Analytical Criteria for Magnetization Reversal in a φ 0 Josephson Junction

The switching of magnetization by electric current pulse in the ${\ensuremath{\varphi}}_{0}$ Josephson junction formed by ordinary superconductors and a magnetic noncentrosymmetric interlayer is studied. The ground state of this junction is characterized by the finite phase difference ${\ensuremath{\varphi}}_{0}$, which is proportional to the strength of the spin-orbit interaction and the exchange field in the normal metal. Based on the Landau-Lifshits-Gilbert and resistively shunted junction model equations we build an analytical description of the magnetization dynamics induced by an arbitrary current pulse. We formulate the criteria for magnetization reversal and, using the obtained results, the form and duration of the current pulse are optimized. The analytical and numerical results are in excellent agreement at $Gr{I}_{p}\ensuremath{\gg}1$, where $G$ is a Josephson-to-magnetic energy ratio, $r$ is a strength of spin-orbit interaction, and ${I}_{p}$ is a value of the current pulse. The analytical result allows one to predict magnetization reversal at the chosen system parameters and explains the features of magnetization reversal in the $G$-$r$ and $G$-$\ensuremath{\alpha}$ diagrams, where $\ensuremath{\alpha}$ is the Gilbert damping. We propose to use such a ${\ensuremath{\varphi}}_{0}$ Josephson junction as a memory element, with the information encoded in the magnetization direction of the ferromagnetic layer.