Pressure and strain tuning of the alternating bilayer-trilayer Ruddlesden-Popper nickelate: crystal and electronic structure

Abstract

We use first-principles calculations to investigate the crystal and electronic structure of the hybrid bilayer-trilayer Ruddlesden-Popper (RP) nickelate La$_7$Ni$_5$O$_{17}$ under hydrostatic pressure and biaxial compressive strain. By analyzing the irreducible representations of the dynamically unstable phonon modes in the high-symmetry $P4/mmm$ structure, we identify a dynamically stable lower-symmetry $C2/c$ structure containing octahedral tilts. The application of both pressure and compressive strain tends to suppress the octahedral tilts, effectively tetragonalizing the structure, in analogy with the conventional RPs. The electronic structure under hydrostatic pressure and strain has similarities, but it differs in the position of the $d_{z^2}$ bonding band from the trilayer block. This band crosses the Fermi level at a pressure of 30 GPa, but it remains below it for any level of compressive strain. This strain-induced modification mirrors the electronic structure changes observed in the conventional bilayer nickelate.

Figures (8)

• Figure 1: Crystal structure of La$_7$Ni$_5$O$_{17}$-2323 and phonon dispersion relation. The high-symmetry space group $P4/mmm$ (a), that displays no octahedral tilts, gives rise to unstable phonon modes (b). The structure obtained by applying distortions according to the irreducible representation of those modes (and relaxing) has $C2/c$ symmetry and contains octahedral tilts (c), characteristic of perovskite nickelates. The phonon dispersion of the $C2/c$ structure exhibits no imaginary frequencies (d), confirming its dynamic stability. Spheres in green, gray, and red in panels (a,c) represent the La, Ni, and O atoms, respectively.
• Figure 2: Evolution of the structural parameters of La$_7$Ni$_5$O$_{17}$-2323 under hydrostatic pressure and its electronic structure at 30 GPa. (a-d) Pressure-dependent evolution of (a) the absolute difference between in-plane lattice constants $|a-b|$; (b) the cross-plane lattice constant $c$; (c) the in-plane Ni-O-Ni bond angle; and (d) the cross-plane Ni-O-Ni bond angle. (e) Electronic band structure at 30 GPa, with colors representing contributions from $d_{x^2-y^2}$ (red) and $d_{z^2}$ (blue) orbitals of the Ni in the inner layer of the trilayer (left), outer layer of the trilayer (middle), and bilayer (right). (f,g) Fermi surface cutoff at the $k_z = 0$ plane, with colors representing (f) contributions from the inner layer of the trilayer (TLi), outer layer of the trilayer (TLo), and bilayer (BL) Ni sites, and (g) contributions from the $d_{x^2-y^2}$ (red) and $d_{z^2}$ (blue) orbitals of Ni.
• Figure 3: Evolution of the structural parameters of La$_7$Ni$_5$O$_{17}$-2323 under biaxial compressive strain and its electronic structure at a -2% biaxial strain. (a-d) Strain-dependent evolution of (a) the in-plane lattice constants with the symmetry starting as $C2/c$; (b) the cross-plane lattice constant $c$; (c) the in-plane Ni-O-Ni bond angle; and (d) the cross-plane Ni-O-Ni bond angle. The star on the right y-axis of (a) marks the in-plane lattice constant at 15 GPa. (e) Electronic band structure at -2% biaxial strain, with colors representing contributions from $d_{x^2-y^2}$ (red) and $d_{z^2}$ (blue) orbitals of the Ni in the inner layer of the trilayer (left), outer layer of the trilayer (middle), and bilayer (right). (f,g) Fermi surface cutoff at the $k_z = 0$ plane, with colors representing (f) contributions from the inner layer of the trilayer (TLi), outer layer of the trilayer (TLo), and bilayer (BL) Ni sites, and (g) contributions from the $d_{x^2-y^2}$ (red) and $d_{z^2}$ (blue) orbitals of Ni.
• Figure 4: Distortions based on the eigenvectors of the phonon modes with imaginary frequencies (labeled on top) at ambient pressure for La$_7$Ni$_5$O$_{17}$-2323 in $P4/mmm$ symmetry. The corresponding irreducible representations are labeled at the bottom.
• Figure 5: Phonon dispersion of La$_7$Ni$_5$O$_{17}$-2323 in $P4/mmm$ symmetry under (a) ambient pressure, (b) 20 GPa, and (c) 30 GPa.