Radio Frequency Techniques

Nonlocal torque operators inab initiotheory of the Gilbert damping in random ferromagnetic alloys

“…These relations reflect the fact that an infinitesimal deviation towards x axis results from an infinitesimal rotation of the magnetization vector around y axis and vice versa. Note that the other components of the Gilbert damping tensor (α µz for µ = x, y, z) are not relevant for the dynamics of small deviations of magnetization direction described by the LLG equation (1). For the groundstate magnetization pointing along a general unit vector m = (m x , m y , m z ), one has to employ the Levi-Civita symbol ǫ µνλ in order to get the Gilbert damping tensor α as…”

“…While a complete picture of magnetization dynamics including, e.g., excitation of magnons and their interaction with other degrees of freedom, is still a challenge for the modern theory of magnetism, remarkable progress has been achieved during the last years concerning the dynamics of the total magnetic moment, which can be probed experimentally by means of the ferromagnetic resonance 1 or by the time-resolved magneto-optical Kerr effect. 2 Time evolution of the macroscopic magnetization vector M can be described by the well-known Landau-Lifshitz-Gilbert (LLG) equation 3,4 …”

Gilbert Damping in Single and Multilayer Ultrathin Films: Role of Interfaces in Nonlocal Spin Dynamics

“…The in-plane FMR (the saturation magnetization and external field are confined to the film plane) experiments were carried out using 10, 24, and 36 GHz systems [10]. The FMR linewidth was measured as the difference in the magnetic fields between the maximum and minimum of the field derivative of the FMR absorption peak, ≠x 00 ͞≠H [10].…”

“…The FMR linewidth was measured as the difference in the magnetic fields between the maximum and minimum of the field derivative of the FMR absorption peak, ≠x 00 ͞≠H [10]. The in-plane resonance fields and resonance linewidths were measured as a function of the azimuthal angle w between the external dc magnetic field H and the Fe in-plane cubic axis.…”

“…They were covered by a 20-ML-thick Au(001) cap layer for protection in ambient conditions. The FMR measurements were used to determine the in-plane fourfold and uniaxial magnetic anisotropies, K 1 and K u , and the effective demagnetizing field perpendicular to the film surface, 4pM eff , as a function of thickness [10]. The results are shown in Fig.…”