Magnetic phases and electron-phonon coupling in La$_3$Ni$_2$O$_7$ under pressure

Motivated by recent reports of pressure-induced superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$, we present a comprehensive investigation into the structural, electronic, magnetic, and phonon properties of this compound across a pressure range of 0 to 29.5 GPa. DFT+U calculations reveal that the A-type antiferromagnetic ground state of La$_3$Ni$_2$O$_7$ persists throughout the studied pressure range. Electronic structure analysis shows that the Ni-$d_{xy}$ and Ni-$d_{z^2}$ orbitals dominate near the Fermi level in both the $Fmmm$ and $Amam$ phases of La$_3$Ni$_2$O$_7$. Phonon dispersion calculations for the $Fmmm$ phase reveal no imaginary modes from 12 to 29.5 GPa, confirming its dynamical stability in this pressure range. The vibrational frequencies of O atoms are substantially higher than those of Ni and La atoms, primarily due to the lower mass of oxygen. At 29.5 GPa, the electron-phonon coupling constant $\lambda$ for the $Fmmm$ phase is calculated to be 0.13. This small value suggests that conventional electron-phonon coupling is insufficient to explain the reported superconductivity in La$_3$Ni$_2$O$_7$, indicating a potentially unconventional mechanism. The study offers nuanced, actionable insights that can strategically inform and direct subsequent experimental investigations into the design and optimization of nickel-based superconducting materials.