1,721,116 research outputs found
Size effects on magnonic mode dynamics in 2D ferromagnetic antidot lattices -- Presentazione poster by R. Zivieri -- Conferenza nazionale
No full textThe size effects on frequencies of collective modes in two-dimensional (2D) arrays of periodic circular antidots (holes) embedded into a ferromagnetic Permalloy material are investigated. The study is performed by calculating the frequency behaviour as a function of the intensity H of the external magnetic field applied in the plane of the system along the y-direction for vanishing Bloch wave vector. The antidot periodicity is a = 420 nm, the thickness is L = 30 nm, whereas the diameters of the holes are d1 = 140 nm, d2 = 180 nm, d3= 220 nm and d4= 260 nm, respectively [1]. The two relevant modes, having an appreciable calculated scattering cross-section, are: 1) the resonant mode of the spectrum, the so-called Fundamental (F) mode, whose spatial profile is confined in the channels; 2) the equivalent mode mainly localized in the horizontal rows of antidots, the Floc mode. Frequencies of collective modes monotonically increase with increasing the mean internal field. However, at a fixed external field the frequencies of F and Floc mode have on opposite behavior as a function of the hole size as shown in Figure 1. Indeed, the mean demagnetizing field experienced by the F mode is anti-parallel to the external field lowering the mean internal field, while for the Floc mode it is parallel and has the effect to increase the internal field.
Moreover, at the centre of the first Brillouin zone, the two lowest spin-wave mode frequencies, namely the edge mode (EM) localized at the antidot borders [2] and the F mode, become soft at a given critical field showing a deep minimum. The intensity of the critical field depends on the hole size and both soft modes do exhibit a finite gap. The softening mechanism is strictly related to the rotation of the static magnetization from the hard to the easy axis marking a reorientational and continuous phase transition. A phenomenological model based on an Hamiltonian density including the different density energy contributions and describing the continuous phase transition is developed. According to this model, the critical field turns out to be equal to the first-order mean demagnetizing field. The mean demagnetizing field was determined according to micromagnetic calculations by averaging over the micromagnetic cells corresponding to the antidot separation. The results of the calculations compare well with experimental data obtained by means of Brillouin light scattering technique for all the diameters investigated [3].
[1] J. Ding, D. Tripathy, A. O. Adeyeye, J. Appl. Phys. 109, (2011) 07D304-1-3.
[2] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, A.O. Adeyeye, S. Neusser, B. Botters, D. Grundler, IEEE Trans. Magn. 46, (2010) 172-178.
[3] R. Zivieri et al., “Soft magnonic modes in two-dimensional permalloy antidot lattices”, J. of Physics: Condens. Matter 25, (2013) 336002-1-7
Band structure and properties of vortex modes in a 2-D magnonic crystal
No full textMagnonic crystals are artificial materials with periodic modulation of the magnetic properties that have recently received large interest from the scientific community. Indeed, the possibility of tuning the propagating properties, speed and allowed/forbidden band width of magnetic collective excitations with an external field has attracted special attention on these systems. However, while in the saturated case the band diagram has been extensively investigated [1], only a few incomplete studies on collective modes in the vortex state have been reported [e.g. Ref. 2]. Here we present a thorough investigation on this subject: employing the dynamical matrix method [3], we performed calculations on a squared 2D lattice of dots in the vortex state, varying the in-plane wavevector components to investigate the first Brillouin zone. We computed the dispersion relations for gyrotropic, azimuthal and radial modes (Fig. 1). Dynamics in vortex states is a complex matter, since the coupling is mainly due to the fluctuations of the magnetization, which is a second order effect, but is more interesting because a slight change of the external field can have dramatic consequences on the information carriers (“magnons”), which can be slowed down even to zero speed: in this way information could be stored or delivered with little energy effort within the same device, which operates either as a memory or a waveguide. We discuss the dynamical coupling of modes with different cell wavefunctions, the corresponding mode dispersion and bandwidth, the effects of interdot coupling on the circular polarization on the modes, the Brillouin Light Scattering cross section of the principal modes. The investigation extends also to vortex states in presence of a nonzero applied field, where the vortex core is no more in the center of the disk, and to the corresponding symmetry breaking in the dispersion relations. This work was supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n°233552 (DYNAMAG).
[1] S. Tacchi, F. Montoncello, M. Madami, G. Gubbiotti, G. Carlotti, L. Giovannini, R. Zivieri , F. Nizzoli, S. Jain, A. O. Adeyeye, and N. Singh, Physical Review Letters, in press (2011).
[2] A. Yu. Galkin, B. A. Ivanov and C. E. Zaspel, Physical Review B, 74, 144419 (2006).
[3] L. Giovannini, F. Montoncello, and F. Nizzoli, Physical Review B 75, 024416 (2007).
Effective quantities and effective rules in two-dimensional ferromagnetic antidot lattices
No full textIn this paper the metamaterial properties of two-dimensional arrays of circular antidots (holes) embedded into a ferromagnetic medium of Permalloy are studied according to both micromagnetic and analytical calculations. The periodicity of the arrays and the diameters of the antidots are in the nanometric range. The collective mode dynamics is described by means of effective physical quantities for the scattering geometry with the external magnetic field applied perpendicularly to the Bloch wave vector in the antidot plane. As an example, the definition of an effective field, incorporating the demagnetizing effects due to the holes, permits to describe the dynamical properties of collective modes in terms of effective properties in the travelling regime. An effective wavelength and a small wave vector are introduced both for extended and localized magnonic modes. By means of these effective quantities it is shown that holes play the role of point defects affecting the spin dynamics in the microwave range. Relations between the effective wavelength and the Bloch wavelength and between the corresponding small wave vector and the Bloch wave vector are found. Some effective rules on the dynamic magnetization, based upon the effective wavelength and the corresponding small wave vector, are derived. An application that exploits the definition of the small wave vector is proposed and an experiment based upon the notion of effective wavelength and small wave vector is suggested
Metamaterial Properties of Two-Dimensional Magnonic Crystals -- Presentazione poster by R. Zivieri - Conferenza nazionale
No full textThe metamaterial properties of two-dimensional magnonic crystals (MCs) are studied according to micromagnetic and analytical calculations. Micromagnetic calculations were performed by using the Dynamical Matrix Method (DMM) extended to periodic systems [1]. The nanometric systems are composed by periodic square arrays of circular antidots (ADs) (holes) embedded into a Permalloy ferromagnetic film [2]. In the calculations the diameter of the holes varies between 10 nm and 120 nm, the array periodicity is a = 800 nm and the thickness is L = 22 nm. The geometry studied is with the external field H perpendicular to the Bloch wave vector K in the sample plane. Since holes are much smaller than the characteristic mode wavelength, the dynamics is described in terms of an effective medium approximation. This description allows us to highlight the metamaterial properties of this class of two-dimensional MCs [3]. Due to the periodicity, frequencies of collective spin modes having Damon-Eshbach-like (DE) character exhibit a band structure and the dispersion shows opening of band gaps at Brillouin zone boundaries. For each collective spin mode an effective wavelength commensurable with the array periodicity is defined. The effective wavelength is related to the scattering from the ADs of the given spin-wave mode. Holes have thus the role of point defects affecting spin dynamics. It is also shown that the effective wavelength and the associated small wave vector are not necessarily equal to their corresponding Bloch quantities.
[1] L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. B 75, 024416 (2007).
[2] R. Zivieri, S. Tacchi, F. Montoncello, L. Giovannini, F. Nizzoli, M. Madami, G. Gubbiotti, G. Carlotti, S. Neusser, G. Duerr, and D. Grundler, Phys. Rev. B 85, 012403 (2012).
[3] R. Zivieri and L. Giovannini, “Metamaterial properties of ferromagnetic antidot lattices” in press in Metamaterials
Collective Vortex Modes in Magnonic Crystals: Multipolar Effects on Dispersion Curves
No full textIt has been recently demonstrated through calculations [1] how collective vortex modes in magnonic crystals can dramatically change their propagation properties as soon as a bias field is applied. Clearly, this fact is potentially helpful in the perspective of magnonic-spin-logic devices, in which the propagation/steadiness of the information carrier (“magnon”) can be given a different binary digit. Employing the dynamical matrix method, we performed calculations on a squared 2D lattice of dots in the vortex state, varying the in-plane
wavevector components to investigate the first Brillouin zone. We computed the dispersion relations for gyrotropic, azimuthal and radial modes. We discuss the dynamical coupling of modes with different cell wavefunctions, which is not purely dipolar as for the modes in saturated states: multipolar contributions are often necessary, and determine the dependence of the bandwidth of a given mode on the lattice parameter. We also discuss how the circular polarization of the modes depends on the Bloch wavevector k and changer as k is changed. When considering a bias magnetic field, in the equilibrium configuration the vortex core sets off the center of the disk: for a class of modes, propagation along the direction of the applied field is slowed down, while perpendicular to the applied field is speeded up. This work was supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n°n°228673 (MAGNONICS).
[1] F. Montoncello and L. Giovannini, Appl. Phys. Lett. 100, 182406 (2012)
Stopping field for collective spin waves at the edge of magnetization reversal
No full textSimilarly to other magnetic systems, even magnonic crystals are characterized by soft modes with a vanishing frequency at the critical field of any given magnetic transition. The profile of these modes has a symmetry that depends on the symmetry change between the initial and final magnetic configurations[1]. The knowledge of the soft mode is not a theoretical-only issue, but can have technological implications, especially in the field of magnonic- and spin-logic devices, where collective spin waves are used for information storage and delivery[2]. Actually, it has been recently demonstrated[3] that the bandwidth of the mode that softens at the critical field, undergoes dramatic variations even when just approaching this critical field. This fact can result either in a band broadening of modes usually non-dispersive (like some end modes), or, vice versa, in a strong band reduction for modes with usually a large bandwidth (as the fundamental mode). In some cases, it is possible to design the magnonic crystal to be characterized by one or another soft mode with the desired symmetry in order to use its bandwidth variation close to the transition field for a specific purpose. We apply this concept to a rectangular array of interacting elliptical dots of Permalloy (i.e., a 2-D magnonic crystal), magnetized along the major axis, and, by calculations with the dynamical matrix method, find out the behavior of the soft mode dispersion at the edge of magnetization reversal. We discuss the correlation among different curves characterizing the magnetic system close to reversal: the magnetization curve, the soft mode frequency vs. field curve, and the frequency vs. wavevector curve. We investigate different aspect ratios for the ellipses, and different magnetic configurations. We show how the soft mode is characterized by a bandwidth that goes to zero at a magnetic field quite distinct from the critical transition field, and we call this field stopping field, because at this field the collective soft mode turns into non-dispersive (stationary). We believe that this feature can be used to design versatile devices, in which information can be stored or delivered at the energy costs of a small magnetic field variation.
[1] F. Montoncello, L. Giovannini, F. Nizzoli, P. Vavassori, and M. Grimsditch, Phys. Rev. B 77, 214402 (2008).
[2] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, M. P. Kostylev, V. S. Tiberkevich, and B. Hillebrands, Phys. Rev. Lett. 108, 257207 (2012). [3] F. Montoncello and L. Giovannini, Applied Physics Letters 104, 242407 (2014)
Information carrier bandwidth and speed tunability in magnonic crystals in the vortex state
No full textMagnonic crystals are artificial materials with periodic modulation of the magnetic properties that have recently received special attention due to the fact that slight changes of the external field can have dramatic consequences on the information carrier (“magnon”) propagation, which can be boosted or delayed even to steadiness: in this way the same device can operate either as a memory or a waveguide. Employing the dynamical matrix method [1], we performed calculations on a squared 2D lattice of dots in the vortex state, varying the in-plane wavevector components to investigate the first Brillouin zone. We computed the dispersion relations for gyrotropic, azimuthal and radial modes. We discuss the dynamical coupling of modes with different cell wavefunctions, which is not purely dipolar as for the saturated states. We discuss how the circular polarization on the modes depends on the Bloch wavevector. We considered also the effects of application of a magnetic field, which moves the vortex core off the center of the disk: for a class of modes, propagation perpendicular to the direction of the applied field is speeded up, while parallel to the applied field is slowed down. These results can be important for designing versatile magnetic filters, in which variation of the applied field direction and intensity can turn the device from a waveguide into a memory, but also for spin logic devices, in which propagation or steadiness of the information carrier along a desired direction can be associated to different binary digits.
[1] L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. B 75, 024416 (2007)
Vortex mode dispersion relations in a 2-D array of interacting disks
No full textSpin-wave propagation in bidimensional arrays of interacting magnetic elements has recently received increased interest in the field of magnonics. Actually, the possibility of tuning the propagating properties, speed and allowed/forbidden band width of magnetic collective excitations with an external field has attracted special attention on these systems. However, while in the saturated case the band diagram has been extensively investigated [1], only a few incomplete studies on collective modes in the vortex state have been reported [e.g. Ref. 2]. Here we present a thorough investigation on this subject: employing the dynamical matrix method [3], we performed calculations on a squared 2D lattice of dots in the vortex state, as a function of the in-plane wavevector, to investigate the first Brillouin zone. We computed the dispersion relations for gyrotropic, azimuthal and radial modes. Dynamics in vortex states is a complex matter, since the coupling is mainly due to the fluctuations of the magnetization, which is a second order effect, but is more interesting because a slight change of the external field can have dramatic consequences on the information carriers (“magnons”), which can be slowed down even to zero speed: in this way information could be stored or delivered with little energy effort within the same device, which operates either as a memory or a waveguide. We discuss the dynamical coupling of modes with different cell wavefunctions, the corresponding mode dispersion and bandwidth, the effects of interdot coupling on the circular polarization on the modes, the Brillouin Light Scattering cross section of the principal modes. The investigation extends also to vortex states in presence of a nonzero applied field, where the vortex core is no more in the center of the disk, and to the corresponding symmetry breaking in the dispersion relations.
This work was supported by the European Community’s Seventh
Framework Programme (FP7/2007-2013) under Grant Agreement n°233552 (DYNAMAG)
Effective Properties of a Two-Dimensional Magnonic Metamaterial -- Presentazione orale by R. Zivieri - Conferenza internazionale
No full textIn this paper the metamaterial properties of a two-dimensional magnonic crystal are studied by doing micromagnetic and analytical calculations. The nanometric system is composed by holes embedded into a Permalloy ferromagnetic film. Since holes are much smaller than the characteristic mode wavelength commensurable with the periodicity, the dynamics is described in terms of effective quantities. Due to this condition also the characteristic wavelength is defined as an effective wavelength. It is shown that the effective wavelength and the corresponding effective wave vector are not necessarily equal to their corresponding Bloch quantities. - Presentazione orale by R. Zivieri - Conferenza internazional
Il progetto “Energie Sisma Emilia”
No full textI disastri naturali, come quelli che si sono verificati in Italia nel secondo dopoguerra e, in particolare, eventi sismici, alluvioni, frane ed esondazioni, richiamano in misura crescente l’attenzione (e non solo quella degli studiosi) sulla fragilità del territorio e sulla necessità di interventi di prevenzione per mitigare i loro effetti economici e sociali. Accanto alla prevenzione, si segnala da più parti, dalle Nazioni Unite alla Commissione Europea, la necessità di far leva sulle capacità di resilienza delle comunità colpite da calamità naturali, agendo quindi sui fattori endogeni dello sviluppo
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