Domain wall effects in ferromagnet-superconductor structures

We investigate how domain structures of the ferromagnet in superconductor-ferromagnet heterostructures may change their transport properties. We calculate the distribution of current in the superconductor induced by magnetic field of Bloch domain walls, e.g., find the “lower critical” magnetization of the ferromagnet that provides vortices in the superconductor.

Figure 1

The SF junction. A sketch of a Bloch domain wall. The magnetization rotates according to Eq. (2). Magnetization in the center of the domain wall is perpendicular to the S film.

Figure 2

(Color online) The plot of $J_y\left(x\right)∕\left(cM\right)$ as a function of $x∕{\lambda }_L$ in the case of the thick SF bilayer, $d_S,d_F⪢{\lambda }_L$. The parameter $\pi \delta ∕\left(2{\lambda }_L\right)=0.2,0.5,1,2,4$ (from top to bottom in the left panel).

Figure 3

(Color online) The plot of $J_y\left(x\right)∕\left(cM\right)$ as a function of $x∕L$ in the case of the thick SF bilayer, $d_S,d_F⪢{\lambda }_L$. We use $\delta ∕L=0.02$ and parameter ${\lambda }_L∕L=0.005,0.01,0.025,0.05,0.1,0.25$ (from top to bottom in the left panel).

Figure 4

(Color online) The plot of $2\lambda J_y\left(x\right)∕\left(cM{d}_F\right)$ as a function of $x∕\left(2\lambda \right)$ in the case of the thin SF bilayer, $d_S,d_F⪡{\lambda }_L$. The parameter $\pi \delta ∕\left(4\lambda \right)=0.2,0.5,1,2,4$ (from top to bottom in the left panel).

Figure 5

(Color online) The plot of $J_y\left(x\right)∕\left(cM\right)$ as a function of $x∕L$ in the case of the thin SF bilayer, $d_S,d_F⪡{\lambda }_L$. We use $\delta ∕L=0.02$, $d_F∕L=0.1$ and parameter $\lambda ∕L=0.05,0.1,0.25,0.75$ (from top to bottom in the left panel).