Phase diagram and neutron spin resonance of superconducting NaFe$_{1-x}$Cu$_x$As

TL;DR

This study investigates the phase diagram and spin excitations in NaFe$_{1-x}$Cu$_x$As, revealing superconductivity near 2% Cu doping, a transition to insulating phases at higher doping, and the role of electronic correlations in superconductivity.

Contribution

It provides the first detailed phase diagram and neutron scattering analysis of NaFe$_{1-x}$Cu$_x$As, highlighting the importance of electronic correlations and impurity effects in its superconducting and magnetic properties.

Findings

Superconductivity appears near 2% Cu doping with suppressed magnetic order.

A high-energy, weakly dispersive neutron spin resonance is observed.

The system transitions to an insulating antiferromagnetic phase near 50% Cu doping.

Abstract

We use transport and neutron scattering to study the electronic phase diagram and spin excitations of NaFe$_{1-x}$Cu$_x$As single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\approx2\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\approx 50\%$. Using transport measurements, we demonstrate that the resistivity in NaFe$_{1-x}$Cu$_x$As exhibits non-Fermi-liquid behavior near $x\approx1.8\%$. Our inelastic neutron scattering experiments reveal a single neutron spin resonance mode exhibiting weak dispersion along $c$-axis in NaFe$_{0.98}$Cu$_{0.02}$As. The resonance is high in energy relative to the superconducting transition temperature $T_{\rm c}$ but weak in intensity, likely resulting from impurity effects. These results are similar to other iron pnictides superconductors despite the superconducting phase in NaFe$_{1-x}$Cu$_x$As is continuously connected to an antiferromagnetically ordered insulating phase near $x\approx 50\%$ with significant electronic correlations. Therefore, electron correlations is an important ingredient of superconductivity in NaFe$_{1-x}$Cu$_x$As and other iron pnictides.

Full text

I Introduction

Superconductivity in copper-oxides is obtained by electron- or hole-doping into their antiferromagnetically ordered insulating parent compounds with strong electron correlations PALee ; keimer . Superconductivity in iron pnictides, on the other hand, is derived from parent compounds that are bad metals kamihara ; stewart ; pdai . Despite the metallic ground state of the parent compounds, strong electronic correlations are suggested to be present in iron pnictides QSi2008 ; HIshida2010 ; TMisawa2012 , especially in heavily hole-doped systems FHardy2013 ; LdeMedici2014 ; MNakajima2014 . In addition to replacing $A$ in $A$Fe2As2 ($A=$ Ca, Sr, Ba) with alkaline metals (K, Na, Rb, Cs) stewart ; pdai , hole-doping in iron pnictides can be achieved through Mn or Cr doping on Fe site although no superconductivity is induced in these cases AThaler2011 ; ASSefat2009 . Doping Cu on Fe site presents an intriguing case, whereas at low doping levels Cu is suggested to dope electrons SIdeta2013 , at higher concentrations Cu has a 3$d^{10}$ configuration and acts as a hole-dopant VKAnand2012 ; YJYan2013 . However, in Cu doped $A$Fe2As2, resistivity remains $\rho<1\text{m}\Omega\cdot\text{cm}$ throughout the whole phase diagram with no signs of strengthened electronic correlations YJYan2013 . As the As atoms within the same unit cell of $A$Fe2-xCuxAs2 can form [As]${}^{-3}\equiv$ [As-As]-4/2 covalent bond with increasing Cu-doping and reducing As-As distance VKAnand2012 ; YJYan2013 , large Cu-doping therefore has little effect on the valence of Fe and $A$Cu2As2 becomes a $sp$-metal without electron correlations as predicted by band structure calculations DJSingh09 .

Since the crystal structure of NaFe1-xCuxAs does not allow the formation of As-As covalent bond [Fig. 1(a)] AFWang2013 , heavily doped NaFe1-xCuxAs is a candidate system to tune the strength of electronic correlations YSong . Recent transport AFWang2013 , scanning tunneling microscopy (STM) CYe2015 , angle-resolved photoemission spectroscopy CEMatt2016 , and optical conductivity ACharnukha measurements demonstrated that with significant ($>10\%$) Cu doping, NaFe1-xCuxAs acquires an insulating ground state. Diffraction measurements revealed short-range Fe-Cu cation order and magnetic order develops as the system becomes insulating. With increasing $x$, the Fe-Cu cation order and magnetic order continuously increase in correlation lengths, and become long-range when $x\approx 50\%$ YSong . The antiferromagnetically ordered insulating state in NaFe1-xCuxAs is a result of significant electronic correlations YSong . Compared to Cu-doped $A$Fe2As2, NaFe1-xCuxAs is more correlated because of its larger iron pnictogen height which results in a small magnetic excitation bandwidth ZPYin2011 ; CZhang2013 , hole-doping effect of Cu in NaFe1-xCuxAs is not counteracted by the formation of As-As covalent bonds and the local potential differences between Cu and Fe reduces the hopping between Fe sites YSong . Since the antiferromagnetically ordered Mott insulating phase of NaFe1-xCuxAs at $x\approx 0.5$ is continuously connected to an albeit somewhat far away superconducting phase at $x\approx 0.02$ AFWang2013 ; YSong , it would be important to elucidate whether the superconducting state in NaFe1-xCuxAs AFWang2013 is similar to other iron pnictide systems.

One hallmark of unconventional superconductivity in iron pnictides is the appearance of a neutron spin resonance mode in the superconducting state at the antiferromagnetic (AF) ordering wave vector of their parent compounds christianson ; pdai ; scalapino ; DSInosov2011 . The energy of the resonance approximately scales with the superconducting transition temperature $T_{\rm c}$ or the superconducting gap $\Delta$ DSInosov2011 ; GYu . The appearance of the resonance mode is typically accompanied by gapping of the normal state spectral weight below the resonance energy christianson ; pdai ; scalapino ; DSInosov2011 . Both the resonance and the associated spin gap are typically interpreted as due to quasi-nested Fermi surfaces that results in a collective bound-state inside the superconducting gap scalapino ; Eschrig ; PJHirschfeld . Within this picture, the resonance mode is evidence for unconventional superconductivity with sign-changing superconducting order parameters on different parts of the Fermi surface christianson . The resonance in BaFe2As2-derived superconductors display significant dispersion along $c$-axis in the underdoped regime SChi09 , and becomes $L$-independent in the well-overdoped region CHLee2013 . In electron-doped NaFe1-xCoxAs, two resonance modes are seen in underdoped compositions CZhang2013 , with the lower-energy-mode gradually losing spectral weight upon further doping before disappearing near optimal doping CZhang2016 ; CZhang2013b . The energy of the single resonance mode in well-overdoped NaFe1-xCoxAs does not scale with $T_{\rm c}$, likely due to multi-orbital physics and impurity effects CZhang2016 . Since superconducting domes are absent in Cu-doped $A$Fe2As2 NNi2010 ; YJYan2013 , it is unclear if superconductivity induced by Cu-doping has similar electronic and magnetic properties as their electron/hole-doped counterparts. As NaFe1-xCuxAs exhibits bulk superconductivity similar to those of NaFe1-xCoxAs AFWang2013 , superconducting NaFe1-xCuxAs offers a unique case to study the effect of the stronger impurity potential of Cu AFWang2013 ; MGKim2012 on the resonance mode.

In this work, we use transport and magnetic susceptibility measurements to characterize NaFe1-xCuxAs with $x\leq 0.06$ and inelastic neutron scattering to study the neutron spin resonance in slightly overdoped NaFe0.98Cu0.02As. The temperature dependence of resistivity display an evolution from Fermi liquid behavior in NaFeAs, to non-Fermi-liquid behavior near $x=0.018$ and back to Fermi-liquid behavior near $x=0.032$, pointing to a funnel of quantum critical behavior near optimal doping. A single resonance mode that disperses weakly along $c$-axis is seen in NaFe0.98Cu0.02As, similar to slightly overdoped NaFe1-xCoxAs CZhang2013b . Similar to what was found in heavily overdoped NaFe1-xCoxAs CZhang2016 , the resonance mode is at an higher energy than what is expected from scaling with $T_{\rm c}$, likely related to the stronger impurity potential of Cu compared to Co AFWang2013 ; MGKim2012 , despite the low Cu concentration of $2\%$. The presence of both a putative quantum critical point in the phase diagram and a neutron spin resonance in superconducting NaFe1-xCuxAs is similar to other iron pnictide superconductors. Since NaFe1-xCuxAs can be continuously tuned to an antiferromagnetically ordered insulating phase with significant electronic correlations near $x\approx 0.5$ YSong , these results suggest electronic correlations to be an essential ingredient of superconductivity in iron pnictides.

II Experimental results

Single crystals of NaFe1-xCuxAs were prepared using the self-flux method method as described in previous work NSpyrison2012 . Inductively coupled plasma atomic emission spectroscopy previously revealed the actual Cu concentration to be similar to the nominal one for $x\lesssim 20\%$ YSong , we therefore quote nominal concentrations throughout this work, which is also consistent with previous report on NaFe1-xCuxAs in the superconducting region AFWang2013 . Resistivity and magnetic susceptibility measurements were carried out using commercial systems from Quantum Design. Resistivity is measured with the four-probe method, and magnetic susceptibility is measured upon warming with an in-plane magnetic field of 20 Oe after zero-field-cooling. Inelastic neutron scattering experiments were carried out using the HB-3 triple-axis spectrometer at the High Flux Isotope Reactor (HFIR) and the Hybrid Spectrometer (HYSPEC) at the Spallation Neutron Source, both at Oak Ridge National Laboratory. The experiment at HB-3 used a pyrolitic graphite monochromtor, analyzer and filter after the sample, the collimation used is 48′-40′ -sample-40′-120′ and the final neutron energy is fixed to $E_{\rm f}=14.7$ meV. HYSPEC is a time-of-flight chopper spectrometer with a movable strip-shaped detector bank that has much fewer pixels along the vertical direction compared to the horizontal direction. Detected neutron counts from the middle third of the pixels along the vertical direction are binned making it function like a triple-axis spectrometer with a position-sensitive-detector, and by rotating the sample and the detector bank, maps of the scattering plane can be obtained. Fixed incident energy $E_{\rm i}=15$ meV is used for the experiment on HYSPEC. Momentum transfer ${\bf Q}=(Q_{x},Q_{y},Q_{z})$ is presented in reciprocal lattice units (r.l.u.) as $(H,K,L)$, with $H=Q_{x}a/2\pi$, $K=Q_{y}b/2\pi$ and $L=Q_{z}c/2\pi$. We adopt the chemical unit cell for the orthorhombic phase of NaFe1-xCuxAs, in this notation $a\approx b\approx 5.56$ and $c\approx 7.05$ for NaFeAs sli . The orthorhombic unit cell is twice the volume of the tetragonal unit cell [Fig. 1(a)], in this notation magnetic Bragg peaks are seen at ${\bf Q}=(1,0,L)$ with $L=0.5,1.5,2.5\ldots$, corresponding to half of the magnetic unit cell along $c$-axis [Fig. 1(b)]. 8 high-quality single crystals with a total mass of 6.04 grams were co-aligned in the $[H,0,L]$ scattering plane [Fig. 1(c)].

Figure 2 summarizes magnetic susceptibility and resistivity measurements. As can be seen in Fig. 2(a) optimal superconductivity with $T_{\rm c}\approx 11.8$ K is obtained near $x=0.018$ in agreement with previous results AFWang2013 . Normalized resistivity in NaFe1-xCuxAs with $x=0.004$, 0.014, 0.018, 0.022, 0.025 and 0.032 are shown in Fig. 2(c) through Fig. 2(h). For underdoped samples ($x=0.004$ and 0.014), resistivity exhibits clear kinks at $T_{\rm s}$ and $T_{\rm N}$ before vanishing in the superconducting state below $T_{\rm c}$. Resistivity data in the tetragonal paramagnetic metallic state are fit to the empirical form $\rho=\rho_{0}+AT^{n}$ for all measured samples [inset of Fig. 2(e)], similar to previous work on NaFe1-xCoxAs GTan2016 ; AFWang2013b . A Fermi-liquid corresponds to $n=2$, whereas linear resistivity ($n=1$) is often observed near a quantum critical point SKasahara2010 ; JGAnalytis2014 . Doping dependence of $n$ for NaFe1-xCuxAs is summarized in Fig. 2(b), revealing clear evolution from $n\approx 2$ in NaFeAs to $n\approx 1$ for $x=0.018$, and back to $n\approx 2$ for $x=0.032$. Similar behavior has been observed in other iron pnictide systems SKasahara2010 ; JGAnalytis2014 ; GTan2016 ; AFWang2013b ; HLuo2012 . Based on magnetic susceptibility and resistivity measurements, we construct the phase diagram of NaFe1-xCuxAs near the superconducting dome as shown in Fig. 1(d), the obtained phase diagram is consistent with previous results AFWang2013 .

Constant-${\bf Q}$ scans at ${\bf Q}=(1,0,L)$ for slightly overdoped NaFe0.98Cu0.02As ($T_{\rm c}=11.8$ K and no static magnetic signal is observed) measured using HB-3 are summarized in Figure 3. Scans above ($T=14$ K) and below ($T=2$ K) $T_{\rm c}$ for $L=0$, 0.5 and 1 are shown in Fig. 3(a), (c) and (e), respectively. The corresponding 2 K data after subtracting 14 K data are similarly shown in Fig. 3(b), (d) and (f). A clear resonance mode that displays a weak $c$-axis dispersion accompanied by a spin gap at lower energies can be clearly seen. For $L=0.5$ [Fig. 3(d)], corresponding to the magnetic zone center in magnetically ordered NaFeAs, the resonance is centered at around $E\approx 5.5$ meV. Similarly for $L=0$ and 1 [Fig. 3(b), (f)], corresponding to the magnetic zone boundary along $c$-axis in magnetically ordered NaFeAs, the resonance is centered at $E\approx 6.5$ meV. The resonance mode at $L=0.5$ also appears to be sharper than for $L=0$ and 1, this behavior is different from slightly overdoped NaFe0.955Co0.045As in which width of the resonance mode does not depend on $L$ CZhang2013b .

$H$-scans at the peak of the resonance mode for $L=0.5$ ($E=5.5$ meV) is shown in Fig. 4. At both 2 K and 14 K, a clear peak is observed, with the peak at 2 K only slightly stronger than the one at 14 K [$\approx 23\%$ stronger from area of fits in Fig. 4(a)], meaning the resonance is weak compared to the normal state excitations in contrast to slightly overdoped NaFe1-xCoxAs CZhang2013b in which the resonance mode dominates the magnetic excitations in the superconducting state. Given the normal state spin fluctuations have indistinguishable intensities in Co- and Cu-doped BaFe2As2 MGKim2012 , it is reasonable to assume the normal state intensities in Co- and Cu-doped NaFeAs are also similar. Therefore, compared to NaFe0.955Co0.045As CZhang2013b , the resonance mode in NaFe0.98Cu0.02As is also quantitatively much weaker. The width of the magnetic peak for $E=5.5$ meV at 2 K [FWHM = 0.228(8) (r.l.u.)] and 14 K [FWHM = 0.25(1) (r.l.u.)] are similar with the peak in the superconducting state slightly narrower, similar to slightly overdoped NaFe1-xCoxAs CZhang2013b . The change in peak width can be seen more clearly by examining the difference of 2 K and 14 K data [Fig. 4(b)], which is significantly narrower than the 14 K data itself [Gaussian peak in red dashed line], with FWHM = 0.17(3) (r.l.u.). This suggests that the effect of superconductivity is not only to enhance intensity at the energy of the resonance mode, but also to increase the correlation length of magnetic excitations. The resonance being more well-defined in momentum space compared the normal state excitations can result from reduction of damping due to opening of the superconducting gap, or the resonance mode intrinsically having a longer correlation length. A weak neutron spin resonance mode is seen in Ba(Fe1-xRux)2As2 near optimal doping and ascribed to weakened electronic correlations JZhao2013 . In comparison, the weak resonance in NaFe0.98Cu0.02As is likely due to impurity effects given electronic correlations in superconducting NaFe1-xCoxAs and NaFe1-xCuxAs should be similar.

Our results are further substantiated by data obtained using HYSPEC in Figure 5 and 6. Constant-energy maps of the $[H,0,L]$ scattering plane are shown in Figure 5 at $T=1.6$ K and 12 K, as can be clearly seen magnetic excitations form rods centered at $H=1$ with little $L$-dependence in both the normal and the superconducting state. In magnetically ordered NaFeAs, $c$-axis polarized spin waves exhibit a spin gap of $E_{\rm g}\approx 4.5$ meV at ${\bf Q}=(1,0,0.5)$ and $E_{\rm g}\approx 7$ meV at ${\bf Q}=(1,0,1)$ YSong2013 . Upon Co-doping into the slightly overdoped regime, magnetic excitations become $L$-independent CZhang2013b . Therefore, the reduction of effective $c$-axis magnetic coupling by doping Cu doping into NaFeAs is similar to doping Co, such behavior is also seen in Ni-doped BaFe2As2 LWHarriger2009 . By comparing the Fig. 5(a) and (b) or Fig. 5(c) and (d), which are plotted to the same color scale, it is clear that the intensities differ little in the superconducting and normal state, consistent with resonance mode being weak. In addition to the magnetic signal, we also observe streaks of spurious scattering of unknown origin [dashed line in Fig. 5(a)]. While the spurious signal overlaps with the magnetic signal at $L=0.5$, the magnetic signal at $L=0$ is reasonably far away. In Fig. 6(a) we show the 1.6 K data subtracted by 12 K data by binning points with $L=0\pm 0.2$, which avoids potential contamination from the spurious signal. Similar to Fig. 3(b) and (f), a resonance that is rather broad in energy is seen. The temperature dependence of the resonance mode at $L=0$ is shown in Fig. 6(b), an superconducting-order-parameter-like increase below $T_{\rm c}$ is observed.

III Discussion and Conclusion

The weak resonance mode in NaFe1-xCuxAs is likely a result of the stronger impurity potential of Cu, which is also likely responsible for the lower optimal $T_{\rm c}$ in NaFe1-xCuxAs AFWang2013 compared to NaFe1-xCoxAs GTan2016 ; AFWang2013b and the near-absence of superconductivity in Ba(Fe1-xCux)2As2 NNi2010 . Compared to Ba(Fe1-xCux)2As2 in which superconductivity is nearly absent, the presence of a superconducting dome in NaFe1-xCuxAs may be related to the lower Cu concentration needed to suppress the magnetic order. In a similar vein, lower concentration of Ni in NaFe1-xNixAs was found to cause magnetic order to remain long-range and commensurate approaching optimal superconductivity CDCao2016 , in contrast to Co- and Ni-doped BaFe2As2 in which the magnetic order becomes short-range and incommensurate near optimal-doping DKPratt2011 ; HQLuo2012 . The impurity potential and concentration of dopants therefore has significant effects on the physical properties of iron pnictide superconductors.

The resonance mode in slightly overdoped NaFe0.98Cu0.02As with $T_{\rm c}=11.8$ K is at $E\approx 5.5$ meV for $L=0.5$, corresponding to $E_{\rm r}\approx 5.5k_{\rm B}T_{\rm c}$. This is higher than $E_{\rm r}\approx 4.3k_{\rm B}T_{\rm c}$ suggested for doped BaFe2As2 DSInosov2011 and $E_{\rm r}\approx 4.5k_{\rm B}T_{\rm c}$ in slightly overdoped NaFe0.955Co0.045As CZhang2013b but lower than $E_{\rm r}\approx 7.1k_{\rm B}T_{\rm c}$ in heavily overdoped NaFe0.92Co0.08As CZhang2016 . Therefore, due to multi-orbital physics and impurity effects, there appears to be no simple relationship between $E_{\rm r}$ and $T_{\rm c}$ in doped NaFeAs. Specifically, both the concentration of dopants [slightly overdoped and heavily overdoped NaFe1-xCoxAs] and impurity potential of dopants [slightly overdoped NaFe1-xCoxAs and NaFe1-xCuxAs] seem to increase the ratio $E_{\rm r}/k_{\rm B}T_{\rm c}$. In cuprate superconductors it was found spectral weight of the resonance mode scales linearly with $(E_{\rm c}-E_{\rm r})/E_{\rm c}$ MKChan2016 , where $E_{\rm c}$ is threshold of the particle-hole continuum. This means as $E_{\rm r}$ moves closer to the particle-hole continuum, spectral weight of the resonance also collapses. A similar effect might also contribute to the weak resonance mode in NaFe0.98Cu0.02As, as the high ratio of $E_{\rm r}$ and $k_{\rm B}T_{\rm c}$ suggests the resonance is likely closer to the particle-hole continuum compared to NaFe0.955Co0.045As.

Similarly, the broader resonance at $L=0$ and 1 compared to $L=0.5$ in NaFe0.98Cu0.02As [Fig. 3(b), (d) and (f)] may be due to the mode at $L=0$ and 1 being at a higher energy, and experience stronger interactions with particle-hole excitations that broaden the mode. Alternatively, spin-orbit coupling found to be present in many iron pnictide superconductors Borisenko and causes energy-splitting of resonance modes polarized along different crystallographic directions Korshunov13 ; yusong_BKFA , also results in broadening of the resonance mode seen in unpolarized neutron scattering experiments. Polarized neutron scattering experiments are needed to distinguish between these scenarios.

The superconducting phase in NaFe1-xCuxAs near $x\approx 0.02$ can be continuously tuned to the antiferromagnetically ordered insulating phase with significant electronic correlations near $x\approx$0.5 through a region of short-range cation and magnetic order YSong , pointing to the possibility of the generic phase diagram of iron pnictides to be anchored around a Mott-insulating state LdeMedici2014 ; CYe2015 . The observation of a spin resonance mode in superconducting NaFe1-xCuxAs demonstrates that the superconducting state is similar to other iron pnictide superconductors, and therefore electronic correlations should be an integral part of the physics of iron pnictide superconductors.

IV Acknowledgments

The single crystal growth and neutron scattering work at Rice is supported by the U.S. DOE, BES under contract no. DE-SC0012311 (P.D.). A part of the material synthesis work at Rice is supported by the Robert A. Welch Foundation Grant No. C-1839 (P.D.). Research at BNU and IOP are supported by the National Basic Research Program of China (973 Program, Grants No. 2012CB821401), National Natural Science Foundation of China (Grants No. 11374011), and the Fundamental Research Funds for the Central Universities (Grants No. 2014KJJCB27). Research at Oak Ridge National Laboratory’s HFIR was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.