Spin Crossover of Local Copper-Oxygen States in the HTSC Cuprate La\(_{2-x}\)Sr\(_x\)CuO\(_4\) Under the c-Axis Pressure

In this work, the change in the energy and structure of local many-particle states of HTSC cuprate La\(_{2-x}\)Sr\(_x\)CuO\(_4\) under the uniaxial compression along the c-axis is studied. Local copper-oxygen states are obtained using exact diagonalization of the CuO\(_6\) octahedron as a part of the GTB method for the five-band p-d model. The dependence of interatomic distances on the c-axis compression is calculated according to Hooke’s law using elastic constants; the influence of interatomic distances on the on-site energies and hopping integrals is obtained using linear extrapolation of the results of ab initio calculations and the theory of MT-orbitals, respectively. The c-axis compression leads to a decrease in the energy of hole states with the nature of the \(a_{1g}\) symmetry orbitals. At a pressure value of \(P_{c1}^{\left( c \right) } = 11.8\) GPa, a spin crossover between the Zhang-Rice singlet and the triplet state \(B_1\) occurs. At higher pressures, a second spin crossover between two-hole states and a crossover of single-hole states with different orbital compositions were also detected. Taking into account the competition of various local states with changing the value of uniaxial compression, the effective five-band Hubbard model is formulated to describe the electronic structure of quasiparticle excitations.