On the presence of mid-gap states in CaV4O9

TL;DR

This study uses exact diagonalizations to analyze the $J_1-J_2$ model on a depleted square lattice, revealing spin gap phases with plaquette order and mid-gap states relevant to CaV4O9's magnetic properties.

Contribution

It provides new insights into the magnetic phases and mid-gap states in CaV4O9 by analyzing the $J_1-J_2$ model with finite cluster exact diagonalizations.

Findings

Spin-spin correlations indicate plaquette order in the spin gap phase.

Presence of singlet states within the singlet-triplet gap for certain $J_2/J_1$ ratios.

Mid-gap states are significant for understanding exchange interactions in CaV4O9.

Abstract

Using exact diagonalizations of finite clusters with up to 32 sites, we study the $J_1-J_2$ model on the 1/5 depleted square lattice. Spin-spin correlation functions are consistent with plaquette order in the spin gap phase which exists for intermediate values of $J_2/J_1$. Besides, we show that singlet states will be present in the singlet-triplet gap if $J_2/J_1$ is not too small ($J_2/J_1 \gtrsim 0.47$). We argue that this property should play a central role in determining the exchange integrals in ${\rm CaV}_4{\rm O}_9$