F. Nizzoli - Academia.edu (original) (raw)
Papers by F. Nizzoli
Journal of Physics: Condensed Matter, 1993
ABSTRACT
Journal of Physics: Conference Series, 2010
Micro-focused Brillouin light scattering (-BLS) technique is employed to study the magnetization... more Micro-focused Brillouin light scattering (-BLS) technique is employed to study the magnetization dynamics of a single elliptical NiFe nanoring. Spin waves spectra, recorded at different positions within the ring, compare very well to the results of dynamical micromagnetic simulations, confirming the exact spatial symmetry and localization region of each of the detected modes. In addition, a comparison with the spectra acquired by conventional Brillouin light scattering on a large array of identical nanorings enables us to show the superiority of -BLS for the study of stationary and localised modes within nanomagnets.
SPIE Proceedings, 1989
ABSTRACT
We present a theoretical model to obtain analytically the spin modes frequencies of cylindrical m... more We present a theoretical model to obtain analytically the spin modes frequencies of cylindrical magnetic dots in the vortex state as a function of an external applied field. In the calculations both the core and the out-of-core ex- change and dipolar fields induced by surface and volume charges are taken into account. Because of the radial sym- metry the linearized integro-differential Landau-Lifshitz equation of motion may be put into a differential form. The analytical solution of the differential equation is a linear combination of Bessel functions of the first and of the second kind of integer order times their correspond- ing angular functions. The wave vector quantization is determined by applying general radial boundary condi- tion at the dot lateral surface. The linearized equation of motion is put into a matrix form and an analytic expres- sion for the spin modes frequencies is obtained from the vanishing of the coe±cient determinant. The spin exci- tations with higher freq...
An analytical model able to calculate frequencies of surface spin modes in vortex-state ferromagn... more An analytical model able to calculate frequencies of surface spin modes in vortex-state ferromagnetic cylindrical dots at zero applied field is formulated. In dots of nanometric radius, the radial eigenvectors of the nonaxially symmetric modes are Bessel functions of order one or greater than one, while the axially symmetric modes correspond to zero order Bessel functions. Instead, in dots of radius R in the micrometric range the radial eigenvectors of the whole set of modes are Bessel functions of order one [1]. The calculated frequencies are compared to experimental data for Permalloy (Py) disks. A deviation of the frequency dispersion from the linear dependence from (L/R)^1/2 where L is the thickness is demonstrated in dots of moderate aspect ratio L/R. Furthermore, the 3D dipolar contribution is calculated exactly and its effect on the spin modes frequencies is discussed. The results are compared with the ones of a micromagnetic approach. The study is extended to ferromagnetic r...
We present a combined experimental and micromagnetic study of spin excitations in chains of dense... more We present a combined experimental and micromagnetic study of spin excitations in chains of dense magnetic dots. The samples consist of long chains of rectangular dots with rounded corners having lateral dimensions of 715 x 450 nm2 and 1025 x 450 nm2, respectively with edge-to-edge separation below 100 nm. The frequency dispersion of the spin wave excitations was measured by Brillouin Light Scattering (BLS) technique for a given applied in-plane magnetic field H and as a function of q (Bloch wave vector) directed along the chains of dots. Micromagnetic calculations, performed by using the dynamical matrix method enabled us to interpret the frequency dispersion of collective spin modes. Calculated dispersions were compared with BLS ones in the Voigt geometry (q perpendicular to H). -- Presentazione poster by R. Zivieri - Conferenza internazional
Physica Status Solidi (a), 1993
Tris-sarcosine calcium chloride, (CH3NHCH2COOH)3CaC12 (TSCC), is a uniaxial ferroelectric with a ... more Tris-sarcosine calcium chloride, (CH3NHCH2COOH)3CaC12 (TSCC), is a uniaxial ferroelectric with a Curie temperature of approximately 130 K /l/. It has orthorhombic symmetry in both phases characterized by the space group D2h in the paraelectric phase and C2v in the ferroelectric one /2/. TSCC is a very interesting ferroelectric material because of the quantum effect on the phase transition which has been observed in mixed crystals of calcium chloride and bromide compounds /3/.
Physical Review B, 2000
ABSTRACT
Physical Review B, 2003
The quantized mode spectrum of standing spin waves and edge modes in cylindrical Permalloy dots w... more The quantized mode spectrum of standing spin waves and edge modes in cylindrical Permalloy dots with a radius R in the range between 100 and 500 nm, thickness Lϭ50 nm, and separation 2R, is examined from both experimental and theoretical points of view. Brillouin scattering measurements in the Damon-Eshbach geometry give evidence of a marked discretization of the spectra with respect to that of the continuous Permalloy film. The modes can be classified into two distinct families according to their frequency. The upper one consists of the usual Damon-Eshbach, dipole-exchange modes. The modes belonging to the lower family, instead, oscillate parallel to the applied field and are reminescent of the backward modes of the film. Brillouin measurements performed with the applied field parallel to the transferred spin-wave wave vector, confirm this interpretation. The frequencies of these waves have been calculated using a simple theoretical model including the exchange field. Also, a laterally confined mode belonging to this family is observed and its frequency is independent on the dot radius.
Physical Review B, 2000
ABSTRACT
Physica B: Condensed Matter, 2004
We have recently developed two methods to calculate the magnetic normal modes of a magnetic nano-... more We have recently developed two methods to calculate the magnetic normal modes of a magnetic nano-particle. One of the methods is based on a conventional micromagnetic approach in which the time evolution of the magnetization of each cell is monitored. After filtering in frequency domain, the magnetic normal modes can be reconstructed. The second method is based on solving the same micromagneitc system in a dynamical matrix formulation. The results of the two methods, applied to a rectangular parallelepiped of Fe, will be presented and compared.
IEEE Transactions on Magnetics, 2002
Both the static and the dynamical magnetic properties of a square array of circular permalloy dot... more 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 of 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 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.
IEEE Transactions on Magnetics, 2010
In this work we formulate a generalized theoretical model to describe the nonlinear dynamics obse... more In this work 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.
Journal of Applied Physics, 2003
The dynamic properties of a squared array of cylindrical Ni81Fe19 dots with thickness L=50 nm, ra... more 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.
Journal of Physics C Solid State Physics
ABSTRACT
Journal of Physics F Metal Physics
The dynamical matrix of simple metals is set up by evaluating the total electron energy to third ... more The dynamical matrix of simple metals is set up by evaluating the total electron energy to third order in the electron ion pseudopotential. In this way three body unpaired non central forces arising from the off diagonal elements of the dielectric matrix are explicitly introduced. Since the usual on Fermi sphere approximation to a nonlocal pseudopotential gives a completely unreliable estimate of third order contributions and a full non local calculation is not feasible, a procedure is given to construct an average local potential, which disposes of most of the non locality and allows for a realistic calculation of the contributions of the unpaired forces to the lattice dynamics of simple metals. The phonon frequencies and the elastic constants of Li, Na, Al and Pb are evaluated. The results show that third order corrections are very important for Pb, while for the other metals they are about 10%. This indicates that three-body central forces are essential in order to describe the l...
Journal of Physics C: Solid State Physics, 1983
ABSTRACT The theory of the Brillouin scattering from the surface of a semi-infinite medium, devel... more ABSTRACT The theory of the Brillouin scattering from the surface of a semi-infinite medium, developed previously, is extended to coated surfaces of cubic materials. The Brillouin cross section is obtained for any scattering geometry and for p and s polarisation of the incident and scattered light. The formulae for the cross section contain contributions from the ripple and the elasto-optic scattering mechanisms for the film as well as for the substrate. The theory is applied to a silica film deposited on crystalline silicon and the behaviour of the cross section against the film thickness is investigated. The authors find that there are strong interference effects among the various contributions to the cross-section, so that the intensity of the spectral lines dramatically oscillates by changing the thickness. Although in general the ripple scattering mechanism is the dominant one it is found that the elasto-optic coupling in the silica film is not negligible and sometimes is even prevailing. The discrete phonon spectrum (Rayleigh, Sezawa, Lamb modes) and the continuous spectrum (resonances, mixed modes) are both studied.
Springer Series on Wave Phenomena, 1986
First order light scattering from collective excitations in transparent materials (fluids, sol id... more First order light scattering from collective excitations in transparent materials (fluids, sol ids) has been studied since the beginning of the century [1,2]. More recently (since 1965) light scattering has been used to investigate acoustic and optic surface vibrations. Two different points of view can be adopted. In fact, surface phonons can be detected which are either externally excited with a variety of different techniques or naturally present in the sample at a finite temperature T due to thermal excitations (thermal noise). The two different methods have been developed rather independently.
Physical review. B, Condensed matter, Jan 15, 1992
ABSTRACT
Journal of Physics: Condensed Matter, 1993
ABSTRACT
Journal of Physics: Conference Series, 2010
Micro-focused Brillouin light scattering (-BLS) technique is employed to study the magnetization... more Micro-focused Brillouin light scattering (-BLS) technique is employed to study the magnetization dynamics of a single elliptical NiFe nanoring. Spin waves spectra, recorded at different positions within the ring, compare very well to the results of dynamical micromagnetic simulations, confirming the exact spatial symmetry and localization region of each of the detected modes. In addition, a comparison with the spectra acquired by conventional Brillouin light scattering on a large array of identical nanorings enables us to show the superiority of -BLS for the study of stationary and localised modes within nanomagnets.
SPIE Proceedings, 1989
ABSTRACT
We present a theoretical model to obtain analytically the spin modes frequencies of cylindrical m... more We present a theoretical model to obtain analytically the spin modes frequencies of cylindrical magnetic dots in the vortex state as a function of an external applied field. In the calculations both the core and the out-of-core ex- change and dipolar fields induced by surface and volume charges are taken into account. Because of the radial sym- metry the linearized integro-differential Landau-Lifshitz equation of motion may be put into a differential form. The analytical solution of the differential equation is a linear combination of Bessel functions of the first and of the second kind of integer order times their correspond- ing angular functions. The wave vector quantization is determined by applying general radial boundary condi- tion at the dot lateral surface. The linearized equation of motion is put into a matrix form and an analytic expres- sion for the spin modes frequencies is obtained from the vanishing of the coe±cient determinant. The spin exci- tations with higher freq...
An analytical model able to calculate frequencies of surface spin modes in vortex-state ferromagn... more An analytical model able to calculate frequencies of surface spin modes in vortex-state ferromagnetic cylindrical dots at zero applied field is formulated. In dots of nanometric radius, the radial eigenvectors of the nonaxially symmetric modes are Bessel functions of order one or greater than one, while the axially symmetric modes correspond to zero order Bessel functions. Instead, in dots of radius R in the micrometric range the radial eigenvectors of the whole set of modes are Bessel functions of order one [1]. The calculated frequencies are compared to experimental data for Permalloy (Py) disks. A deviation of the frequency dispersion from the linear dependence from (L/R)^1/2 where L is the thickness is demonstrated in dots of moderate aspect ratio L/R. Furthermore, the 3D dipolar contribution is calculated exactly and its effect on the spin modes frequencies is discussed. The results are compared with the ones of a micromagnetic approach. The study is extended to ferromagnetic r...
We present a combined experimental and micromagnetic study of spin excitations in chains of dense... more We present a combined experimental and micromagnetic study of spin excitations in chains of dense magnetic dots. The samples consist of long chains of rectangular dots with rounded corners having lateral dimensions of 715 x 450 nm2 and 1025 x 450 nm2, respectively with edge-to-edge separation below 100 nm. The frequency dispersion of the spin wave excitations was measured by Brillouin Light Scattering (BLS) technique for a given applied in-plane magnetic field H and as a function of q (Bloch wave vector) directed along the chains of dots. Micromagnetic calculations, performed by using the dynamical matrix method enabled us to interpret the frequency dispersion of collective spin modes. Calculated dispersions were compared with BLS ones in the Voigt geometry (q perpendicular to H). -- Presentazione poster by R. Zivieri - Conferenza internazional
Physica Status Solidi (a), 1993
Tris-sarcosine calcium chloride, (CH3NHCH2COOH)3CaC12 (TSCC), is a uniaxial ferroelectric with a ... more Tris-sarcosine calcium chloride, (CH3NHCH2COOH)3CaC12 (TSCC), is a uniaxial ferroelectric with a Curie temperature of approximately 130 K /l/. It has orthorhombic symmetry in both phases characterized by the space group D2h in the paraelectric phase and C2v in the ferroelectric one /2/. TSCC is a very interesting ferroelectric material because of the quantum effect on the phase transition which has been observed in mixed crystals of calcium chloride and bromide compounds /3/.
Physical Review B, 2000
ABSTRACT
Physical Review B, 2003
The quantized mode spectrum of standing spin waves and edge modes in cylindrical Permalloy dots w... more The quantized mode spectrum of standing spin waves and edge modes in cylindrical Permalloy dots with a radius R in the range between 100 and 500 nm, thickness Lϭ50 nm, and separation 2R, is examined from both experimental and theoretical points of view. Brillouin scattering measurements in the Damon-Eshbach geometry give evidence of a marked discretization of the spectra with respect to that of the continuous Permalloy film. The modes can be classified into two distinct families according to their frequency. The upper one consists of the usual Damon-Eshbach, dipole-exchange modes. The modes belonging to the lower family, instead, oscillate parallel to the applied field and are reminescent of the backward modes of the film. Brillouin measurements performed with the applied field parallel to the transferred spin-wave wave vector, confirm this interpretation. The frequencies of these waves have been calculated using a simple theoretical model including the exchange field. Also, a laterally confined mode belonging to this family is observed and its frequency is independent on the dot radius.
Physical Review B, 2000
ABSTRACT
Physica B: Condensed Matter, 2004
We have recently developed two methods to calculate the magnetic normal modes of a magnetic nano-... more We have recently developed two methods to calculate the magnetic normal modes of a magnetic nano-particle. One of the methods is based on a conventional micromagnetic approach in which the time evolution of the magnetization of each cell is monitored. After filtering in frequency domain, the magnetic normal modes can be reconstructed. The second method is based on solving the same micromagneitc system in a dynamical matrix formulation. The results of the two methods, applied to a rectangular parallelepiped of Fe, will be presented and compared.
IEEE Transactions on Magnetics, 2002
Both the static and the dynamical magnetic properties of a square array of circular permalloy dot... more 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 of 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 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.
IEEE Transactions on Magnetics, 2010
In this work we formulate a generalized theoretical model to describe the nonlinear dynamics obse... more In this work 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.
Journal of Applied Physics, 2003
The dynamic properties of a squared array of cylindrical Ni81Fe19 dots with thickness L=50 nm, ra... more 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.
Journal of Physics C Solid State Physics
ABSTRACT
Journal of Physics F Metal Physics
The dynamical matrix of simple metals is set up by evaluating the total electron energy to third ... more The dynamical matrix of simple metals is set up by evaluating the total electron energy to third order in the electron ion pseudopotential. In this way three body unpaired non central forces arising from the off diagonal elements of the dielectric matrix are explicitly introduced. Since the usual on Fermi sphere approximation to a nonlocal pseudopotential gives a completely unreliable estimate of third order contributions and a full non local calculation is not feasible, a procedure is given to construct an average local potential, which disposes of most of the non locality and allows for a realistic calculation of the contributions of the unpaired forces to the lattice dynamics of simple metals. The phonon frequencies and the elastic constants of Li, Na, Al and Pb are evaluated. The results show that third order corrections are very important for Pb, while for the other metals they are about 10%. This indicates that three-body central forces are essential in order to describe the l...
Journal of Physics C: Solid State Physics, 1983
ABSTRACT The theory of the Brillouin scattering from the surface of a semi-infinite medium, devel... more ABSTRACT The theory of the Brillouin scattering from the surface of a semi-infinite medium, developed previously, is extended to coated surfaces of cubic materials. The Brillouin cross section is obtained for any scattering geometry and for p and s polarisation of the incident and scattered light. The formulae for the cross section contain contributions from the ripple and the elasto-optic scattering mechanisms for the film as well as for the substrate. The theory is applied to a silica film deposited on crystalline silicon and the behaviour of the cross section against the film thickness is investigated. The authors find that there are strong interference effects among the various contributions to the cross-section, so that the intensity of the spectral lines dramatically oscillates by changing the thickness. Although in general the ripple scattering mechanism is the dominant one it is found that the elasto-optic coupling in the silica film is not negligible and sometimes is even prevailing. The discrete phonon spectrum (Rayleigh, Sezawa, Lamb modes) and the continuous spectrum (resonances, mixed modes) are both studied.
Springer Series on Wave Phenomena, 1986
First order light scattering from collective excitations in transparent materials (fluids, sol id... more First order light scattering from collective excitations in transparent materials (fluids, sol ids) has been studied since the beginning of the century [1,2]. More recently (since 1965) light scattering has been used to investigate acoustic and optic surface vibrations. Two different points of view can be adopted. In fact, surface phonons can be detected which are either externally excited with a variety of different techniques or naturally present in the sample at a finite temperature T due to thermal excitations (thermal noise). The two different methods have been developed rather independently.
Physical review. B, Condensed matter, Jan 15, 1992
ABSTRACT