Site dilution of quantum spins in the honeycomb lattice

Abstract

We consider the effect of random site dilution on a honeycomb lattice of quantum spins described by the antiferromagnetic Heisenberg spin-$S$ model. Using linear spin-wave theory, we compute the zero-temperature magnetization and density of states as a function of dilution up to the classical percolation threshold. Several subtle issues regarding the treatment of quasidivergent zero-energy modes, which appear in the real-space formulation of the spin-wave problem, are clarified. For $S>1∕2$, the spin-wave theory is well defined in the sense that results at all dilution concentrations are consistent with the underlying assumptions of the theory. For $S=1∕2$, however, the approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the stochastic series expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo calculation: (i) an improved estimate for the staggered magnetization of the undiluted system ${m}_{\mathrm{av}}(L\ensuremath{\rightarrow}\ensuremath{\infty})=0.2677(6)$ and (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. We have used the computed staggered magnetization and density of states to analyze neutron scattering experiments and N\'eel temperature measurements of two quasi-two-dimensional diluted honeycomb systems: (i) ${\mathrm{Mn}}_{p}{\mathrm{Zn}}_{1\ensuremath{-}p}\mathrm{P}{\mathrm{S}}_{3}$ (a diluted $S=5∕2$ system) and (ii) $\mathrm{Ba}{({\mathrm{Ni}}_{p}{\mathrm{Mg}}_{1\ensuremath{-}p})}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ (a diluted $S=1$ system). We have found that our calculations are in good agreement with the experimental data.