Order by disorder from nonmagnetic impurities in a two-dimensional quantumspin liquid

We consider doping of nonmagnetic impurities in the spin-1/2, 1/5-depleted square lattice. This structure, whose undoped phase diagram offers both mag netically ordered and spin-liquid ground states, is realized physically in CaV4O9. Doping into the ordered phase results in a progressive loss of orde r, which becomes complete at the percolation threshold. By contrast, doping into the spin liquids creates a phase of weak but long-ranged antiferromag netic order, a true order-by-disorder phenomenon. We study the phase diagra m of the doped system by computing the static susceptibility and staggered magnetization using a stochastic series-expansion quantum Monte Carlo techn ique.