Dipole-exchange modes in transversely magnetized ferromagnetic stripes

We present a theory of dipole-exchange modes in transversely magnetized ferromagnetic stripes of rectangular cross sections: a comparison is made with experimental results on Permalloy stripes. The model applies to very thin stripes (of the order of the exchange length): the magnetization is considered uniform over their thickness, and we consider modes of long wavelength along the longitudinal direction of the stripes. An applied magnetic field saturates the stripes along the transverse direction, and we also consider the effect of the exchange and dipolar fields. Under these assumptions we obtain the frequencies and shapes of the modes either considering free or pinned boundary conditions. We obtain good agreement with measurements of the frequency spectra in Permalloy nano wires of several rectangular cross sections: this happens for modes with appreciable amplitude throughout the samples. There is frequency disagreement for edge modes due to limitations of the model, since the effects of roughness, corners and imperfections at the edges of the samples are quite relevant in this case.