Magnetic Excitation Spectra in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$: A Two-Particle Approach within a Combination of the Density Functional Theory and the Dynamical Mean-Field Theory Method

We study the magnetic excitation spectra in the paramagnetic state of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ from the ab initio perspective. Both the one-particle and the magnetic two-particle excitation spectra are determined within the combination of the density functional theory and the dynamical mean-field theory method. This method reproduces all the experimentally observed features in inelastic neutron scattering and relates them to both the one-particle excitations and the collective modes. The magnetic excitation dispersion is well accounted for by our theoretical calculation in the paramagnetic state without any broken symmetry; hence, nematic order is not needed to explain the inelastic neutron scattering experimental data.

Figure 1

The Feynman diagrams for the Bethe-Salpeter equation. It relates the two-particle Green’s function ($\chi$) with the polarization (${\chi }^0$) and the local irreducible vertex function (${\Gamma }_{\mathrm{loc}}^{\mathrm{irr}}$). The nonlocal two-particle Green’s function is obtained by replacing the local propagator by the nonlocal propagator.

Figure 2

(a) The constant energy plot of the theoretical dynamical structure factor $S(\mathbf{q},\omega )$ ($=\frac{{\chi }^{\prime \prime }(\mathbf{q},\omega )}{1-e^{-\hslash \omega /k_{B}T}}$) at different energies (50, 75, 125, and 150 meV) in the paramagnetic state ($T=386\mathrm{K}$) of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ as a function of momentum $\mathbf{q}=(H,K,L)$. $L$ is here fixed at 1. (b) The corresponding inelastic neutron scattering data from Ref. 13.

Figure 3

$S(\mathbf{q},\omega )$ along the special path in the Brillouin zone marked by a red arrow in the inset on the right. The inset shows the body-centered tetragonal (black line) and the unfolded (blue line) Brillouin zone. Black dots with error bars correspond to INS data from Ref. 13. The white dashed line shows the isotropic Heisenberg spin wave dispersion.

Figure 4

(a) The wave vector $K$ dependence ($H=1$, $L=1$) of $S(\mathbf{q},\omega )$ at several frequencies. (b) The corresponding INS data at $\omega =19$ and (c) 128 meV reproduced from Ref. 13. The red circles correspond to the paramagnetic state at $T=150\mathrm{K}$ and the blue diamonds to the magnetic state at $T=7\mathrm{K}$.

Figure 5

(a) The Fe $d$ orbital resolved dynamical magnetic susceptibility at $T=386\mathrm{K}$ for distinct wave vectors $\mathbf{q}=(1,0,1)$, $(0,1,1)$, $(0,0,1)$, and $(1,1,1)$. Different colors correspond to different orbital contributions. (b) The Fermi surface in the $\Gamma$ and $Z$ plane at $T=73\mathrm{K}$ colored by the orbital characters: $d_{xz}$ (blue), $d_{yz}$ (green), and $d_{xy}$ (red). The small symbols mark the regions in the Fermi surface, where nesting for the wave vector $\mathbf{q}=(1,0,1)$ is good. (c) The zoom-in of $A(\mathbf{k},\omega )$ along the path marked by a black dashed line in (b). The green open circles indicate the two relevant bands of $d_{xy}$ character which give rise to the peak in magnetic excitation spectra near 230 meV at $\mathbf{q}=(1,1,1)$. (d) $A(\mathbf{k},\omega )$ computed in one Fe atom per unit cell at $T=73\mathrm{K}$. The green arrows mark the same bands which give rise to the 230 meV peak. The DFT bands are overlaid by white dashed lines. The blue arrows mark corresponding DFT bands of $d_{xy}$ character.