Is the nature of magnetic order in copper-oxides and in iron- pnictides different?

We use the results of first-principles electronic structure calculations and a strong coupling perturbation approach, together with general theoretical arguments, to illustrate the differences in super-exchange interactions between the copper-oxides and iron-pnictides. We show that the two magnetic ground states can be understood in a simple manner within the same theoretical foundation. Contrary to the emerging view that magnetic order in the iron-pnictides is of itinerant nature, we argue that the observed magnetic moment is small because of frustration introduced by the electrons of the Fe orbitals as they compete to impose their preferred magnetic ordering. The copper-oxide layers present in the high-Tc superconducting families are turned into superconductors by introducing dopants that create electrons or holes in these otherwise antiferromagnetic (AF) insulating layers [1]. The proximity of antiferromagnetism to superconductivity has led to the general view that this form of magnetic order is intimately related to the mechanism of superconductivity in these materials [2]. In the recently discovered iron-pnictide based superconductors [3–8], which exhibit superconductivity at relatively high-Tc, the copperoxide layer is replaced by an iron-pnictide layer. Interest in the new materials, reminiscent of that seen when the cuprates were discovered more than two decades ago, is due to the fact that many unsuccessful attempts were made to replace the copper-oxide layer in high-Tc materials to facilitate practical applications. The parent compounds of these iron-pnictide materials, like the copperoxide parent materials, show a spin-density-wave order [9, 10] illustrated in Fig. 1(a). Unlike the copper-oxides, the parent compounds in the iron-pnictides, such as the pure LaOFeAs, are metallic, but are magnetically ordered and non-superconducting and they become superconductors by doping with electrons or holes. The copper-oxide parent compounds are well described as spin-1/2 Heisenberg quantum antiferromagnets [2]. Furthermore, it is widely believed that superconductivity in copper-oxides arises when, by doping the quantum antiferromagnet, the carriers (holes or electrons) form a strongly correlated Anderson-Mott type system with the spin-spin correlations playing a fundamental role in the superconductivity mechanism. After the discovery of the iron-pnictide superconductors, there is an emerging view that the magnetism in these compounds is of itinerant type [11–14] and that these systems are different from the cuprates and in fact weakly correlated. This is an important issue to settle, because any further theoretical analysis of other properties of this new family of materials, including the still unknown superconductivity mechanism, depends on it. Here we focus on this issue and seek a broader framework to reconcile the different forms of magnetic order and to explain the magnetic properties in both families of materials with the same approach. Our arguments are inspired by the results of Ref. [15], where first-principles electronic structure calculations based on density functional theory (DFT) were combined with a strong coupling expansion to obtain an effective low-energy Hamiltonian which describes the electrons occupying the five Fe orbitals. In the present work, we address the nature of the magnetic order in the iron-pnictide and the copper-oxide based materials using a more general scheme, which is