Magnetocrystalline anisotropy in iron garnets originates from the interplay between lattice symmetry, cation site preference, and spin-orbit coupling mediated by oxygen. We develop a dual order parameter framework that quantitatively connects site-selective occupation of inequivalent dodecahedral ($24c$) sublattices to the magnetic anisotropy energy in Bi substituted yttrium iron garnet (Bi:YIG). We introduce a site-order parameter ${\eta }_{\text{so}}$ (sublattice imbalance between $\alpha$ and $\beta$ within $24c$) and a composition parameter ${\eta }_{\text{co}}$ (total Bi fraction on $24c$) and use density-functional theory across 13 representative $({\eta }_{\text{so}},{\eta }_{\text{co}})$ states. $K({\eta }_{\text{so}},{\eta }_{\text{co}})$ obeys a compact Landau-type expansion dominated by a large odd-in-${\eta }_{\text{so}}$ linear term and a weaker even-in-${\eta }_{\text{so}}$ curvature. The fitted map yields an analytic switching boundary $K=0$ in the $({\eta }_{\text{so}},{\eta }_{\text{co}})$ plane and order-resolved three-dimensional surfaces and weight maps that make the hierarchy (linear $\gg$ quadratic $\gg$ cubic) explicit. This unified framework rationalizes growth-induced anisotropy trends in Bi:YIG and suggests actionable routes for engineering uniaxial anisotropy via controlled $A$-sublattice ordering.

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• Magnetic anisotropy
• Order parameters
• Complex oxides
• Density functional calculations