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We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical $(1/S)$ expansion we find that quantum fluctuations of spins induce a long-range order that breaks the fourfold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case $S=1/2$ and find a useful phenomenology to describe the bond-ordered phases.
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Tchernyshyov et al. (2003) studied this question.
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