Extrinsic and Intrinsic Nonlinear Planar Hall Effect in T_d-MoTe₂

T_d-MoTe₂, a semimetallic material with broken inversion symmetry, allows a rich variety of nonlinear transport phenomena which may manifest intriguing quantum geometry of the band structure. Here, we report the observation of a nonlinear planar Hall effect in T_d-MoTe₂ over a broad temperature range (2 to 150 K). The nonlinear Hall voltage scales quadratically (linearly) with the applied electric (magnetic) field and shows distinct angular dependence on the in-plane magnetic field: a cosine (sine) relationship when the electric field aligns with the a axis (b axis). Combined first-principles calculations and scaling analysis of experimental data reveal two scaling terms, including an intrinsic contribution from Berry connection polarizability of band structure and an extrinsic nonlinear Drude-like contribution. This study not only expands the understanding of nonlinear Hall transport mechanisms in low-symmetry materials but also suggests potential applications in precision magnetic field sensing and electronic devices exploiting directional charge transport.