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

Abstract

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 et. al. Phys. Rev. Lett. 99, 137203 (2007)] that, upon dilution of the magnetic rare-earth ions (Dy 3+ and Ho 3+ ) by non-magnetic Yttrium (Y 3+ ) ions, the residual entropy depends non-monotonically on the concentration of Y 3+ 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 the present 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.

Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method

“…The size dependence is very small, and the size difference is not appreciable with this scale of plot. We observed the nonmonotonic concentration dependence of the residual entropy, which was experimentally reported [6,7]. We also plot the generalized Pauling approximation [6]:…”

Disordered kagomé spin ice

“…8 We find that the residual entropy is generally increasing with the amount of disorder in the system; a finding that is consistent with measurements made in physically diluted spin ice systems. 3,4 Statistically speaking, the introduction of disorder removes frustration at vertices in the material, which impacts the dynamics in such a way that the path to the perfectly charge ordered state is blocked and the number of arrangements, and hence the residual entropy, increases as the number of missing magnets increases.…”

“…The results of the simulations including disorder are consistent with that measured in physical systems. 3,4 …”

“…[1][2][3][4][5][6] In spin ice pyrochlores, such as Dy 2 Ti 2 O 7 , the magnetic moments of the Dy 3+ ions align along the tetrahedral axes of the crystal and these systems transition from ferromagnetic to antiferromagnetic spin ordering at low temperatures. At low temperatures these systems follow the "spin ice rules", where at each vertex two spins point inward and two spins point outward.…”

“…This compares to real spin ice materials as they have been found to have nonmagnetic defects. 3,4 The removal of a single magnet at a vertex leads to local ferromagnetic coupling as the frustration is eliminated at the corresponding vertices; impacting the spin dynamics. A related study has been carried out on doped colloidal artificial spin ice.…”