Classical Antiferromagnet on a Hyperkagome Lattice

Abstract

Motivated by recent experiments on ${\mathrm{Na}}_4{\mathrm{Ir}}_3{\mathrm{O}}_8$ [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This “hyperkagome” lattice consists of corner-sharing triangles. We present the results of large-$N$ mean field theory and Monte Carlo computations on $O(N)$ classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model ($N=3$) via “order by disorder,” representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.