Electronic Structure and Dynamical Correlations in Antiferromagnetic BiFeO$_3$

Abstract

We study the electronic structure and dynamical correlations in antiferromagnetic BiFeO$_3$, a prototypical room-temperature multiferroic, using a variety of static and dynamical first-principles methods. Conventional static Hubbard corrections (DFT+$U$, DFT+$U$+$V$) incorrectly predict a deep-valence Fe $3d$ peak (around $-7\,\text{eV}$) in antiferromagnetic BiFeO$_3$, in contradiction with hard-X-ray photoemission. We resolve this failure by using a recent generalization of DFT+$U$ to include a frequency-dependent screening -- DFT+$U(ω)$ -- or using a dynamical Hubbard functional (dynH). The screened Coulomb interaction $U(ω)$, computed with spin-polarized RPA and projected onto maximally localized Fe $3d$ Wannier orbitals, is expressed as a sum-over-poles, yielding a self-energy that augments the Kohn--Sham Hamiltonian. This DFT+$U(ω)$ approach predicts a fundamental band gap of $1.53\,\text{eV}$, consistent with experiments, and completely eliminates the unphysical deep-valence peak. The resulting simulated HAXPES spectrum reproduces the experimental lineshape with an accuracy matching or exceeding that of far more demanding DFT+DMFT calculations. Our work demonstrates the critical nature of dynamical screening in complex oxides and establishes DFT+$U(ω)$ as a predictive, computationally efficient method for correlated materials.

Figures (5)

• Figure 1: (a) Conventional (top) and primitive (bottom) $R3c$BiFeO3 unit cells. Bi atoms are purple, and FeO$_6$ octahedra are colored by Fe spin orientation (spin-up: red; spin-down: blue). (b) Band structure from PBEsol (white dashed lines) compared with the DFT+$U(\omega)$ spectral function and projected density of states. Dynamical correlations increase the fundamental gap from 1.03 to 1.53 and introduce significant incoherent spectral weight.
• Figure 2: Real and imaginary parts of the dynamically screened on-site Coulomb interaction $U(\omega)$ for Fe $3d$ orbitals. The static limit is $U_0 = 2.56eV$, and the bare limit is $U_\infty = 21.75eV$.
• Figure 3: Disentangling static vs. dynamical effects on the Fe $3d$ PDOS. A static DFT+$U$ calculation using $U=3.74eV$ (top) produces a spurious Fe peak. In contrast, a dynamical $\text{DFT}+U_{\text{diag}}(\omega)$ calculation averaging only the diagonal elements (middle), which has the same large static limit but includes dynamics, correctly eliminates this artifact, closely matching the result from DFT+$U(\omega)$ with full averaging (bottom).
• Figure 4: Comparison of simulated HAXPES spectra with experimental data from Refs. mazumdar_valence_2016paul_investigation_2018 (points). The DFT+$U(\omega)$ spectrum (orange) provides the best overall agreement with experiment, eliminating the spurious peak of static DFT+$U$+$V$ (red, dashed) and matching or exceeding the accuracy of DFT+DMFT (purple).
• Figure 5: Relative intensity of HAXPES features. The plot shows the intensity ratios of valence features I, II, and III relative to peak V. The DFT+$U(\omega)$ results fall within the experimental range (grey bars), while the DFT+DMFT paul_investigation_2018 method consistently overestimates these ratios.