We present a detailed study of the spin-torque diode effect in CoFeB/MgO/CoFe/NiFe magnetic tunnel junctions. From the evolution of the resonance frequency with magnetic field at different angles, we clearly identify the free-layer mode and find an excellent agreement with simulations by taking into account several terms for magnetic anisotropy. Moreover, we demonstrate the large contribution of the out-of-plane torque in our junctions with asymmetric electrodes compared to the in-plane torque. Consequently, we provide a way to enhance the sensitivity of these devices for the detection of microwave frequency
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