Antiferromagnetism weakening with Y-substitution in the TbRhIn$_5$ intermetallic system

We report measurements of the temperature dependence specific heat, magnetic susceptibility in single crystals of the series of intermetallic compounds Tb$_{1-x}$Y$_x$RhIn$_5$ (nominal concentrations $x= 0.15, 0.30, 0.40, 0.50$ and $0.70$). A mean field approximation to simulate the macroscopic properties along the series has been used. Neutron diffraction data in powdered sample of nominal concentration Tb$_{0.6}$Y$_{0.4}$RhIn$_5$ reveal AFM propagation vector $k=[\frac{1}{2}~0~\frac{1}{2}]$ with the magnetic moments oriented close to the tetragonal \textit{c} axis. We discuss the role of combined effects of crystalline electric field (CEF) perturbations and dilution in the magnetic properties evolution with Y content. In particular, we suggest that changes in the Tb-In first neighbors distances, i.e. the TbIn$_3$ cuboctahedra distortion, are responsible for changes in the Tb crystalline potential and the possible reorientation of Tb magnetic moments for $x>$0.4. This reflects non negligible variations of the $B^{m}_{n}$ crystal field parameters and the energy levels splitting with \textit{x}.