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Using a simple model of multi-band superconductors, which can be applied inparticular to Fe\nobreakdash-based pnictides, we calculate the Josephsoncurrent $I_{\text{J}}$ in a tunnel junction composed by such superconductors.We employ the tunneling Hamiltonian method and quasiclassical Green'sfunctions. We study both the case of coexistence of the superconducting($\Delta $) and magnetic (SDW---spin density wave) order parameters and thecase when only the superconducting order parameter exists. We show that thecurrent $I_{\text{J}}$ depends on the mutual orientation of magnetization ofthe SDW in the case of non-ideal nesting when the coexistence ofsuperconducting and magnetic order parameters is possible as it takes place inFe\nobreakdash-based pnictides. It is found that the realization of the$\pi$\nobreakdash-junction is possible in both cases. We compare our resultsfor multi-band superconductors without the SDW with those obtained earlier andfind that they coincide if the tunneling matrix elements are real. If theseelements are complex, a new term appears in the formula for the Josephsoncritical current.

Realization of the $\pi$-state in junctions formed by multi-band superconductors with a spin-density-wave