SrVoFeAs as Compared with Other Fe-based Superconductors
One of the most popular scenarios for the superconductivity in Fe-based superconductors (FeBSC) posits that the bosons responsible for electronic pairing are spin-fluctuations with a wave vector spanning the hole Fermi surfaces (FSs) near and the electron FSs near M points. So far all FeBSC for which neutron data are available do demonstrate such excitations, and the band structure calculations so far were finding quasi-nested FSs in all FeBSC, providing for a peak in the spin susceptibility at the desired wave vectors. However, the newest addition to the family, SrVOFeAs, has been calculated to have a very complex FS with no visible quasi-nesting features. It was argued therefore that this material does not fall under the existing paradigm and calls for revisiting our current ideas about what is the likely cause of superconductivity in FeBSC. In this paper, I show that the visible complexity of the FS is entirely due to the V-derived electronic states. Assuming that superconductivity in SrVOFeAs, as in the other FeBSC, originates in the FeAs layers, and the superconducting electrons are sensitive to the susceptibility of the FeAs electronic subsystem, I recalculate the bare susceptibility, weighting the electronic states with their Fe character, and obtain a susceptibility that fully supports the existing quasi-nesting model. Besides, I find that the mean-filed magnetic ground state is the checkerboard in V sublattuce and stripes in the Fe sublattice.
The recently discovereddisc () Fe-based high-temperature superconductors (FeBSC) represent a challenging case for the theory of superconductivity. They appear to be rather different from cuprates in terms of their electronic structure, magnetic order, correlation effects, and superconducting symmetryreview (). So far the most popular suggestion for the pairing mechanism has been one that assigns the role of an intermediate boson to spin fluctuations with wave vectors close to Q=( (in the two-Fe Brillouin zone). There are two ways to generate such spin fluctuations: one assumes superexchange between the second neighbors in the Fe lattice and the other exploits the fact that the non-interacting spin susceptibility calculated using the one-electron band structure has a peak, or better to say a broad maximum close to ( (see review Ref. review, ). A strong argument in favor of the latter scenario was the case of FeSe, where the parent magnetic compound FeTe shows an antiferromagnetic order at a different wave vector. both in the experiment and in the calculations, but the calculated spin susceptibility is still peaked Q=( and the experiment also observes spin fluctuations with the same wave vector. Also, the fact that FeBSC lack strong Coulomb correlationsAnis (); Tom () speaks against the former alternative.
Recently, however, a new FeBSC, SrVOFeAs, has been discovered which seemingly violates this so far meticulously observed rule. The calculated Fermi surface (FS)WEP () appears to be much more complex than in the other investigated FeBSC, and there is no visual indication of any quasinesting topology. Lee and PickettWEP () argued that SrVOFeAs represents “a new paradigm for Fe-pnictide superconductors”, and inferred that “there is no reason to expect an s symmetry of superconducting order parameter ( a different sign on the two FSs) in SrVOFeAs.
I have repeated the calculations of Lee and Pickett and have obtained the FS that was similar to theirsnote () (Fig. 1). I have also verified that the bare susceptibility without any account for the matrix elements
indeed does not have any peak at Q=( (Fig. 2). In fact, it has a peak at an entirely different wave vector, as anticipated by Lee and Pickett. However, this does not take into account the fact that the calculated Fermi surface is really a superposition of two FS systems, one originating from the FeAs planes, and the other from VO ones. While there is some hybridization between the two systems of bands (at least along the XM direction; see Ref. WEP, for details), as well as a magnetic coupling and a magnetic moment on V, and maybe even Coulomb correlation effects on V site, electrons derived from the Fe -orbitals couple mostly with the spin fluctuations on the Fe sites. This is a simple consequence of the Hund’s rule. With that in mind, I colored the parts of the Fermi surface in Fig. 1 that have predominantly Fe character.
Imagine now that the unpainted parts of the FS disappear. What remains after this mental tour de force closely resembles the familiar FSs of other FeBSC. Taking into account the above argument regarding the special role of the Fe spin fluctuations, we can rewrite Eq. 1 as
where is the relative weight of the Fe orbitals in the wave function. The result (Fig. 3), as expected, shows the same structure as for the other pnictides, especially for the real part of susceptibility, which is the one relevant for superconductivity.
I conclude that, unfortunately, SrVOFeAs, despite being an interesting and in many aspects unusual FeBSC, does not represent a new paradigm, but rather falls into the same class as other pnictides. It is also worth noting that while it has been established both experimentallyAnis (); Tom () and computationallyAnis (); Antoin () that the FeAs subsystem is only weakly correlated, this had not been obvious a priori, and it is not obvious for the V-O subsystem in SrVOFeAs. Being essentially in a vanadium oxide layer (and vanadium oxide is strongly correlated in the bulk form), V in SrVOFeAs may be subject to strong Hubbard correlations that would remove V states from the Fermi levelLDAU (). Thus, strictly speaking, the conclusion above should be formulated as follows: even if SrVOFeAs is a weakly correlated metal and the FS calculated within the density functional theory is realistic, the fact that the overall topology seems on the first glance to be different from other pnictides is misleading and the spin fluctuation spectrum is likely to be rather similar.
At the end, let me briefly touched upon a separate, but equally (if not more) interesting issue of the magnetic ground state and magnetic properties of SrVOFeAs within the density functional theory (DFT). It is well knowreview () that DFT seriously overestimates the tendency to magnetism in FeBSCs, so that the calculated ground state appears strongly antiferromagnetic even in the materials that sho no long range magnetic order (phosphates, selenide). This is routinely ascribed to the mean-filead character of DFT. However, it is of course interesting to see what is the (magnetic) ground state in the mean filed, even when in real life the ground state is paramagnetic. For all FeBSCs studied so far the antiferromagnetic stripe magnetic structure is by far the lowest in energy (energy gain of the order of 200 meV per Fe compared to a nonmagnetic solution), while the ferromagnetic structure is barely stable if at all.
Most likely, the DFT ground state of FeBSCs is also antiferromagnetic in-plane. However, even the nonmagetic unit cell contains 16 atoms, which makes it extremely difficult to investigate the energy landscape for possible antiferromagnetic pattern. Thus, it makes sense to study possible ferro(ferri)magnetic solutions, in hope to extract at least some useful information. This approach was adapted in Ref. Shein () (although these authors do not present any nonmagnetic calculations, actually relevant for superconductivity). They found a solution with a moment on V ( but not on Fe. Lee and Pickett found another, ferrimagnetic solution, with opposite moments on V and Fe, the former being largerLP (). Using different starting configurations, I was able to converge to three different ground states within the same symmetry, as shown in the Table, as well as to two lower-symmetry states, as illustrated in Fig. 4(b,c,d): interlayer antiferromagnetic V sublattice, where the V layers are ferromagnetic, and antiferromagnetically stacked, while Fe is nonmagnetic, and Fe-checkerboard, where Fe forms a Neel plane and V in nonmagnetic. After that, I have calculated two configurations in the double (four formula units) cell, which I feel are the most relevant because of the superexchange interaction in the V layers: V-checkerboard with nonmagnetic Fe, and V-checkerboard combined with the stripe order in the Fe layers (Fig. 4)
A few observations are in place: (1) the state found in Ref. Shein () is not the ground state even within that symmetry; (2) unlike all other FeBSCs, FeAs planes can support a very stable ferromagnetic state; (3) the interaction between V and Fe is ferromagnetic, that is, not of superexchange character, (4) the magnetic coupling between V and Fe is so weak that V does not induce any magnetization on Fe, unless one already starts with a magnetic Fe; (5) It is more important, from the total energy point of view, to have magnetic moment on V that on Fe — a bit surprising, given that V has a weaker Hund’s rule coupling; (6) V sublattice itself has a net antiferromagnetic interaction: if Fe is not magnetic, V orders antiferromagnetically; (7) Unless some more exotic ground state will be discovered, the total energy is minimized when V layers order in the Neel (checkerboard) fashion, while Fe orders the same way as in other pnictides, forming stripes; (8) most importantly, a number of very different magnetic states are nearly degenerate in energy. This last fact may be the key to the experimental fact that the actual material is paramagnetic despite the fact that on the mean field level it is more magnetic than other pnictides. This is an extremely intriguing situation and the magnetism SrVOFeAs deserves a more elaborated experimental and theoretical study that is beyond the scope of this paper.
|V-cb + Fe-stripes||2.2|
I thank W.E. Pickett and D. Parker for stimulating discussions related to this work. I also acknowledge funding from the Office of Naval Research.
After this paper was accepted for publication, I became aware of another band structure calculationChina (). These author have considered the “Shein-Ivanovskii” half-FM states and two antiferromagnetic states, with the checkerboard (Neel) and stripe ordering in the Fe subslattice, and unspecified, presumably ferromagnetic, ordering in the V subsystem. As clear from the above, neither in this states represents an energy minimum even within the corresponding symmetry group, therefore these authors arrived to an incorrect conclusion that the lowest-energy magnetic state is characterized by Neel order in the Fe subsystem.
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