfaces

We report a first-principles investigation of the atomic and electronic properties at perfect defective (001) surfaces antiperovskite ${\mathrm{Sr}}_{3}\mathrm{Sn}\mathrm{O}$. first performed thermodynamical study structure terminations demonstrated that SrSn-terminated should be most stable one, either with $(1\ifmmode\times\else\texttimes\fi{}1$) or $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstruction induced by formation Sn vacancies. detailed surface gap states obtained for these surfaces, which we compare those other terminations, also having relatively low energies. These states, located near Fermi level, could have major contribution to transport properties. Due lack inversion symmetry associated surface, predict they experience spin splittings, an important property spin-orbitronic applications. Finally, found ${\mathrm{Sr}}_{2}\mathrm{O}$-terminated display ferromagnetic ordering resulting from population $4d$ orbitals Sr atoms this lead spin-polarized two-dimensional electron gas.