Magnetic properties and critical behaviors of the nodal-line semimetal candidate ErIn₃

The AuCu3-type intermetallic compounds ReIn3 (Re = a rare earth ion) with type-IV magnetic space groups are predicted to show topologically nontrivial electronic states. Here, we grow ErIn3 single crystals, and study their magnetic properties and critical behaviors by means of the magnetic susceptibility, and magnetization isotherm measurements. Combining a detailed analysis of the magnetic susceptibility and isothermal magnetization, we find that this compound harbors a complicated magnetic phase diagram, and its magnetic moment arrangement appears not to simply follow the fashion as observed in the isostructural counterpart GdIn3 (it adopts a conventional type-C magnetic structure that belongs to type-IV magnetic space groups). A careful study of the magnetic properties around the antiferromagnetic (AFM)-paramagnetic transition yields the critical exponents beta = 0.309 (0.297), gamma = 1.117 (1.038), and delta = 4.617 (4.454), indicating that the tricritical mean field model or the three-dimensional Ising model works for ErIn3's magnetic behaviors and the presence of a long-range AFM interaction therein. Besides, the exchange interaction distance J(r) similar to r (-4.665) as well confirms a long-range magnetic coupling in ErIn3. Our results offer the clues that the magnetic structure varies from one member of ReIn3 family to another, and to confirm their electronic features in the AFM phases further experimental and theoretical studies are still desired.