Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

A. V. Sadovnikov, S. A. Odintsov, E. N. Beginin, S. E. Sheshukova, Yu. P. Sharaevskii, and S. A. Nikitov

Phys. Rev. B 96, 144428 – Published 24 October 2017

Abstract

We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

Received 5 May 2017
Revised 8 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.144428

Physics Subject Headings (PhySH)

Electrical generation of spin carriers Ferromagnetism Magnetization switching Spin waves

Magnetic insulators

Brillouin scattering & spectroscopy Landau-Lifschitz-Gilbert equation Micromagnetic modeling Microwave techniques Rigorous coupled-wave analysis

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. V. Sadovnikov^*

Laboratory “Metamaterials”, Saratov State University, Saratov 410012, Russia and Kotel'nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia

S. A. Odintsov, E. N. Beginin, S. E. Sheshukova, and Yu. P. Sharaevskii

Laboratory “Metamaterials”, Saratov State University, Saratov 410012, Russia

S. A. Nikitov

Laboratory “Metamaterials”, Saratov State University, Saratov 410012, Russia and Kotel'nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009, Russia

^*sadovnikovav@gmail.com

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Vol. 96, Iss. 14 — 1 October 2017

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Images

Figure 1
(a) Schematic view of side-coupled magnonic stripes and cartoon of BLS experiment. BLS measurement was performed in backscattering configuration. On the inset: relative effective gap $d_{eff} / d$ as a function of stripe's width. (b) Internal magnetic field profile $H_{i} (y)$ for SCMSs (top) and the transverse profile of the symmetric $Φ_{s} (y)$ and antisymmetric $Φ_{as} (y)$ modes (bottom). The spacing between stripes is depicted with shaded area. (c) The dispersion measured using VNA (open squares) and dispersion characteristics of symmetric and antisymmetric modes of SCMSs of width 100 $μ m$ (dashed curves), 200 $μ m$ (solid curves), and 1 mm (dotted curves). All the shown data were obtained at $H_{0} = 1200$ Oe.
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Figure 2
Normalized color-coded BLS intensity map recorded at the excitation frequency of $f_{1} = 5.1$ GHz. Power level of input signal is labeled above each map. Edges of stripes are guided with dotted lines. $L$ denotes the spin-wave coupling length for each map.
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Figure 3
Snapshots of the out-of-plane component of dynamic magnetization (a) and distribution of spin-wave amplitude (b) calculated by the means of micromagnetic simulations at the excitation frequency of $f_{1} = 5.1$ GHz. Edges of stripes are guided with dotted lines. (c) Calculated longitudinal profile of spin-wave amplitude in first ( $Ψ_{1}$ ) and second ( $Ψ_{2}$ ) stripe. The data of BLS experiment are shown with open symbols. (d) Frequency dependence of $L$ is shown with open circles (BLS data), solid curve (micromagnetic simulation), and dotted curve (FEM simulation). All the shown data were obtained at $H_{0} = 1200$ Oe.
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Figure 4
(a) Experimentally measured transmission coefficient $T_{0}$ as a function of $x$ coordinate at $P_{0} = - 25$ dBm (open circles) and $P_{0} = 23$ dBm (closed squares). Solid and dashed curves depict the results of numerical simulation; power dependency of coupling length (b) and transmission factor (c), measured by BLS (triangles) and numerically simulated using micromagnetic simulation (MMS), FEM, and coupled GLEs (as labeled in box). (d) Mode $y$ profiles $Φ_{1, 2}$ of separated stripes at $P_{0} = 0$ dBm (dashed curve) and $P_{0} = 23$ dBm (solid curves). (e) Nonlinear differential phase shift in each stripe $Δ ϕ_{NL} 1, 2$ (dashed and dotted curves) and overlap integral $C$ (solid curve) as a function of input power. The data were obtained for $f = 5.1$ GHz and $H_{0} = 1200$ Oe.
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Figure 5
(a) Dynamic amplitude of SW $h_{0}$ (solid curve) and coupling length (dashed curve) as a function of saturation magnetization in YIG. (b) The map of $P_{0} (f)$ demonstrating the regimes of spin-wave dynamics. Yellow region corresponds to the SW transmission through the first magnetic stripe, blue—to the second. The dashed, solid, and dotted curves correspond to the values of $T$ , denoted at the top of map. (c) Transmission of SW through the first stripe $S_{1}$ measured with VNA in linear (solid green curve) and nonlinear (dotted red curve) regime. Calculation results are shown with dashed and dash-dotted curves. (d) Coupling length as a function of distance between stripes (solid curve) and internal magnetic field in the center of the stripe (dotted curve—simulation; open squares—BLS experiment). (e) Threshold power $P_{th}$ of spin-wave switching as a function of spacing between stripes and internal magnetic field. (f) Threshold power (solid curve) and coupling length (dotted curve) as a function of the stripes' width. Open circles denote the experimental data.
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