Josephson Effect in Magnetic Superconductors with Spiral Magnetic Order

It is shown that in magnetic superconductors with spiral magnetic order the Josephson current has an additional contribution which depends: (i) on the relative orientation (magnetic phase) $\theta =\theta_{L}-\theta_{R}$ of magnetizations on the left ($L$) and right ($R$) banks of the contact, (ii) on the junction helicity $\chi =\chi_{L}\chi_{R}$, (with spiral helicity $\chi _{L(R)}=\pm 1$), i.e. $J=[J_{c}-J_{\chi}\cos \theta ]\sin \phi$ with $\phi =\phi_{L}-\phi_{R}$. The ratio $R_{\chi}\equiv J_{\chi}/J_{c}$ is calculated as a function of the superconducting order parameter $\Delta$, the exchange field energy $h$ and the wave vector $Q$ of the spiral magnetic structure. The $\pi$-Josephson contact can be realized in such a system in some region of parameters. Some possible consequences of this new phase relation is also analyzed.