While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of 4f magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic Yb$^{3+}$ triangular lattice planes with pseudospin $s=1/2$ at low temperatures, are an ideal platform to study these new phenomena. Competing frustrated interactions may lead to an absence of magnetic order associated to a gapless spin liquid ground state with a huge linear specific heat exceeding that of many heavy fermions, whereas the application of a magnetic field induces anisotropic magnetic order with successive transitions into different long ranged ordered structures. In this comparative study, we discuss our experimental findings in terms of a unified crystal-field and exchange model. We combine electron paramagnetic resonance (EPR) experiments and results from neutron scattering with measurements of the magnetic susceptibility, isothermal magnetization up to full polarization, and specific heat to determine the relevant model parameters. The impact of the crystal field is discussed as well as the symmetry-compatible form of the exchange tensor, and we give explicit expressions for the anisotropic g factor, the temperature dependence of the susceptibility, the exchange-narrowed EPR linewidth and the saturation field.
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