Dilution effects in spin 7/2 systems. The case of the antiferromagnet GdRhIn$_5$

We report the structural and magnetic characterization of La-substituted Gd$_{1-x}$La$_x$RhIn$_5$ ($x\leq$ 0.50) antiferromagnetic (AFM) compounds. The magnetic responses of pure GdRhIn$_5$ are well described by a $S=7/2$ Heisenberg model. When Gd$^{3+}$ ions are substituted by La$^{3+}$, the maximum of the susceptibility and the inflection point of the magnetic specific heat are systematically shifted to lower temperatures accompanied by a broadening of the transition. The data is qualitatively explained by a phenomenological model which incorporates a distribution of magnetic regions with different transition temperatures ($T_N$). The universal behaviour of the low temperature specific heat is found for La (vacancies) concentrations below $x=0.40$ which is consistent with spin wave excitations. For $x=0.5$ this universal behaviour is lost. The sharp second order transition of GdRhIn$_5$ is destroyed, as seen in the specific heat data, contrary to what is expected for a Heisenberg model. The results are discussed in the context of the magnetic behavior observed for the La-substituted (Ce,Tb,Nd)RhIn$_5$ compounds.