Range of the t--J model parameters for CuO$_{2}$ plane: experimental data constraints

TL;DR

This paper constrains the parameters of the t-J model for CuO$_{2}$ planes by deriving the hopping integral from the three-band Hubbard model, using experimental data to narrow parameter uncertainties and validate the model's spectral features.

Contribution

It provides experimentally constrained ranges for the t-J model parameters based on the three-band Hubbard model and experimental data, clarifying the model's applicability.

Findings

Fixed t/J ratio range for holes: 2.4 to 2.7

Fixed t/J ratio range for electrons: 2.5 to 3.0

Validated the formation of Frenkel excitons and charge-transfer spectrum features

Abstract

The t-J model effective hopping integral is determined from the three-band Hubbard model for the charge carriers in CuO$_{2}$ plane. For this purpose the values of the superexchange constant $J$ and the charge-transfer gap $E_{gap}$ are calculated in the framework of the three-band model. Fitting values of $J$ and $E_{gap}$ to the experimental data allows to narrow the uncertainty region of the three-band model parameters. As a result, the $t/J$ ratio of the t-J model is fixed in the range $2.4 \div 2.7$ for holes and $2.5 \div 3.0$ for electrons. Formation of the Frenkel exciton is justified and the main features of the charge-transfer spectrum are correctly described in the framework of this approach.