Magnon Modes of Microstates and Microwave-Induced Avalanche in Kagome Artificial Spin Ice with Topological Defects

We investigate spin dynamics of microstates in artificial spin ice (ASI) in ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ nanomagnets arranged in an interconnected kagome lattice using microfocus Brillouin light scattering, broadband ferromagnetic resonance, magnetic force microscopy, x-ray photoemission electron microscopy, and simulations. We experimentally reconfigure microstates in ASI using a 2D vector field protocol and apply microwave-assisted switching to intentionally trigger reversal. Our work is key for the creation of avalanches inside the kagome ASI and reprogrammable magnonics based on ASIs.

Figure 1

Gray scale FMR spectra map of sample $A$ for a field protocol of (a) $-90\to +90\mathrm{mT}$ and (b) $-90\to +45\to 0\mathrm{mT}$ at $\varphi =0°$. To enhance the contrast, we show the difference between neighboring spectra (derivative). White arrows represent sweep direction of $H$. (c) Definition of $T1$, $T2$, and $T3$ nanobars with respect to the magnetic field direction. (d) Magnetic force microscopy image of sample $A$ after a field protocol of $-91.2\to +44.1\to 0\mathrm{mT}$ along $\varphi =0°$ (the $x$ axis points upwards). Stray fields detected by MFM are colored in blue (red) consistent with two-in-one-out (one-in-two-out) configuration. The additional colored dots and arrows highlight positions explored by micro-BLS in Fig. 2. The integrated CPW is apparent.

Figure 2

BLS intensities measured for different external field values when the laser spot was placed on the centers of nanobars indicated by (a) orange, (b) magenta, (c) cyan, and (d) green filled circles in Fig. 1. We observe resonance peaks obeying $df/dH<0$ in (a) and (b), and $df/dH>0$ for (c) and (d). The resonance frequencies highlighted by symbols in (a) to (d) are overlaid on FMR data in Fig. 1. (e) Representative sketch illustrating charges on vertices (colored filled circles) and magnetization directions (bold arrows) of the kagome ASI extracted near the CPW (light green) from combined analysis of MFM and BLS data, respectively (see Supplemental Material Fig. S2 for the complete map [19]). The colors of arrows highlighting studied nanobars are consistent with spectra shown in (a) to (d).

Figure 3

(a) Sketches of charge configurations (blue and red spheres) and magnetization vectors $\mathbf{M}$ (arrows) for configurations $C1$ to $C5$. (b) BLS intensities measured at the central position on $T1$ nanobars belonging to the configurations displayed above the spectra at ${\mu }_{0}H=25\mathrm{mT}$. (c) Spatially resolved BLS intensity maps at 25 mT for fixed frequencies in configurations $C1$ to $C5$ displayed above. Here, red (blue) color corresponds to maximum (minimum) BLS intensity. (d)–(h) Simulated spatial distribution of power absorption in $T1$ and $T2$ nanobars for configurations $C1$ to $C5$ at ${\mu }_{0}H=25\mathrm{mT}$. Red (blue) color corresponds to $0.2\mathrm{k}(\mathrm{A}/\mathrm{m}{)}^2$ [$0\mathrm{k}(\mathrm{A}/\mathrm{m}{)}^2$] reflecting spin-precessional amplitude $M_z^2$.

Figure 4

Gray scale FMR spectra of sample $A$ for field protocols of (a) a major loop with $90\to -90\mathrm{mT}$ at $\varphi =20°$ and (b) after first applying $90\to -76\mathrm{mT}$ [yellow arrow in (a)], a minor loop with $-76\to 0\mathrm{mT}$ at $\varphi =20°$ and then $0\to +90\mathrm{mT}$ at $\varphi =-20°$. The solid white arrows indicate field sweep directions. We show the difference between neighboring spectra (derivative). The dashed blue colored lines highlight regimes attributed to particular microstate configurations shown on the top. The black arrows indicate field directions with respect to the bow-tie subgroup. XPEEM images taken at remanence (c) before and (d) after applying a microwave signal at 9.3 GHz. The magnetization of white (black) colored nanobars points along (opposite to) the magnetic field which was applied under microwave irradiation. The CPW appears in light-gray color. (e) Difference between XPEEM images shown in (c) and (d). Nanobars switched by microwaves are shown in white color. The blue solid arrow indicates the x-ray and magnetic field direction.