L. Giovannini

Combined Frequency-Amplitude Nonlinear Modulation: Theory and Applications

In this paper, we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal. The derived analytical solution may give a satisfactory explanation of recent laboratory observations on magnetic spin-transfer oscillators and fully agrees with results of micromagnetic calculations. Since the theory has been developed independently of the mechanism causing the nonlinearities, it may encompass the description of modulation processes of any physical nature, a promising feature for potential applications in the field of communication systems.

Elastic and elasto‐optic properties of thin films of poly(styrene) spin coated onto Si(001)

Brillouin light scattering (BLS) has been used to study a series of three thin films of poly(styrene) spin coated onto Si(001) wafers. Poly(styrene) molecular weights Mw of 30 000 and 600 000 were used, and the film thicknesses h were in the range 1730 A<h<3750 A. It was found that the poly(styrene) films have isotropic elastic symmetry and that all of the films can be described by the same set of two independent elastic constants c11=5.7±0.15 GPa and c44=1.39±0.03 GPa. Both c11 and c44 were determined unambiguously using a least‐squares‐fitting procedure by observation of the longitudinal guided and Rayleigh modes of the poly(styrene) films. Calculations have been performed of the BLS spectra which include both surface ripple and elasto‐optic light scattering mechanisms. From comparisons of the relative mode intensities in the measured and calculated BLS spectra, it is found that the values of the elasto‐optic coefficients for poly(styrene) are k11=−1.4±0.4 and k12=−1.6±0.4.

Brillouin scattering by pseudosurface acoustic modes on (11(mean)1) GaAs

The authors have studied the propagation of pseudosurface acoustic modes on the (11(mean)1) plane of GaAs. From a calculation of the surface density of phonon states, two resonances are found in the continuum of modes, corresponding to the pseudosurface acoustic modes, called PSM and HFPSM. Experimental evidence for these modes is given by Brillouin spectra taken for different directions on the (11(mean)1) plane of a GaAs crystal. They found a good agreement between the experimental spectra and the theoretical cross sections, calculated taking into account both the ripple and the elasto-optic contributions to the scattering process.

Asymmetry of spin wave dispersions in a hexagonal magnonic crystal

We report a study of the dispersion of spin waves in a hexagonal array of interacting ferromagnetic nanodisks for two orthogonal orientations of the in-plane applied magnetic field, i.e., either parallel or perpendicular to the direction of first neighbour disks. The experimental data were modelled using the dynamical matrix method, and the results were interpreted in terms of the effective wave vector model. We have found that spin waves propagating in the two orthogonal directions exhibit marked asymmetry concerning the existence of maxima/minima in their dispersion curves and the sign of their group velocities.

Vortex mode dynamics and bandwidth tunability in a two-dimensional array of interacting magnetic disks

We calculate the spin wave spectrum and band diagram of a planar array of interacting disks in the vortex state at zero and finite applied field. We found that the circular polarization of modes depends on the Bloch wavevector k, and that the apparent spin wave profile can change as k increases from Γ to zone boundary as a consequence of the array periodicity, although the cell function remains the same. Focusing on the gyrotropic mode, we found that application of an external field can reduce or enhance the mode bandwidth, and hence slow down or boost the information carrier propagation along orthogonal directions.

Lagrangian formulation of the linear autonomous magnetization dynamics in spin-torque auto-oscillators

Abstract A Lagrangian formalism is used to find steady-state solution of the Landau–Lifshitz–Gilbert–Slonczewski equation corresponding to the linear autonomous dynamics of a magnetic auto-oscillatory system subject to the action of a spin-polarized electric current. In such a system, two concurrent dissipative mechanisms, arising from the positive intrinsic dissipation and the negative current-induced one, take place simultaneously and make the excitation of a steady precessional motion of the magnetization vector conceivable. The proposed formulation leads to the definition of a complex generalized non-Hermitian Eigenvalue problem, both in the case of a macrospin model and in the more general case of an ensemble of magnetic particles interacting each other through magnetostatic and exchange interactions. This method allows to identify the spin-wave normal modes which become unstable in the presence of the two competing dissipative contributions and provides an accurate estimation of the value of the excitation threshold current.

Spin mode calculations in nanometric magnetic rings: Localization effects in the vortex and saturated states

We study how a varying applied magnetic field influences the localization of the spin excitations in a Permalloy nanoring. The eigenfrequencies and eigenvectors of the excitations are calculated directly in the frequency domain with the dynamical matrix method, which recently proven to be successful in explaining the spin mode spectrum measured by the Brillouin scattering in rings [G. Gubbiotti et al., Phys. Rev. Lett. 97, 247203 (2006)]. When the ring is in the vortex equilibrium state at a field different from zero, we found that the localization of the (m,0) azimuthal modes may take place either where the internal field has a minimum or a maximum, depending on the mode frequency and index m. The saturated phase is characterized by a variety of modes, which may localize in the lateral arms of the ring, in the upper/lower sectors in the direction of the applied field, and at the inner or outer borders.

Effect of Interdot Separation on Collective Magnonic Modes in Chains of Rectangular Dots

The behavior of collective spin excitations in chains of rectangular NiFe dots is studied as a function of interdot separation. Dots have thickness of 40 nm and lateral dimensions of 715 × 450 nm2. They are put side by side along the major axis and the interdot separation is varied in the range 55-625 nm. Brillouin light scattering experiments have been performed at normal incidence (exchanged wave vector q = 0) and with the external magnetic field applied along the chain length. A satisfactory interpretation of the experimental data is achieved by magnonic bands calculations based on the dynamical matrix method. Such calculations have been performed at both the center and the border of the first Brillouin zone, in the case of Bloch wave vector q parallel to the applied field. In this way we can predict the amplitude of modes frequency oscillation (magnonic band), which is an important property to identify the behavior of a one-dimensional magnonic meta-material.

Soft spin modes and magnetic transitions in trilayered nanodisks in the vortex state

We present calculations of spin dynamics of a trilayered cylindrical nanodot with circular cross section, which is made of two permalloy disks with the same diameter (200 nm) and different thicknesses (20 and 10 nm), separated by a nonmagetic 10 nm thick spacer. The calculations are performed within the framework of the dynamical matrix method. Due to the different layer thicknesses, the ground state of this system at zero applied field is the vortex configuration in both layers. This system is the ideal one to investigate the dynamics of vortex modes in multilayered dots: we calculate doublets of gyrotropic, radial, and azimuthal modes, which are in phase and out-of-phase in the two layers. The dependence of these modes on vortex polarity and node number is investigated. The modes are studied as a function of a tangential magnetic field. The transition to the saturated state occurs at different critical fields for the two layers. In the proximity of these critical points, the magnetization discontinuitie...

Angle-resolved spin wave band diagrams of square antidot lattices studied by Brillouin light scattering

The Brillouin light scattering technique has been exploited to study the angle-resolved spin wave band diagrams of squared Permalloy antidot lattice. Frequency dispersion of spin waves has been measured for a set of fixed wave vector magnitudes, while varying the wave vector in-plane orientation with respect to the applied magnetic field. The magnonic band gap between the two most dispersive modes exhibits a minimum value at an angular position, which exclusively depends on the product between the selected wave vector magnitude and the lattice constant of the array. The experimental data are in very good agreement with predictions obtained by dynamical matrix method calculations. The presented results are relevant for magnonic devices where the antidot lattice, acting as a diffraction grating, is exploited to achieve multidirectional spin wave emission.