Conductivity Anisotropy in the Antiferromagnetic State of Iron Pnictides

Recent experiments on iron pnictides have uncovered a large in-plane resistivity anisotropy with a surprising result: The system conducts better in the antiferromagnetic $x$ direction than in the ferromagnetic $y$ direction. We address this problem by calculating the ratio of the Drude weight along the $x$ and $y$ directions, $D_x/D_y$, for the mean-field $\mathbf{Q}=(\pi ,\mathbf{0})$ magnetic phase diagram of a five-band model for the undoped pnictides. We find that $D_x/D_y$ ranges between $0.2<D_x/D_y<1.7$ for different interaction parameters. Large values of the orbital ordering favor an anisotropy opposite to the one found experimentally. On the other hand, $D_x/D_y$ is strongly dependent on the topology and morphology of the reconstructed Fermi surface. Our results point against orbital ordering as the origin of the observed conductivity anisotropy, which may be ascribed to the anisotropy of the Fermi velocity.

Figure 1

(a) $U$ vs $J/U$ magnetic phase diagram superposed to the magnetization showing the paramagnetic (black), high moment (HM), and low moment (LM) magnetic phases. The magnetic moment reaches values as high as $3.4{\mu }_B$. The color scale emphasizes the region with magnetic moments smaller than $2{\mu }_B$. (b) Drude ratio with largest values of $D_x/D_y>1$ corresponding to small values of the magnetization. (c) Orbital ordering $n_{yz}-n_{zx}$. It correlates well with the difference between the partial density of states of $d_{yz}$ and $d_{zx}$ at the Fermi level; see 27.

Figure 2

Fermi surfaces (left) and velocities (right) at different points of the phase diagram in the extended (Fe) Brillouin zone. The Fermi surfaces are weighted by their spectral weight. The corresponding $U$ and $J$ values, as well as the obtained anisotropy of the Drude ratio, magnetic moment in Bohr magnetons and the magnetic state appear on top of each figure.

Figure 3

(a) Fermi surface in the paramagnetic state for $U$, $J=0$. (b) Band structure for $U=2.2\mathrm{eV}$ and $J/U=0.07$ corresponding to the LM state, in red. The linewidth gives a measure of the spectral weight. The paramagnetic bands, in black, are shown as a reference. The position of the Dirac cones along $\Gamma X$ is marked with arrows.