Non-trivial role of interlayer cation states in iron-based superconductors

Non-trivial role of interlayer cation states in iron-based superconductors

Daniel Guterding guterding@itp.uni-frankfurt.de Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany    Harald O. Jeschke Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany    I. I. Mazin Code 6393, Naval Research Laboratory, Washington, DC 20375, USA    J. K. Glasbrenner [ National Research Council/Code 6393, Naval Research Laboratory, Washington, DC 20375, USA    E. Bascones Instituto de Ciencia de Materiales de Madrid, ICMM-CSIC, Cantoblanco, 28049 Madrid, Spain    Roser Valentí Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
Abstract

Unconventional superconductivity in iron pnictides and chalcogenides has been suggested to be controlled by the interplay of low-energy antiferromagnetic spin fluctuations and the particular topology of the Fermi surface in these materials. Based on this premise, one would also expect the large class of isostructural and isoelectronic iron germanide compounds to be good superconductors. As a matter of fact, they, however, superconduct at very low temperatures or not at all. In this work we establish that superconductivity in iron germanides is suppressed by strong ferromagnetic tendencies, which surprisingly do not originate from changes in bond-angles or -distances with respect to iron pnictides and chalcogenides, but are due to changes in the electronic structure in a wide range of energies happening upon substitution of atom species (As by Ge and the corresponding spacer cations). Our results indicate that superconductivity in iron-based materials may not always be fully understood based on or model Hamiltonians only.

pacs:
71.20.-b, 74.24.Ha, 74.70.Xa, 75.30.Et

Present address: ]Department of Computational and Data Sciences and Computational Materials Science Center, George Mason University, 4400 University Drive, Fairfax, VA 22030

Introduction.- After the initial discovery of high-temperature superconductivity in doped LaFeAsO Kamihara2008 , a large variety of other iron pnictides and chalcogenides have been shown to be superconductors Hosono2015a , with some reports of the transition temperature as high as 100 K Ge2015 . On the other hand, isoelectronic and isostructural iron germanides are either non-superconducting Avila2004 ; Ran2011 ; Kim2015 ; Liu2012 or possibly superconduct at very low temperatures Zou2014 ; Chen2016 . The currently most intensively debated material is YFeGe, for which superconductivity below 2 K has been reported Chen2016 . Its electronic structure is very similar to that of CaFeAs in the collapsed tetragonal phase, but with significant hole-doping Chen2016 ; Singh2014 ; Subedi2014 . This led to speculation Chen2016 about a connection between superconductivity in YFeGe and the collapsed phase of the extremely hole-doped pnictide, KFeAs Ying2015 ; Nakajima2015 ; Guterding2015B . Furthermore, Wang et al. Wang2016B recently found YFeGe to be close to a magnetic instability and X-ray absorption and photoemission experiments show evidence for strong spin-fluctuations Sirica2015 and moderate correlation effects Xu2016 in this material.

Figure 1: (Color online) Crystal structures of RbFeAs, YFeGe, NaFeAs and MgFeGe. The unit cells and interatomic distances are true to scale. The numbers next to the unit cells indicate the nominal valence of atoms at the same vertical positions.

It is generally agreed that magnetism plays an important role in superconductivity of Fe-based superconductors (FeBS) Hirschfeld2011 ; Chubukov2012 ; Hosono2015a ; Glasbrenner2015 ; Guterding2016 ; Davis2013 ; Hu2016 ; Si2016 . It is therefore natural to ask whether the magnetic tendencies in iron germanides are fundamentally different from those in iron pnictides and chalcogenides Bascones2016 and why that is the case. In a first attempt to understand the lack of superconductivity in Fe germanides, a few authors investigated the electronic properties of the isoelectronic and isostructural materials MgFeGe and LiFeAs Jeschke2013 ; Yin2014 ; Ding2014 . The former is a paramagnetic metal, while the latter is a superconductor. An important conclusion was that the dominant magnetic exchange interactions in MgFeGe are ferromagnetic, while those in LiFeAs are antiferromagnetic. The microscopic origin of this different behavior was, however, not further explored.

In this Letter we show that (i) the presence of ferromagnetic tendencies is a general trait in iron germanides, which is detrimental for superconductivity, and that (ii) the ferromagnetic tendencies arise from the interaction of the cation spacer with the FeGe layer. In fact, the hole-doping or collapse of the -axis in YFeGe are not essential for this behavior, but the key is in substitution of As by Ge and the corresponding substitution of monovalent or divalent spacers by divalent or trivalent cations, respectively. This modifies the electronic bandstructure in a wide range of energies at and away from the Fermi level and creates ferromagnetic tendencies which suppress superconductivity. Hence, one can go from As to Se/Te, right in the periodic table, and find further FeBS, but not to the left towards Ge. In agreement with recent NMR measurements Wiecki2015 , our study highlights the role of presence or absence of ferromagnetic fluctuations in determining the value of in FeBS.

Our analysis shows that conventional low-energy models of FeBS, which only incorporate the Fe and (=As, Se, Ge, …) states are in some cases not sufficient to explain key features of FeBS. Although these models usually reproduce the Fermi surface very well, they do not reflect the physical instabilities of the actual materials because they neglect the interaction with the spacer between the Fe layers. Even though bulk FeSe does not contain spacer layers, our arguments may be relevant for intercalates BurrardLucas2013 ; Guterding2015A ; Sun2015 , alkali-dosed thick films Wen2016 and FeSe monolayers on SrTiO Ge2015

Materials and Methods.- We compare isoelectronic iron arsenides and iron germanides from (i) the so-called hole-doped 122-family where iron is in a nominal oxidation Fe with occupation Yin2011 ; Backes2014 ; Backes2016 and (ii) the so-called 111-family with Fe in a configuration Yin2011 ; Ferber2012 ; Lee2012 . The crystal structures of RbFeAs, YFeGe, NaFeAs and MgFeGe are shown in Fig. 1, where we also indicate the nominal valences of the atoms in each compound. Lattice constants and internal positions in this figure were taken from experiment Venturini1996 ; Parker2009 ; Liu2012 ; Eilers2015 .

The most obvious structural difference between iron arsenides and iron germanides is shrinking of the -axis (Fig. 1). From NaFeAs to MgFeGe it is not as pronounced as from RbFeAs to YFeGe, where Ge - bonds may form (in MgFeGe direct Ge-Ge bonding is not possible). Although these materials are isoelectronic, the germanides have a stronger charge transfer between the Fe (= As, Ge) and the spacer layers.

The isoelectronic substitution of As by Ge, Rb by Y, and Na by Mg was simulated within the virtual crystal approximation (VCA). To disentangle effects originating from direct atomic substitution from effects coming from small changes of bond-distances and -angles in real materials, we performed all calculations for the 122-family with the experimental structural parameters of YFeGe Venturini1996 and those for the 111-family with the experimental structural parameters of MgFeGe Liu2012 . The technical details of our DFT calculations can be found in Ref. Supplement, .

We also analyze the density of states by using the extended Stoner model Andersen1977 ; Mazin1997 , which is a simple tool for understanding the origin of itinerant ferromagnetism (see Ref. Supplement, for details). The paramagnetic state is unstable towards ferromagnetism if the conditions and are fullfilled at some , where is the paramagnetic density of states averaged over an energy window that contains a sufficient number of states to realize an Fe moment and is the Stoner parameter Supplement .

Results.- We first calculated the DFT energies of various spin configurations. By means of the VCA we interpolated between RbFeAs and YFeGe [via SrFe(AsGe)] and between NaFeAs and MgFeGe. Using a two-dimensional Heisenberg model to parametrize the DFT energies (see Ref. Supplement, for more details) we observe that the nearest-neighbor exchange coupling universally changes from antiferromagnetic to ferromagnetic when going continuously from As to Ge without changing the electron count, while all other exchange couplings are almost unaffected (Fig. 2). Only in the 111-family the next-nearest-neighbor exchange is also reduced, but it does not change sign. At the germanide end-point the ferromagnetic becomes the dominant exchange interaction.

Figure 2: (Color online) Calculated Heisenberg exchange parameters for (a) the VCA interpolation between RbFeAs and YFeGe [via SrFe(AsGe)] and (b) the VCA interpolation between NaFeAs and MgFeGe. Lines are guides to the eye. The error bars represent the statistical errors of the fit. The inset of (b) shows the structure of the two-dimensional Heisenberg model we use to fit the DFT energies. is the nearest-neighbor coupling in the square lattice of Fe atoms, while is the next-nearest neighbor coupling. and are longer-range exchange couplings. Positive values of J correspond to antiferromagnetic exchange. Note that all calculations were performed in the crystal structures of YFeGe and MgFeGe respectively.

Remarkably, we also obtained a large ferromagnetic for NaFeAs after we expanded the structure used for Fig. 2 by 10% along the -axis but kept all distances within the FeAs layer unchanged by the expansion. These results indicate that NaFeAs can also be turned ferromagnetic by separating the FeAs layers and by shifting Na further away from the layers.

From this analysis we conclude that previous suggestions Wang2016B that iron germanides and iron pnictides show similar magnetic behavior don’t hold. While both families have a stripe antiferromagnetic ground state in the DFT calculations, the nature of excitations is entirely different. This is reflected in the presence of a nearest neighbor ferromagnetic exchange in iron germanides and antiferromagnetic in the iron pnictides despite the very similar crystal structure and electronic structure at the Fermi level. In particular, the results on the expanded NaFeAs suggest that the origin of this different behavior lies dominantly in the relative separation between the spacer and the Fe plane.

A further distinctive feature of the germanides is that the magnetism of Fe in YFeGe appears to be rather peculiar. There is a low- and a high-moment solution for Fe, the former more stabilized for shorter Fe-Ge bond length Supplement (in pnictides, either a high-spin solution is realized, or magnetism collapses completely).

Figure 3: (Color online) Effective density of states in the extended Stoner model as a function of magnetic moment for (a) RbFeAs and YFeGe and (b) NaFeAs and MgFeGe. The colored bars on the right -axis indicate the calculated inverse Stoner parameters for the respective case. All calculations were performed in the crystal structures of YFeGe and MgFeGe respectively.
Figure 4: (Color online) Total density of states calculated from DFT for (a) RbFeAs, (b) YFeFe, (c) NaFeAs and (d) MgFeGe. The shaded areas below the curves correspond to the energy range needed to realize a moment of or per iron respectively within the extended Stoner model. All calculations were performed in the crystal structures of YFeGe and MgFeGe respectively.

To understand in a simple framework the origin of the magnetic behavior presented above we investigate the effective density of states as a function of the magnetic moment within the extended Stoner model (see Fig. 3). We observe that (i) iron germanides have in general a higher DOS at the Fermi level and (ii) a significant number of states is shifted from higher energies towards the Fermi level, as compared to pnictides. This is signalled by the strong increase of the effective DOS at low moments (see Fig. 3 where results for YFeGe versus RbFeAs and MgFeGe versus NaFeAs are shown). Interestingly, the changes in the high-moment region () are marginal, while they are considerable in the low-moment region (). Furthermore, we find that the Stoner parameter is almost independent of the material and that lies between 0.7 eV and 0.75 eV. Therefore, by looking for crossings of with in Fig. 3, we establish that the extended Stoner criterion for ferromagnetism is fulfilled in iron germanides, but not in pnictides. Moreover, the metastability of different magnetic moments in YFeGe is also evident from this analysis, as the effective DOS almost fulfills the extended Stoner criterion also for large moments of about .

Fig. 4 shows the total calculated DOS for RbFeAs vs. YFeGe and NaFeAs vs. MgFeGe, where we colored the energy regions corresponding to magnetic moments of (blue) and (red) in the extended Stoner model. The energy range corresponding to is compressed when going from arsenides to germanides, while the energy range corresponding to even increases marginally in germanides. As the density of states in the window shown is dominated by Fe states, this implies that the bandwidth of some of the Fe states is selectively reduced in iron germanides, while the overall bandwidth is about constant Supplement .

Discussion.- One of the principal questions in the theory of the Fe-based superconductors is what should be the minimal chemical model to explain the essential physics and, above all, superconductivity. It was recognized that the effective Fe-only (“-only”) model does not work in some materials, but it has been believed so far that the electronic properties of iron-based superconductors were exclusively controlled by the Fe layers (=As, Se, Ge, …) as described by the so-called “-model”. Thereby the role of all other constituents was reduced to charge reservoirs.

We have established in this work that iron germanides have a general tendency towards ferromagnetism which proves detrimental for superconductivity even though the Fermi surface is very similar to that of isoelectronic pnictides. Most importantly, this tendency can be traced down to the flattening of some bands near the Fermi level and a modified electronic bandstructure in a wide range of energies at and away from the Fermi level. Neither the collapse of the -axis, nor the hole-doping of the 122 germanides are essential for the emergence of ferromagnetism. However, the character and position of the intercalating species, normally considered irrelevant and not explicitly included in any theory or model, plays a decisive role.

Our findings have important implications for iron-based superconductivity in general: (i) The Fermi surface geometry and topology is an important, but not the only condition for emerging superconductivity. The character of spin fluctuations, even on the level of the simple ferromagnetic-antiferromagnetic dichotomy, may be qualitatively different in seemingly similar materials. (ii) A quantitative theory of in iron-based superconductors must include the interaction between all constituents of the unit cell, including, in some cases, the interlayer spacers. (iii) While FeGe layers are not necessarily ferromagnetic, the fact that they have to be spaced with different elements (e.g., Mg vs. Na, or Y vs. Sr) drives them ferromagnetic. (iv) In a more general way, it does matter what we place next to or on top of an Fe-ligand layer. This observation may be directly related to an apparent role that interfacial effects play in high- Fe chalcogenides, such as FeSe monolayers deposited on specially prepared surfaces or KFeSe filaments embedded in the magnetic KFeSe phase.

Acknowledgements.
Acknowledgments.- DG, HOJ and RV thank the German Research Foundation (Deutsche Forschungsgemeinschaft) for financial support through grant SPP 1458. IIM was supported by ONR through the NRL basic research program and by the Alexander von Humboldt foundation. JKG acknowledges the support of the NRC program at NRL. EB acknowledges funding from Ministerio de Economía y Competitividad vía Grant No. FIS2014-53219-P and from Fundación Ramón Areces and thanks R. Rurali and X. Cartoixa for early calculations. The authors thank S. L. Bud’ko and P. C. Canfield for helpful discussions.

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See pages 1 of supplement.pdf See pages 2 of supplement.pdf See pages 3 of supplement.pdf See pages 4 of supplement.pdf See pages 5 of supplement.pdf See pages 6 of supplement.pdf See pages 7 of supplement.pdf See pages 8 of supplement.pdf See pages 9 of supplement.pdf

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