Resonant inelastic x-ray scattering in layered trimer iridate Ba4Ir3 O10 : the density functional approach

TL;DR

Ba$_4$Ir$_3$O$_{10}$ exhibits a delicate interplay between spin–orbit coupling, electron correlations, and a trimer-based Ir network that stabilizes an insulating ferrimagnetic ground state driven by both dimerization at Ir$_1$ and Mott physics at Ir$_2$. Using fully relativistic DFT with GGA+$U$ and a core-hole–aware RIXS formalism, the authors compute XAS/XMCD and Ir L$_3$ and O K edge RIXS spectra that agree with experiments, identifying intra-$t_{2g}$ excitations below $2.3$ eV, a $t_{2g} \rightarrow e_g$ peak near $3.7$ eV, and higher-energy charge-transfer features. They find best agreement for $U_{ m eff} \approx 1.3$ eV on Ir$_2$, with Ir$_2$ supporting a $J_{ m eff}=1/2$ state while Ir$_1$ hosts molecular-orbital–like states due to strong dimerization; this underlines the necessity of site-resolved treatments in 5$d$ oxide trimers. The results demonstrate a robust first-principles pathway to interpret RIXS in complex SOC–driven systems and highlight the significant role of covalency and lattice geometry in shaping low-energy excitations and magnetic behavior.

Abstract

We have investigated the electronic structure of Ba4Ir3O10 within the density-functional theory (DFT) using the generalized gradient approximation while considering strong Coulomb correlations (GGA+U) in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. Ba4Ir3O10 has a quasi-2D structure composed of buckled sheets, which constitute corner-connected Ir3O12 trimers containing three distorted face-sharing IrO6 octahedra. The Ir atoms are distributed over two symmetrically inequivalent sites: the center of the trimer (Ir1) and its two tips (Ir2). The Ir1 - Ir2 distance within the trimer is quite small and equals to 2.58 A at low temperature. As a result, the clear formation of bonding and antibonding states at the Ir1 site occurs. The large bonding-antibonding splitting stabilizes the dyz-orbital-dominant antibonding state of t2g holes and produces a wide energy gap at the Fermi level. However, the energy gap opens up only with taking into account strong Coulomb correlations at the Ir2 site. Therefore, we have quite a unique situation when the insulating state is driven by both the dimerization at the Ir1 site and Mott insulating behavior at the Ir2 one. We have investigated resonant inelastic x-ray scattering (RIXS) spectra at the Ir L3 edge. The calculated results are in good agreement with experimental data. The RIXS spectrum possesses several sharp features below 2.1 eV corresponding to transitions within the Ir t2g levels. The excitation located from 2.1 to 4.6 eV is due to t2g to eg and O2p to t2g transitions. The wide structure situated at 6.2-12 eV appears due to charge transfer and O2p to eg transitions. We have also presented comprehensive theoretical calculations of the RIXS spectrum at the oxygen K edge.

Figures (10)

• Figure 1: (Color online) The schematic representation of Ba$_4$Ir$_3$O$_{10}$ in the monoclinic structure with the space group $P2_1/a$ (No. 14).
• Figure 2: (Color online) The orbital-resolved Ir $t_{2g}$ partial density of states [in states/(atom eV)] for Ba$_4$Ir$_3$O$_{10}$ calculated in the GGA for the nomagnetic solution at the Ir$_1$ site (a), and the Ir$_2$ site (b). The results of the ferrimagnetic (FiM) solution (c) and the GGA+$U$ results (d) for the Ir$_2$ site.
• Figure 3: (Color online) The energy band structure of Ba$_4$Ir$_3$O$_{10}$ and 5$d$ partial density of states for Ir$_1$ (the upper panel) and Ir$_2$ (the middle panel) calculated in the fully relativistic Dirac GGA+SO approximation. The circles are proportional in size to their orbital character projected onto the basis set of Ir $d_{3/2}$ (the relativistic quantum number $\kappa$ = 2, the blue curve) and $d_{5/2}$ ($\kappa$ = $-$3, the red curve) states; (the lower panel) the energy bands calculated in the GGA+SO+$U$ approximation with $U_{\rm{eff}}$ = 1.3 eV.
• Figure 4: (Color online) The phase diagram in the $U_{\rm{eff}}-$SOC plane for Ba$_4$Ir$_3$O$_{10}$ (the blue curve) in comparison with Sr$_2$IrO$_4$AKB24a (the red curve). The curves separate metal (under the curves) and Mott insulator (above the curves) states for Ba$_4$Ir$_3$O$_{10}$ and Sr$_2$IrO$_4$, connected via a first-order phase transition. The horizontal lines indicate the value of Hubbard $U_{\rm{eff}}$ for which the energy band gap opens up.
• Figure 5: (Color online) The energy band structure and total density of states (DOS) [in states/(cell eV)] for Ba$_4$Ir$_3$O$_{10}$ calculated in the GGA+SO+$U$ approach ($U_{\rm{eff}}$= 1.3 eV).