  We investigate 1D quantum systems that support Majorana bound states at
interfaces between topologically distinct regions. In particular, we show that
there exists a duality between particle-hole and spin degrees of freedom in
certain spin-orbit-coupled 1D platforms such as topological insulator edges.
This duality results in a spin analogue of previously explored `fractional
Josephson effects'---that is, the spin current flowing across a magnetic
junction exhibits 4\pi-periodicity in the relative magnetic field angle across
the junction. Furthermore, the interplay between the particle-hole and spin
degrees of freedom results in unconventional magneto-Josephson effects, such
that the Josephson current is a function of the magnetic field orientation with
periodicity 4\pi.
