F. Nizzoli

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.

Finite size effects in patterned magnetic permalloy films

Electron beam lithography has been used to prepare 250-A-thick square-shaped permalloy dots whose width and separation are in the range between 1 and 4 μm. The static and dynamic magnetic properties of these structures have been investigated by complementary techniques such as magneto-optic Kerr effect (MOKE), magnetic force microscopy (MFM), and Brillouin light scattering (BLS). Longitudinal MOKE enabled us to compare the hysteresis loops of the specimens with different dot size and interdot separation, showing a marked influence of the demagnetizing field inside the dots. MFM images recorded at zero applied field showed that, depending on the interdot spacing, there is a prevalence of either four- or seven-domain patterns together with a minority of nonsolenoidal patterns that possess a net magnetic moment. BLS from thermally activated spin waves were then used to determine the intrinsic magnetic parameters of the permalloy films and to show evidence of the discretization of the spin-wave peak due to th...

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.

Magnetic properties of submicron circular permalloy dots

Both the static and the dynamical magnetic properties of a square array of circular permalloy dots, characterized by a magnetic vortex configuration of the magnetization, have been investigated by means of magneto-optical Kerr effect and Brillouin light scattering (BLS) from thermally excited spin waves. The measured hysteresis loop can be satisfactorily reproduced by micromagnetic simulations, showing that the vortex configuration is stable over a wide range of applied field. The high frequency response of the dots was analyzed by BLS measurements performed under an external magnetic field intensity large enough to uniformly magnetize the dots. Evidence is given of a marked discretization of the spin wave spectrum with respect to the case of the continuous permalloy film, where only one peak, corresponding to the Damon-Eshbach mode, was detected. The experimental frequencies have been compared to those calculated using a recently developed analytical model for a flat uniformly magnetized cylindrical dot.

Spin wave modes in submicron cylindrical dots

The dynamic properties of a squared array of cylindrical Ni81Fe19 dots with thickness L=50 nm, radius R=100 nm, and separation 2R have been investigated by Brillouin light scattering. The sample was prepared by means of electron-beam lithography and evaporation in ultrahigh vacuum. The lateral confinement of spin waves within each dot causes a marked discretization of the spin wave spectrum. Several discrete peaks were measured in the saturated state as a function of both the incidence angle of light and the applied magnetic field. The detected modes are classified as surface dipolar and bulk magnetostatic modes at frequencies higher and lower than the Kittel uniform mode, respectively.

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...

Spin modes of triangular magnetic nanodots in the vortex, Y, and buckle states

We present a complete investigation on the spin normal modes of triangular nanoparticles in the vortex, Y, and buckle states. In order to get a micromagnetic representation of an equilateral triangle, we choose a base side of 360 nm and a height of 310 nm, while the thickness is 20 nm. This choice allows the vortex state as an equilibrium configuration at zero applied field. We calculate the principal modes of the three magnetic configuration through the dynamical matrix method and discuss in detail their frequencies and their profiles on the basis of the internal field behavior. We also explain the onset of the irregular nodal surfaces in the mode profiles beyond a critical node number, depending on the underlying magnetic configuration. The modes with nodal surfaces parallel to the direction of variation of the internal field are found to occur in a series with identical node number but different localization: this is related to the reduced coherent length of the modes because of the strongly varying in...