Complete mapping of the spin-wave spectrum in vortex state nano-disk
  We report a study on the complete spin-wave spectrum inside a vortex state nano-disk. Transformation of this spectrum is continuously monitored as the nano-disk becomes gradually magnetized by a perpendicular magnetic field and encouters a second order phase transition to the uniformly magnetized state. This reveals the bijective relationship that exists between the eigen-modes in the vortex state with the ones in the saturated state. It is found that the gyrotropic mode can be continuously viewed as a uniform phase precession, which uniquely softens (its frequency vanishes) at the saturation field to transform above into the Kittel mode. By contrast the other spin-wave modes remain finite as a function of the applied field while their character is altered by level anti-crossing. 
Boris Taurel, Thierry Valet, Vladimir V. Naletov, Nicolas Vukadinovic,   Gr\'egoire de Loubens, and Olivier Klein
cond-mat.mes-hall