Magnetization curve of a square-lattice Heisenberg antiferromagnet

We calculate the uniform magnetization of a spin-1/2 Heisenberg square lattice antiferromagnet at $T=0$ in magnetic fields up to the saturation field in the framework of spin-wave theory including quantum corrections of the second order in $1/S$. External field generally suppresses zero-point fluctuations, which leads to an upward curvature of the magnetization curve at low fields and logarithmic singularity close to the saturation.