Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation

Dmytriiev, O.; Dvornik, Mykola; Mikhaylovskiy, R. V.; Franchin, Matteo; Fangohr, Hans; Giovannini, L.; Montoncello, F.; Berkov, D. V.; Semenova, E.K.; Gorn, N. L.; Prabhakar, Anil; Kruglyak, V. V.

doi:10.1103/physrevb.86.104405

Cited by 27 publications

(16 citation statements)

References 49 publications

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“…Hereω is the driving frequency. Dynamical magnetic susceptibility functions can be related directly to the eigenmodes of the dynamical matrix in the presence of damping [29,52]. Using the expressions in Sec.…”

Section: Dynamical Magnetic Susceptibilitymentioning

confidence: 99%

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Zero modes in magnetic systems: General theory and an efficient computational scheme

2014

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The presence of topological defects in magnetic media often leads to normal modes with zero frequency (zero modes). Such modes are crucial for long-time behavior, describing, for example, the motion of a domain wall as a whole. Conventional numerical methods to calculate the spin-wave spectrum in magnetic media are either inefficient or they fail for systems with zero modes. We present a new efficient computational scheme that reduces the magnetic normal-mode problem to a generalized Hermitian eigenvalue problem also in the presence of zero modes. We apply our scheme to several examples, including two-dimensional domain walls and Skyrmions, and show how the effective masses that determine the dynamics can be calculated directly. These systems highlight the fundamental distinction between the two types of zero modes that can occur in spin systems, which we call special and inertial zero modes. Whereas the inertial modes are generic Goldstone modes related to a broken continuous symmetry, the special modes arise naturally when two broken continuous symmetries coexist. Our method is suitable for both conservative and dissipative systems. For the latter case, we present a perturbative scheme to take into account damping, which can also be used to calculate dynamical susceptibilities.

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Section: Dynamical Magnetic Susceptibilitymentioning

confidence: 99%

“…(39) and (42) to calculate the corrected u 1k ,u 1k to an error of only O(η 2 ) and then use Eq. (52).…”

Section: Dynamical Magnetic Susceptibilitymentioning

confidence: 99%

Zero modes in magnetic systems: General theory and an efficient computational scheme

2014

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“…This yields an aspect ratio for the whole array of ∼1/10. It has been shown 62,63 that this aspect ratio guarantees a negligibly small influence of the borders on the central part of the system and also an insignificant difference of the dipolar field in the central two nanowires, which we simulated, to the dipolar field in these nanowires in an infinite array, which could be obtained by further decreasing the aspect ratio. Thus, the arrays studied here can be considered effectively infinite in the sense described above, i.e., "quasi-infinite."…”

Section: Details Of the Experiments And Micromagnetic Simulation Pmentioning

confidence: 99%

Static and dynamic magnetic properties of densely packed magnetic nanowire arrays

et al. 2013

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The static and dynamic magnetic properties of magnetic nanowire arrays with high packing density (>0.4) and wire diameter much greater than the exchange length have been studied by static and time-resolved magneto-optical Kerr effect measurements and micromagnetic simulations. The nanowires were formed by electrodeposition within a nanoporous template such that their symmetry axes lay normal to the plane of the substrate. A quantitative and systematic investigation has been made of the static and dynamic properties of the array, which lie between the limiting cases of a single wire and a continuous ferromagnetic thin film. In particular, the competition between anisotropies associated with the shape of the individual nanowires and that of the array as a whole has been studied. Measured and simulated hysteresis loops are largely anhysteretic with zero remanence, and the micromagnetic configuration is such that the net magnetization vanishes in directions orthogonal to the applied field. Simulations of the remanent state reveal antiferromagnetic alignment of the magnetization in adjacent nanowires and the formation of vortex flux closure structures at the ends of each nanowire. The excitation spectra obtained from experiment and micromagnetic simulations are in qualitative agreement for magnetic fields applied both parallel and perpendicular to the axes of the nanowires. For the field parallel to the nanowire axes, there is also good quantitative agreement between experiment and simulation. The resonant frequencies are initially found to decrease as the applied field is increased from remanence. This is the result of a change of mode profile within the plane of the array from nonuniform to uniform as the ground state evolves with increasing applied field. Quantitative differences between experimental and simulated spectra are observed when the field is applied perpendicular to the nanowire axes. The dependence of the magnetic excitation spectra upon the array packing density is explored, and dispersion curves for spin waves propagating within the array parallel to the nanowire axis are presented. Finally, a tunneling of end modes through the middle region of the nanowires was observed. The tunneling is more efficient for wires forming densely packed arrays, as a result of the extended penetration of the dynamic demagnetizing fields into the middle of the wires and due to the lowering of the tunneling barrier by the static demagnetizing field of the array.

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“…A comprehensive study, both experimentally and by micromagnetic simulation, of a densely packed array of permalloy nanowires with wire diameter much greater than the exchange length demonstrated new features of SW dynamics in nanowires (Dmytriiev et al, 2012). Particularly, the tunneling of end modes was observed, which is more efficient in arrays with smaller distance between nanowires, due to the common action of static and dynamic parts of the dipolar field in an array.…”

Section: Collective Sw Modes In Arrays Of Interacting Nanowiresmentioning

confidence: 96%

“…SW play a significant role in technologically important processes, as the spin reorientation transition and the formation of reversal modes, which influence the hysteretic properties and stability of magnetic nanostructures (Chipara et al, 2002). This theoretical achievement encouraged the subsequent experimental and theoretical investigations that during the last 15 years created a comprehensive picture of magnetization dynamics in both individual nanowires and nanowire arrays (Dmytriiev et al, 2012;Nielsch and Stadler, 2007). From this point of view, investigations of SW in nanostructures play a significant role as a way of a testing novel magnetic materials.…”

Section: Sws In Magnetic Nanowiresmentioning

confidence: 99%

Spin waves and electromagnetic waves in magnetic nanowires

Pardavi‐Horváth

Tartakovskaya

2015

Magnetic Nano- And Microwires

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Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation

Cited by 27 publications

References 49 publications

Zero modes in magnetic systems: General theory and an efficient computational scheme

Zero modes in magnetic systems: General theory and an efficient computational scheme

Static and dynamic magnetic properties of densely packed magnetic nanowire arrays

Spin waves and electromagnetic waves in magnetic nanowires

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