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The in-plane superexchange interaction $J$ of cuprate superconductors haslong been suggested to be an important parameter for exploring theirhigh-temperature superconductivity. The bilayerBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ is the most studied system with high-qualitysingle crystals in the wide doping range with the the same structure and phase.So far, the lattice parameter dependence of $J$ in its antiferromagnetic parentcompound Bi$_2$Sr$_2$CaCu$_2$O$_{8}$ has not been established. By combiningRaman scattering and x-ray diffraction techniques on the same sample in thesame pressure environment, we obtain the evolution of both the two-magnonspectrum and the structural parameters with pressure up to nearly 30 GPa, Therelationship between pressure or the in-plane lattice parameter and $J$ is thusestablished for Bi$_2$Sr$_2$CaCu$_2$O$_{8}$. Over the studied pressure range,superconductivity does not appear in this parent compound based on a sensitivemagnetic measurement technique. The effects of pressure and chemical doping onthe superexchange interaction and structure and their implications forsuperconductivity are discussed from the comparison of the obtainedexperimental data with the existing experiments. The results and findingsprovide valuable information for the understanding of superconductivity and thefuture theory developments for superconductivity in cuprates.

Lattice effect on the superexchange interaction in antiferromagnetic Bi$_2$Sr$_2$CaCu$_2$O$_8$