Effect of magnons on the 0-π transition in a superconductor/half-metallic ferromagnet/superconductor junction

We study the Josephson effect in an s-wave superconductor/dirty half-metal/s-wave superconductor (SC/HM/SC) junction by taking account of the spin dynamics due to the magnon excitation in the HM. Using the fourth order perturbation theory for the tunneling Hamiltonian and Green's function method, we formulate the Josephson critical current in a SC/HM/SC junction. In the tunneling process from the SC to the HM and vice versa, we consider the effect of spin flip tunneling due to the magnon excitation at the interface. As a result, it is found that the spin triplet pair correlation propagates into the HM and the Josephson current flows. We find that the Josephson critical current shows the damped oscillation as a function of the thickness of the HM and the 0-π transition occurs. Moreover, we show that the 0-π transition occurs by changing temperature. The 0-π transition results from magnon excitations in the HM. This proposes a new mechanism with respect to the 0-π transition.