1,721,053 research outputs found
Softening of spin waves calculated under a Hamiltonian approach: importance for information delivery, and in the understanding of reversal avalanches in macrospin networks
No full textSpin waves (SWs) have became the subject of an intense theoretical and experimental investigation due to their potentiality as dissipationless information carriers for spintronic logic gates and waveguides. Differently from the Fourier analysis of a system’s magnetic response after proper excitation, the Hamiltonian approach [1] allows the computation of the whole set of SW modes, independently of the excitation symmetry and action, as an eigenvalue/eigenvector problem; moreover, the modes can be in principle computed arbitrarily close to the critical field for any magnetization change (“transition”), e.g. magnetization reversal, vortex-to saturation transition, etc. The last property is particularly suitable to the calculation of soft modes [2], i.e. SWs with a frequency going to zero at the critical field: at the critical field, this modes are known to trigger the transition by transferring their symmetry to the static magnetization, determining a specific instability that leads the system to reconfigure in a different way. Besides the theoretical interest in describing many kind of changes of the magnetization configuration, soft modes have surprising properties of great importance for spintronics, as a asymmetric broadening of their bandwidth [3] (with different group velocity in different directions), and for a dynamic explanation of the complexity of reversal avalanches (Dirac strings) in macrospin networks like artificial quasicrystals and artificial spin ices [4].
[1] L. Giovannini, F. Montoncello and F. Nizzoli, Phys. Rev B 75, 024416 (2007)
[2] F. Montoncello et al., Phys. Rev. B 77, 214402 (2008)
[3] F. Montoncello and L. Giovannini, Appl. Phys. Lett. 104, 242407 (2014)
[4] F. Montoncello et al., Journal of Magnetism and Magnetic Materials 423, 158 (2017)
Spin Waves in complex systems: how hybridization can be a source of entanglement for computing and sensing
No full textSpin Waves are the coherent oscillations of the magnetic moments of a medium, their propagation does not involve energy dissipation by Joule effect, and in periodic systems their wave function profile can be non-uniform and crucially dependent on the (tunable) symmetry of the underlying magnetization[1]. Their intrinsic wave nature, together with the quantization of their energy, suggests to use them to implement an entangled state superposition, which can collapse due to any symmetry breaking in the underlying magnetization texture[2,3]. The symmetry breaking can result from the measurement of any external quantity in sensing applications (e.g., a tiny external field or induced anisotropy) or from an intentional operation in computing applications[4]. With the help of micromagnetic simulations, we present an overview of two different situations of state superposition: spin waves in a vortex magnetization state [5], and spin waves occurring as hybrids in a lattice of macrospins (elongated elements). In both cases, we suggest how to address the Bloch sphere through the complex amplitude of the spin-wave profiles, how to implement a gate operation which preserves the entanglement, and how to break the symmetry (i.e., the measurement) and force the system to collapse in one of the originally irreducible states, producing a result detectable, in principle, by any space-resolved spectroscopy (e.g., micro-focused Brillouin light scattering or X-ray microscopy[6,7]).
References:
[1] R. Negrello, F. Montoncello, M.T. Kaffash et al., APL Mater. 10, 091115 (2022).
[2] Dany Lachance-Quirion et al., Appl. Phys. Express 12, 070101 (2019).
[3] M. Mohseni, V.I. Vasyuchka, V.S. L’vov, A.A. Serga and B. Hillebrands, Communications Physics 5, 196(2022).
[4] C. L. Degen, F. Reinhard, and P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017).
[5] G. Gubbiotti, M. Madami, S. Tacchi, et al., Phys. Rev. Lett. 97, 247203 (2006).
[6] T. Sebastian, K. Schultheiss, B. Obry, B. Hillebrands and H. Schultheiss, Front. Phys. 3, 35 (2015).
[7] Nick Träger, Felix Groß, Johannes Förster et al., Scientific Reports 10, 18146 (2020).
*We acknowledge grant 2023-FAR.L-FIRD_DFST_MF (Fondo di Ateneo per la Ricerca, University of Ferrara, Italy
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)
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)
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).
Activation of magnetic normal modes by spin polarized current in nanopillars with different cross sections
No full textWe investigated the activation of spin modes by a spin-polarized current in Permalloy magnetic nanopillars with different cross sections (lateral dimensions varying within 200-500 nm) and with point contacts (diameter: 30 nm) in different positions along the pillar section. In our study we neglected the Oersted field, the dipolar interaction between fixed and free layer, and temperature effects. We calculated the magnetic normal mode frequencies and spatial profiles of the free layer through the Dynamical Matrix Method (DMM). The space-resolved power response of the dynamic magnetization of the free layer under the influence of the polarized current was calculated through a full micromagnetic framework combined with a micromagnetic spectral mapping technique. The magnetization in the fixed layer was assumed exactly uniform, while in the free layer (thickness of 5 nm), the magnetic equilibrium configuration was calculated in three cases of different symmetry: quasi-uniform state, S-state, vortex state. In order to analyze the perturbation that a spin current induces on the magnetic ground state, we considered a short current pulse in the perpendicular-to-plane spin-polarized current configuration. We found that the spin polarized current activates a sub-set of the modes calculated within the DMM framework. We found as well that the profile of the activated modes critically depends on the symmetry properties of the underlying magnetic ground state, and that the distribution of the applied current across the pillar section determines a phase relation requirement on the magnetic oscillation. A simple selection rule is proposed, correlated to the transferred spin torque
Application of the dynamical matrix approach to the investigation of spin excitations in nanometric dots
No full textThe dynamical matrix method, which has been recently introduced for spin mode calculations in magnetic nano-dots, is reviewed. The method is a hybrid of micro-magnetic simulations (i.e. the dot is approximated out of small cells) and an eigenvalue/eigenvector approach, which requires the computation of a matrix, whose elements represent the torque acting on each cell. We apply this
method to calculate the normal modes of dots of different shape (parallelepipeds, disks, ellipses and rings), material (Fe, Permalloy) and magnetization state (saturated, vortex, with and without external field). In each case, the equilibrium configuration is preliminarily computed and then used to perform the dynamical calculation, which yields the eigenvalues (frequencies) and eigenvectors (profiles) of the spin modes. The modes are classified according to the orientation of the nodal lines with respect to the local magnetization, and are investigated in their frequency dependence on the wave-vector, nodal number and applied field. Many physical features are discussed, such as the
existence of localized modes in saturated dots, the hybridization between modes, the interaction of modes with the out-of-plane vortex core in cylindrical dots, the dependence of the mode frequency on the eccentricity in elliptical dots
Bandwidth variation of collective spin waves at the edge of magnetic transitions
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. 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. Actually, it has been recently demonstrated that the bandwidth of the mode that softens at the critical transition field, undergoes dramatic variations even when just approaching this critical field. This fact can result in a band broadening also for modes usually non-dispersive (like some end modes). In some cases, it is possible to design the magnonic crystal to be characterized by a soft mode with the desired symmetry, in order to use its bandwidth variation close to the transition field for a specific purpose. We show this concept as emerging from calculations within the dynamical matrix method: first, for square arrays of disks in the saturated and also in the vortex state, then for rectangular arrays of interacting elliptical dots, magnetized along the minor and also major axis, and find out the behavior of the soft mode dispersion close to different magnetic transitions. We discuss the correlation among: the magnetization curve, the soft mode frequency vs. field curve, and the frequency vs. wavevector curve. In the vortex-to-saturated transition 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 nondispersive (stationary). We believe that this features might be used to design versatile devices, in which information can be stored or delivered at the energy costs of a small magnetic field variation
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