Evidence of quantum criticality in the doped Haldane systemY2BaNiO5

Abstract

Experimental bulk susceptibility $\ensuremath{\chi}(T)$ and magnetization $M(H,T)$ of the $S=1$ Haldane chain system doped with nonmagnetic impurities, ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Zn}}_{x}{\mathrm{O}}_{5}$ $(x<~0.08),$ are analyzed. A numerical calculation for the low-energy spectrum of noninteracting open segments describes well experimental data above 4 K. Below 4 K, we observe power-law behaviors $\ensuremath{\chi}(T)\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\alpha}}$ and $M(H,T)\ensuremath{\sim}{T}^{1\ensuremath{-}\ensuremath{\alpha}}{f}_{\ensuremath{\alpha}}(H/T),$ with $\ensuremath{\alpha}(<1)$ depending on the doping concentration x. This observation suggests the appearance of a gapless quantum phase due to a broad distribution of effective couplings between the dilution-induced moments.