  Using gauge theory for Spin(7)-manifolds of dimension 8, we develop a
procedure, called Spin-rotation, which transforms a (stable) holomorphic
structure on a vector bundle over a complex torus of dimension 4 into a new
holomorphic structure over a different complex torus. We show non-trivial
examples of this procedure by rotating a decomposable Weil abelian variety into
a non-decomposable one. As a byproduct, we obtain a Bogomolov type inequality,
which gives restrictions for the existence of stable bundles on an abelian
variety of dimension 4, and show examples in which this is stronger than the
usual Bogomolov inequality.
