Ferromagnetism in ZnO films doped with 5 at% of Sc, Ti, V, Fe, Co, or Ni is observed at room temperature, but not for Cr, Mn, or Cu. The magnetic moments are 1.9 and 0.5 μB/atom for Co- and Ti-substituted oxides, respectively, and 0.3 μB/Sc for Sc-substituted ZnO. Magnetization is highly anisotropic, varying by a factor of three depending on the orientation of the applied field relative to the R-cut sapphire substrates. The results are explained by a spin-split donor impurity band model, which accounts for ferromagnetism in insulating or conducting high-k oxides with magnetic ion concentrations far below the percolation threshold. The variation of ferromagnetism with oxygen pressure during film growth suggests a link between ferromagnetism and defect concentration. The study examines the systematic variation of magnetism in (Zn1-xMx)O films with different transition metals M at fixed concentration x = 5%, varying x for M = Co, and varying oxygen pressure during film growth. Films were prepared by pulsed-laser deposition using a KrF excimer laser. The films are transparent and strongly textured, showing only the (110) reflection of the wurtzite structure. The composition was determined by EDAX analysis. Substitution of Co cations in the tetrahedral sites of the wurtzite structure was confirmed by optical spectroscopy. Characteristic optical absorption bands were identified with d-d transitions of Co²+ ions. The magnetic moment varies systematically across the (Zn0.95M0.05)O series, with maxima near Ti and Co. No moment was observed for Cr, Mn, Cu, or Zn. Ferromagnetism in (Zn0.95Sc0.05)O is surprising as neither Zn²+ nor Sc³+ are magnetic ions. The magnetization anisotropy is large, with the moment being greatest when the field is applied perpendicular to the film plane. The moment per Co varies significantly in the plane of the film. The films show n-type conductivity at low oxygen pressure and insulating behavior at higher pressure. The magnetic moment decreases as the carrier concentration increases. The model explains the magnetic moment variation in terms of random distribution of Co ions and antiferromagnetic coupling. The spin-split donor impurity band model explains the ferromagnetism in high-k dielectrics doped with transition-metal ions. The large anisotropy and giant moments are unusual and may arise from the impurity band's d character or oriented magnetic point defects. The valence of the substitutional 3d ions changes along the series, with Co being divalent and Ti trivalent. The electronic structure calculations are needed to define the roleFerromagnetism in ZnO films doped with 5 at% of Sc, Ti, V, Fe, Co, or Ni is observed at room temperature, but not for Cr, Mn, or Cu. The magnetic moments are 1.9 and 0.5 μB/atom for Co- and Ti-substituted oxides, respectively, and 0.3 μB/Sc for Sc-substituted ZnO. Magnetization is highly anisotropic, varying by a factor of three depending on the orientation of the applied field relative to the R-cut sapphire substrates. The results are explained by a spin-split donor impurity band model, which accounts for ferromagnetism in insulating or conducting high-k oxides with magnetic ion concentrations far below the percolation threshold. The variation of ferromagnetism with oxygen pressure during film growth suggests a link between ferromagnetism and defect concentration. The study examines the systematic variation of magnetism in (Zn1-xMx)O films with different transition metals M at fixed concentration x = 5%, varying x for M = Co, and varying oxygen pressure during film growth. Films were prepared by pulsed-laser deposition using a KrF excimer laser. The films are transparent and strongly textured, showing only the (110) reflection of the wurtzite structure. The composition was determined by EDAX analysis. Substitution of Co cations in the tetrahedral sites of the wurtzite structure was confirmed by optical spectroscopy. Characteristic optical absorption bands were identified with d-d transitions of Co²+ ions. The magnetic moment varies systematically across the (Zn0.95M0.05)O series, with maxima near Ti and Co. No moment was observed for Cr, Mn, Cu, or Zn. Ferromagnetism in (Zn0.95Sc0.05)O is surprising as neither Zn²+ nor Sc³+ are magnetic ions. The magnetization anisotropy is large, with the moment being greatest when the field is applied perpendicular to the film plane. The moment per Co varies significantly in the plane of the film. The films show n-type conductivity at low oxygen pressure and insulating behavior at higher pressure. The magnetic moment decreases as the carrier concentration increases. The model explains the magnetic moment variation in terms of random distribution of Co ions and antiferromagnetic coupling. The spin-split donor impurity band model explains the ferromagnetism in high-k dielectrics doped with transition-metal ions. The large anisotropy and giant moments are unusual and may arise from the impurity band's d character or oriented magnetic point defects. The valence of the substitutional 3d ions changes along the series, with Co being divalent and Ti trivalent. The electronic structure calculations are needed to define the role