Resistive State of Superconductor-Ferromagnet-Superconductor Josephson Junctions in the Presence of Moving Domain Walls

We describe resistive states of the system combining two types of orderings—a superconducting and a ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor-ferromagnet-superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the finite slope of Shapiro steps as the characteristic feature of the regime with domain wall oscillations driven by the ac external current flowing through the junction.

Figure 1

(a) Sketch of the system under consideration. Superconducting electrodes forming a Josephson junction are placed on top of a ferromagnetic strip. The position of DWs in the strip can be controlled by the normal current $j_N$. (b) A simplified model of the Josephson junction region. A Néel-type DW is present in the interlayer. The Josephson supercurrent flows in the $F$ region in the $x$ direction.

Figure 2

IV characteristics of the SFS junction with a DW at rest (blue) and a moving DW (red). $\beta =1$, $\alpha =0.1$, $eK{d}_W/(\pi j_c)=5$, $t_d=40t_J$, where $t_J=1/2eR{I}_c$. Upper-left insert: Shapiro steps for $I(t)=I+0.3I_c\cos \omega t$, $\omega =15t_d^{-1}$. Axis labeling is the same as in the main figure. Bottom-right insert: the equivalent circuit scheme of the junction.

Figure 3

$V(t)$ for rectangular current impulses. Different curves correspond to different impulse periods $T$. For all the panels the solid lines correspond to $\beta =1$ (the anomalous phase due to the DW motion is nonzero) and the dashed lines are for $\beta =0$ (the anomalous phase shift is zero). (a) $j=0.5j_c$, $T=3t_d$ (blue), $T=2t_d$ (yellow), $T=t_d$ (red); (b) $j=1.2j_c$, $T=1.25t_d$ (blue), $T=0.83t_d$ (yellow), $T=0.42t_d$ (red). Insert: $j=1.2j_c$, $T=1.25t_d$ (the part of the main panel on a large scale). For all the curves $\alpha =0.1$, $eK{d}_W/(\pi j_c)=5$, $t_d=40t_J$.