Spin-wave nonreciprocity and magnonic band structure in a thin permalloy film induced by dynamical coupling with an array of Ni stripes

M. Mruczkiewicz, P. Graczyk, P. Lupo, A. Adeyeye, G. Gubbiotti, and M. Krawczyk

Phys. Rev. B 96, 104411 – Published 11 September 2017

Abstract

An efficient way for control of the spin wave propagation in a magnetic medium is the use of periodic patterns known as magnonic crystals (MCs). However, the fabrication of MCs especially bicomponents, with periodicity in nanoscale, is a challenging task due to the requirement for sharp interfaces. An alternative method to circumvent this problem is to use homogeneous ferromagnetic film with a modified periodically surrounding. In this work we demonstrate that the magnonic band structure is formed in thin Py film due to dynamical magnetostatic coupling with the array of Ni stripes. We show that the band gap width can be systematically tuned by changing separation between film and stripes. We show also the effect of nonreciprocity, which is seen at the band gap edge which is shifted from the Brillouin zone boundary and also in nonreciprocal interaction of propagating spin waves in Py film with the standing waves in Ni stripes. Our findings open a possibility for further investigation and exploitation of the nonreciprocity and band structure in magnonic devices.

Received 13 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.104411

Physics Subject Headings (PhySH)

Spin waves

Magnetic multilayers Nanowires

Bloch-Floquet theorem Brillouin scattering & spectroscopy Finite-element method Landau-Lifschitz-Gilbert equation Magnetization measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Mruczkiewicz¹, P. Graczyk², P. Lupo³, A. Adeyeye³, G. Gubbiotti⁴, and M. Krawczyk^2,*

¹Institute of Electrical Engineering, Slovak Academy of Sciences, Dubravska cesta 9, 841 04 Bratislava, Slovakia
²Faculty of Physics, Adam Mickiewicz University in Poznan, Umultowska 85, 61-614 Poznan, Poland
³Information Storage Materials Laboratory, Department of Electrical and Computer Engineering, National University of Singapore, 117576 Singapore
⁴Istituto Officina dei Materiali del CNR (CNR-IOM), Sede Secondaria di Perugia, c/o Dipartimento di Fisica e Geologia, Università di Perugia, I-06123 Perugia, Italy

^*krawczyk@amu.edu.pl

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Vol. 96, Iss. 10 — 1 September 2017

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Images

Figure 1
(a) SEM image of the Ni wires after the first stage of the fabrication process. (b) Schematic representation of the cross-sectional view of the sample (unit cell) under investigation. It is composed of a homogeneous Py film ( $t_{Py} = 30 nm$ ) and an array of Ni stripes ( $t_{Ni} = 30 nm$ ) beneath it. The SWs propagate along the $x$ axis, which is perpendicular to the magnetic field (the $z$ direction). Periodic boundary conditions (PBC) are assumed along the $x$ axis.
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Figure 2
Measured BLS spectrum (points) and fitted Lorentzian curve of the peaks on the Stokes and anti-Stokes side of the spectrum at $k = 13.9 rad / μ m$ in the bilayer composed of Py and Ni films. (b) Dispersion relation of SWs. The red (black) lines and square dots show the points collected from the anti-Stokes (Stokes) side of the spectra, i.e., from the waves propagating in the $+ x$ and $- x$ direction, respectively. The dots are measured data, lines refer to the calculations. In the insets, the SW amplitude for two waves at the same wave number propagating in opposite directions is shown. (c) The difference in frequencies between SWs propagating in the opposite directions obtained from the Stokes and anti-Stokes sides of BLS spectra in (b) in dependence of the wave number for the external magnetic field 500 Oe. The red dotted line is a guide to the eye.
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Figure 3
The dispersion relation of SWs measured with BLS in Py film with the array of the Ni wires beneath it. The data for three samples with separation $t_{Cr} = 0, 10$ , and 30 nm between Py film and Ni NWs are shown. The magnetic field is in-plane of the film and along Ni wires, it has magnitude 500 Oe. The vertical dashed lines mark the Brillouin zone boundaries. The thin lines (dense small dots) mark the numerical results for Py film and Ni NWs with separation $t_{Cr} = 30 nm$ and pinning on the Py surface.
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Figure 4
(a) Magnonic band structure computed for the Py film with the array of Ni wires separated by 0, 10, and 30 nm of Cr. The vertical dashed line points at the first Brillouin zone border. The empty circles labeled (b)–(e) indicate the modes of the sample with $t_{Cr} = 10 nm$ from the second BZ, which are equivalent to the BZ center. Their SW amplitude space distributions are shown in (b)–(e). (f) and (g) The magnitude of stray dynamic magnetostatic field for DE mode with the same frequency (10.3 GHz) but opposite slopes, equivalent to the waves propagating in opposite directions.
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Figure 5
Enlarged view of the dispersion relation from Fig. 4 around the magnonic band gap (marked with a gray bar for sample with $t_{Cr} = 30 nm$ ) (a), and around the anticrossings (dotted circle) of the DE band with the mode localized in Ni wires (b).
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