A theoretical model for the calculation of the quantized spectrum of spin modes frequencies in cylindrical magnetic dots of radius ranging from the nanometric to the submicrometric scale in the vortex ground state is presented [1]. We take into account of the core energy showing its effect on the spin dynamics. At zero applied field the surface modes at lower frequencies present as radial eigenvectors Bessel functions of high orders (m . 1), while the axially symmetric modes at higher frequencies correspond to zero order Bessel functions. The out-of-core and core dipolar field components are calculated exactly for both axially symmetric and diametrically symmetric vortex spin modes and the effect on the spin dynamics is studied. A comparison of this calculation with the spin modes frequencies obtained using the local approximation is performed both considering a dependence of the dynamic magnetization from the dot thickness and assuming uniform magnetization. The dynamics of volume modes in the vortex state is also quantitatively studied within this model. The frequency splitting of the m = + -1 modes [2] is explained in terms of the different energy contribution of the two corresponding spin modes dipolar fields and compares well with available experimental data. An expression for the gyrotropic mode, classified in this framework as a pseudo- Goldstone excitation because of the presence of a static core field, is derived and its frequency is compared to the measured one for various aspect ratios. The model is generalized [3] to determine the spin dynamics in the vortex state, but under an external applied field. Both the regime when the vortex centre is inside the dot and that when it is outside it are considered and their effect on the quantized spin modes is studied. It is shown that the spin modes profiles are affected by the broken symmetry induced by the external field. The spin modes frequencies also depend from additional effective fields absent at vanishing applied field. [1] R. Zivieri and F. Nizzoli, Phys. Rev. B 71 (2005) 014411 [2] R. Zivieri in preparation [3] R. Zivieri in preparation -- Presentazione orale by R. Zivieri - Conferenza internazionale
Theory of spin modes in the vortex state -- Presentazione orale by R. Zivieri - Conferenza internazionale
ZIVIERI, Roberto
2006
Abstract
A theoretical model for the calculation of the quantized spectrum of spin modes frequencies in cylindrical magnetic dots of radius ranging from the nanometric to the submicrometric scale in the vortex ground state is presented [1]. We take into account of the core energy showing its effect on the spin dynamics. At zero applied field the surface modes at lower frequencies present as radial eigenvectors Bessel functions of high orders (m . 1), while the axially symmetric modes at higher frequencies correspond to zero order Bessel functions. The out-of-core and core dipolar field components are calculated exactly for both axially symmetric and diametrically symmetric vortex spin modes and the effect on the spin dynamics is studied. A comparison of this calculation with the spin modes frequencies obtained using the local approximation is performed both considering a dependence of the dynamic magnetization from the dot thickness and assuming uniform magnetization. The dynamics of volume modes in the vortex state is also quantitatively studied within this model. The frequency splitting of the m = + -1 modes [2] is explained in terms of the different energy contribution of the two corresponding spin modes dipolar fields and compares well with available experimental data. An expression for the gyrotropic mode, classified in this framework as a pseudo- Goldstone excitation because of the presence of a static core field, is derived and its frequency is compared to the measured one for various aspect ratios. The model is generalized [3] to determine the spin dynamics in the vortex state, but under an external applied field. Both the regime when the vortex centre is inside the dot and that when it is outside it are considered and their effect on the quantized spin modes is studied. It is shown that the spin modes profiles are affected by the broken symmetry induced by the external field. The spin modes frequencies also depend from additional effective fields absent at vanishing applied field. [1] R. Zivieri and F. Nizzoli, Phys. Rev. B 71 (2005) 014411 [2] R. Zivieri in preparation [3] R. Zivieri in preparation -- Presentazione orale by R. Zivieri - Conferenza internazionaleI documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
