A low-field disordered-free-moment phase in site-diluted spin-gap antiferromagnets

Site dilution of spin-gapped antiferromagnets leads to localized free moments, which can order antiferromagnetically in two and higher dimensions. A very important question of high experimental relevance is: what is the response of the diluted system to an applied magnetic field? This is a very complicated problem since the exponentially decaying interactions between the free moments introduce a large variety of energy scales, which respond differently to the field. Here we show how a weak magnetic field drives this order-by-disorder state into a novel \emph{disordered-free-moment} phase, characterized by the formation of local singlets between neighboring moments and by localized moments aligned antiparallel to the field. This disordered phase is characterized by the absence of a gap, as it is the case in a Bose glass. The associated field-driven quantum phase transition is consistent with the universality of a superfluid-to-Bose-glass transition. The robustness of the disordered-free-moment phase and its prominent features, in particular a series of \emph{pseudo}-plateaus in the magnetization curve, makes it accessible and relevant to experiments.