A detailed magnetization study for the novel FeSe superconductor is carried out to investigate the behavior of the intrinsic magnetic susceptibility $chi$ in the normal state with temperature and under hydrostatic pressure. The temperature dependencies of $chi$ and its anisotropy $Delta chi=chi_{|}-chi_{bot}$ are measured for FeSe single crystals in the temperature range 4.2-300 K, and a substantial growth of susceptibility with temperature is revealed. The observed anisotropy $Delta chi$ is very large and comparable with the averaged susceptibility at low temperatures. For a polycrystalline sample of FeSe, a significant pressure effect on $chi$ is determined to be essentially dependent on temperature. Ab initio calculations of the pressure dependent electronic structure and magnetic susceptibility indicate that FeSe is close to magnetic instability with dominating enhanced spin paramagnetism. The calculated paramagnetic susceptibility exhibits a strong dependence on the unit cell volume and especially on the height $Z$ of chalcogen species from the Fe plane. The change of $Z$ under pressure determines a large positive pressure effect on $chi$ which is observed at low temperatures. It is shown that the literature experimental data on the strong and nonmonotonic pressure dependence of the superconducting transition temperature in FeSe correlate qualitatively with calculated behavior of the density of electronic states at the Fermi level.
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