Low Magnetization and Anisotropy in the Antiferromagnetic State of Undoped Iron Pnictides

We examine the magnetic phase diagram of iron pnictides using a five-band model. For the intermediate values of the interaction expected to hold in the iron pnictides, we find a metallic low moment state characterized by antiparallel orbital magnetic moments. The anisotropy of the interorbital hopping amplitudes is the key to understanding this low moment state. This state accounts for the small magnetization measured in undoped iron pnictides and leads to the strong exchange anisotropy found in neutron experiments. Orbital ordering is concomitant with magnetism and produces the large $zx$ orbital weight seen at $\Gamma$ in photoemission experiments.

Figure 1

Calculated ($\pi ,0$) mean-field magnetic phase diagram of the five-band Hamiltonian in Eq. (1). Patterned areas (for $U\gtrsim 3$) correspond to gapped states. The following color code applies: gray corresponds to the paramagnetic (PM) state; red to a low magnetic moment (LM) state showing orbital magnetizations $m_{\gamma }$ with opposite signs; blue to high magnetization (HM) with parallel $m_{\gamma }$ which corresponds at large $U$ to an $S_z=2$ state; white is an intermediate $S_z=1$ moment state; and green is the $S_z=0$ state. The $S_z=2$, $S_z=1$, and $S_z=0$ states are illustrated from top to bottom on the right. Magnetic moment $m$ and gap are assumed to be finite when larger than 0.001.

Figure 2

(a) Total magnetic moment for three different values of $J$ as a function of $U$. (b) Orbital magnetic moments $m_{\gamma }$, (c) OO $n_{yz}\mathrm{\text{−}}{n}_{zx}$ and gap, and (d) orbital filling $n_{\gamma }$ as a function of $U$ for $J/U=0.07$. The low magnetic moment state arising for $2\le U\le 2.8$ is due to the partial cancellation of opposite magnetic moments on different orbitals.

Figure 3

(a) Dependence on $\alpha$ of the first nearest neighbors hopping amplitudes mostly responsible for the stability of the low magnetic moment state and the orbital ordering. For other hopping amplitudes see 19. (b) Direct Fe-Fe and indirect (via As) contributions to $t_{yz,yz}^x$ and $t_{yz,yz}^y$ showing a strong anisotropy. (c) Sketch of the low magnetic moment state on three neighboring sites of the Fe plane and the largest hoppings involved in its stabilization.

Figure 4

(a) Anisotropy $J_{\mathrm{eff}}^y/J_{\mathrm{eff}}^x$ of the magnetic exchange from a strong coupling approach and (b) orbital ordering $n_{yz}-n_{zx}$ as a function of $U$ and $J$. The anisotropy appears mostly within the $S_z=0$ and low moment states [green and red (LM) regions in Fig. 1]. The orbital ordering accompanies the magnetization within a wide range of parameters but is not correlated with the exchange anisotropy.