Origin of spin-gap in CaV${}_4$O${}_9$: effect of frustration and lattice distortion

Abstract

We study the origin of spin-gap in recently discovered material CaV${}_4$O${}_9$. We analyze the spin-$1/2$ Heisenberg model on the $1/5$ depleted square lattice with nearest neighbor (nn) and next nearest neighbor (nnn) interactions, in terms of the singlet and triplet states of the 4-spin plaquettes and 2-spin dimers. Phase diagram of the model is obtained within a linear ``spin-wave"-like approximation, and is shown to agree well with the earlier results of QMC simulations for nn interactions. We further propose that the special lattice structure of CaV${}_4$O${}_9$ naturally leads to lattice distortions, which enhances the spin-gap via a spin-Peierls mechanism.

4 pages, RevTex, 2 postscript figures. Latex file and figures have been uuencoded