Possibility of a π Josephson junction and switch in superconductors with spiral magnetic order

It is shown in tunneling junctions made of two magnetic superconductors with spiral magnetic order that the Josephson current depends on the magnetic phase, $\theta ={\theta }_L-{\theta }_R,$ as well as the spiral helicity, $\chi ={\chi }_L{\chi }_R.$ The former describes the relative orientation of magnetizations on the left (L) and right (R) banks of the contact, while the latter characterizes the left (right)-handed spiral with respect to the surface unit vector. The Josephson current ${J=(J}_c-J_{-\chi }\cos \theta )\sin \phi$ is calculated as a function of the superconducting order parameters, ${\Delta }_{L\left(R\right)\mathrm{}},$ the exchange energies, $h_{L\left(R\right)\mathrm{}},$ and the spiral wave vectors, ${\mathbf{Q}}_{L\left(R\right)\mathrm{}}.$ It turns out that the π Josephson junction can be realized in some range of microscopic parameters. A possibility of making switches, which are based on this new phase relation, is also analyzed.