A Mott insulator continuously connected to iron pnictide superconductors

Iron-based superconductivity develops near an antiferromagnetic order and out of a bad-metal normal state, which has been interpreted as originating from a proximate Mott transition. Whether an actual Mott insulator can be realized in the phase diagram of the iron pnictides remains an open question. Here we use transport, transmission electron microscopy, X-ray absorption spectroscopy, resonant inelastic X-ray scattering and neutron scattering to demonstrate that NaFe1−xCuxAs near x≈0.5 exhibits real space Fe and Cu ordering, and are antiferromagnetic insulators with the insulating behaviour persisting above the Néel temperature, indicative of a Mott insulator. On decreasing x from 0.5, the antiferromagnetic-ordered moment continuously decreases, yielding to superconductivity ∼x=0.05. Our discovery of a Mott-insulating state in NaFe1−xCuxAs thus makes it the only known Fe-based material, in which superconductivity can be smoothly connected to the Mott-insulating state, highlighting the important role of electron correlations in the high-Tc superconductivity.

Supplementary Figure 8 |Schematic depiction of the in-plane AF ordering in NaFe 0.5 Cu 0.5 As (left panel) used by the electronic structure calculations.Rows of Cu atoms (red) turn out to carry no magnetic moment, whereas spins of Fe atoms (blue) take on the arrangement similar to the parent compound NaFeAs (right panel) with the in-plane ordering wave-vector Q = (1,0) in the orthorhombic notation. The rows of Cu atoms alternate in the c-direction, according to the experimentally determined Ibamspacegroup. Note that the spin polarization axis is depicted symbolically and is not representative of the actual spin orientation relative to the crystalline axes.

Supplementary Note 1: Fe and Cu ordering in NaFe 1-x Cu x As as seen in diffraction measurements
The crystal structure of NaFe 0.56 Cu 0.44 As obtained from single crystal neutron diffraction refinement is shown in Supplementary Table S1. We collected 120 reflections at Bragg peaks associated with the NaFeAs structure and measured 95 super-lattice peak positions. 22 super-lattice peaks with measurable intensities are identified (Supplementary Table S2), these peaks are refined together with Bragg peaks associated with the NaFeAs structure (not shown). Due to twinning the measured intensity at (H,K,L) have contributions from (H,K,L) from twin 1 and (H,L,K) from twin 2. Population of the twins is roughly 2:1 for this particular sample. Due to formation of Fe-Cu stripes, y positions of Na and As also shift from their high symmetry position 0.25 by δ Na and δ As , respectively.
The crystal structure for NaFe 0.56 Cu 0.44 As in Supplementary Table 1 approximates the ideal structure of NaFe-0.5 Cu 0.5 As as shown in Figure 1(d), where Fe and Cu order into stripes forming a structural analog of the stripe magnetic order in NaFeAs. This reduces the symmetry of the system to Ibamspace group. We adopt a unit cell similar to the orthorhombic structural unit cell of NaFeAs throughout the rest of paper as shown in Figure 1(d) unless otherwise stated. Compared to the Ibam notation used in Supplementary Table 1,a, b and c in this notation correspond to b, c, and half of a in the Ibamnotation.Inthe notation used in Figure 1 To illustrate the effect of Fe-Cu ordering seen in neutron diffraction experiments, calculated neutron powder diffraction profiles for NaFe 0.5 Cu 0.5 As with (i) disordered Fe and Cu and δ As = δ Na = 0, (ii) ordered Fe and Cu and δ As = δ Na = 0 and (iii) ordered Fe and Cu with δ As = δ Na = -0.01 are compared in Supplementary Figure 1 assuming b = c(Ibam notation). With this assumption, case (i) becomes tetragonal with P4/nmm symmetry. In case (ii) where Fe-Cu order into stripes, the only effect is to induce super-lattice peaks without affecting the intensity of nuclear Bragg peaks already present in case (i). For case (iii), introducing non-zero δ As andδ Na , nuclear Bragg peaks already present in case (i) change only slightly.
Given these considerations and for NaFe 1-x Cu x As with x<0.5 the already weak super-lattice peaks become weaker and broader with decreasing doping [Supplementary Figure 5(f)]weuse P4/nmm space group appropriate for NaFeAs in the tetragonal state [1] to fit the our room temperature neutron powder diffraction (NPD) data for NaFe 1-x Cu x As. Doing so the information related to Fe-Cu ordering is neglected but other aspects of the structure can still be reliably obtained. Sincethe Fe-Cu ordering exists already at room temperature [ Figure 2(c)], it will be interesting in future work to see if an order-disorder transition occurs at elevated temperatures where P4/nmm symmetry can be recovered with Fe and Cu becoming disordered and δ As = δ Na = 0 corresponding to case (i).
The NPD refinementresultsfor NaFe 1-x Cu x As with x = 0.016, 0.18, 0.39 and 0.44 at room temperature are shown in Supplementary Figures2(a)-(d) and the refined structuralparameters are shown in Supplementary Table 3. Na and As occupancies are assumed to be 1, refinements of their occupancies also yield values close to 1. Given the similar scattering lengths of Fe and Cu, the occupancies of these two elements are set to values determined from ICP.The NPD data at 4K for NaFe 1-x Cu x As with x = 0.44 is shown in Supplementary Figure 2(e). Only one super-lattice/magnetic peak is clearly seen as shown in the inset, so it is not possible to reliably refine δ As and δ Na from NPD data. Instead this data is used to estimate size of the ordered moment, refining the ordered moment for the magnetic structure in Figure 1 The absorption peak at 930.7eV in SrCuO 2 due to Cu 2+ is absent in NaFe 1-x Cu x As(x = 0.44), demonstrating Cu 1+ valence in heavily Cu-doped NaFe 1-x Cu x As samples. Previous results on Cu in different valence states [3]showa chemical shift of ~2 eV between the absorption peaks for Cu 1+ and Cu 2+ .Thisagrees with our observation that the sharp absorption peak (931.8 eV) in NaFe 1-x Cu x As (x = 0.44) is higher than the Cu 2+ absorption peak in SrCuO 2 , suggesting that Cu in NaFe 1-x Cu x As assumes the Cu 1+ oxidation state. The two overlapping peaks at ~ 935.5 eV and 936.5 eV are likely due to traces of unreacted elemental Cu. We have further searched for magnetic excitations with resonant inelastic X-ray scattering (RIXS)CuL 3 edge, but did not observe indication for magnetic modes for any of the sampled momentum transfers, typical scans at Q = (0.23,0.23) are shown in Supplementary Figure 3(b).The absence of magnetic excitations is expected for Cu 1+ with a Cu 3d 10 electronic configuration. Thus, both XAS and RIXS results confirm that Cu is in the nonmagnetic Cu 1+ state and the elastic magnetic order observed by neutron scattering is entirely due to Fe.

Supplementary Note 3: Additional neutron scattering results
The ordered moment sizes were estimated from normalizing rocking scans of magnetic peaks against a weak nuclear Bragg peak (2, 0, 0) in single crystal elastic neutron scattering measurements. While super-lattice peaks occur at (1, 0, 0.5) and equivalent wave-vectors and magnetic peaks occur at (0, 1, 0.5) and equivalent positions, they overlap in reciprocal spacedue to twinning. Supplementary Figure 4 shows scans along the [H, 0, L]/[0, K, L] directions at 3.6 K and 300 K for the x = 0.44 sample. In Supplementary Figure5(a), the Q-dependence of magnetic peak intensities are shown, the magnetic intensities are obtained from rocking scans at 3.6 K after correcting for the super-lattice contributions using the ratio of peak intensities at 3.6 K and 300 K shown in Supplementary Figure4 and the Lorentz factor. In Supplementary Figure5(b)-(c), the calculated Q dependence of magnetic peak intensities are plotted for spins oriented along a, b and c assuming Fe 2+ magnetic form factor. Comparing the measured Q-dependence in Supplementary Figure5(a) and the calculated Q-dependence in Supplementary Figure5(b)-(c), we conclude that the ordered magnetic moments are oriented predominantly along the aaxis. To conclusively determine the orientation of the ordered magnetic moment, we carried out detailed polarized neutron scattering experiments. Since in our notation magnetic peaks occur at (0, K, L) with K = 1, 3, 5… and L = 0.5, 1.5, 2.5… but not (H, 0, L) positions, we only see magnetic signal from [0, K, L] scattering plane. We define neutron polarization directions along momentum transfer Q as x, perpendicular to Q but in the [0, K, L] scattering plane as y and perpendicular to the scattering plane as z as shown in Supplementary Figure6(a). As our neutron scattering samples have twin domains, we cannot distinguish the (H, 0, L) from the (0, K, L) positions in these measurements.
Since SF neutron diffraction is only sensitive to spin components perpendicular to both momentum transfer Q and neutron polarization direction, one can conclusively determine the spin components along all crystallographic axes M a , M b and M c from the observed magnetic peaks. M a , M b and M c can be obtained via,

Paramagnetic phase:
We first studied the non-magnetic phase of NaFe 0.5 Cu 0.5 As, using the space group Ibam deduced from the highresolution TEM and single crystal neutron diffraction measurements [Supplementary Table 1]. The electronic density of states calculated with DFT-GGA method is shown in Supplementary Figure 9(b). The calculations indicate that NaFe 0.5 Cu 0.5 As is expected to be a good metal, with the DOS at the Fermi level of 2.5 states per formula unit (f.u.). It is instructive to compare this value to the DOS in the parent compound NaFeAs [ Supplementary Figure 9(a)], which is actually lower at ~2.0 states per f.u. This is understood because in NaFeAs, the Fermi level lies near a trough of the DOS, whereas in NaFe 0.5 Cu 0.5 As, it sits of the shoulder of the Fe d-state peak. This is also consistent with the fact that the Fe d-electron bandwidth is narrower than in NaFeAs, resulting in a larger DOS.
At first sight, the theoretical finding of the metallic behavior is puzzling, given the experimental observation of the insulating nature of NaFe 0.56 Cu 0.44 As. Conceivably, this may be an indication of the failure of the ab initio theory, since strong electron correlations are notoriously difficult to capture with DFT. To estimate the effect of the Coulomb repulsion U, we have performed a DFT+U calculation [4] on NaFe 0.5 Cu 0.5 As using the interaction strength U = 3.15 eV and Hund's coupling J = 0.4 eV calculated in Ref. [5]. Curiously, although Coulomb repulsion does reduce the DOS by creating a pseudogap like feature at the Fermi level, it still predicts NaFe 0.5 Cu 0.5 As to be a metal (DOS(E F ) ~2.1 states/f.u.) rather than an insulator in the paramagnetic state, as shown in Supplementary Figure 9(c). This is in stark contrast to the experimentally measured resistivity, which exhibits insulating behavior even in the paramagnetic phase, above the AF ordering temperature in NaFe 0.5 Cu 0.5 As [see Figure 2(f) in the main text]. Clearly, strong electron correlations are present that are not captured properly by the DFT or DFT+U calculations in the paramagnetic phase.

Antiferromagnetic phase:
We have also calculated the AF configuration of NaFe 0.5 Cu 0.5 As, which turns out to be more stable than the paramagnetic state by 0.28 eV/f.u. in our DFT-GGA calculations. We note that the antiferromagnetic order lowers the symmetry of the paramagnetic Ibam space group down to its subgroup I222. The Fe magnetic moments order in the (ab)-plane according to the experimentally observed Q = (1,0) wave-vector, as depicted schematically in the left panel of Supplementary Figure 8. The value of the ordered moment is predicted by DFT to be 2.77 µ B on Fe site, larger than the experimentally measured ordered moment of ~1.4 µ B per Fe. We find that the Cu moment is essentially zero (~0.02 µ B ), consistent with the full shell Cu 1+ (d 10 ) configuration inferred from the experiments. Calculations within the DFT-GGA formalism show that the electronic density of states at the Fermi level is severely suppressed in the AF state, as shown in Supplementary Figure 10(a). Including the effect of the Coulomb repulsion using the DFT+U approach opens up a spectral gap of about 0.1 eV at the Fermi level, resulting in the true insulating state. The DFT+U also predicts Cu ions to be nonmagnetic, while stabilizing an even higher ordered moment on Fe sites (3.29 µ B per Fe).
It is instructive to compare the ab initio AF calculations with the experiment. In DFT and DFT+U calculations, the entire ordered moment comes from Fe site, while Cu ions are non-magnetic. While this is consistent with our experimental results, the predicted moment is much larger (2.77 µ B in GGA) than the experimentally measured value of ~ 1.4 µ B .
In conclusion, theoretical electronic structure calculations based on DFT and DFT+U indicate that the value of Coulomb repulsion is not large enough by itself to result in the paramagnetic Mott insulating state in NaFe 0.5 Cu 0. 5 As, which appears to contradict the observed insulating behavior of resistivity [ Fig. 1(f) in the main text]. Allowing the possibility of an AF ordering amplifies the effect of Coulomb interaction, resulting in an insulating magnetic ground state. However, the theory predicts the average value of the ordered moment per Fe site too large compared with the experimental value from neutron diffraction. This deficiency of DFT in exaggerating the ordered Fe moment is well documented in other materials in the iron pnictide family [5,6]. The electronic structure calculations do capture correctly an enhanced propensity to AF ordering when compared to the parent compound NaFeAs, which has a very small ordered moment ~0.1 µ B /Fe [1]. This is consistent with the electronic correlations becoming stronger upon Cu doping.