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Long-Range Magnetic Interactions in the Multiferroic Antiferromagnet $\rm MnWO_4$

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.