Shaping non-reciprocal caustic spin-wave beams

Abstract

A caustic is a mathematical concept describing the beam formation when the beam envelope is reflected or refracted by a manifold. While caustics are common in a wide range of physical systems, caustics typically exhibit a reciprocal wave propagation and are challenging to control. Here, we utilize the highly anisotropic dispersion and inherent non-reciprocity of a magnonic system to shape non-reciprocal emission of caustic-like spin wave beams in an extended 200 nm thick yttrium iron garnet (YIG) film from a nano-constricted rf waveguide. We introduce a near-field diffraction model to study spin-wave beamforming in homogeneous in-plane magnetized thin films, and reveal the propagation of non-reciprocal spin-wave beams directly emitted from the nanoconstriction by spatially resolved micro-focused Brillouin light spectroscopy (BLS). The experimental results agree well with both micromagnetic simulation, and the near-field diffraction model. The proposed method can be readily implemented to study spin-wave interference at the sub-micron scale, which is central to the development of wave-based computing applications and magnonic devices.

Figures (4)

• Figure 1: (a) Sketch of the spin wave profiles along half a wavelength for oppositely propagating waves in DE configuration, together with the ac field generated by the antenna.(b) Superposition of in-plane Fourier components of the ac magnetization $\lvert\tilde{m}_u\rvert$ (black-red scale bar), and ac field $\mathfrak{Re}(\tilde{h}_u)$ (green-blue scale bar) for a 500 nm square segment (white dotted line is the isofrequency curve). (c) NFD, and (d) MuMax3 simulations in the DE-like configuration at 7.9 GHz for a 50 nm thick YIG film magnetized along $v$ axis under a bias field of 200 mT. (e),(f) Same as (a), (b) for bias field along along $u$-axis, showing out-of-plane ac field $\mathfrak{Im}(\tilde{h}_{\xi})$. (g) MuMax3, and (h) NFD simulations in the BVW-like configuration.
• Figure 2: (a) Scanning microscope image of a 400 nm-wide and 2 $\mu$m-long constricted stripline. (b) 2D-field distribution of the in-plane $h_u$, and (c) out-of-plane $h_{\xi}$ components of the excitation field obtained via COMSOL MULTIPHYSICS. (d) BLS measurement at 7.5 GHz, and a bias field $\mu_0 H_\mathrm{ext}$=$\pm$188 mT applied in the $v$-direction. (e) Corresponding MuMax3 simulations, and (f) NFD simulations for both bias field polarities. (g) In-plane Fourier components of the dynamic magnetization $\lvert\tilde{m}_u\rvert$. (h) Real part of the in-plane Fourier component of the ac field $\mathfrak{Re}(h_u)$. (i) Imaginary part of the out-of-plane Fourier component of the ac field $\mathfrak{Im}(h_\xi)$ (dotted line is the isofrequency).
• Figure 3: (a) BLS measurement at 7.5 GHz, and a +188 mT (left) and -188 mT (right) bias field applied along $u$. (b) Corresponding MuMax3, and (c) NFD simulations for both bias field polarities. (d) In-plane component $h_v$ of the microwave field obtained with COMSOL MULTIPHYSICS. (e) Sketch of the chiral coupling occurring at the edges of the constriction in the BVW-like configuration. (f) Superposition of the in-plane Fourier components of ac magnetization $\lvert\tilde{m}_v\rvert$ (black-yellow color scale), and ac field $\lvert h_v\rvert$ (red-blue color scale) indicating the effective caustic locations.
• Figure 4: (a) BLS measurement showing the angular dependence of the field and frequency. (b) Summary of caustic existence conditions. (Top) Frequency dependence of amplitude $|m_x|_\mathrm{max}$, which corresponds to the maximum amplitude of $|m_x|$ at $u$=10 $\mu$m in the NFD simulations (black lines are for BVW-configuration, colored lines for DE-configuration). (Bottom) Comparison between measured caustic angles and theoretical values $\theta_c=\pi/2-(\widehat{\vec{v_g},\vec{H}_{ext}})$ extracted from the isofrequency curve at the corresponding applied fields. (black dashed line corresponds to FMR condition in field and frequency).