# Itinerant Nature of Magnetism in Iron Pnictides: A first principles study 

Yu-Zhong Zhang, 1 Ingo Opahle, 1 Harald O. Jeschke, 1 and Roser Valent´ı 1 

$^{1}$Institut f¨ ur Theoretische Physik, Goethe-Universit¨ at Frankfurt, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany 

(Dated: October 24, 2018) 

Within the framework of density functional theory we investigate the nature of magnetism in various families of Fe-based superconductors. (i) We show that magnetization of stripe-type anti- ferromagnetic order always becomes stronger when As is substituted by Sb in LaOFeAs, BaFe 2 As 2 and LiFeAs. By calculating Pauli susceptibilities, we attribute the magnetization increase obtained after replacing As by Sb to the enhancement of an instability at ( π, π ). This points to a strong con- nection between Fermi surface nesting and magnetism, which supports the theory of the itinerant nature of magnetism in various families of Fe-based superconductors. (ii) We find that within the family LaOFe P n ( P n =P, As, Sb, Bi) the absence of an antiferromagnetic phase in LaOFeP and its presence in LaOFeAs can be attributed to the competition of instabilities in the Pauli susceptibility at ( π, π ) and (0 , 0), which further strengthens the close relation between Fermi surface nesting and experimentally observed magnetization. (iii) Finally, based on our relaxed structures and Pauli susceptibility results, we predict that LaOFeSb upon doping or application of pressure should be a candidate for a superconductor with the highest transition temperature among the hypothetical compounds LaOFeSb, LaOFeBi, ScOFeP and ScOFeAs while the parent compounds LaOFeSb and LaOFeBi should show at ambient pressure a stripe-type antiferromagnetic metallic state. 

After the discovery of the first high- T$_{c}$ iron-based su- perconductor La[O$_{1}$$_{−}$$_{x}$F$_{x}$]FeAs 1 (denoted as 1111 com- pound), the superconducting transition temperature was rapidly raised up to 55 K with substitution of La by Sm $^{2}$. While various other families of Fe-based super- conductors were reported afterwards, like the 122 com- pounds AE Fe$_{2}$As$_{2}$ ( AE =Ca,Sr,Ba) $^{3–9}$, the 111 com- pounds A FeAs ( A =Li,Na) 10–15 and the 11 compounds Fe Ch ( Ch =Se,Te) $^{16–18}$, the transition temperature has always been lower than the highest one observed in the 1111 systems. Besides the continuous experimental at- tempts to pursue higher superconducting transition tem- peratures in the Fe-based compounds and deeper under- standing of high- T$_{c}$ superconductivity $^{19}$, a great effort to understand the origin of their phase diagram has also been made on the theoretical side. 

Although it is widely believed that magnetically medi- ated rather than phonon-mediated pairing dominates the superconducting state due to its proximity to a stripe- type antiferromagnetic phase $^{20–37}$, the origin of the mag- netism is still highly under debate. Some of the ex- perimental work and theoretical studies based on den- sity functional theory (DFT) support an itinerant sce- nario of magnetism due to the fact that the electron and hole sheets of the Fermi surface are nearly nested 23,38–44 and correlation effects are not very strong, resulting in a metallic state of the parent compounds $^{45–48}$. In con- trast, some authors favor a localized picture 21,34,35,49–53 since DFT calculations fail to reproduce the experimen- tally observed band splitting in the stripe-type antifer- romagnetic phase $^{54}$. In these studies the observed small magnetic moment is attributed to highly frustrated su- 

PACS numbers: 74.70.-b 74.25.Ha 74.25.Jb,71.15.Mb,71.15.Pd 

## I. INTRODUCTION 

perexchange interactions which explain the observed low energy spin excitations well $^{55}$. Apart from the oppos- ing viewpoints above, various other interpretations co- exist, such as those that propose that the magnetism could come from the local Hund’s rule coupling 56 or from the coexistence of localized and itinerant electrons $^{57–60}$. A recent LDA+U calculation explains the small mag- netic moment by formation of magnetic multipoles 62 while LDA+DMFT (dynamical mean field theory) cal- culations in conjunction with angle resolved photoemis- sion (ARPES) experiments suggest that involvement of non-local fluctuations may be crucial $^{61}$. Further, a recent DMFT calculation stressed the importance of the inter- play between frustrated and unfrustrated bands within a two-band Hubbard model at half-filling $^{63}$. Among these theories, it is presently hard to decide which is the most promising for the observed magnetism in the parent com- pounds of the iron-based superconductors. 

In fact, one of the most popular theories mentioned above, the itinerant scenario of magnetism, was recently substantially challenged both by experiment 64 and den- sity functional theory calculations $^{65}$. On the one hand, an ARPES study on the 11 compound Fe$_{1+}$$_{x}$Te shows no evidence of a Fermi surface nesting at ( π, 0) 64 while mag- netic order with such a wave vector is detected by neutron scattering $^{66}$. On the other hand, a DFT calculation on LaOFeAs, BaFe$_{2}$As$_{2}$ and LiFeAs based on a pseudopo- tential method 65 reveals that the magnetic moments are enhanced in all compounds by replacing As with Sb while the Fermi surface nesting with a nesting vector of ( π, π ) is found with this substitution to be enhanced only in the 1111 compound but suppressed in the 122 and 111 compounds. These studies question altogether the appli- cability of the theory of itinerant magnetism to the 11, 

