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Abstract Non‐collinear antiferromagnets (AFMs) are an exciting new platform for studying intrinsic spin Hall effects (SHEs), phenomena that arise from the materials’ band structure, Berry phase curvature, and linear response to an external electric field. In contrast to conventional SHE materials, symmetry analysis of non‐collinear antiferromagnets does not forbid non‐zero longitudinal and out‐of‐plane spin currents with polarization and predicts an anisotropy with current orientation to the magnetic lattice. Here, multi‐component out‐of‐plane spin Hall conductivities are reported in L1₂‐ordered antiferromagnetic PtMn₃thin films that are uniquely generated in the non‐collinear state. The maximum spin torque efficiencies (ξ  =J_S /J_e ≈ 0.3) are significantly larger than in Pt (ξ  ≈  0.1). Additionally, the spin Hall conductivities in the non‐collinear state exhibit the predicted orientation‐dependent anisotropy, opening the possibility for new devices with selectable spin polarization. This work demonstrates symmetry control through the magnetic lattice as a pathway to tailored functionality in magnetoelectronic systems.