The use of spin waves (SW) in magnonic crystals (MCs) as information carriers has been the target of intense investigation in recent years, particularly in relation with the possibility of controlling their Bragg diffraction and dispersion relations by an applied field, and their peculiarity in the context of dissipationless computing, since SWs don't involve charge motion and ohmic losses. Hence, depending on the applied field, a MC device can turn from a memory to an efficient waveguide in correspondence to the dynamic change of the SW carrier. In the context of high density informaton storage/delivery, it is particularly desirable (but scarcely explored) that more than a signal could flow, independently and with no interference, from source to drain across the same material device. However, due to the long-range nature of the magnetic dipolar interaction, it is not trivial to find out a two-dimensional (2D) periodic magnetic system, in which the magnetization dynamics involve two specific and distinct regions of it for all modes in two complete frequency bands, and, at the same time, the two bands are enough separated in frequency. In this work, we investigate a special 2D Permalloy MC, designed in such a way that SWs can propagate in distinct regions of it, depending on the frequency band they belong to, so to guarantee complete signal independence. We characterize the two spin wave types, by determining the two localization areas and the extension of the corresponding bands. The basic idea is considering two superposed sublattices, and using shape anisotropy to differentiate in energy the dynamics within the two sublattice elements: in this way, the excitations corresponding to different sublattice elements are forced to belong to different frequency ranges. This task is attained with the following MC design (Fig. 1-a): a main (primary) square sublattice, with a short lattice constant (15 nm), is made of cubes with a side of 5 nm, that is slightly lower than the exchange correlation length (5.5 nm, in our case), and exactly corresponding to the micromagnetic elemental cell. A secondary square sublattice, with a long lattice constant (60 nm), is made of larger prism particles, with identical thickness and width, but with a double length: 10×5×5 nm3 (hence consisting of two micromagnetic cells). In this way, the dipolar energy in smaller particles is much larger than in bigger particles, and this is a condition necessary to both increase the frequency of the modes localized in larger particles, and determine a fast decay of the mode oscillation outside that region. An external magnetic field of constant magnitude, B0= 0.1 T, is then applied at different directions. We study the system within the micromagnetic framework, computing the equilibrium magnetization by the software OOMMF [1] and the spin wave dynamics by the dynamical matrix method (DMM) [2]. We find that, in agreement with predictions, the modes computed at different wavevectors belong to one or another specific frequency band, depending on the region of localization: within the corresponding bands, the magnetic excitation of an element of a sublattice doesn’t interfere with the dynamics of the other sublattice (Fig. 1-b,c). We calculate the dispersion relations of the two modes belonging to the two sublattices (Fig. 2-a,b), and show how they don’t cross with each other within the whole Brillouin zone: the two frequency bands are separated by a large frequency gap. We compute the maximum value of the frequency gap (6 GHz), and show its dependence on the SW propagation direction. Then we discuss the results on the basis of the internal field variations, and compare our actual dual band system with other systems (e.g., end modes and bulk modes in ordinary arrays of dots) in which a possibly wide frequency gap doesn’t meet an independent propagation in disjoint parts of the MC. We also discuss the importance, for the dual property, of shape anisotropy and nanometric size of the MC constituents, in the perspective of providing essential information to an experimental validation: i.e, exciting two simultaneous SW signals in the same MC device, with small antennas placed in different MC sublattice elements. References: [1] M. J. Donahue and D. G. Porter, OOMMF User’s Guide, Version 1.0, NIST, Gaithersburg, Md, USA, 1999. [2] L. Giovannini, F. Montoncello, and F. Nizzoli, Physical Review B, 75, (2007) 024416.

### Design and basic Spin Wave dynamics of a Dual Band Magnonic Crystal

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*MONTONCELLO, Federico;GIOVANNINI, Loris*

##### 2017

#### Abstract

The use of spin waves (SW) in magnonic crystals (MCs) as information carriers has been the target of intense investigation in recent years, particularly in relation with the possibility of controlling their Bragg diffraction and dispersion relations by an applied field, and their peculiarity in the context of dissipationless computing, since SWs don't involve charge motion and ohmic losses. Hence, depending on the applied field, a MC device can turn from a memory to an efficient waveguide in correspondence to the dynamic change of the SW carrier. In the context of high density informaton storage/delivery, it is particularly desirable (but scarcely explored) that more than a signal could flow, independently and with no interference, from source to drain across the same material device. However, due to the long-range nature of the magnetic dipolar interaction, it is not trivial to find out a two-dimensional (2D) periodic magnetic system, in which the magnetization dynamics involve two specific and distinct regions of it for all modes in two complete frequency bands, and, at the same time, the two bands are enough separated in frequency. In this work, we investigate a special 2D Permalloy MC, designed in such a way that SWs can propagate in distinct regions of it, depending on the frequency band they belong to, so to guarantee complete signal independence. We characterize the two spin wave types, by determining the two localization areas and the extension of the corresponding bands. The basic idea is considering two superposed sublattices, and using shape anisotropy to differentiate in energy the dynamics within the two sublattice elements: in this way, the excitations corresponding to different sublattice elements are forced to belong to different frequency ranges. This task is attained with the following MC design (Fig. 1-a): a main (primary) square sublattice, with a short lattice constant (15 nm), is made of cubes with a side of 5 nm, that is slightly lower than the exchange correlation length (5.5 nm, in our case), and exactly corresponding to the micromagnetic elemental cell. A secondary square sublattice, with a long lattice constant (60 nm), is made of larger prism particles, with identical thickness and width, but with a double length: 10×5×5 nm3 (hence consisting of two micromagnetic cells). In this way, the dipolar energy in smaller particles is much larger than in bigger particles, and this is a condition necessary to both increase the frequency of the modes localized in larger particles, and determine a fast decay of the mode oscillation outside that region. An external magnetic field of constant magnitude, B0= 0.1 T, is then applied at different directions. We study the system within the micromagnetic framework, computing the equilibrium magnetization by the software OOMMF [1] and the spin wave dynamics by the dynamical matrix method (DMM) [2]. We find that, in agreement with predictions, the modes computed at different wavevectors belong to one or another specific frequency band, depending on the region of localization: within the corresponding bands, the magnetic excitation of an element of a sublattice doesn’t interfere with the dynamics of the other sublattice (Fig. 1-b,c). We calculate the dispersion relations of the two modes belonging to the two sublattices (Fig. 2-a,b), and show how they don’t cross with each other within the whole Brillouin zone: the two frequency bands are separated by a large frequency gap. We compute the maximum value of the frequency gap (6 GHz), and show its dependence on the SW propagation direction. Then we discuss the results on the basis of the internal field variations, and compare our actual dual band system with other systems (e.g., end modes and bulk modes in ordinary arrays of dots) in which a possibly wide frequency gap doesn’t meet an independent propagation in disjoint parts of the MC. We also discuss the importance, for the dual property, of shape anisotropy and nanometric size of the MC constituents, in the perspective of providing essential information to an experimental validation: i.e, exciting two simultaneous SW signals in the same MC device, with small antennas placed in different MC sublattice elements. References: [1] M. J. Donahue and D. G. Porter, OOMMF User’s Guide, Version 1.0, NIST, Gaithersburg, Md, USA, 1999. [2] L. Giovannini, F. Montoncello, and F. Nizzoli, Physical Review B, 75, (2007) 024416.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.