Magnetic Bose condensation vs. magnon localization in a model magnet with site dilution

We report on the theoretical field-temperature phase diagram of anisotropic coupled S=1 chains with site dilution, modeling the magnetic behavior of doped NiCl$_2$-\emph{tetrakis} thiourea (DTN). In absence of doping, this compound clearly displays field-induced Bose-Einstein condensation of magnons [V. Zapf \emph{et al.}, Phys. Rev. Lett. {\bf 98}, 047205 (2007)], as revealed by the mean-field scaling of the field-induced ordering temperature, $T_c \sim |H-H_c|^{\phi}$ with $\phi=2/3$. The critical field $H_c$ corresponds to a $T=0$ quantum phase transition (QPT) between a spin gap phase and a gapless ordered phase. Here we show that site dilution opens a novel gapless spin-liquid phase close to the ordering transition, corresponding to a \emph{Bose glass} phase of localized magnons. Disorder leads to a radical change in the universality class of the QPT (which turns into a \emph{quantum percolation} transition), and in the critical temperature scaling, which exhibits a novel universal exponent $\phi\approx 1.2$. A crossover to mean-field scaling of $T_c$ at finite temperature is observed, and explained via a scenario of \emph{thermal percolation} of magnons.