Interaction between Superconducting Vortices and a Bloch Wall in Ferrite Garnet Films

A theoretical model for how Bloch walls occurring in in-plane magnetized ferrite garnet films can serve as efficient magnetic micromanipulators is presented. As an example, the walls’ interaction with Abrikosov vortices in a superconductor in close contact with a garnet film is analyzed within the London approximation. The model explains how vortices are attracted to such walls, and excellent quantitative agreement is obtained for the resulting peaked flux profile determined experimentally in ${\mathrm{NbSe}}_2$ using high-resolution magneto-optical imaging of vortices. In particular, this model, when generalized to include charged magnetic walls, explains the counterintuitive attraction observed between vortices and a Bloch wall of opposite polarity.

Figure 1

Magneto-optical image of the vortex distribution near a Bloch wall in a Bi-substituted lutetium iron garnet film placed on top of a superconducting ${\mathrm{NbSe}}_2$ crystal with transition temperature of 7.2 K. The slightly uncrossed analyzer and polarizer setting used here implies that the dark wall and the bright vortices have opposite field polarities. Image dimensions are $70\times 70\mu {\mathrm{m}}^2$.

Figure 2

Top: MO image showing a zigzag Bloch wall in a FGF separating two domains with antiparallel in-plane magnetization. Bottom: Sketch of an in-plane magnetized FGF with a Bloch wall placed above a superconductor. The magnetic charges along the vertical sides of the wall can lead to a net attraction between a wall and vortices, as seen in Fig. 1.

Figure 3

The calculated forces on the vortex from the Bloch wall: $F^{\perp }$ is repulsive and $F^{\parallel }$ is attractive. Their sum $F^{vw}$ changes sign at $x^{*}\approx 1\mu \mathrm{m}$. The parameters used here are: $\sin \phi =0.34$, $2W=0.6\mu \mathrm{m}$, $h=0.8\mu \mathrm{m}$, $a=140\mathrm{nm}$, $\lambda =200\mathrm{nm}$, and $M_s=50\mathrm{kA}/\mathrm{m}$.

Figure 4

The excess vortex density $\delta N(x)$ near the Bloch wall for various wall width $2W$ calculated using $L=160\mu \mathrm{m}$ and the other parameter values as indicated in the caption of Fig. 3.

Figure 5

Top: Distribution of vortices formed in the presence of a Bloch wall. The image was taken after the wall, seen in Fig. 1, was removed by an in-plane field of the order of a few $\mu \mathrm{T}$ applied perpendicular to the indicated $x$ axis. Bottom: Vortex density obtained from the image (each symbol represents one vortex) together with the theoretical curve calculated for $L=160\mu \mathrm{m}$, ${\Phi }_0{N}_0=0.3\mathrm{mT}$ and remaining parameters as listed in the caption of Fig. 3.