Ordered ground states of kagome magnets with generic exchange anisotropy

There is a growing family of rare-earth kagome materials with dominant nearest-neighbor interactions and strong spin-orbit coupling. The low symmetry of these materials makes theoretical description complicated, with six distinct nearest-neighbor coupling parameters allowed. In this article, we ask what kinds of classical, ordered, ground states can be expected to occur in these materials, assuming generic (i.e., non-fine-tuned) sets of exchange parameters. We use symmetry analysis to show that there are only five distinct classical ground state phases occurring for generic parameters. The five phases are: (i) a coplanar, twofold degenerate state with vanishing magnetization (A(1)), (ii) a noncoplanar, twofold degenerate state with magnetization perpendicular to the kagome plane (A(2)), (iii) a coplanar, sixfold degenerate state with magnetization lying within the kagome plane (E-coplanar), (iv) a noncoplanar, sixfold degenerate state with magnetization lying within a mirror plane of the lattice (E-noncoplanar(6)), (v) a noncoplanar, twelvefold degenerate state with magnetization in an arbitrary direction (E-noncoplanar(12)). All five are translation invariant (q = 0) states. Having found the set of possible ground states, the ground state phase diagram is obtained by comparing numerically optimized energies for each possibility as a function of the coupling parameters. The state E-noncoplanar(12) is extremely rare, occupying