Investigation of the spectral properties and magnetism of ${\mathrm{BiFeO}}_3$ by dynamical mean-field theory

Using the local density approximation plus dynamical mean-field theory (LDA+DMFT), we have computed the valence-band photoelectron spectra and magnetic excitation spectra of ${\mathrm{BiFeO}}_3$, one of the most studied multiferroics. Within the DMFT approach, the local impurity problem is tackled by the exact diagonalization solver. The solution of the impurity problem within the LDA+DMFT method for the paramagnetic and magnetically ordered phases produces result in agreement with the experimental data on electronic and magnetic structures. For comparison, we also present results obtained by the $\mathrm{LDA}+U$ approach which is commonly used to compute the physical properties of this compound. Our LDA+DMFT derived electronic spectra match adequately with the experimental hard x-ray photoelectron spectroscopy and resonant photoelectron spectroscopy for Fe $3d$ states, whereas the $\mathrm{LDA}+U$ method fails to capture the general features of the measured spectra. This indicates the importance of accurately incorporating the dynamical aspect of electronic correlation among Fe $3d$ orbitals to reproduce the experimental excitation spectra. Specifically, the LDA+DMFT derived density of states exhibits a significant amount of Fe $3d$ states at the position of Bi lone pairs, implying that the latter are not alone in the spectral scenario. This fact might modify our interpretation about the origin of ferroelectric polarization in this material. Our study demonstrates that the combination of orbital cross sections for the constituent elements and broadening schemes for the spectral functions are crucial to explain the detailed structures of the experimental electronic spectra. Our magnetic excitation spectra computed from the LDA+DMFT result conform well with the inelastic neutron scattering data.

Figure 1

Total and projected density of states of ${\mathrm{BiFeO}}_3$ in the valence band, calculated using the LSDA+$U$ method with $U=6$ eV and $J=0.9$ eV. The top of the valence band is set to zero.

Figure 2

Total and projected density of states of ${\mathrm{BiFeO}}_3$ in the valence band, calculated using the LDA+DMFT method with $U=6$ eV and $J=0.9$ eV. The result from the PM and AFM phase are shown. The AFM data are shifted along $y$ axis for better visualization. The top of the valence band is set to zero.

Figure 3

(a) and (b) Imaginary part of the hybridization function computed using the LSDA+$U$ and LDA+DMFT methods, respectively. (c) and (d) Symmetry-resolved partial DOS for the Fe $3d$ orbitals calculated using the LSDA+$U$ and LDA+DMFT methods, respectively. The LDA+DMFT calculations are performed in the PM phase. The LDA+DMFT calculation in the AFM configuration produces an identical result to the PM configuration (see text).

Figure 4

A comparison between the RPES spectra [36] and theoretical spectra for Fe $3d$ states of ${\mathrm{BiFeO}}_3$ computed using the LSDA+$U$ and LDA+DMFT methods. The LDA+DMFT spectra are calculated in the PM and AFM phases. The theoretical calculations are performed using $U=6$ eV and $J=0.9$ eV. The experimental data are shifted to align with the calculated valence-band edge (see text).

Figure 5

A comparison between the HAXPES spectra [36] and theoretical spectra of ${\mathrm{BiFeO}}_3$ computed using the LSDA+$U$ and LDA+DMFT methods. The LDA+DMFT spectra are shown for the PM and AFM phases. The theoretical calculations are performed using $U=6$ eV and $J=0.9$ eV. The experimental data are shifted to align with the calculated valence-band edge (see text).

Figure 6

Atom and orbital-projected spectral states of ${\mathrm{BiFeO}}_3$, calculated using the LSDA+$U$ and LDA+DMFT (PM phase) methods. The calculations are done with interaction parameters $U=6$ eV and $J=0.9$ eV. All the spectra are normalized in intensity with respect to the Bi $5d$ states (data not shown). The LDA+DMFT derived spectra for the AFM phase are identical to the spectra for the PM phase (see text).

Figure 7

Adiabatic magnon spectra of ${\mathrm{BiFeO}}_3$ calculated using the exchange parameters and magnetic moment provided by the LDA+DMFT method. The open squares (red) indicate the experimental data of Ref. [57].

Figure 8

Theoretical spectra of Fe $3d$ states calculated using the LDA+DMFT method (PM phase) for different combinations of $U$ and $J$ values. The inset shows the spectra for two different values of $J$, while $U$ is fixed. The result from the AFM phase is identical to this result (see text).

Figure 9

The Fe $3d$ DOS are calculated using the LDA+DMFT method (PM phase) for 15 and 20 auxiliary bath orbitals. The result for the AFM phase is identical to this result.

Figure 10

The valence band HAXPES spectra of ${\mathrm{BiFeO}}_3$ at two temperatures measured at a photon energy of 2.1 keV.