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Current-induced magnetization excitations are studied for a spin-torque oscillator (STO) composed of a nanopillar with a perpendicular polarizer layer (PL), a MgO barrier layer, and a planar free layer (FL). By applying direct current and perpendicular-to-plane magnetic field, we measure resistance and radio-frequency electrical signal of the STO, which reflect magnetization motions of both PL and FL. Examination of the experimental results reveals that large-cone-angle magnetization oscillation occurs in the FL regardless of the current direction, whereas the PL magnetization shows principally either synchronized excitation with the FL oscillation or thermal-induced ferromagnetic resonance (FMR), depending on the current direction. Utilizing macrospin simulations, we show that hybridization of the excitation modes of the PL and FL through mutual dipolar field explains the magnetization dynamics. When the current flows from the PL to the FL, large-cone-angle oscillation of the FL magnetization occurs with the same rotation direction as that of FMR of the PL magnetization, leading to emergence of the synchronized excitation modes. On the other hand, when the current flows from the FL to the PL, the magnetization motions of the two layers have opposite rotation directions, and consequently, the PL and FL show their respective intrinsic excitation modes.