Josephson effect due to the long-range odd-frequency triplet superconductivity in SFS junctions with Néel domain walls

We consider a SFS Josephson junction made of two superconductors S and a multidomain ferromagnet F with an in-plane magnetization. We assume that the neighboring domains of the ferromagnet are separated by Néel domain walls. An odd-frequency triplet long-range component of superconducting correlations arises in the domain walls and spreads into the domains over a long distance of the order ξ_T=√D∕2πT, where D is the diffusion coefficient (dirty limit is implied). We calculate the contribution of this component to the Josephson current in the situation when conventional short-range components exponentially decay over the thickness of the F layer and can be neglected. In the limit when the thickness of the F layer is much smaller than the penetration length of the long-range component, we find that the junction is in the π state. We also analyze a correction to the density of states due to the long-range triplet component.