We consider the structure of anisotropic exchange interactions in ytterbium-based insulating rare-earth magnets built from edge-sharing octahedra. We argue the features of trivalent ytterbium and this structural configuration allow for a semiquantitative determination of the different anisotropic exchange regimes that may manifest themselves in such compounds. The validity of such superexchange calculations is tested through comparison to the well-characterized breathing pyrochlore compound ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$. With this in hand, we then consider applications to three-dimensional pyrochlore spinels as well as two-dimensional honeycomb and triangular lattice systems built from such edge-sharing octahedra. We find an extended regime of robust emergent weak anisotropy with dominant antiferromagnetic Heisenberg interactions as well as smaller regions with strong anisotropy. We discuss the implications of our results for known compounds with the above structures, such as the spinels $A{\mathrm{Yb}}_2{X}_4$ ($A=\mathrm{Cd}$, Mg, $X=\mathrm{S}$, Se) and the triangular compound ${\mathrm{YbMgGaO}}_4$, which have recently been put forth as promising candidates for exploring unconventional magnetic phenomena. Finally, we speculate on implications of our calculations for the $R_2{M}_2{\mathrm{O}}_7$ pyrochlore compounds and some honeycomb ytterbium magnets.

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• Exchange interaction
• Frustrated magnetism
• Magnetic anisotropy
• Spin liquid