Spin-gapless semiconductors (SGSs), with intrinsic magnetism, $100\%$ spin polarization, and zero-gap band crossing points, have attracted great scientific interest owing to their potential applications in spintronics. In this Letter, using first-principles calculations and symmetry analysis, we demonstrate that the realistic material ${\mathrm{Sr}}_2{\mathrm{CuF}}_6$ is a spintronic material with multiple dimensions of spin-gapless semiconducting states. Tetragonal ${\mathrm{Sr}}_2{\mathrm{CuF}}_6$ has a zero-dimensional zero-gap nodal point, a one-dimensional zero-gap nodal line, and a two-dimensional nearly zero-gap nodal surface in one spin direction. Moreover, it hosts a wide band gap in the other spin direction. Our results extend the SGS members from nodal point SGSs and nodal line SGSs to nodal surface SGSs. Furthermore, we report a SGS candidate in an experimentally realized material exhibiting different dimensions of zero-gap points in momentum space. It is hoped that spintronic materials with multiple dimensions of spin-gapless semiconducting states may have significant applications in new-generation spintronics.

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• Electronic structure
• Spin polarization
• Spintronics
• Half-metals
• Magnetic systems
• Topological materials
• Band structure methods