Electronic Structure of KFe$_2$Se$_2$ from First Principles Calculations
Electronic structure and magnetic properties for iron-selenide KFeSe are studied by first-principles calculations. The ground state is collinear antiferromagnetic with calculated 2.26 magnetic moment on Fe atoms; and the , coupling strengths are calculated to be 0.038 eV and 0.029 eV. The states around are dominated by the Fe-3d orbitals which hybridize noticeably to the Se-4p orbitals. While the band structure of KFeSe is similar to a heavily electron-doped BaFeAs or FeSe system, the Fermi surface of KFeSe is much closer to FeSe system since the electron sheets around is symmetric with respect to - exchange. These features, as well as the absence of Fermi surface nesting, suggest that the parent KFeSe could be regarded as an electron doped 11 system with possible local moment magnetism.
pacs:74.70.-b, 74.25.Ha, 74.25.Jb, 74.25.Kc
The discovery of iron-based compounds, typically represented by LaFeAsOKamihara et al. (2008) (1111-type), BaFeAsRotter et al. (2008) (122-type) and FeSePitcher et al. (2008); Tapp et al. (2008)(11-type), has triggered enormous enthusiasm in searching for the new high transition temperature superconductors without copperChen et al. (2008, 2008); Ren et al. (2008); Wen et al. (2008); Wang et al. (2008). Ever since the discovery, density functional studies have been performed to explore the electronic structure and the pairing mechanism of the system. Calculations have been performed on LaFeAsODong et al. (2008); Singh and Du (2008); Yildirim (2008); Mazin et al. (2008); Cao et al. (2008); Ma and Lu (2008); Ma et al. (2008), and the ground state is found to be a collinear anti-ferromagnetism (COL) state. The magnetic ordering was proposed to be the consequence of the Fermi surface nesting phenomenaDong et al. (2008); Singh and Du (2008); Mazin et al. (2008) , which is also present in the BaFeAs parent compoundSingh (2008). The Fermi surface nesting is thus considered closely related with the superconducting (SC) phenomena since it is suppressed in SC phase. On the other hand, the - Heisenberg model based on a local moment pictureSi and Abrahams (2008); Yildirim (2008); Ma et al. (2008) was also proposed to account for the magnetic structure. It is also found that the band energy dispersion of these compounds should be calculated using the unrelaxed experimental structure in order to compare with the experimentsKasinathan et al. (2009); Rullier-Albenque et al. (2010), and that the ordered magnetic moments on Fe atom are systematically overestimated in density functional calculations.
Recently, another substance with similar chemical composition, KFeSe, has been producedGuo et al. (2010). The material is reported to be iso-structural to BaFeAs, and the superconductivity as high as 30 K is reported when it is intrinsically doped (KFeSe with ). Question thus arises that whether this material represents a new family or it is one of the discovered class. More specifically, since KFeSe is structurally close to BaFeAs but chemically close to FeSe, it is interesting to clarify which one is closer to its electronic structure.
In this paper, we report our first-principles study of this compound. We demonstrate that the electronic structure of the parent KFeSe could be regarded as an electron doped 11 system, instead of the structurally much closer BaFeAs. All the calculations were performed with the Quantum ESPRESSO codeGiannozzi et al. (2009), while an accurate set of PAW dataCao et al. (2010) were employed throughout the calculation. A 48 Ry energy cut-off ensures the calculations converge to 0.1 mRy, and all structures were optimized until forces on individual atoms were smaller than 0.1 mRy/bohr and external pressure less than 0.5 kbar. For non-magnetic (NM) and checkerboard anti-ferromagnetic (CBD) states, a Monkhorst-Pack k-gridMonkhorst and Pack (1976) was found to be sufficient; while for the collinear anti-ferromagnetic (COL) state and bi-collinear anti-ferromagnetic (BIC) state, and Monkhorst-Pack k-grid were needed to ensure the convergence to 1 meV/Fe, respectively. The PBE flavor of general gradient approximation (GGA) to the exchange-correlation functionalPerdew et al. (1996) was applied throughout the calculations.
We first examine several possible spin configurations for KFeSe (TABLE 1). The column expt indicates calculation with experimental structure and non-magnetic spin configuration, while the structures are fully optimized (lattice constants as well as internal coordinates) for NM/CBD/COL/BIC columns. It is therefore apparent that the collinear phase, which is 57 meV/Fe lower than the NM phase, is the ground state of KFeSe. This magnetic state ordering was also double-checked with full-potential linearized augmented plane wave (FLAPW) method using the elk codeelk (). A body-centered tetragonal (bct) to base-centered orthorhombic (bco) phase transition is also present in the process, although the orthorhombicity is almost negligible. Although the phase transition is not yet observed in the experiments, the resistivity measurement shows an abrupt change around KGuo et al. (2010), which we propose to be due to the bco-bct phase transition. The magnetic moment on Fe atoms turns out to be 2.26 /Fe for the collinear phase, which is similar to those obtained in PAW calculations for BaFeAsCao et al. (2010). In order to estimate the magnetic coupling strength, we incorporate the - Heisenberg model, defined by
Where, is the spin operator (of magnitude ) at the site , and denote the summation over the nearest neighbor and the next nearest neighbor sites, and are the nearest neighbor and the next nearest neighbor exchange interactions, respectively. By calculating the total energy per Fe atom for the CBD and COL states and assuming , we obtain meV and meV, respectively.
Calculations with LaFeAsO, BaFeAs, and FeSe systems suggest that the band dispersions and DOS of these systems should be studied without structural optimization in order to compare with the experimentsMazin et al. (2008); Singh and Du (2008); Cao et al. (2008); Singh (2008); Subedi et al. (2008); Singh et al. (2009); Singh (2009); although their energetic properties as well as magnetism should be explored with structural relaxation. We followed this procedure, and the discussion in the rest of this paper will primarily focus on the calculations with unrelaxed (experimental) structure unless we explicitly specify. Firstly, we present the density of states (DOS), as well as the projected density of states (PDOS) calculations (FIG. 1). The DOS and PDOS of KFeSe resemble those of BaFeAs systems, and exhibit typical characteristics of the layered structure. The contribution from Fe-3d and Se-4p orbitals dominates the states from eV to eV, while most of the K-4s contribution locates from eV to eV. A closer examination of the PDOS data shows that over 90% of the states from eV to are from the Fe-3d orbitals, and that the Fe-3d/Se-4p orbital hybridizes considerably from eV to eV and from to eV.
We further calculated the band structure for KFeSe, as shown in FIG. 2. Since the Se atom (4s4p) outermost shell has 1 more electron than the As atom (4s4p), the FeSe layer could be regarded as highly electron-doped. In fact, the band structure of KFeSe shows that the Fe-3d and Fe-3d bands are fully occupied, whereas these bands were the origin of the hole pockets in the BaFeAs systems. At , the 3d and 3d bands becomes degenerate due to the crystal symmetry. We define the energy difference between these two bands and the Fermi level at to be , and the difference between these two bands and the 3d band at to be (FIG. 2). The latter is due to the slightly deformed tetrahedral crystal field by the 4 Se atoms around the Fe atom. For the KFeSe systems, and are 18 meV and 13 meV, respectively; while for the BaFeAs systems, they are -297 meV and 204 meV, respectively. Similar to the BaFeAs band structure, the bands close to from to are mostly flat, except for the one cross the Fermi level which is due to the hybridization of Fe-3d and Se-4p orbitals. It is worthy noting that the structural relaxation does not change the number of bands across the Fermi level, nor the orbital character of these bands for KFeSe, in contrast to the cases for LaFeAsO and BaFeAs. However, the structural optimization expands the band splittings to 314 meV, and shifts the top of fully occupied d bands to 149 meV.
The band structure we obtained is then fitted using the maximally localized Wannier function (MLWF) method Souza et al. (2001); Mostofi et al. (2008) (FIG. 2) to obtain a model Hamiltonian for reconstructing the Fermi surfaces. To perform the fitting, we chose the 16 bands from eV to eV, and 16 initial guess orbitals including the Fe-3d and Se-4p to ensure the fitting quality. Nevertheless, it is possible to fit the band structure with slightly worse quality with the 10 Fe-3d orbitals only, in order to reduce the Hamiltonian size. Applying the symmetry, the number of orbitals could be further brought down to five.
We show the parent KFeSe Fermi surface in FIG. a. The Fermi surface of the parent KFeSe consists of two sheets around -point and one sheet around . Despite of the similarities between the KFeSe and the BaFeAs systems, two distinctions are apparent. First of all, the two sheets around points in KFeSe are much more symmetric than those in BaFeAs. If we define to be the k-vector from the point to the Fermi surface sheet, where denotes the angle formed by the vector and - (as shown in FIG. c), we could further define . For the two sheets around in KFeSe, both yield , while for the BaFeAs system the inner sheet has and the outer sheet has . This feature suggests that the electronic structure of KFeSe is in fact much closer to FeSe instead of BaFeAs. Secondly, the sheets around are completely different between KFeSe and BaFeAs or FeSe. Three sheets were observed for BaFeAs or FeSe system, which constitutes the three hole pockets for the system. For KFeSe system, only one sheet exists around (0,0,) axis, which is highly 3-D and vanishes around . Thus, the Fermi surface nesting effect is absent in the parent KFeSe compound. Nevertheless, one could achieve FeSe-like fermi surface using the rigid band model simply by shifting down the fermi level (FIG. c), or effectively by hole doping. From the band structure calculation, the Fermi level has to be shifted down by 0.2 eV in order to recover the Fermi surface nesting effect. The DOS result indicates that shifting down by 0.2 eV corresponds to 1.0 hole doping effectively, or completely removing K from KFeSe. Due to the loss of Fermi surface nesting, the magnetism of KFeSe is not simply due to the Fermi surface nesting effect. Instead, it is possible that the localized Fe-3d orbitals plays an essential role in the magnetism. Using the same model, we could also obtain the Fermi surface for KFeSe (), as shown in FIG. b, which could be an analogue to an electron-doped 11 system.
Finally, we study the -dependence of the magnetic coupling strength and using the GGA+ method, to test if the COL configuration remains as the ground state if there is electron correlation beyond LDA. A series of from 1.0 eV to 6.0 eV were used to optimize the lattice constants as well as the internal coordinates for NM/CBD/COL configurations, and then and under different were fitted using . Both and show linear dependence with respect to the on-site energy , and the collinear state remains the ground state within a reasonable range.
In conclusion, we have studied the electronic structure of KFeSe using first-principles calculations. The ground state of KFeSe turns out to be collinear anti-ferromagnetic configuration with 2.26 magnetic moment on Fe atoms, similar to BaFeAs. The and coupling strengths are calculated to be 0.038 eV and 0.029 eV, respectively. Although the band structure is similar to heavily electron-doped BaFeAs, the Fermi surface suggests that the system is much closer to an electron-doped FeSe system. The Fermi surface nesting effect is absent in the parent KFeSe compound, thus the antiferromagnetism is possibly due to the local moments instead of the itinerant electrons. Since the KFeSe is electron-doped, the superconductivity could be introduced with hole-doping or, effectively, K or Fe deficiencies.
We would like to thank Hong Ding and Gang Wang for calling our attention to the KFeSe compound reported in Ref.Guo et al. (2010). We also thank Guanghan Cao, Xiaoyong Feng, and Qimiao Si for helpful discussions. This work was supported by the NSFC, the 973 Project of the MOST and the Fundamental Research Funds for the Central Universities of China (No. 2010QNA3026). All the calculations were performed on Hangzhou Normal University College of Science High Performance Computing Center.
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