Coupled vortex oscillations in mesoscale ferromagnetic double-disk structures

Coupled resonance modes in connected ferromagnetic double-dot structures have been investigated as a function of the overlap between the dots, both experimentally and via micromagnetic simulations. An asymmetry is observed in the frequency spectrum about zero field. Softening of the magnetization during vortex core precession when the cores are near the overlap region results in low-frequency modes and a splitting corresponding to different polarity combinations. A range of vortex resonance frequencies are identified that can be tuned by varying the overlap area. This study provides insight into the control of the dynamic response in coupled mesoscale magnetic structures.

Figure 1

(a) AFM images for 1-$\mu$m diameter disks with edge-to-edge separation of 130 nm and connected disks with contact length (CL) of 220 nm. (b) Frequency spectrum for separated disks as a function of $H$. (c)–(f) Frequency spectra for CL $=$ 220, 450, 615, and 740 nm, respectively.

Figure 2

Micromagnetically simulated magnetization configurations for connected disks of diameter 1$\mu$m with CL $=$ 200-nm and 20-nm thick Ni${}_{80}$Fe${}_{20}$ for vortex cores (a) near the overlapping region and (b) at the opposite boundary edges. The color coding shows the azimuthal angle of the local magnetization vector. Micromagnetically simulated volume charge density ($\nabla ·M$) for a connected disk (c) with $\mathrm{CL}=200$ nm when the cores are pushed far apart and for a single disk (d).

Figure 3

Micromagnetically simulated volume charge density ($\nabla ·M$) for connected disks with $\mathrm{CL}=600$ nm when the cores are pushed close to the CL by an applied field for (a) $p_1{p}_2=-1$ and (b) $p_1{p}_2=+1$.

Figure 4

(a) and (b) shows the plots of the potential well profiles for left disk as a function of normalized $M_X$ for $H=-100$ and $+$100 Oe for $p_1{p}_2=-1$ and $\mathrm{CL}=200$ nm. Solid lines are the quadratic fits to the curves.

Figure 5

Plot of ${\omega }_r$ as a function of $H$ for various CL values. Inset shows the simulated magnetization configuration for CL $=$ 600 nm when the cores are near the overlapping region, with the color coding showing the azimuthal angle of the local magnetization vector.

Figure 6

Sketches of the relative motion of the two cores in connected disks for $p_1{p}_2=+1$ and $-1$ are shown in (a) and (b), respectively. The outer thick arrows correspond to the chirality of in-plane magnetization in the two disks.