Long-range superharmonic Josephson current and spin-triplet pairing correlations in a junction with ferromagnetic bilayers

The long-range spin-triplet supercurrent transport is an interesting phenomenon in the superconductor/ ferromagnet (S/F) heterostructure containing noncollinear magnetic domains. Here we study the long-range superharmonic Josephson current in asymmetric S/F-1/F-2/S junctions. It is demonstrated that this current is induced by spin-triplet pairs vertical bar up arrow up arrow > -vertical bar down arrow down arrow > or vertical bar up arrow up arrow > + vertical bar down arrow down arrow > in the thick F-1 layer. The magnetic rotation of the particularly thin F-2 layer will not only modulate the amplitude of the superharmonic current but also realise the conversion between vertical bar up arrow up arrow > -vertical bar down arrow down arrow > and vertical bar up arrow up arrow > + vertical bar down arrow down arrow >. Moreover, the critical current shows an oscillatory dependence on thickness and exchange field in the F-2 layer. These effect can be used for engineering cryoelectronic devices manipulating the superharmonic current. In contrast, the critical current declines monotonically with increasing exchange field of the F-1 layer, and if the F-1 layer is converted into half-metal, the long-range supercurrent is prohibited but vertical bar up arrow up arrow > still exists within the entire F-1 region. This phenomenon contradicts the conventional wisdom and indicates the occurrence of spin and charge separation in present junction, which could lead to useful spintronics devices.