Multiple magnetic phases and magnetization plateaus in TbRh6Ge4

We probe the magnetic order in single crystals of $\mathrm{Tb}{\mathrm{Rh}}_{6}{\mathrm{Ge}}_{4}$ using electrical transport, magnetization, and thermodynamic measurements. $\mathrm{Tb}{\mathrm{Rh}}_{6}{\mathrm{Ge}}_{4}$ crystallizes in the noncentrosymmetric tetragonal $\mathrm{Li}{\mathrm{Co}}_{6}{\mathrm{P}}_{4}$-type structure, where the Tb ions form a triangular lattice in the basal plane and chains along the $c$ axis. This compound undergoes a second-order antiferromagnetic transition at ${T}_{N}=12.7$ K, which is followed by an additional transition at ${T}_{M}=2.8$ K. When fields are applied along the easy $c$ axis, multiple metamagnetic transitions are observed, where there are plateaus at 1/9 and 1/3 of the saturation magnetization. We map the field-temperature phase diagram revealing complex magnetism, where antiferromagnetic coupling within the basal plane may lead to significant magnetic frustration.