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The altermagnetism influences the electronic states allowing the presence ofnon-relativistic spinsplittings. Since altermagnetic spin-splitting is presentalong specific k-paths of the 3D Brillouin zone, we expect that thealtermagnetic surface states will be present on specific surface orientations.We unveil the properties of the altermagnetic surface states considering threerepresentative space groups: tetragonal, orthorhombic and hexagonal. Wecalculate the 2D projected Brillouin zone from the 3D Brillouin zone. We studythe surfaces with their respective 2D Brillouin zones establishing where thespin-splittings with opposite sign merge annihilating the altermagneticproperties and on which surfaces the altermagnetism is preserved. Looking atthe three principal surface orientations, we find that for several cases twosurfaces are blind to the altermagnetism, while the altermagnetism survives forone surface orientation. Which surface preserves the altermagnetism dependsalso on the magnetic order. We show that an electric field orthogonal to theblind surface can activate the altermagnetism. Our results predict whichsurfaces to cleave in order to preserve altermagnetism in surfaces orinterfaces and this paves the way to observe non-relativistic altermagneticspin-splitting in thin films via spin-resolved ARPES and to interface thealtermagnetism with other collective modes. We open future perspectives for thestudy of altermagnetic effects on the trivial and topological surface states.

Altermagnetic surface states: towards the observation and utilization of altermagnetism in thin films, interfaces and topological materials