  We propose a systematic magnetic-flux-free approach to detect, manipulate and
braid Majorana fermions in a semiconductor nanowire-based topological Josephson
junction by utilizing the Majorana spin degree of freedom. We find an intrinsic
$\pi$-phase difference between spin-triplet pairings enforced by the Majorana
zeros modes (MZMs) at the two ends of a one-dimensional spinful topological
superconductor. This $\pi$-phase is identified to be a spin-dependent
superconducting phase, referred to as the spin-phase, which we show to be
tunable by controlling spin-orbit coupling strength via electric gates. This
electric controllable spin-phase not only affects the coupling energy between
MZMs but also leads to a fractional Josephson effect in the absence of any
applied magnetic flux, which enables the efficient topological qubit readout.
We thus propose an all-electrically controlled superconductor-semiconductor
hybrid circuit to manipulate MZMs and to detect their non-Abelian braiding
statistics properties. Our work on spin properties of topological Josephson
effects potentially opens up a new thrust for spintronic applications with
Majorana-based semiconductor quantum circuits.
