Synthesis and Characterization of Magnesium Co-Substituted M-Type Ferrites BaFe_12-x-yMg_xM_yO₁₉ with M = Zr, Hf

M-type hexaferrites are widely used in magnetic applications, and tailoring their properties via aliovalent substitution requires a detailed understanding of charge compensation and cation distribution. In this work, Mg²⁺/M⁴⁺ (M = Zr, Hf) co-substituted BaFe₁₂O₁₉ was synthesized via Na₂CO₃ flux and comprehensively characterized by wavelength-dispersive X-ray spectroscopy, powder and single-crystal X-ray diffraction, Rietveld refinement, X-ray absorption near-edge structure, and magnetic measurements. Increasing substitution levels x, y in BaFe_12-x-yMg_xM_yO₁₉ result in increasing lattice parameters and decreasing the room-temperature magnetic parameters saturation magnetization, remanence, and coercivity, while remanence and coercivity increase at low temperatures. Secondary phases form for nominal substitution ≥ 1. Zr⁴⁺ and Hf⁴⁺ preferentially occupy the 4f₂ site, whereas Mg²⁺ is distributed over multiple sites, as indicated by polyhedral volume analysis. Wavelength-dispersive X-ray spectroscopy confirms homogeneous elemental distribution within individual crystals but reveals significant variation in substitution levels within batches. The maximum degree of substitution for the tetravalent metals was y ≈ 1.2-1.7, with lower Mg incorporation of x ≈ 0.9-1.1. Charge compensation was found to be partially achieved via vacancy formation, while minor Fe²⁺ contributions cannot be excluded.