The properties of the two-dimensional antiferromagnet of spin 1/2 on a
square lattice with nearest- and next-nearest-neighbors interactions
in a strong magnetic field close to saturation are studied in terms of
the equivalent Bose-gas problem. A phase with a gap in the elementary
excitations spectrum, short-range-ordered ground state, and a corresp
onding plateau in the magnetization curve is shown to exist in the int
erval of fields between the first and second critical fields h0 < h <
h01. Its existence is closely related to the two-particle attraction i
n the vicinity of the wave vector p0u over arrow pointing right = (pi,
pi). In the interval between the second and third critical fields h01
< h < h(cf) the system behaves as a quasi-one-dimensional magnetic ph
ase with long-range order in the ground state and a gapless mode. The
magnetization depends on field linearly, with logarithmic corrections.