Spin-wave dynamics in permalloy/cobalt magnonic crystals in the presence of a nonmagnetic spacer

P. Malagò, L. Giovannini, R. Zivieri, P. Gruszecki, and M. Krawczyk

Phys. Rev. B 92, 064416 – Published 12 August 2015

Abstract

In this paper, we theoretically study the influence of a nonmagnetic spacer between ferromagnetic dots and a ferromagnetic matrix on the frequency dispersion of the spin-wave excitations in two-dimensional bicomponent magnonic crystals. By means of the dynamical matrix method we investigate structures that are inhomogeneous across the thickness represented by square arrays of cobalt or permalloy dots in a permalloy matrix. We show that the introduction of a nonmagnetic spacer significantly modifies the total internal magnetic field, especially at the edges of the grooves and dots. This permits the manipulation of the magnonic band structure of spin waves localized either at the edges of the dots or in matrix material at the edges of the grooves. According to the micromagnetic simulations two types of end modes were found. The corresponding frequencies are significantly influenced by the end modes’ localization region. We also show that, with the use of a single ferromagnetic material, it is possible to design a magnonic crystal preserving the properties of bicomponent magnonic crystals and magnonic antidot lattices. Finally, the influence of the nonmagnetic spacers on the technologically relevant parameters such as group velocity and magnonic bandwidth are discussed.

Received 16 April 2015
Revised 24 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.064416

Authors & Affiliations

P. Malagò¹, L. Giovannini¹, R. Zivieri¹, P. Gruszecki², and M. Krawczyk²

¹Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via G. Saragat 1, I-44122 Ferrara, Italy
²Faculty of Physics, Adam Mickiewicz University in Poznań, Umultowska 85, 61-641 Poznan, Poland

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 92, Iss. 6 — 1 August 2015

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) System 1: Top view of the primitive cell and its perpendicular cross section in a bicomponent MC consisting of Co square dots in square array partially immersed in Py. Nonmagnetic spacer (white area) of 10 nm thickness separates the bottom of Co dots from Py. (b) System 2-Co: similar to S1 but with full separation of Co dots (200 nm wide) from Py (10 nm of nonmagnetic spacer from the bottom and lateral sides of Co). (c) System S2-Py: one-component MC with geometry equal to $S 2^{Co}$ but with Py dot. (d) System 3: MC created by square array of square grooves in Py film partially filled with Py dots. Dots are separated from the matrix by 10-nm-thick nonmagnetic spacer. (e) System 4: square array of square Co dots. Red dashed lines in the perpendicular cross sections point at the planes $(z = 5 and 25 nm)$ used in Figs. 2–2 to visualize the spatial profiles of SW modes.
Reuse & Permissions
Figure 2
Differential scattering cross section calculated for S1 at the center of the BZ. The arrows label the modes with the highest scattering cross section in the center of the first BZ investigated in this paper.
Reuse & Permissions
Figure 3
Dispersion relation in the first BZ along the direction perpendicular to the external magnetic field. (a) Dispersion relation of the most relevant modes in S1: end mode of the dot $(E M_{d})$ , Damon-Eshbach–like mode (DE), and DE-like mode in horizontal rows $(D E^{HR})$ are shown. (b) Dispersion relation in $S 2^{Co}$ . The additional dispersion relation of the end mode in Py film $(E M_{f})$ and backwardlike volume SW $(B A^{HR})$ are shown. (c) Dispersion relation of the most relevant modes in $S 2^{Py}$ . (d) Dispersion relation in S3. (e) Dispersion relation in the array of Co dots (S4). The black dashed lines in (b)–(d) mark dispersion relation of DE mode in homogeneous Py film of 10 nm thickness calculated according to Ref. [49].
Reuse & Permissions
Figure 4
Spatial profiles (real part of the out-of-plane component of the dynamic magnetization vector) for SWs with large differential scattering cross section in the center of the Brillouin zone. The spatial profiles of SW modes from the bottom part of the Py film (in the plane $z = 5 nm$ in left column) and in the plane crossing dots (for $z = 25 nm$ in right column) are shown in $3 \times 3$ primitive cells, i.e., on the planes marked in Fig. 1 with red dashed lines. (a) Spatial profiles of EM, $D E^{HR}$ , and DE modes in S1. (b) Spatial profiles of $E M_{d}, E M_{f}, D E^{HR}, B A^{HR}$ , and DE modes in $S 2^{Co}$ . (c) Spatial profiles of $E M_{d}, E M_{f}$ , DE, $B A^{HR}$ , and $D E^{HR}$ modes in $S 2^{Py}$ . (d) Spatial profiles of $E M_{f}$ , DE, $E M_{d}, B A^{HR}$ , and $D E^{HR}$ modes in S3. (e) Spatial profiles of EM and DE modes in S4.
Reuse & Permissions
Figure 5
The $y$ component of the total magnetic field calculated for (a) S1, (b) $S 2^{Co}$ , (c) $S 2^{Py}$ , and (d) S3 along the $y$ axis and averaged along $x$ , for four different values of $z$ : $z = 5 nm$ (in full Py film, black dot-dashed line), $z = 15 nm$ (crossing Py and spacer below the dots, red dashed line), $z = 25 nm$ (crossing Py matrix and middle of dots, green dotted line), and $z = 35 nm$ crossing Co dots (only in S1 and $S 2^{Co}$ , blue solid line). The gray vertical rectangles mark the nonmagnetic spacers which separate the dot from the matrix. The insets on the top show a sketch of MCs with lines along which the total magnetic field is calculated.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics