Microscopic origin of the linear temperature increase of the magnetic susceptibility of BaFe${}_2$As${}_2$

Employing a combination of ab initio band-structure theory and dynamical mean-field theory we explain the experimentally observed linear temperature increase of the magnetic susceptibility of the iron pnictide material BaFe${}_2$As${}_2$. The microscopic origin of this anomalous behavior is traced to a sharp peak in the spectral function located approximately 100 meV below the Fermi level. This peak is due to the weak dispersion of two-dimensional bands associated with the layered crystal structure of pnictides.

Figure 1

Uniform magnetic susceptibility $\chi \left(T\right)$ of BaFe${}_2$As${}_2$ calculated within LDA+DMFT (squares) in comparison with experimental data of Wang et al. (Ref. 4) (circles and triangles). The line is a least-square fit to the last six points of the computed data. The inset shows the theoretical curve for the full temperature interval.

Figure 2

LDA+DMFT results for the orbitally resolved Fe 3$d$ susceptibilities ${\chi }_{\alpha }\left(T\right)$ with $\alpha =xy$, $yz$, $xz$, $3z^2-r^2$, $x^2-y^2$ of BaFe${}_2$As${}_2$ vs. temperature obtained from the derivative of the magnetization.

Figure 3

Comparison of the total Fe 3$d$ spectral function of BaFe${}_2$As${}_2$ as obtained from LDA+DMFT (solid line) and LDA (shaded area), respectively.

Figure 4

Orbitally resolved Fe 3$d$ spectral functions of BaFe${}_2$As${}_2$ obtained within LDA+DMFT (solid lines) in comparison with LDA results (filled areas). The Fermi energy is set to 0 eV.

Figure 5

Fe 3$d$ spectral functions of BaFe${}_2$As${}_2$ computed within LDA+DMFT in the temperature range 232–580 K. The Fermi energy corresponds to 0 eV.

Figure 6

LDA+DMFT results for the orbitally resolved Fe 3$d$ susceptibilities ${\chi }_{\alpha }^{\mathrm{RPA}}\left(T\right)$ with $\alpha =xy$, $yz$, $xz$, $3z^2-r^2$, $x^2-y^2$ of BaFe${}_2$As${}_2$ vs. temperature, obtained from the RPA expression for the susceptibility in Eq. (7).

Figure 7

LDA+DMFT results for the uniform magnetic susceptibility of a one-band model with the noninteracting Fe $d_{xy}$ DOS of BaFe${}_2$As${}_2$ as a function of temperature. Upper panel: Results computed according to Eq. (4); the inset shows the spectral function of the interacting system. Lower panel: RPA results for the uniform magnetic susceptibility using Eq. (7); the divergence of the susceptibility for $\mu =0.2$ eV at about 300 K is an artifact of the RPA.

Figure 8

Spin susceptibility ${\chi }_1\left(T\right)$ of a model defined by the density of states (8) calculated from Eq. (6) for different values of the peak position. The inset shows the density of states plotted relative to the Fermi energy (zero energy).

Figure 9

Band structure and spectral functions computed for BaFe${}_2$As${}_2$; the Fermi energy corresponds to 0 eV. (a) Dispersion curves calculated within LDA (dashed curves), contributions of the orbitals with $d_{xy}$ symmetry (fat bands), energy bands of a two-orbital model obtained as a projection onto the $d_{xy}$ states (solid curves). (b) Spectral function of the $d_{xy}$ orbital from LDA. (c) Energy bands of a model corresponding to the real hopping parameters. (d) Spectral function of the model Hamiltonian (9).

Figure 10

Spectral functions of Hamiltonian (9) calculated in the basis of bonding (solid curve) and antibonding (dashed curve) wave functions. The total spectral function is shown by a dotted line. The Fermi energy is set to zero.