Tunable magnetization dynamics in artificial spin ice via shape anisotropy modification

Ferromagnetic resonance (FMR) is performed on kagome artificial spin ice (ASI) formed of disconnected ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ nanowires. Here we break the threefold angular symmetry of the kagome lattice by altering the coercive field of each sublattice via shape anisotropy modification. This allows for distinct high-frequency responses when a magnetic field is aligned along each sublattice and additionally enables simultaneous spin-wave resonances to be excited in all nanowire sublattices, unachievable in conventional kagome ASI. The different coercive field of each sublattice allows selective magnetic switching via global field, unlocking novel microstates inaccessible in homogeneous-nanowire ASI. The distinct spin-wave spectra of these states are detected experimentally via FMR and linked to underlying microstates using micromagnetic simulation.

Figure 1

SEM of device and 40 by $100\mu m$ ASI array. Two copper GSG type waveguides are deposited on top also via EBL with thickness of 200 nm. The CPWs are connected to a VNA to measure the power reflection, ${\mathrm{S}}_{11}$. Angle $\theta$, used throughout script, are defined in the top left of the figure where $0^{\circ }$ is along the length of the medium nanowire. (b) SEM of the structure used to determine the width, lengths, and end-to-end distances of the nanowires. (c) AFM image for nanowire height characterisation. (d) MFM image showing nanowires obeying pseudo-ice-rule consistent with the presence of geometric frustration.

Figure 2

(a), (b), and (c) are experimental magnetic field sweeps from positive to negative aligned along the length of the narrow, medium, and wide nanowires, respectively, as illustrated by the inset and arrow. (d), (e), and (f) are the corresponding micromagnetic simulations with inset showing geometry used with periodic boundary conditions applied. The labeled modes in Figs. (a)–(f) are illustrated in the spatial pixel power plots in (g), (h), and (i) at 1.5 kOe along the direction of the white arrow. The N, M, and W modes are located in the bulk of the narrow, medium, and wide nanowires, respectively. The S mode is the result of magnetization curling at the ends of the wide nanowire. (j) and (k) are the magnetization profiles of the wide nanowire at 1.5 kOe offset by $\pm {60}^{\circ }$ resulting in the S mode. (l) is the magnetization profile of the wide nanowire when the field is aligned along the length in which case the S mode is not present. The N mode in (h) and (i) is not detected experimentally due to relatively lower volume compared to the other two nanowires. This fact combined with the S mode only occurring in (g) and (h) explains the different mode numbers for each of the three cases.

Figure 3

(a) is the experimental frequency dependence of the absorbed power for three angles. The M-mode peak height is measured as shown by the dotted lines and arrows. These are normalized by the peak height at $0^{\circ }$. (b) shows the normalized power, $\alpha$, for all angles which varies sinusoidally. The errors are estimated from the variation in the power of the broadband frequency and error propagation is calculated. There is a relative increase in the peak height at ${45}^{\circ }$ which occurs where the modes are brought closer together as can be seen in (c) which shows the full angular dependence where each result is divided by $\alpha$ so they are displayed more clearly. The green triangles, blue squares, and red circles show the peak positions and error bars show the full width at half maximum (FWHM) for the narrow, medium, and wide modes, respectively. Colored spectra indicate when the field is aligned along a particular nanowire. (d) is the simulated angular dependence which is normalized to the maximum peak across all spectra so the relative peak size as a function of the angle is discernible. Each of the four possible permutations of nanowire frequency ordering regions are indicated between (c) and (d) and the dotted lines indicate the mode positions switching. The NMW region is where the four mode case is possible in other regions the N mode is too weak to be detected. There is a switching of the M and N modes at ${25}^{\circ }$ where the MNW region begins where it is possible to have three modes. Next is the MWN region which contains the coincidental angle where the three modes come close together. Finally the NWM mode where it is possible to have a case with two detectable modes. The S mode is suppressed here as the field is more closely aligned with the length of the wide nanowire

Figure 4

(a) shows results from angular dependent simulation around the region where the three modes N (green triangles), M (blue squares), and W (red circles) are brought close together. The error bars show the FWHM. (b)–(e) illustrate the modes coming together and then apart again as the angle is varied. The insets show the relative orientation of the ASI. (d) shows the modes coming close together at ${52}^{\circ }$ with an increase in relative amplitude. The full bandwidth (defined as between where the resonance starts and ends) of the cumulative peak is used to integrate the power pixel map in (f) which shows resonance in all sublattices over a 600 MHz range.

Figure 5

A minor loop field protocol is performed starting from $-200$ to 200 Oe and increasing by 200 Oe after each minor loop up to 1 kOe along the length of the wide nanowire. (a) is the experimental result of the fourth minor loop with range $-800$ to 800 Oe. The field is swept from negative to positive as illustrated in the inset. (b) is the simulated FMR for the current ASI structure. The labeled modes correspond to the power pixel plots in (e). (c) is the simulation result where the width of half of the wide nanowires are reduced by 35 nm which introduces a new mode [vi]. (d) and (g) are the simulated hysteresis minor loops for the field protocol for the sample structure and further modified structure, respectively. The white dots indicate the location within the hysteresis that the magnetization and power pixel plots are analyzed. (e) and (h) are the magnetization state at $-0.8$ kOe for the sample and further modified structure, respectively, where the color wheel in the top left corner shows the magnetization direction and the white arrow shows applied field direction. (f) [i–iii] and (i) [iv–vi] show the corresponding power pixel plots at $-600$ Oe for the sample and modified structure, respectively. A video of the simulated minor loop protocols is available in the Supplemental Material [29].