Figure 5. Real and imaginary parts of the eigenvalue of the coupled spin motion in azimuthal angle on different current densities.

The eigenvalues (ε) and eigenvectors of the coupled spin motion in azimuthal angle have been obtained with the method described in the text. Among the eigenvalues, the eigenvalue whose real part is the largest is plotted as a function of external field in the case of s = 0.8 nm. (a),(b) Real part Re(ε) calculated on the positive and negative current biases, respectively. Re(ε) has a tendency to increase with the increasing current densities. However, it becomes smaller and goes below zero around 45 mT irrespective of the current densities and polarities. (c),(d) Imaginary part Im(ε) calculated on the positive and negative current biases, respectively. Im(ε) shows similar frequency gap as the experiments and micromagnetic calculations. The relative phase of the spin oscillation between the FL and TPL has been identified through the eigenvectors. The schematic diagrams of the corresponding coupled spin motion are depicted in the inset of (c) and (d).