  $\gamma$-triclinic and $\alpha$-monoclinic polymorphs of CoV$_{2}$O$_{6}$ are
two of the few known transition metal ion based materials that display stepped
$1/3$ magnetization plateaus at low temperatures. Neutron diffraction [M.
Markkula et al. Phys. Rev. B 86, 134401 (2012)], x-ray dichroism [N. Hollmann
et al. Phys. Rev. B 89, 201101(R) (2014)], and dielectric measurements [K.
Singh et al. J. Mater. Chem. 22, 6436 (2012)] have shown a coupling between
orbital, magnetic and structural orders in CoV$_{2}$O$_{6}$. We apply neutron
inelastic scattering to investigate this coupling by measuring the spin-orbit
transitions in both $\alpha$ and $\gamma$ polymorphs. We find the spin-exchange
and anisotropy in monoclinic $\alpha$-CoV$_{2}$O$_{6}$ to be weak in comparison
with the spin-orbit coupling $\lambda$ and estimate an upper limit of
$|J/\lambda| \sim$ 0.05. However, the spin exchange is larger in the triclinic
polymorph and we suggest the excitations are predominately two dimensional. The
local compression of the octahedra surrounding the Co$^{2+}$ ion results in a
direct coupling between higher energy orbital levels, the magnetic ground
state, and elastic strain. CoV$_{2}$O$_{6}$ is therefore an example where the
local distortion along with the spin-orbit coupling provides a means of
intertwining structural and magnetic properties. We finish the paper by
investigating the low-energy magnetic fluctuations within the ground state
doublet and report a magnetic excitation that is independent of the local
crystalline electric field. We characterize the temperature and momentum
dependence of these excitations and discuss possible connections to the
magnetization plateaus.
