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Compounds of transition metal ions with strong spin-orbit coupling recentlyattracted attention due to the possibility to host frustrated bond-dependentanisotropic magnetic interactions. In general, such interactions lead tocomplex phase diagrams that may include exotic phases, e.g. the Kitaev spinliquid. Here we report on our comprehensive analysis of the global phasediagram of the extended Kitaev-Heisenberg model relevant to honeycomb latticecompounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed methodbased on spin coherent states that enabled us to resolve arbitrary spinpatterns in the cluster ground states obtained by exact diagonalization. Globaltrends in the phase diagram are understood in combination with the analyticalmappings of the Hamiltonian that uncover peculiar links to known models -Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice - orreveal entire manifolds of exact fluctuation-free ground states. Finally, ourstudy can serve as a methodological example that can be applied to other spinmodels with complex bond-dependent non-Heisenberg interactions.

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models