Field-induced magnetic transitions in the quasi-two-dimensional heavy-fermion antiferromagnets Ce_(n)RhIn_(3n+2) (n=1 or 2)

We have measured the field-dependent heat capacity in the tetragonal antiferromagnets CeRhIn$_{5}$ and Ce$_{2}$RhIn$_{8}$, both of which have an enhanced value of the electronic specific heat coefficient $\gamma \sim 400$ mJ/mol-Ce K$^{2}$ above $T_{N}$. For $T<T_{N},$ the specific heat data at zero applied magnetic field are consistent with the existence of an anisotropic spin-density wave opening a gap in the Fermi surface for CeRhIn$_{5},$ while Ce$_{2}$RhIn$_{8}$ shows behavior consistent with a simple antiferromagnetic magnon. From these results, the magnetic structure, in a manner similar to the crystal structure, appears more two-dimensional in CeRhIn$_{5}$ than in Ce$_{2}$RhIn$_{8}$ where only about 12% of the Fermi surface remains ungapped relative to 92% for Ce$_{2}$RhIn$_{8}$. When $B||c,$ both compounds behave in a manner expected for heavy fermion systems as both $T_{N}$ and the electronic heat capacity decrease as field is applied. When the field is applied in the tetragonal basal plane ($B||a$), CeRhIn$_{5}$ and Ce$_{2}$RhIn$_{8}$ have very similar phase diagrams which contain both first- and second-order field-induced magnetic transitions .