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Controlling Magnetic Order, Magnetic Anisotropy, and Band Topology in Semimetals ${\rm Sr(Mn_{0.9}Cu_{0.1})Sb_2}$ and ${\rm Sr(Mn_{0.9}Zn_{0.1})Sb_2}$

Neutron diffraction and magnetic susceptibility studies show that orthorhombic single-crystals of topological semimetals ${\rm Sr(Mn_{0.9}Cu_{0.1})Sb_2}$ and ${\rm Sr(Mn_{0.9}Zn_{0.1})Sb_2}$ undergo three dimensional C-type antiferromagnetic (AFM) ordering of the Mn$^{2+}$ moments at $T_N = 200\pm10$ and $210\pm12$ K, respectively, significantly lower than that of the parent SrMnSb$_2$ with $T_N=297 \pm 3$ K. Magnetization versus applied magnetic field (perpendicular to MnSb planes) below $T_N$ exhibits slightly modified de Haas van Alphen oscillations for the Zn-doped crystal as compared to that of the parent compound. By contrast, the Cu-doped system does not show de Haas van Alphen magnetic oscillations, suggesting that either Cu substitution for Mn changes the electronic structure of the parent compound substantially, or that the Cu sites are strong scatterers of carriers that significantly shorten their mean free path thus diminishing the oscillations. Density functional theory (DFT) calculations including spin-orbit coupling predict the C-type AFM state for the parent, Cu-, and Zn-doped systems and identify the $a$-axis (i.e., perpendicular to the Mn layer) as the easy magnetization direction in the parent and 12.5% of Cu or Zn substitutions. In contrast, 25% of Cu content changes the easy magnetization to the $b$-axis (i.e., within the Mn layer). We find that the incorporation of Cu and Zn in SrMnSb$_2$ tunes electronic bands near the Fermi level resulting in different band topology and semi-metallicity. The parent and Zn-doped systems have coexistence of electron and hole pockets with opened Dirac cone around the Y-point whereas the Cu-doped system has dominant hole pockets around the Fermi level with a distorted Dirac cone. The tunable electronic structure may point out possibilities of rationalizing the experimentally observed de Haas van Alphen magnetic oscillations.