  The spin-wave excitations of the multiferroic $\rm MnWO_4$ have been measured
in its low-temperature collinear commensurate phase using high-resolution
inelastic neutron scattering. These excitations can be well described by a
Heisenberg model with competing long-range exchange interactions and a
single-ion anisotropy term. The magnetic interactions are strongly frustrated
within the zigzag spin chain along c axis and between chains along the a axis,
while the coupling between spin along the b axis is much weaker. The balance of
these interactions results in the noncollinear incommensurate spin structure
associated with the magnetoelectric effect, and the perturbation of the
magnetic interactions leads to the observed rich phase diagrams of the
chemically-doped materials. This delicate balance can also be tuned by the
application of external electric or magnetic fields to achieve magnetoelectric
control of this type of materials.
