  The ordered magnetic states of MnWO4 at low temperatures were examined by
evaluating the spin exchange interactions between the Mn2+ ions of MnWO4 on the
basis of first principles density functional calculations and by performing
classical spin analysis with the resulting spin exchange parameters. Our work
shows that the spin exchange interactions are frustrated within each zigzag
chain of Mn2+ ions along the c-direction and between such chains of Mn2+ ions
along the a-direction. This explains the occurrence of a spiral-spin order
along the c- and a-directions in the incommensurate magnetic state AF2, and
that of a uudd spin order along the c- and a-directions in the commensurate
magnetic state AF1. The ferroelectric polarization of MnWO4 in the spiral-spin
state AF2 was examined by performing Berry phase calculations for a model
superstructure to find that the ferroelectric polarization occurs along the
b-direction, in agreement with experiment.
