Within the field of magnetism, magnetic frustration is a generous source of new phases of matter with unusual and exciting physical properties. Magnetic order is dictated by the interdependence of local electronic states and their real-space interactions decorating materials lattices. These local states can compete or work together to drive differing magnetic states of matter, ranging from the typical collinear (anti)ferromagnets to more exotic, highly-entangled ground states with emergent phenomena in small spin systems (S = 1/2). These correlated phases are predicted to arise in materials lattices that incite multiple equivalent interactions without a readily apparent magnetic ground state configuration in so called magnetic frustration. In turn, this frustration can lead to massively degenerate classical ground states hinting that instead a novel entangled phase could arise from the competition. Even with decades of research in this field, frustrated magnets remain an exciting and growing field of research as new magnetic phases arediscovered.

Herein, the physical properties of insulating lanthanide-based frustrated magnets areexplored from select members of the ALnX2 (A = alkali, Ln = lanthanide, X = chalcogenide) family of materials. This materials family crystallizes in various structures dictated by the ratio of the lanthanide radius to the alkali and chalcogenide radii, and this thesis focuses on two frustrated crystal lattices in this family, the equilateral triangular lattice and the elongated diamond lattice. We find that triangular lattice NaYbO2 does not conventionally order to 50 mK and instead contains an unconventional quantum disordered ground state that is tunable in an external magnetic field. However, structurally-similar triangular lattice KCeO2 magnetically orders below 300 mK with a small magnetic moment. Additionally, we show how the Heisenberg J1 - J2 model can be applied to the elongated magnetic diamond lattice in LiYbO2 and NaCeO2 where collinear or spiral magnetic order arises depending on the ratio of J2/J1. In LiYbO2, spiral magnetic order undergoes an incommensurate-to-commensurate structure under an external field below 1 K while NaCeO2 exhibits long range collinear antiferromagnetic order below 3.2 K. Overall, these materials studies advance the dependence of frustrated magnetic phases on external parameters, lanthanide character, and lattice geometry.