F. Montoncello

Tunable short-wavelength spin wave excitation from pinned magnetic domain walls

Miniaturization of magnonic devices for wave-like computing requires emission of short-wavelength spin waves, a key feature that cannot be achieved with microwave antennas. In this paper, we propose a tunable source of short-wavelength spin waves based on highly localized and strongly pinned magnetic domain walls in ferroelectric-ferromagnetic bilayers. When driven into oscillation by a microwave spin-polarized current, the magnetic domain walls emit spin waves with the same frequency as the excitation current. The amplitude of the emitted spin waves and the range of attainable excitation frequencies depend on the availability of domain wall resonance modes. In this respect, pinned domain walls in magnetic nanowires are particularly attractive. In this geometry, spin wave confinement perpendicular to the nanowire axis produces a multitude of domain wall resonances enabling efficient spin wave emission at frequencies up to 100 GHz and wavelengths down to 20 nm. At high frequency, the emission of spin waves in magnetic nanowires becomes monochromatic. Moreover, pinning of magnetic domain wall oscillators onto the same ferroelectric domain boundary in parallel nanowires guarantees good coherency between spin wave sources, which opens perspectives towards the realization of Mach-Zehnder type logic devices and sensors.

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.

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.

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...

Experimental Evidence of Field-Induced Localization of Spin Excitations in NiFe Elliptical Rings by Micro-Focused Brillouin Light Scattering

Micro-focused Brillouin light scattering has been exploited as a scanning probe technique to investigate the spatial localization and symmetry of magnetic excitations in elliptical nanorings. The interpretation of the experimental data has been achieved using the dynamical matrix method. Special attention is paid to the investigation of the soft-mode involved in the vortex-to-onion transition, to the localization of modes as a function of the external field, and to the to identification of the vortex chirality of a single ring.

A continuous excitation approach to determine time-dependent dispersion diagrams in 2D magnonic crystals

We propose an alternative micromagnetic approach to determine the spin wave dispersion relations in magnonic structures. Characteristic of the method is that a limited area of the system is continuously excited with a spatially uniform oscillating field, tuned at a given frequency. After a transitory time, the regime magnetization dynamics is collected and a spatial Fourier analysis on it determines the frequency vs wave vector relation. Combining several simulations in any predetermined range of frequencies, at any resolution, we investigate the dispersion relations for different kinds of magnonic crystals: a dot array, an antidot array, and a bicomponent film. Especially compared to traditional pulse-excitation methods this technique has many advantages. First, the excitation power is concentrated at a single frequency, allowing the corresponding spin waves to propagate with very low attenuation, resulting in a higher k-space resolution. Second, the model allows to include very large wave vector components, necessary to describe the high-frequency response of non-quantized spin waves in quasi-continuous systems. Finally, we address some possible experimental opportunities with respect to excitation/detection techniques over large distances and the observation of the odd/even symmetry of spin waves using Brillouin light scattering.