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Ferromagnetic resonance of exchange-coupled perpendicularly magnetized bilayers

Strong ferromagnetic interlayer exchange couplings $J$ in perpendicularly magnetized systems are becoming increasingly desirable for applications. We study whether ferromagnetic interlayer exchange couplings can be measured by a combination of broadband ferromagnetic resonance methods and magnetometry hysteresis loops. For this we model the switching and the eigenexcitations in bilayer systems comprising a soft layer coupled to a thicker harder layer that possesses higher perpendicular magnetic anisotropy. For large $J >0$ the switching fields are essentially independent of $J$ but the frequency of the optical eigenmode of the bilayer and the linewidth of the acoustical and optical eigenmode are directly sensitive to the coupling. We derive a corpus of compact analytical expressions to analyze these frequencies, their linewidth and discuss the meaning thereof. We illustrate this corpus on a system mimicking the fixed layers of a magnetic tunnel junction meant for spin torque applications.