  We study quantum magnetism of interacting spinor bosons at integer fillings
hopping in a square lattice in the presence of non-Abelian gauge fields. In the
strong coupling limit, it leads to the Rotated ferromagnetic Heisenberg model
(RFHM) which is a new class of quantum spin model. We introduce Wilson loops to
characterize frustrations and gauge equivalent classes. For a special
equivalent class, we identify a new spin-orbital entangled commensurate ground
state. It supports not only commensurate magnons, but also a new gapped
elementary excitation: in-commensurate magnons with two gap minima continuously
tuned by the SOC strength. At low temperatures, these magnons lead to dramatic
effects in many physical quantities such as density of states, specific heat,
magnetization, uniform susceptibility, staggered susceptibility and various
spin correlation functions. The commensurate magnons lead to a pinned central
peak in the angle resolved light or atom Bragg spectroscopy. However, the
in-commensurate magnons split it into two located at their two gap minima. At
high temperatures, the transverse spin structure factors depend on the SOC
strength explicitly. The whole set of Wilson loops can be mapped out by
measuring the specific heat at the corresponding orders in the high temperature
expansion. We argue that one gauge may be realized in current experiments and
other gauges may also be realized in near future experiments. The results
achieved along the exact solvable line sets up the stage to investigate
dramatic effects when tuning away from it by various means. We sketch the
crucial roles to be played by these magnons at other equivalent classes, with
spin anisotropic interactions and in the presence of finite magnetic fields.
Various experimental detections of these new phenomena are discussed. Rotated
Anti-ferromagnetic Heisenberg model are also briefly mentioned.
