We report detailed thermal expansion and magnetostriction experiments on GdCoIn$_5$ and GdRhIn$_5$ single crystal samples that show a sudden change in the dilation at a field B$^ast$ for temperatures below the Neel transition temperature TN. We prese
nt a first-principles model including crystal-field effects, dipolar and exchange interactions, and the dependence of the exchange couplings with lattice distortions in order to fully account for the magnetostriction and magnetic susceptibility data. The mean-field solution of the model shows that a transition between metastable states occurs at the field B$^ast$. It also indicates that two degenerate phases coexist in the sample at temperatures below TN. This allows to explain the lack of observation, in high resolution x-ray experiments, of an orthorhombic distortion at the Neeel transition even though the magnetic structure breaks the tetragonal symmetry and the magnetoelastic coupling is significant. These conclusions could be extended to other tetragonal Gd-based compounds that present the same phenomenology.
We investigate the effects of an applied magnetic field on the magnetic properties of the antiferromagnet GdCoIn$_5$. The prominent anisotropy observed in the susceptibility below $T_N$ is rapidly suppressed by a field of just a few Tesla. Further ev
idence of this low energy-scale is obtained from magnetoresistance and magnetostriction experiments. The lattice lenght, particulary, shows a sudden change below 2 Tesla when the magnetic field is applied perpendicular to the crystallographic $hat{c}$-axis. The experimental results as a whole can be attributed to a small but non negligible higher-order crystalline electric field.
