Homogeneous magnetization dynamics below T c of EuO: Effects of spin waves and anisotropy

Using a broadband reflectometer, the dynamic susceptibility χ(ω) of a EuO sphere has been measured from 0.3 to 20 GHz at temperatures ranging between 4.2 K and Tc=69.5 K. For fields applied parallel to the hard [100] direction one heavily damped Lorentzian is observed which for internal fields H larger and smaller than the anisotropy field arises from the dynamics of the homogeneous and the wall magnetization, respectively. For fields near HA applied along one of the easy [111] axes, both processes contribute to χ(ω) but with increased and decreased values of the resonances and damping frequencies of the homogeneous and wall processes, respectively. The homogeneous process is identified by the static susceptibility χz(0) which obeys the H−1/2 divergence due to spin waves. Its line shape is explained by a frequency variation of the kinetic coefficient of the relaxation damping, Lz(ω)=Lz(0)/[1+(iω/ωc)]. The characteristic frequency, ωc/2π=18 GHz, turns out to be independent of temperature and magnetic field, and is related to the relaxation rate of the long-wavelength longitudinal magnetization fluctuations. The field and temperature variation of the kinetic coefficient of the relaxation can be described by the same scaling function, Lz(χz(T,H)), as previously observed above Tc. Based on results of numerical mode-coupling work, this behavior is associated with the dipolar anisotropy of the magnetic fluctuations.