  We propose a scheme to braid Majorana zero modes (MZMs) through steering the
spin degree of freedom, without moving, measuring, or more generically fusing
the modes. For a spinful Majorana system, we show that braiding two MZMs is
achieved by adiabatically reversing the Majorana spins, which topologically
corresponds to twisting two associated worldribbons, the extention of
worldlines that track the braiding history of MZMs. We demonstrate the
feasibility of applying the current scheme to the
superconductor/2D-topological-insulator/ferromagnetic-insulator (SC/2DTI/FI)
hybrid system which is currently under construction in experiment. A single
braiding of two MZMs is precisely achieved by adiabatically reversing the FI
magnetization, not relying on details of the reversing path, and the braiding
operation is shown to be stable against local imperfections such as the static
and dynamical disorder effects. The stability is a consequence of the intrinsic
connection of the current scheme to topological charge pumping. The proposed
device involves no auxiliary MZMs, rendering a minimal scheme for observing
non-Abelian braiding and having advantages with minimized errors for the
experimental demonstration.
