Coupling of Circuit Structures to Magnetostatic Modes of Ferromagnetic Resonators

The coupling between a current-carrying circuit structure and the magnetostatic modes of a general ferromagnet, such as a YIG resonator, is examined. A small-signal theory is presented that describes the excitation of an arbitrary mode in terms of an effective susceptibility matrix; this description leads to a simple method for calculating the z parameters of the resonator and coupling structure combination. This result is tested by comparison with other theory and with experiment. Applied to the case of a uniform field exciting the uniform mode of an ellipsoidal resonator, it reduces to Carter´s well-known formula. Applied to the case of a particular nonuniform field exciting the main mode of a thin square resonator, it predicts the experimental finding that the coupling strength depends only on the resonator´s thickness. This last case illustrates the extended generality of our result which allows the treatment of situations where the RF magnetization and field are not uniform.