Nonmonotonic residual entropy in diluted spin ice: A comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results

Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, are highly frustrated magnetic systems. Their low-temperature strongly correlated state can be mapped onto the proton disordered state of common water ice. As a result, spin ices display the same low-temperature residual Pauling entropy as water ice, at least in calorimetric experiments that are equilibrated over moderately long-time scales. It was found in a previous study [X. Ke, Phys. Rev. Lett. 99, 137203 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.137203] that, upon dilution of the magnetic rare-earth ions (Dy3+ and Ho3+) by nonmagnetic yttrium (Y3+) ions, the residual entropy depends nonmonotonically on the concentration of Y3+ ions. A quantitative description of the magnetic specific heat of site-diluted spin ice materials can be viewed as a further test aimed at validating the microscopic Hamiltonian description of these systems. In this work, we report results from Monte Carlo simulations of site-diluted microscopic dipolar spin ice models (DSIM) that account quantitatively for the experimental specific-heat measurements, and thus also for the residual entropy, as a function of dilution, for both Dy2-xYxTi2O7 and Ho2-xYxTi2O7. The main features of the dilution physics displayed by the magnetic specific-heat data are quantitatively captured by the diluted DSIM up to 85% of the magnetic ions diluted (x=1.7). The previously reported departures in the residual entropy between Dy2-xYxTi2O7 versus Ho2-xYxTi2O7, as well as with a site-dilution variant of Pauling's approximation, are thus rationalized through the site-diluted DSIM. We find for 90% (x=1.8) and 95% (x=1.9) of the magnetic ions diluted in Dy2-xYxTi2O7 a significant discrepancy between the experimental and Monte Carlo specific-heat results. We discuss possible reasons for this disagreement.