Ferromagnetic resonance modes in trilayer artificial spin ices subject to interfacial Dzyaloshinskii-Moriya interaction

Abstract

Artificial spin ices are metamaterials that can host several ferromagnetic resonances as well as spin waves. As the field advances towards the creation of three-dimensional geometries, a trilayer square artificial spin ice has been already found to exhibit many interesting properties. Here, we numerically investigate a strongly-coupled trialyer square artificial spin ice under the effect of interfacial Dzyaloshinskii-Moriya interaction (DMI). This interaction affords non-reciprocity to waves, leading to changes in the standing wave modes established in confined geometries. We find that the interplay between the non-reciprocity, an applied field, and the stray field within the artificial spin ice results in frequency split additional edge modes. The edge modes are favored by the DMI sign and exhibit destructive and constructive interference depending on both the DMI magnitude and the external magnetic field. Our results demonstrate the non-reciprocity in small nanoislands can affect the long-range states stabilized in the artificial spin ice due to the strong coupling between layers.

Figures (8)

• Figure 1: Schematic of a trilayer element composed of a top Py layer (light blue) and a bottom CoFe layer (dark blue) separated by a nonmagnetic spacer of thickness $G$. The stadium-shaped nanoislands have dimensions $L = 200$ nm, $W = 100$ nm, and $T = 5$ nm.
• Figure 2: Hysteresis loops for a trilayer element for gaps of (a-b), $5$ nm, (c-d) $20$ nm, and (e-f) $40$ nm. The hysteresis curves of Py are shown in (a), (c), and (e) while the hysteresis curve of CoFe are shown in (b), (d), and (f). In all cases, the field sweep from positive to negative field is shown by blue curves and the sweep from negative to positive field is shown by black dashed curves.
• Figure 3: Ferromagnetic resonance for a trilayer element for gaps of (a-b), $5$ nm, (c-d) $20$ nm, and (e-f) $40$ nm. The FMR of Py are shown in (a), (c), and (e) while the FMR of CoFe are shown in (b), (d), and (f).
• Figure 4: Schematic of a trilayer square ASI where each element is the trilayer shown in Fig. \ref{['fig:geometry']}. The center-to-center distance is $d=300$ nm.
• Figure 5: DMI-dependent spectra for trilayer ASIs for the cases in which DMI has the same sign for (a) Py and (b) CoFe; and DMI is opposite values for (c) Py and (d) CoFe. In the latter pannels, the sign of the x-axis represents the DMI parameters for the Py layer. For dominant modes are identified: bulk (B), edge (E), and two standing-wave modes, M1 and M2.