Transverse instabilities of multiple vortex chains in magnetically coupled ${\text{NbSe}}_2/\text{permalloy}$ superconductor/ferromagnet bilayers

Using scanning tunneling microscopy and Ginzburg-Landau simulations, we explore vortex configurations in magnetically coupled ${\text{NbSe}}_2/\text{permalloy}$ superconductor/ferromagnet bilayer. The permalloy film with stripe domain structure induces periodic local magnetic induction in the superconductor, creating a series of pinning-antipinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-one-dimensional arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the system becomes nonlinear due to a change in both the number of vortices and the confining potential. The longitudinal instabilities of the resulting vortex structures lead to vortices “levitating” in the antipinning channels.

Figure 1

(Color online) (a) Fabrication of magnetically coupled superconductor/ferromagnet structure: on a single crystal ${\text{NbSe}}_2$ a thin layer of insulating ${\text{SiO}}_2$ is evaporated followed by a $1\text{−}\mu \text{m}$-thick permalloy. After cleaving the ${\text{NbSe}}_2$ down to submicron thickness, fresh atomically flat surface is exposed to the STM probe. (b) Magnetic force microscope images of the stripe domain pattern in Py at 0 and 2000 Oe applied field perpendicular to the surface of the film at room temperature. Scan area is $20\times 20\mu {\text{m}}^2$.

Figure 2

(Color online) (a) STM images of vortex configurations in ${\text{NbSe}}_2$ at 4.2 K. Applied magnetic field values (in Oe) perpendicular to the surface of the superconductor are shown in the upper right corner. The white dotted lines show the underlying magnetic stripe domain boundaries. The scanning area is $0.7\times 0.7\mu {\text{m}}^2$. (b) Cooper-pair density plots, calculated at $-105$ and $-165\text{Oe}$ [in comparison with (a); see marked area], obtained for $D=1\mu \text{m}$ (plot sizes are $1.087\times 2.176$ and $1.087\times 2.193\mu {\text{m}}^2$, respectively).

Figure 3

(Color online) (a) Same as Fig. 2, but for $H=\pm 300$ and $\pm 400\text{Oe}$. (b) Cooper-pair density plots, calculated at $-325$ and $-385\text{Oe}$, for $D=1\mu \text{m}$ (plot sizes are $1.087\times 2.176$ and $1.087\times 2.193\mu {\text{m}}^2$, respectively).

Figure 4

(Color online) The equilibrium vortex phase diagram of the ${\text{NbSe}}_2$ film at $T=4.2\text{K}$ as a function of thickness of the underlying Py film $D$ and external perpendicular field $H$ (the domain structure of the Py film is assumed to be unperturbed by the applied field). $N$ denotes the number of vortex chains along the positive magnetic domains [illustrated by ${\left|\psi \right|}^2$ contour plots on the right, dark (light) color—low (high) density]. At high fields, vortices penetrate areas above negative magnetic domains.

Figure 5

(Color online) Average vortex spacing along the chain, prior to $N\to N+1$ chain configurational transition (color coding corresponding to Fig. 4), as a function of the thickness of the Py film.