Classical Chiral Antiferromagnet on a Kagome Lattice

Extensive ground-state degeneracy in classical spin systems has motivated the study of these systems' quantum counterparts in search of topological phases of matter. But the possibility of entropic ground-state selection---order-by-disorder---has also motivated the study of these systems in their own right. Among these is the kagome Heisenberg antiferromagnet (KHAFM) whose low-$T$ classical phase exhibits coplanar order. Like the KHAFM, the so-called ``kagome chiral model'' whose interactions are defined by the scalar triple product of neighboring spins has a large classical ground-state degeneracy. Furthermore, the two ground-state manifolds exhibit remarkable similarity, but linear spin-wave analysis reveals crucially differing dynamics. All coplanar KHAFM ground-states are equivalent at harmonic order and have flat bands, but the kagome chiral model admits flat bands only for certain states among its analogous ``triaxial'' ground-states: The only zero modes of the kagome chiral model are zero to all orders. Although this undoes the standard argument for order-by-disorder, the set of ground-states having the greatest number of zero modes forms a $Z_2$ spin liquid which may be stabilized by other means.