Abstract
I review recent work in collaboration with D.~Heidarian (D.~Heidarian and K.~Damle, Phys. Rev. Lett. 95, 127206 (2005)) and T.~Senthil (K.~Damle and T.~Senthil, Phys. Rev. Lett. 97, 067202 (2006)) on the low temperature spin-nematic ordering of $S=1$
kagome and triangular lattice antiferromagnets in which there is sufficiently strongly single-ion anisotropy $D$
that dominates over the antiferromagnetic exchange $J$. I contrast this behaviour
with that of $S3/2$ magnets with $D J$---these display interesting
order-by-disorder effects that lead to characteristic spin-density wave
states that have been identified in collaboration with A.~Sen
and A.~Vishwanath (A.~Sen, K.~Damle, and A.~Vishwanath, preprint (2007)).
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