Magnetic Field Effects in Frustrated Low-Dimensional Magnets

We investigate the frustrated two-dimensional S = 1/2 next nearest neighbor anisotropic Heisenberg antiferromagnet on a square lattice as described by the $J_{1a,b} - J_2$ model. We use spin-wave theory and exact diagonalization for finite tiles including a new method for the finite size scaling procedure. We present results obtained from the extension of our numerical method to finite magnetic fields as well as from spin-wave theory. The induced uniform and the staggered moment in the antiferromagnetically ordered phases in the presence of a magnetic field are calculated. They deviate strongly from classical behaviour depending on frustration ratio $J_2//J_{1a,b}$ and the $J_{1a,b}$ exchange anisotropy. The magnetization becomes strongly nonlinear and is suppressed from the classical value. This is due to enhanced quantum fluctuations already at moderate frustration