It remains a challenge to understand the unconventional mechanisms that cause high-T_C superconductivity in cuprate superconductors, high-T_C multiferroicity in CuO, or low-dimensional magnetism in the spin-Peierls transition compounds such as CuGeO₃. A common feature of all these copper oxide compounds (containing Cu2+ ions) is the presence of large magnetic superexchange interactions J. It is a general strategy to apply chemical and/or physical pressure in order to tune these exotic properties. Here we show theoretically, for the first time, the impact of physical pressure on J on CuO, for which we predict a strong enhancement of the low-dimensionality of the magnetic interactions and the spin-frustration at high-pressures. Such modifications are expected to strongly influence the multiferroic properties of CuO. We finally demonstrate that PBE0 hybrid DFT calculations provide reliable J values for a wide range of copper(II) oxides compounds, i.e. CuGeO₃, BaCu₂Si₂O₇, BaCu₂Ge₂O₇, and La₂CuO_4.

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