We report detailed thermal expansion and magnetostriction experiments on ${\mathrm{GdCoIn}}_5$ and $\mathrm{GdRh}{\left({\mathrm{In}}_{1-x}{\mathrm{Cd}}_x\right)}_5$ ($x=0$ and 0.025) single-crystal samples that show a sudden change in the dilation at a field $B^{★}$ for temperatures below the Néel transition temperature $T_N$. We present a first-principles model including crystal-field effects, dipolar and exchange interactions, and the dependence of the latter 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 $B^{★}$. It also indicates that two degenerate phases should coexist at temperatures below $T_N$, which may explain the lack of observation, in high-resolution x-ray experiments, of an orthorhombic distortion at the Néel transition, even though the experimentally determined magnetic structure breaks the tetragonal symmetry and the magnetoelastic coupling from our model is significant. These conclusions could be extended to other tetragonal Gd-based compounds that present the same phenomenology.

• Received 29 May 2018
• Revised 15 August 2018

DOI:https://doi.org/10.1103/PhysRevB.99.134406