Role of Shape Ellipticity on Dipole-Exchange Spin Waves in Ferromagnetic Nanorings

The properties of the quantized spin-wave frequencies and the transition field between the two stable magnetization states (the low-field vortex state and the higher-field onion state) are studied for elliptical nanorings. The dependences of these quantities on the nanoring sizes and the degree of ellipticity are examined over a wide range of values for the applied magnetic field and its orientation. The novel effects introduced when the symmetry axes of the inner elliptical edges of the rings are rotated relative to those of the outer elliptical edge are also studied. To characterize these effects, our theory makes use of a Hamiltonian-based dipole-exchange methodology, adapted from that used to elucidate the spin-wave modes in circular nanorings. It is found that spin-wave frequencies and the behavior of the transition field(s) depend sensitively on the degree of ellipticity, the rotation angle of the inner elliptical edge with respect to the outer elliptical edge, and the direction of the applied field relative to the nanoring axes.