  Atomtronics has the potential for engineering new types of functional
devices, such as Josephson junctions (JJs). Previous studies have mainly
focused on JJs whose ground states have 0 or $\pi $ superconducting phase
difference across the junctions, while arbitrarily tunable phase JJs may have
important applications in superconducting electronics and quantum computation.
Here we show that a phase tunable JJ can be implemented in a spin-orbit coupled
cold atomic gas with the magnetic tunneling barrier generated by a
spin-dependent focused laser beam. We consider the JJ confined in either a
linear harmonic trap or a circular ring trap. In the ring trap, the magnetic
barrier induces a spontaneous mass current for the ground state of the JJ,
demonstrating the magnetoelectric effects of cold atoms.
