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

Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation
Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation
We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing arrays of magnetic inclusions of arbitrary shapes. The method fully takes into account the spectrum of spin waves confined in the inclusions. We evaluate the method by considering a particular case of a metamaterial formed by a stack of identical two-dimensional (2D) periodic hexagonal arrays of disk-shaped magnetic inclusions in a nonmagnetic matrix. Two versions of the method are considered. The first approach is based on a simple semianalytical theory that uses the numerically calculated susceptibility tensor of an isolated inclusion as input data for an analytical calculation in which the magnetodipole interaction between inclusions within each 2D array is taken into account. In the second approach, we employ micromagnetic packages with periodic boundary conditions to calculate the susceptibility of the whole 2D periodic array of such inclusions. The comparison of the two approaches reveals the necessity of retaining higher-order terms in the analytical calculation of the magnetodipole interaction via the multipole expansion. Models limited to the dipolar term can lead to remarkable underestimation of the effect of the magnetodipole interaction, in particular, for modes localized near the edge regions of inclusions. To calculate the susceptibility tensor of an isolated inclusion, we have implemented two different methods: (a) a method based on micromagnetic simulations, in which we have compared three different micromagnetic packages: the finite-element package nmag and the two finite differences packages oommf and micromagus; and (b) the modified dynamical matrix method (DMM). The comparison of the different micromagnetic packages and the DMM (based on the calculation of the susceptibility tensor of an isolated inclusion) demonstrate that their results agree to within 3%. Frequency regions in which the metamaterial is characterized by the negative permeability are identified. We speculate that the proposed methodology could be generalized to more complex arrangements of magnetic inclusions, e.g., to those with multiple periods or fractal arrangements, as well as to arrays of inclusions with a distribution of properties.
1550-235X
[11pp.]
Dmytriiev, O.
d21ec0f9-b61a-487c-8aac-dbbf06c8350b
Dvornik, M.
0cbb8bdc-1ad7-408c-a936-56e46fb947d0
Mikhaylovskiy, R.V.
1fa1e312-c783-45b3-a999-9bd958dbfe8d
Franchin, Matteo
9e00aaa2-959e-420f-854c-3b43aece85e3
Fangohr, H.
9b7cfab9-d5dc-45dc-947c-2eba5c81a160
Giovannini, L.
50ed5794-1627-4d6a-bbad-4b5e3bf5b9c9
Montoncello, F.
e669c409-cbd3-4a18-96af-a3cd73ed08f5
Berkov, D.V.
8761928a-3ce2-4e86-b616-4f9dcaa327e7
Semenova, E.K.
e016596c-6edd-4871-8fd4-f34d926e187d
Gorn, N.L.
c340312c-4565-4fb5-853a-7892ab744f97
Prabhakar, A.
dd188e7d-1e2e-4b42-8c61-e094e0678375
Kruglyak, V.V.
1e597fe0-10cd-468f-97f0-cb19c12b4939
Dmytriiev, O.
d21ec0f9-b61a-487c-8aac-dbbf06c8350b
Dvornik, M.
0cbb8bdc-1ad7-408c-a936-56e46fb947d0
Mikhaylovskiy, R.V.
1fa1e312-c783-45b3-a999-9bd958dbfe8d
Franchin, Matteo
9e00aaa2-959e-420f-854c-3b43aece85e3
Fangohr, H.
9b7cfab9-d5dc-45dc-947c-2eba5c81a160
Giovannini, L.
50ed5794-1627-4d6a-bbad-4b5e3bf5b9c9
Montoncello, F.
e669c409-cbd3-4a18-96af-a3cd73ed08f5
Berkov, D.V.
8761928a-3ce2-4e86-b616-4f9dcaa327e7
Semenova, E.K.
e016596c-6edd-4871-8fd4-f34d926e187d
Gorn, N.L.
c340312c-4565-4fb5-853a-7892ab744f97
Prabhakar, A.
dd188e7d-1e2e-4b42-8c61-e094e0678375
Kruglyak, V.V.
1e597fe0-10cd-468f-97f0-cb19c12b4939

Dmytriiev, O., Dvornik, M., Mikhaylovskiy, R.V., Franchin, Matteo, Fangohr, H., Giovannini, L., Montoncello, F., Berkov, D.V., Semenova, E.K., Gorn, N.L., Prabhakar, A. and Kruglyak, V.V. (2012) Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation. Physical Review B, 86 (10), [11pp.]. (doi:10.1103/PhysRevB.86.104405).

Record type: Article

Abstract

We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing arrays of magnetic inclusions of arbitrary shapes. The method fully takes into account the spectrum of spin waves confined in the inclusions. We evaluate the method by considering a particular case of a metamaterial formed by a stack of identical two-dimensional (2D) periodic hexagonal arrays of disk-shaped magnetic inclusions in a nonmagnetic matrix. Two versions of the method are considered. The first approach is based on a simple semianalytical theory that uses the numerically calculated susceptibility tensor of an isolated inclusion as input data for an analytical calculation in which the magnetodipole interaction between inclusions within each 2D array is taken into account. In the second approach, we employ micromagnetic packages with periodic boundary conditions to calculate the susceptibility of the whole 2D periodic array of such inclusions. The comparison of the two approaches reveals the necessity of retaining higher-order terms in the analytical calculation of the magnetodipole interaction via the multipole expansion. Models limited to the dipolar term can lead to remarkable underestimation of the effect of the magnetodipole interaction, in particular, for modes localized near the edge regions of inclusions. To calculate the susceptibility tensor of an isolated inclusion, we have implemented two different methods: (a) a method based on micromagnetic simulations, in which we have compared three different micromagnetic packages: the finite-element package nmag and the two finite differences packages oommf and micromagus; and (b) the modified dynamical matrix method (DMM). The comparison of the different micromagnetic packages and the DMM (based on the calculation of the susceptibility tensor of an isolated inclusion) demonstrate that their results agree to within 3%. Frequency regions in which the metamaterial is characterized by the negative permeability are identified. We speculate that the proposed methodology could be generalized to more complex arrangements of magnetic inclusions, e.g., to those with multiple periods or fractal arrangements, as well as to arrays of inclusions with a distribution of properties.

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Published date: 4 September 2012
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 351899
URI: https://eprints.soton.ac.uk/id/eprint/351899
ISSN: 1550-235X
PURE UUID: f5606976-6cf4-4912-a36e-83b568310ec3

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Date deposited: 30 Apr 2013 13:25
Last modified: 20 Sep 2018 16:31

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Contributors

Author: O. Dmytriiev
Author: M. Dvornik
Author: R.V. Mikhaylovskiy
Author: Matteo Franchin
Author: H. Fangohr
Author: L. Giovannini
Author: F. Montoncello
Author: D.V. Berkov
Author: E.K. Semenova
Author: N.L. Gorn
Author: A. Prabhakar
Author: V.V. Kruglyak

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