The magnetic behaviour of Dy$_2$Ir$_2$O$_7$ -- beyond the mean field approximation.

The magnetic properties of a pyrochlore iridate Dy$_2$Ir$_2$O$_7$ prepared by the CsCl flux method were investigated by means of specific heat and magnetization measurements. The low temperature behaviour was confirmed to be consistent with previously published results, whereas the high temperature data and their analysis are presented for the first time. At 128 K, a bifurcation of magnetization measured under zero field cooled and field cooled regimes coincides with an onset of the anomaly in specific heat pointing to an ordering of the iridium sublattice. Further, our high-temperature magnetization and specific heat data are interpreted in the frame of the previously determined crystal field scheme for Dy$_2$Ir$_2$O$_7$. The difference between calculations and experimental data, represented by 20 K specific heat anomaly, suggests the behaviour of studied iridate beyond the mean field approximation. This is in contrast with the rest of the heavy rare-earth pyrochlore iridates, where the mean field approximation constitutes an adequate description.