Vortex chain states in a ferromagnet/superconductor bilayer

The discrete vortex lattices in a ferromagnet/superconductor bilayer are studied when the ferromagnet has periodic stripe domains with an out-of-plane magnetization. The vortices are assumed to be situated periodically on chains in the stripe domains. Only up to two vortex chains per domain configurations are considered. When the domain period is fixed, the threshold magnetization is calculated at which the transition from the Meissner state to the mixed state occurs. When the domain period is not fixed, the equilibrium domain size and vortex positions are calculated, depending on the domain’s magnetization and the domain wall energy. In equilibrium, the vortices in the neighbor domains are halfway shifted, while they are next to each other in the same domain.

Figure 1

Proposed configurations for $N=1$ and $N=2$ states.

Figure 2

Phase diagram showing transition from the Meissner state to the mixed state, depending on $m{\varphi }_0∕{\epsilon }_0$ and $\Lambda ∕L$. The region below the $N=1$ curve corresponds to the Meissner state, while the $N=1$ state exists in the area between the $N=1$ and $N=2$ curves. The $N=2$ state becomes energetically favorable above the $N=2$ curve.

Figure 3

The phase diagram for the third case $N=2$ state. The $N=2$ state becomes stable in the region above the curve.

Figure 4

$L∕\Lambda$ versus $m{\varphi }_0∕{\epsilon }_0$ for the third configuration.

Figure 5

$b∕\Lambda$ versus $m{\varphi }_0∕{\epsilon }_0$ for the third configuration.

Figure 6

$a∕\Lambda$ versus $m{\varphi }_0∕{\epsilon }_0$ for the third configuration.