Influence of spin-phonon coupling on antiferromagnetic spin fluctuations in FeSe under pressure: First-principles calculations with van der Waals corrections

The electronic structures, lattice dynamics, and magnetic properties of crystal β-FeSe under hydrostatic pressure have been studied by using the first-principles electronic structure calculations with van der Waals corrections. With applied pressure, the energy bands around the Fermi energy level consisting mainly of Fe-$3d$ orbitals show obvious energy shifts and occupation variations, and meanwhile the frequencies of all optical phonon modes increase. Among these phonon modes, the A1g mode, which relates to the Se height from the Fe-Fe plane, shows a clear frequency jump in a pressure range between 5 and 6 GPa. This is also the pressure range within which the highest superconducting transition temperature Tc of FeSe is reached in experiments. In comparison with other phonon modes, the atomic displacement due to the zero-point vibration of the A1g mode induces the strongest fluctuation of local magnetic moment on Fe under pressures from 0 to 9 GPa, and the induced fluctuation reaches a maximum around 5 GPa. These results suggest that the effect of phonon via spin-phonon coupling could not be completely omitted when exploring the superconducting mechanism in iron-based superconductors.