Superconducting Spintronics with Magnetic Domain Walls

The recent experimental demonstration of spin-polarized supercurrents offer a venue for establishment of a superconducting analogue to conventional spintronics. Whereas domain wall motion in purely magnetic structures is a well-studied topic, it is not clear how domain wall dynamics may influence superconductivity and if some functional property can be harnessed from such a scenario. Here, we demonstrate that domain wall motion in superconducting systems offers a unique way of controlling the quantum state of the superconductor. Considering both the diffusive and ballistic limits, we show that moving the domain wall to different locations in a Josephson junction will change the quantum ground state from being in a 0 state to a $\pi$ state. Remarkably, we also show that domain wall motion can be used to turn on and off superconductivity: the position of the domain wall determines the critical temperature $T_c$ and thus if the system is in a resistive state or not, causing even a quantum phase transition between the dissipationless and normal state at $T=0$. In this way, one achieves dynamical control over the superconducting state within a single sample by utilizing magnetic domain wall motion.