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In this paper, we demonstrate the feasibility of nonlinear spin-orbit interactions in thin films of materials with second-order nonlinear susceptibility. Remarkably, the nonlinear tensor can mix the longitudinal and transverse components of the pump field. We observe experimentally our theoretical predictions in the process of second-harmonic generation from a thin film of aluminum gallium arsenide, a material platform widely spread for its role in the advancement of active, nonlinear, and quantum photonic devices. 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