  We investigate the effects of long-range interaction on the magnetic
excitations and the competition between magnetic phases on a frustrated square
lattice. Applying the spin wave theory and assisted with symmetry analysis, we
obtain analytical expression for spin wave spectrum of competing Neel and (pi,
0) stripe states of systems containing any-order long-range interactions. In
the specific case of long-range interactions with power-law decay, we found
surprisingly that staggered long-range interaction suppresses quantum
fluctuation and enlarges the ordered moment, especially in the Neel state, and
thus extends its phase boundary to the stripe state. Our findings only
illustrate the rich possibilities of the roles of long-range interactions, and
advocate future investigations in other magnetic systems with different
structures of interactions.
