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The $\varphi_0$ Josephson junctions formed by ordinary superconductors and amagnetic non-centrosymmetric interlayer are studied. We derive an analyticalsolution for the magnetization dynamics induced by an arbitrary current pulseand formulate the criteria for magnetization reversal. Using the obtainedresults, the form and duration of the current pulse are optimized. Theagreement between analytical and numerical investigations is reached in thecase of a large product of the ratio Josephson to magnetic energy, strength ofspin-orbit interaction and a minimal value of the current pulse. The obtainedresults allow one to predict magnetization reversal at the chosen systemparameters.

Analytical criteria for magnetization reversal in $\varphi_0$ Josephson junction