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

TL;DR

This paper investigates the origin of the spin-gap in CaV$_4$O$_9$, highlighting the roles of frustration, lattice distortion, and a spin-Peierls mechanism, supported by theoretical modeling and comparison with quantum Monte Carlo results.

Contribution

It introduces a detailed analysis of the spin-gap in CaV$_4$O$_9$ using a Heisenberg model and proposes lattice distortions enhance the gap through a spin-Peierls mechanism.

Findings

Phase diagram aligns with QMC results for nn interactions.

Lattice distortions can enhance the spin-gap.

Lattice structure naturally leads to spin-Peierls mechanism.

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.