Compared to its ferromagnetic (FM) counterpart, the Griffiths singularity arising from antiferromagnetic (AF) rare regions remains much less explored. Here, we investigate this rare-region effect in Fe-doped perovskite manganites ${\mathrm{La}}_{0.67}{\mathrm{Sr}}_{0.33}{\mathrm{Mn}}_{1-y}{\mathrm{Fe}}_y{\mathrm{O}}_3$ (LSMFO). We observe that Fe doping suppresses the long-range FM order and induces a metal-to-insulator transition at a percolation threshold $y_c^{\mathrm{MI}}\simeq 0.18$, dual to the insulator-to-metal transition at $x_c^{\mathrm{IM}}\simeq 0.175$ in ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ (LSMO). Extending this percolation duality, we find corroborating evidence for a dual AF Griffiths phase in LSMFO, with a percolation threshold $y_c^{\mathrm{AG}}$ closely mirroring that of the FM Griffiths phase in LSMO $(x_c^{\mathrm{FG}}\simeq 0.07)$. Furthermore, we demonstrate that strong disorder and frustration, mediated by the Griffiths rare regions, destabilize both long-range FM and AF correlations, culminating in a low-temperature spin glass state for $y\ge 0.18$. Our work thus establishes a unified perspective for understanding rare-region effects in systems involving competing FM and AF exchange interactions.

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• Doping effects
• Electrical conductivity
• Lattice dynamics
• Magnetic phase transitions
• Percolation
• Phase diagrams