The discovery in 2001 of superconductivity in some heavy fermion compounds of the $RM{\mathrm{In}}_5$ $(R=4f$ or $5f$ elements; $M=\text{Co}$, Rh, Ir) family, has triggered an enormous amount of research into understanding the physical origin of superconductivity and its relation with magnetism. Although many properties have been clarified, there are still crucial questions that remain unanswered. One of these questions is the particular role of the transition metal in determining the value of critical superconducting temperature $\left(T_C\right)$. In this work, we analyze an interesting regularity that is experimentally observed in this family of compounds, where the lowest Néel temperatures are obtained in the Co-based materials. We focus our analysis on the $\mathrm{Gd}M{\mathrm{In}}_5$ compounds and perform density-functional-theory-based total-energy calculations to obtain the parameters for the exchange coupling interactions between the magnetic moments located at the ${\mathrm{Gd}}^{3+}$ ions. Our calculations indicate that the ground state of the three compounds is a $C$-type antiferromagnet determined by the competition between the first- and second-neighbor exchange couplings inside ${\mathrm{GdIn}}_3$ planes and stabilized by the couplings across $M{\mathrm{In}}_2$ planes. We then solve a model with these magnetic interactions using a mean-field approximation and quantum Monte Carlo simulations. The results obtained for the calculated Néel and Curie-Weiss temperatures, the specific heat, and the magnetic susceptibility are in very good agreement with the existent experimental data. Remarkably, we show that the first-neighbor interplane exchange coupling in the Co-based material is much smaller than in the Rh and Ir analogs which leads to a more two-dimensional magnetic behavior in the former. This result explains the observed lower Néel temperature in Co-115 systems and may shed light on the fact that the Co-based 115 superconductors present the highest $T_C$.

• Received 4 November 2014

DOI:https://doi.org/10.1103/PhysRevB.91.014409