Abstract
Strong interplay of spin and charge/orbital degrees of freedom is the fundamental characteristic of the iron-based superconductors (FeSCs), which leads to the emergence of a nematic state as a rule in the vicinity of the antiferromagnetic state. Despite intense debate for many years, however, whether nematicity is driven by spin or orbital fluctuations remains unsettled. Here, by use of transport, magnetization, and 75As nuclear magnetic resonance (NMR) measurements, we show a striking transformation of the relationship between nematicity and spin fluctuations (SFs) in Na1−xLi x FeAs; For x ≤ 0.02, the nematic transition promotes SFs. In contrast, for x ≥ 0.03, the system undergoes a non-magnetic phase transition at a temperature T0 into a distinct nematic state that suppresses SFs. Such a drastic change of the spin fluctuation spectrum associated with nematicity by small doping is highly unusual, and provides insights into the origin and nature of nematicity in FeSCs.
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Introduction
Nematicity, i.e., spontaneous breaking of the C4 symmetry of the crystal, has emerged as a research focus recently in the iron-based superconductors (FeSCs), because the nematic state can provide a clue to the understanding of high temperature superconductivity in these materials1,2,3,4,5,6,7,8. Currently two major scenarios have been proposed for the origin of nematicity: magnetic and charge/orbital9. The former assumes that the nematic state are entirely induced by the interband spin fluctuations (SFs). The latter scenario treats its origin as charge density waves or orbital orders.
The magnetic scenario is believed to be realized in the 122-family of FeSCs10,11,12, particularly because a scaling relation was found between the spin fluctuations in nuclear magnetic resonance (NMR) and the shear modulus in the tetragonal phase of Ba(Fe1−xCo x )2As210. On the other hand, the most simple compound FeSe is best described by the orbital scenario since nematic order occurs without any signature of the spin fluctuation enhancement13,14,15. In FeSCs other than FeSe, however, the SDW transition temperature TSDW is quite close to the nematic one Tnem, imposing limitations on investigating the interplay of nematicity and SFs in detail. Thus it is much desirable to find a system in which one can effectively tune SFs and nematicity in wide phase spaces, e.g., temperature and chemical doping.
From this point of view, NaFeAs, which is isostructural and isoelectronic to well investigated LiFeAs, is worth attention. LiFeAs shows only a superconducting (SC) ground state without a signature of nematicity or magnetism16,17,18. In contrast, NaFeAs is featured by the three successive transitions at low T; a nematic transition at Tnem~55 K is followed by a SDW at TSDW~45 K and by a filamentary SC transition at ~8 K. In this respect, the study of (Na,Li)FeAs may allow a full spectrum of emergent orders coming from a delicate balance among competing orders by Li (Na)-substitution into Na (Li) layers in NaFeAs (LiFeAs). However, the study of such isoelectronic doping has been extremely challenging because (Na,Li)FeAs becomes easily phase separated due to distinct chemistry of Na and Li metals.
In this work, we report the successful growth of homogeneous Na1−xLi x FeAs single crystals and the investigation of their electronic phase diagram up to x = 0.1. We found that with a systematic increase of x, the SDW is suppressed for x ≥ 0.03, giving way to the SC state with the full Meissner shielding. Strikingly, also for x ≥ 0.03, 75As spin–lattice relaxation measurements show a sharp anomaly at a well-defined temperature T0, evidencing a non-magnetic phase transition before entering the bulk SC state. Our comprehensive data further show that, above a critical doping xc~0.03, spin and nematic fluctuations become strongly entangled, resulting in a charge/orbital ordered state below T0. This implies that the nature of a nematic state could vary depending on the underlying electronic structure. Furthermore, our rich phase diagram strongly suggests that the normal state of FeSCs from which superconductivity emerges is far more complex than previously known.
Results and discussion
Crystal structure
Figure 1a presents the crystal structure and Fig. 1b shows the variation of the c-axis lattice parameter of the Na1−xLi x FeAs single crystals, which decreases systematically with increasing x up to 0.06 and then levels off from 0.08. The c value was extracted from the (00l) reflections in the diffraction pattern measured along the ab-plane of the single crystals (Supplementary Fig. 1a) which suggests the absence of any other impurity phase. To determine the crystalline phase, we also performed the powder x-ray diffraction of the ground Na0.95Li0.05FeAs single crystal (Supplementary Fig. 1b) and the pattern could be successfully refined by the tetragonal P4/nmm structure as in the parent NaFeAs19.
Transport and magnetization measurements
The temperature (T) dependence of resistivity (ρ) of the selected Na1−xLi x FeAs single crystals is displayed in the T range from 3 to 300 K, and near the SC transition in Fig. 1d, e, respectively. Each resistivity curve was normalized by the value at 300 K (ρ/ρ300K) and shifted vertically for clarity (for the original resistivity data, see Supplementary Fig. 2). For the undoped crystal, ρ decreases smoothly exhibiting a typical metallic behavior with decreasing T, showing up several anomalous features at low T, an upturn at ~54 K (magenta arrow), a first drop (black arrow) at ~41 K, and a second drop to reach finally zero resistivity state (blue arrow) at ~7.7 K, which are identified as the nematic (Tnem), the SDW (TSDW), and the SC (\(T_{\mathrm{c}}^\rho\)) transition temperatures, respectively. Tnem and TSDW appear more clearly in the derivative curves of dρ/dT as a deviation point (magenta arrow in Fig. 1f) and a local maximum or minimum (black arrow in Fig. 1f). At \(T_{\mathrm{c}}^\rho\) ~ 7.7 K, the corresponding magnetic susceptibility (χ) (Fig. 1c) decreases abruptly, allowing us to assign Tc from χ, \(T_{\mathrm{c}}^\chi\) ~ 7.0 K. These transport and magnetization data are overall consistent with those found in previous reports on NaFeAs (refs.19,20,21,22,23,24).
With the same criteria applied on the parent NaFeAs, we could extract the \(T_{\mathrm{c}}^\rho\) (\(T_{\mathrm{c}}^\chi\)), TSDW, Tnem, and Meissner shielding fractions for the whole region (0 ≤ x ≤ 0.1). With increasing doping within 0 ≤ x ≤ 0.02, both Tnem and TSDW are rapidly suppressed. For x = 0.03, the dρ/dT curve reveals a jump which is assigned to Tnem, but does not show an anomaly associated with TSDW. The magnetization data show that the SC volume fraction in the parent compound is very small in agreement with the previous results and increases weakly with doping up to x~0.03. Upon further doping (x = 0.04, 0.05, and 0.06), the SC shielding fraction at T = 2 K reaches 68%, 98%, and 90%, respectively, and the highest Tc = 12.3 K is obtained for x = 0.05, constituting an optimal doping. After the optimal doping, inserting more dopants into the system suppress both the SC shielding fraction and Tc, and eventually superconductivity disappears above x = 0.12.
75As nuclear magnetic resonance
We now turn to 75As NMR measurements on Na1−xLi x FeAs. The 75As nuclei (nuclear spin I = 3/2) possess a large quadrupole moment. For axial symmetry, a magnetic field H perpendicular to the principal axis (crystallographic c-axis in our case) yields two satellite lines whose separation is given by the quadrupole frequency νQ. Figure 2a shows the 75As NMR full spectrum at H = 9.1 T parallel to the ab-plane as a function of Li doping in the tetragonal/paramagnetic (PM) phase (at 60 K). Clearly, νQ = 9.93 MHz for undoped crystal does not change notably with doping, indicating that the local symmetry or the average electric field gradient (EFG) at the 75As is insensitive to Li dopants up to x = 0.06. On the other hand, the linewidth of the spectra progressively increases with increasing doping, which is naturally understood by the increase of chemical disorder due to dopants. It should be noted that the relative linewidth of the satellites with respect to the central one, which could be considered as a measure of chemical homogeneity, remains reasonably small up to ~10 at x = 0.06, in support of the high quality of our samples. Importantly, we do not observe other NMR lines with doping which would have indicated the presence of an impurity phase such as pure LiFeAs. Thus, the evolution of the 75As spectra with doping provides local evidence for the successful incorporation of Li dopants into the Na layers of NaFeAs.
In the magnetically ordered state of NaFeAs, the stripe-like arrangement of Fe moments in the ab-plane, by symmetry, produces hyperfine fields at 75As pointing along the c-axis25, 26. As a direct consequence of two oppositely aligned antiferromagnetic (AFM) sublattices, the 75As central line splits into two AFM lines for H || c. In case of H || ab, the total magnetic field that 75As experiences slightly increases due to the vector sum of the local field along c and the external field along ab, and the magnetic broadening of 75As line occurs accordingly. Therefore, long range AFM order in Na1−xLi x FeAs can be easily confirmed by NMR via a positive shift and a broadening of the 75As line for H || ab, and a large AFM splitting of the line for H || c. Indeed, for the parent (x = 0) and underdoped (x = 0.02) samples, the 75As line for H || ab broadens and shifts to higher frequency (Fig. 2b, c), and at the same time the 75As line for H || c splits into two well-defined AFM lines (Fig. 3f), thereby proving locally the SDW order. Note that the splitting of the 75As line shown in Fig. 2b is due to nemacitiy. Indeed, we determined Tnem for x = 0 and 0.02 by measuring the T dependence of 75As satellite line (Supplementary Fig. 3).
For x ≥ 0.04, on the other hand, the T dependence of the 75As spectrum is clearly told apart from those for x ≤ 0.02 samples. First of all, there is no signature of a static SDW ordering. The 75As line preserves its shape without a shift nor a significant broadening down to low temperatures (see also Supplementary Fig. 4). Second, the T evolution of the 75As spectrum is very similar for the two field orientations H || ab and H || c, which contrasts sharply with the strongly anisotropic behavior observed for x ≤ 0.02. These features indicate that the system for x ≥ 0.04 remains paramagnetic. Remarkably, the intermediate doping, i.e., x = 0.03, yields a very peculiar feature which seemingly separates the two doping regions, x ≤ 0.02 and x ≥ 0.04. That is, the 75As line is considerably broadened below T0 ~ 32 K for both field orientations (see Figs. 2d and 3c.). The nearly isotropic NMR line broadening indicates that an inhomogeneous (short-ranged) magnetism develops. Moreover, we emphasize that T0 for x = 0.03 is higher than TSDW for x = 0.02 and coincides with Tnem (Fig. 4c). Therefore, we conclude that the inhomogeneous line broadening observed for x = 0.03 below T0 is irrelevant to the SDW, but arises from an emerging phase which may involve a short-ranged magnetism.
For x ≥ 0.03, alongside the suppression of the SDW, we observe that the resonance frequency ν of the 75As line in the PM phase is abruptly reduced. This behavior is clearly shown in Fig. 3g in terms of the Knight shift, \({\cal K} \equiv \left( {\nu - \nu _0} \right){\mathrm{/}}\nu _0 \times 100\)% where ν0 is unshifted Larmor frequency. Since the second order quadrupole shift vanishes for H || c, \({\cal K}_{H||c}\) is equivalent to the local spin susceptibility \(\chi _{{\mathrm{spin}}} = \mu _{\mathrm{B}}^2N_{\mathrm{F}}\) where NF is the density of states at the Fermi level. While a gradual reduction of χspin or NF with doping is commonly observed in FeSCs27,28,29, the abrupt large reduction of χspin induced by a moderate doping is very unusual (Supplementary Fig. 5). This may suggest a modification of the Fermi surface geometry near x ~ 0.03, owing to, e.g., a Lifshitz transition30.
Low energy spin fluctuations
Having established that static SDW order is abruptly suppressed at x ~ 0.03, we now investigate low energy spin dynamics, as probed by the spin–lattice relaxation rate divided by temperature (T1T)−1, which is proportional to SFs at very low energy. (T1T)−1 as a function of T and x are shown in Fig. 4. For x = 0 and 0.02, the diverging behavior of (T1T)−1 is immediately followed by an exponential drop with decreasing T. The drastic change of (T1T)−1 at TSDW precisely reflects two important characteristics of a SDW transition. The divergence of (T1T)−1 at TSDW represents the critical slowing down of SFs toward long-range magnetic order and the subsequent exponential drop of (T1T)−1 implies the depletion of low-energy spin excitations, i.e., the opening of a SDW gap. As doping is increased to 0.03, the divergent (T1T)−1 observed for x ≤ 0.02 is greatly suppressed, being consistent with the disappearance of static SDW order for x ≥ 0.03, as discussed above. Unexpectedly, however, (T1T)−1 drops rapidly below T0 > Tc forming a peak, indicating a phase transition at T0. With further increasing doping, the (T1T)−1 peak gradually moves to lower T, but its shape and height remain nearly the same.
The phase transition at T0 observed for x ≥ 0.03 cannot be of magnetic origin. First, the T dependence of the 75As spectrum (Figs. 2 and 3) does not show any signature of static magnetism, particularly for x ≥ 0.04. Second, (T1T)−1 or SFs does not diverge at T0, implying that the magnetic correlation length remains short at T0. Third, the sudden reduction of SFs between x = 0.02 and 0.03 is hardly observed in other FeSCs in which SFs above TSDW is gradually suppressed with increasing doping or pressure toward the optimal region27, 31, 32. Moreover, for x = 0.03, it turns out that T0 nearly coincides with Tnem, as shown in Fig. 4c, implying that the T0 transition is closely related to nematicity. Note that the sharp (T1T)−1 peak at T0 and its doping dependence are well distinguished from those arising from a glassy spin freezing observed in Co-doped BaFe2As233, 34; either significant magnetic broadening or strong doping and field dependence of the (T1T)−1 peak expected for a glassy magnetic state is not observed.
Interestingly, we find that the strong anisotropy of (T1T)−1 above TSDW for x ≤ 0.02 is maintained above T0 for x ≥ 0.03 (see Fig. 4a, b). That is, SFs for H || ab is factor of four stronger than for H || c over the whole doping range investigated. The robust spin fluctuation anisotropy with or without a static SDW order indicates that dynamic SDW fluctuations persist at least up to x = 0.06.
It may be worthwhile to note that below T0 the 75As signal amplitude is notably reduced for both H || ab and H || c, as shown in Figs. 2d–f and 3c–e (see also Supplementary Fig. 4). The suppression of signal intensity indicates that the volume fraction of the sample seen by NMR decreases in the charge/orbital ordered phase. This phenomenon is quite similar to the wipeout effect observed in the charge stripe phase of cuprate superconductors, in which NMR relaxation rates of the nuclei in spin-rich regions become too fast to be detected35,36,37. The underlying mechanism of the signal wipeout in Na1−xLi x FeAs remains unclear and needs further investigation. Interestingly, the similar wipeout of the NMR signal was also observed in the 77Se NMR study of FeSe in the nematic phase which does not involve any static magnetism38.
Phase diagram
Figure 5 presents the temperature-doping phase diagram determined by our NMR and transport/magnetization measurements. When compared to the phase diagram previously known in NaFe1−xA x As (A = Co, Cu, or Rh)23, 24, 39, 40, a difference is the seeming mutual repulsion of the SDW and bulk superconductivity near xc ~ 0.03, similar to that reported in LaFeAsO1−xF x 41 and NaFe1−xCo x As42. However, our data are not sufficiently dense to conclude whether the SDW and SC phases coexist in the narrow doping range near x = 0.03 or completely repel each other.
The most important feature in Fig. 5 is the emergence of a non-magnetic phase below T0 > Tc at optimal doping. Whereas T0(x) is reasonably connected to Tnem for x ≤ 0.02, we note that the phase below T0 cannot be a simple nematic because the strong suppression of SFs below T0 (or spin–gap behavior) is unlikely due to nematicity itself. Although theory predicts that the nematic transition could trigger a pseudogap behavior43, such a pseudogap is only viewed as magnetic precursors whose signature is a sharp increase of the magnetic correlation length. Therefore, we conclude that the phase below T0 should involve a charge/orbital order which could give rise to a featured gap in the spin fluctuation spectrum.
An even more remarkable observation is the critical change of the relationship between SFs and nematicity with doping. For x ≤ 0.02, SFs are enhanced just below the nematic transition at Tnem and diverge at TSDW. For x ≥ 0.03, however, a strong enhancement of SFs precedes the phase transition into a charge/orbital nematic state at T0, but it is suppressed once the charge/orbital nematic state develops. Theoretically, it has been proposed that the strong interplay of spin and charge/orbital degrees of freedom could result in a charge density wave (CDW) state in proximity to a SDW state9, 44,45,46. Following the work9, the competition of these two orders can be described by the effective Ginzburg–Landau functional:
where the χs(q, Ω n ) ~ \([ {\xi _{\mathrm{s}}^{ - 2} + \alpha _{\mathrm{s}}( {q - Q_{x,y}} )^2} ]^{ - 1}\) and χc(q, Ω n ) ~ \([ {\xi _{\mathrm{c}}^{ - 2} + \alpha _{\mathrm{c}}( {q - Q_{x,y}} )^2} ]^{ - 1}\) are dynamical spin and charge susceptibilities, Mx,y and Φx,y are SDW and CDW order parameters with the propagation vectors Q x = (π, 0) and Q y = (0, π), respectively. The coupling constant g in the leading order arises due to small non-ellipticity of the electron and hole pockets and is much smaller than u. The onset of nematic order parameter ϕ with Mx,y = Φx,y = 0 leads to renormalization of the magnetic correlation length \(\xi _s^{ - 2} \to \xi _s^{ - 2} \pm \phi\) (see refs.9, 43). It leads to strong enhancement of SFs below Tnem. The opposite situation happens when the nematic transition coincides with the CDW phase Φ x ≠ 0. The magnetic correlation length changes as \(\xi _{\mathrm{s}}^{ - 2} \to \xi _{\mathrm{s}}^{ - 2} + (u \pm g){\mathrm{\Phi }}_x^2\) leading to suppression of SFs since (u ± g) > 0. This may account for the drastic change of the relationship between nematicity and SFs. Our findings establish Na1−xLi x FeAs as a rich playground for the study of the interplay of spin and charge/orbital degrees of freedom in FeSCs.
Methods
Crystal growth and characterization
High-quality single crystals of Na1−xLi x FeAs were grown by a self-flux technique. Due to high reactivity of metallic Na, Li, Fe and As, all preparation processes were carried out inside an Ar-filled glovebox of which O2 and H2O contents were less than 1 ppm. Pure elemental Na (99.995%, Alfa Aesar), Li (99.9 + %, Sigma Aldrich), As (99.99999 + %, Alfa Aesar) lumps and Fe (99.998%, Puratonic) powder in a molar ratio (Na,Li):Fe:As = 3:2:4 were placed into an alumina crucible, then kept inside a welded Nb container under ~0.8 bar of Ar atmosphere. The welded container was finally sealed in an evacuated quartz ampoule. The ampoule was heated directly up to 1050 °C, stayed at this temperature for 1 h, afterward slowly cooled down to 750 °C with a rate of 3 °C/h and then heater was turned off while the ampoule was still kept in the furnace. 2D plate-like-shaped single crystals with shiny ab-plane surfaces were mechanically detached from a flux and typical sizes were around ~440.3 mm3. Since the grown crystals were highly sensitive to air and moisture, each steps of physical measurement preparations were also done in an Ar-filled glovebox. The crystalline phase was determined by the powder x-ray diffraction using Cu K α radiation at room temperature. To avoid oxidation and compensate the preferred orientation of single crystals, a sealed quartz capillary was adopted with grounded as-grown crystals for powder diffraction measurements. To measure the (00l) reflection peak, a piece of single crystal with the shiny ab-plane surfaces was sandwiched between kapton tapes. Rietveld refinements of the diffraction pattern were performed using Fullprof program. In particular, inductively coupled plasma atomic photoemission spectroscopy (ICP-AES) was carried out on a piece of optimally doped Na0.95Li0.05FeAs to check the elemental composition of Na and Li; a molar ratio of Na and Li was found as Na: Li = 0.944: 0.056, which is close to the expected composition. Electrical resistivity was measured by the conventional four probe technique using a conductive silver epoxy in PPMS™ (Quantum Design). Magnetic susceptibility was measured with a vibrating sample magnetometer in PPMS™ and MPMS™ (Quantum Design).
It should be noted that SC transitions of all the samples were considerably broad as the estimated transition width ΔT extracted at temperatures of 10 and 90% of resistivity maximum was 7.5–15 K. Moreover, all the resistivity curves exhibited a temperature window of showing insulating behavior (dρ/dT < 0) before the onset of SC transition similar to NaFe1−xCu x As system23. In other doped Na 111 systems like NaFe1−xCo x As22 and NaFe1−xRh x As24, robust metallic behavior were observed in broad doping ranges. The former Cu doping was claimed to have isoelectronic doping while the latter two involving large electron doping was inevitably accompanied by large chemical potential shift. As Li does not bring additional charge carriers to the systems, the effect of disorder-induced electron localization on transport is likely pronounced to result in the insulating-like behaviors as in the case of NaFe1−xCu x As system.
Nuclear magnetic resonance
75As (nuclear spin I = 3/2) NMR was carried out in Na1−xLi x FeAs single crystals at an external field of 9.1 T and in the range of temperature 4.2–100 K. Due to the extreme sensitivity of the samples to air and moisture, all the samples were carefully sealed into quartz tubes filled with Ar gas. The sealed sample was reoriented using a goniometer for the accurate alignment along the external field. The 75As NMR spectra were acquired by a standard spin-echo technique with a typical π/2 pulse length 2–3 μs. The nuclear spin–lattice relaxation rate \(T_1^{ - 1}\) was obtained by fitting the recovery of the nuclear magnetization M(t) after a saturating pulse to following fitting function,
where A is a fitting parameter. We also measured 23Na NMR spectra for x = 0.04. As shown in Supplementary Fig. 6, we confirm that the 23Na is barely influenced by the T0 phase transition.
Data availability
The data that support the findings of this study are available from the corresponding authors (S.H.B. or K.H.K.).
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Acknowledgements
This work was financially supported by the National Creative Research Initiative (2010-0018300) and Global Collaborative Research Projects (2016K1A4A3914691) through Korea’s NRF, which is funded by Ministry of Science, ICT and Future Planning (MSIP). The work at Germany has been supported by the Deutsche Forschungsgemeinschaft (Germany) via DFG Research Grants BA 4927/2-1. D.V.E. acknowledges VW-foundation for partial financial support.
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K.H.K. and B.S.L. have proposed and initiated the project. W.H.N., B.S.L., D.B. have grown single crystals and characterized transport and structure properties. S.H.B. performed NMR measurements and analyzed data; S.H.B., D.V.E., and K.H.K. participated in writing of the manuscript. All authors discussed the results and commented on the manuscript.
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Baek, SH., Bhoi, D., Nam, W. et al. Tuning the interplay between nematicity and spin fluctuations in Na1−xLi x FeAs superconductors. Nat Commun 9, 2139 (2018). https://doi.org/10.1038/s41467-018-04471-7
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DOI: https://doi.org/10.1038/s41467-018-04471-7
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