Towards graded-index magnonics: Steering spin waves in magnonic networks

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Towards graded-index magnonics: Steering spin waves in magnonic networks

C. S. Davies, A. Francis, A. V. Sadovnikov, S. V. Chertopalov, M. T. Bryan, S. V. Grishin, D. A. Allwood, Y. P. Sharaevskii, S. A. Nikitov, and V. V. Kruglyak

Phys. Rev. B 92, 020408(R) – Published 20 July 2015; Erratum Phys. Rev. B 95, 019901 (2017)

Abstract

Magnonics explores precessional excitations of ordered spins in magnetic materials—so-called spin waves—and their use as information and signal carriers within networks of magnonic waveguides. Here, we demonstrate that the nonuniformity of the internal magnetic field and magnetization inherent to magnetic structures creates a medium of graded refractive index for propagating magnetostatic waves and can be used to steer their propagation. The character of the nonuniformity can be tuned and potentially programmed using the applied magnetic field, which opens exciting prospects for the field of graded-index magnonics.

Received 2 February 2015
Revised 29 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.020408

Erratum

Erratum: Towards graded-index magnonics: Steering spin waves in magnonic networks [Phys. Rev. B 92, 020408(R) (2015)]

C. S. Davies, A. Francis, A. V. Sadovnikov, S. V. Chertopalov, M. T. Bryan, S. V. Grishin, D. A. Allwood, Y. P. Sharaevskii, S. A. Nikitov, and V. V. Kruglyak

Phys. Rev. B 95, 019901 (2017)

Authors & Affiliations

C. S. Davies¹, A. Francis¹, A. V. Sadovnikov^2,3, S. V. Chertopalov⁴, M. T. Bryan⁵, S. V. Grishin², D. A. Allwood⁵, Y. P. Sharaevskii², S. A. Nikitov^2,3, and V. V. Kruglyak^1,*

¹School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
²Laboratory “Metamaterials,” Saratov State University, Saratov 410012, Russia
³Kotel'nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia
⁴Donetsk National University, 24 Universitetskaya Street, Donetsk 83001, Ukraine
⁵Department of Materials Science and Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom

^*Corresponding author: v.v.kruglyak@exeter.ac.uk

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Issue

Vol. 92, Iss. 2 — 1 July 2015

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Images

Figure 1
A schematic of the TRSKM experiment. (a) The Permalloy microstructures are mounted on top of the CPW, producing a microwave magnetic field $h$ . The scanned optical probe is used to measure the out-of-plane component of the magnetization via the polar Kerr effect. (b) The sample is shown, together with a representative time-resolved Kerr signal acquired in experiments with pulsed excitation and its Fourier spectrum (top inset). In experiments with cw excitation, Kerr images of the spin waves in the highlighted region were acquired at eight time delays, shown by the red points on one cycle of the continuous wave (cw) microwave pump (bottom inset). The frequency $f$ of the microwave is equal to that of the Fourier peak from the top inset. The bias magnetic field $H_{B}$ is applied at different angles $α$ relative to the horizontal symmetry axis of the microstructure.
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Figure 2
Snapshots of spin waves propagating in the arms of the Permalloy T junction. The bias magnetic field $H_{B} = 500 Oe$ is applied parallel (a) and at angles of $α = - 15^{\circ}$ (b) and $α = + 15^{\circ}$ (c) relative to the leg of the junction (i.e., horizontal symmetry axis from Fig. 1). In each case, the top and bottom panels show results of the TRSKM imaging and micromagnetic simulations, respectively. The frequency of the cw pump was 8.24 GHz for experiments, while for simulations it was 7.62 GHz in (a) and 7.52 GHz in (b) and (c). The difference in the frequency values is due to inevitable differences between the measured and simulated samples.
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Figure 3
Spin waves in an asymmetrically magnetized Permalloy T junction. (a) The calculated distributions of the static magnetization (arrows) and the projection of the internal magnetic field onto the magnetization (color scale) are shown for the magnetic field of $H_{B} = 500 Oe$ applied at $15^{\circ}$ to the vertical symmetry axis. Each arrow represents the average of $5 \times 5$ mesh cells. (b) $k_{x}$ spectra of the dynamic magnetization distributions across the leg [gray line in (a)] and along the arms [blue line in (a), amplified $\times 5]$ of the T junction excited at 7.52 GHz are shown by the gray and blue curves, respectively. The $k_{x}$ value of $0.94 μ m^{- 1}$ , indicated by a dashed line, corresponds to maximum spin-wave Fourier amplitude. (c) A construction illustrating the extraction of the group velocities of the incident (index “i”) and reflected (index “r”) beams is shown for the white boxed pixel in (a). For the specific $k_{x}$ value of $0.94 μ m^{- 1}$ [which is indicated by the vertical dashed lines here and in (b)], the group velocities are perpendicular to the characteristic isofrequency curves (purple). The $k_{y}$ value is given by the crossing of the dashed line and the isofrequency curve. Here and in (b), the region shaded yellow has the same size and represents the range of forbidden $k_{x}$ values, as calculated for the white boxed pixel and for pixels on the gray line in (a), respectively. (d) The extracted directional unit vectors of the group velocities $\hat{v}$ and wave vectors $\hat{k}$ are shown for $k_{x}$ values shown by the vertical dashed lines in (b) and (c).
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