FeS: Structure and Composition Relations to Superconductivity and Magnetism

Abstract:

Structure and composition of iron chalcogenides have a delicate relationship with magnetism and superconductivity. In this report we investigate the iron sulfide layered tetragonal phase (t-FeS), and compare with three-dimensional hexagonal phase (h-FeS). X-ray diffraction reveals the absence of structural transitions for both t- and h-FeS below room temperature, and gives phase compositions of Fe0.93(1)S and Fe0.84(1)S, respectively, for the samples studied here. The a lattice parameter of  3.68 Å is significant for causing bulk superconductivity in iron sulfide, which is controlled by composition and structural details such as iron stoichiometry and concentration of vacancy. While h-FeS with a = 3.4436(1) Å has magnetic ordering well above room temperature, our t-FeS with a =3.6779(8) Å shows filamentary superconductivity below Tc = 4 K with less than 15% superconducting volume fraction. Also for t-FeS, the magnetic susceptibility shows an anomaly at ~ 15 K, and neutron diffraction reveals a commensurate antiferromagnetic ordering below TN = 116 K, with wave vector km= (0.25,0.25,0) and 0.46(2) B/Fe. Although two synthesis routes are used here to stabilize t vs h crystal structures (hydrothermal vs solid-state methods), both FeS compounds order on two length-scales of ~1000 nm sheets or blocks and ~ 20 nm smaller particles, shown by neutron scattering. First principles calculations reveal a high sensitivity to the structure for the electronic and magnetic properties in t-FeS, predicting marginal antiferromagnetic instability for our compound (sulfur height of zS  0.252) with an ordering energy of ~11 meV/Fe, while h-FeS is magnetically stable.

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Introduction

 The equiatomic iron chalcogenides of FeCh, with Ch = S, Se, and Te, are difficult to synthesize stoichiometrically due to the existence of a wide solid-solution of phases close to this ratio [1,2,3]. These tetragonal PbO-type structures (space group P4/nmm) are made of square-planar sheets of Fe, which are in a tetrahedral environment with the chalcogens (Fig. 1a), similar coordination to superconducting iron arsenides. It is shown that variations in Fe composition can generate great and wide ranging changes in the physical properties of FeCh.

For the selenide, a major conundrum is the relationship between structure, magnetism, and superconductivity, and their close connection to the chemical Fe:Se ratio. Shortly after the discovery of superconductivity in tetragonal ‘FeSe’ [4], studies documented superconductivity in the true composition ranges of Fe1.01Se to Fe1.025Se that are stabilized by reactions within 300 to 440 C [5,6]. It is found that although Fe1.01Se is the optimal composition for superconductivity with Tc= 8 K that also gives rise to a structural transition (without magnetic order) at Ts = 90 K [7], Fe1.03Se is not a superconductor and does not undergo a structural transition [6].

The tetragonal phase for the tellurides exist in Fe1.06Te to Fe1.17Te composition region, with no superconductivity [8] and an ordered moment of roughly 2 B [9]. Fe1.141Te structurally changes from the tetragonal to a mixed tetragonal/orthorhombic (Pmmn) phase below 76 K, and is completely orthorhombic below Ts = 56 K [8]; there is also incommensurate antiferromagnetic ordering below TN = 63 K with a magnetic ordering wave-vector of km=(0.38,0,0.25) [8]. However, Fe1.076Te is found to transform from tetragonal to monoclinic (P21/m) and antiferromagnetic phase below Ts = TN =75 K [8] with km=(0.25,0,0.25) [8]. A slightly less Fe rich sample with Fe1.068Te gives Ts =TN = 67 K [10].

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Results and discussions  

Magnetism 

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A magnetic structure model that best fits the data giving maximum intensity at the magnetic peak position is composed of spins having antiferromagnetic correlations within the ab plane and ferromagnetic correlation along the c-axis. This is the first evidence of long-range order in tetragonal iron selenide. Fig. 6c shows the magnetic structure of the Fe sublattice with the spins forming cycloids perpendicular to the c-axis with an ordered moment of 0.46(2) B/Fe. For h-FeS in comparison, there are two susceptibility features reported: there is a spin transition in which the spins rotate along the c axis at 450 K [31], and an accompanying structure transition to a different superstructure at TN = 600 K [31,32].

 Electronic structures

We perform first principles calculations using the generalized gradient approximation on both t-FeS and h-FeS structures. For our t-FeS, X-ray diffraction refinement gives a sulfur height zS = 0.252(3) at 20 K, at which we find a marginal antiferromagnetic instability, with an ordering energy of just 11 meV/Fe and staggered moment of 1.16 B. If zS is taken as 0.2602, as found in the earlier experiment at 300 K [19], one finds a substantially larger ordering energy of 49 meV/Fe and staggered moment of 1.61 B. Finally, if t-FeS is allowed to relax to an equilibrium position (zS=0.2362), one converges to a non-magnetic state. The calculations indicate an extreme coupling of magnetism to structure, and that the tetragonal structure has a borderline nearest-neighbor antiferromagnetic instability, with the magnetism strongly dependent on the sulfur height [33]. This is in fact observed in the iron-based superconductors where the calculated magnetic properties are highly sensitive to the exact arsenic height [34]. In fact, the calculated magnetic properties of t-FeS are interrelated to stoichiometry and structure. The calculated density-of-states N(E) in Fig. 7 (here we used our experimental structure) depict a rapid variation of N(E) around the Fermi energy, and one might expect a dependence of magnetic character on stoichiometry. Accordingly, we have simulated Fe-deficient Fe0.85S (relaxed zS=0.2469) within the virtual crystal approximation (VCA) and here find an antiferromagnetic instability, with 41 meV/Fe ordering energy [35]. This calculation is done within the VCA-relaxed structure and in this case we find that relaxation strengthens the magnetism, rather than removing it, as in the stoichiometric case.

The h-FeS is much more magnetic; it is possible to stabilize several antiferromagnetic states along with a ferromagnetic state, all with energies several hundred meV per Fe below the non-magnetic state (Table 2). Hence this is much more of a local-moment system than the tetragonal phase, with much stronger magnetism. The reason for this divergence is strongly related to crystal structure, but for now we will focus on the calculated non-magnetic densities-of-states (we used our experimental structure with the sulfur height zS=0.252; the hexagonal structure has no free coordinates). As is well known for the parent compounds of the Fe-based superconductors, in the tetragonal phase the Fermi level lies in the middle of a pseudogap, with Fermi-level DOS of 1.96/eV unit cell (both spins), and corresponding T-linear specific heat coefficient  of 2.31 mJ/mol-K2 . The DOS is dominated by Fe states, and assuming an Fe Stoner exchange parameter I of 0.75 eV, with 2 Fe per unit cell, the ferromagnetic Stoner criterion IN(EF) > 1 is not satisfied. This is consistent with the lack of a stable ferromagnetic solution and the marginal stability of the antiferromagnetic ground-state [36]. The situation is very different for the h-FeS, with N(EF) well over three times greater at 7.17/eV-u.c.; here there is no pseudogap and there is in fact a Van Hove singularity just 0.2 eV below EF. The Stoner parameter IN(EF) is 2.69, indicating a strong tendency towards magnetism. This is consistent with the finding of numerous stable magnetic states, as depicted in Table 2. We find three separate antiferromagnetic states, along with a ferromagnetic state, to be stable relative to the non-magnetic state, with ordering energies of hundreds of meV per Fe. The great differences in electronic structure in the two phases can be directly tied to the crystal structure, which will be the subject of a separate publication [37]; for now we will simply assert that while the tetragonal phase is well known to have quasi-two-dimensional character, the hexagonal phase is much more 3D and yet also has strong one-dimensional character resulting from c-axis Fe-Fe coupling. The van Hove singularity results from this coupling and yields the higher N(EF), and hence stronger magnetic character in the hexagonal phase.