Field Induced Ordering in Highly Frustrated Antiferromagnets

We predict that an external field can induce a spin ordering in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for $S=1\mathrm{}/2$. The field induced collinear states have a spin gap and produce magnetization plateaus.