Neutron spin resonance as a probe of superconducting gap anisotropy in partially detwinned electron underdoped NaFeCoAs
We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned NaFeCoAs which has coexisting static antiferromagnetic (AF) order and superconductivity ( K, K). In previous INS work on a twinned sample, spin excitations form a dispersive sharp resonance near meV and a broad dispersionless mode at meV at the AF ordering wave vector and its twinned domain . For partially detwinned NaFeCoAs with the static AF order mostly occurring at , we still find a double resonance at both wave vectors with similar intensity. Since characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders, but originate from the superconducting gap anisotropy.
pacs:74.25.Ha, 74.70.-b, 78.70.Nx
The neutron spin resonance is a collective magnetic excitation observed by inelastic neutron scattering (INS) at the antiferromagnetic (AF) ordering wave vector of unconventional superconductors below mignod (); Eschrig (); jmtranquada (); dai (). First discovered in the optimally hole-doped YBaCuO family of copper oxide superconductors mignod (), the mode was also found in iron pnictide superconductors at the AF wave vector in reciprocal space [Figs. 1(a) and 1(b)] kamihara (); cruz (); christianson (); CZhang13 (); NQureshi14 (); lumsden (); schi09 (); dsinosov09 (); steffens (); MGKim13 (); CLZhang13 (); CLZhang14 (), and is considered one of the hall marks of unconventional superconductivity scalapino (). Experimentally, the neutron spin resonance appears as an enhancement of the magnetic spectral weight at an energy in the superconducting state at the expense of normal state spin excitations for energies below it. For iron pnictide superconductors with hole and electron Fermi surfaces near the and points, respectively [Fig. 1(c)] hirschfeld (); chubukov (), the mode is generally believed to arise from sign reversed quasiparticle excitations between the hole and electron Fermi surfaces and occur at an energy below the sum of their superconducting gap energies () Korshunov (); Maier ().
If the energy of the resonance is associated with the superconducting gap energies at the hole and electron Fermi surfaces, it should be sensitive to their anisotropy on the respective Fermi surfaces Maier09 (); Goswami (). Indeed, recent INS experiments on the NaFeCoAs family of iron pnictide superconductors reveal the presence of a dispersive sharp resonance near meV and a broad dispersionless mode at meV at in electron underdoped superconducting NaFeCoAs with static AF order ( K and K) CLZhang13 (); CLZhang14 (). From the electronic phase diagram of NaFeCoAs determined from specific heat GTTan2013 (), scanning tunneling microscopy PCai2013 (), and nuclear magnetic resonance (NMR) SWOh2013 (); LMa2014 () experiments, we know that NaFeCoAs is a bulk superconductor with microscopically coexisting static AF ordered and superconducting phases. For Co-doping near optimal superconductivity around , NaFeCoAs becomes mesoscopically phase separated with static AF ordered and paramagnetic superconducting phases LMa2014 (), similar to the co-existing cluster spin glass and superconducting phases in optimally electron-doped BaFeAs Bernhard2012 (); XYLu2014B (). Since angle resolved photoemission spectroscopy (ARPES) experiments on NaFeCoAs found a large superconducting gap anisotropy in the electron Fermi pockets qqge (), the double resonance may result from orbital-selective pairing induced superconducting gap anisotropy along the electron Fermi surfaces RYu14 (). Upon increasing electron doping to to form superconducting NaFeCoAs ( K), the superconducting gap anisotropy disappears Liu_arpes (); thirupathaiah () and INS reveals only a single sharp resonance coupled with superconductivity clzhang13b ().
Although the superconducting gap anisotropy provided a possible interpretation RYu14 (), the double resonance in underdoped NaFeCoAs may also be due to the coexisting static AF order with superconductivity knolle11 (); WCLv14 (). Since characterizes the explicit breaking of the spin rotational symmetry in the AF ordered state of a completely detwinned sample [Fig. 1(b) and 1(c)] YSong13 (), one should expect magnetic susceptibility anisotropy at and . At the AF ordering wave vector , the resonance appears in the longitudinal susceptibility, whereas the transverse component displays a spin-wave Goldstone mode. At the other momentum , the resonance has both longitudinal and transverse components and is isotropic in space. If the resonance shows distinct energy scales at and , one would expect to find a double resonance in a twinned sample as shown in Fig. 1(e) knolle11 (); WCLv14 (). However, one would then expect a single resonance of energy at and that of energy at in a completely detwinned superconducting sample with static AF order [Fig. 1(f)].
To test if this is indeed the case, we have carried out INS experiments on uniaxial strain partially detwinned NaFeCoAs to study the neutron spin resonance at and . Instead of at and at as expected from the theory of coexisting static AF order with superconductivity knolle11 (); WCLv14 (), we find that both and are present at and as in the twinned case. Therefore, the presence of the double resonance is not directly associated with the breaking of the spin rotational symmetry in detwinned NaFeCoAs. Instead, our results are consistent with the notion that the splitting of the resonance is due to superconducting gap anisotropy in the underdoped NaFeCoAs, suggesting weak direct coupling between spin waves and superconductivity. These results are also consistent with polarized neutron scattering data, where the longitudinal spin excitations of reveals a clear order-parameter-like increase below reminiscent of the resonance, while the transverse spin excitations of the from the spin-wave Goldstone mode have no anomaly across CLZhang14 ().
II. Experimental Results and Theoretical Calculations
We prepared single crystals of NaFeCoAs by the self-flux method CLZhang13 () and cut a large crystal into the rectangular shape along the and directions ( mm, 0.79 g). From NMR measurements LMa2014 (), we know that the tetragonal-to-orthorhombic structural transition happens around K, above and . Our neutron scattering experiments were carried out on the PUMA and BT-7 thermal triple-axis spectrometers at the MLZ, TU Müchen, Germany schi09 (), and NIST center for neutron research (NCNR), Gaithersburg, Maryland jeff (), respectively. In both cases, we used vertically and horizontally focused pyrolytic monochromator and analyzer with a fixed final neutron energy of meV. The wave vector at (,,) in Å is defined as (H,K,L) = (,,) reciprocal lattice unit (r.l.u.) using the orthorhombic unit cell ( Å and Å at 3 K). In this notation, the AF Bragg peaks occur at the positions with and there are no magnetic peaks at [Figs. 1(a) and 1(b)] slli09 (). We have used a detwinning device similar to that of the previous INS work on BaFeNiAs xylu14s (). The samples are aligned in the scattering plane. In this scattering geometry, we can probe the static AF order and spin excitations at both and , thus allowing a conclusive determination of the detwinning ratio and spin excitation anisotropy at these wave vectors. Figure 2(a) and 2(b) shows the temperature differences in transverse elastic scans along the and directions, respectively, for NaFeCoAs between 2 K and 41 K. By comparing the scattering intensity at these two wave vectors, we estimate that the sample is about 58% detwinned. Figure 2(c) shows the temperature dependence of the magnetic order parameters. Consistent with previous data on a twinned sample CLZhang13 (), the uniaxial strain used to detwinn the sample does not seem to alter K and K.
In previous INS work on twinned NaFeCoAs, superconductivity induces a dispersive sharp resonance near meV and a broad dispersionless mode at meV at and CLZhang13 (). To explore what happens in the uniaxial strain detwinned NaFeCoAs, we carried out constant-Q scans at wave vectors [Fig. 2(d)] and [Fig. 2(e)] below and above . While it is difficult to see the resonance in the raw data, the temperature differences between 5 K and 21 K plotted in Fig. 2(f) reveal a sharp peak at meV and a broad peak at meV, in addition to the negative scattering below 3 meV due to a spin gap. These data indicate the presence of a superconductivity-induced sharp resonance and a broad resonance above a spin gap, similar to the results on twinned samples CLZhang13 (). Surprising, there are no observable differences for the resonance at and , suggesting that the double resonance is not directly associated with the twinning state of the sample.
To confirm the conclusion of Fig. 2, we carried out constant-energy scans near and at and above and below . Figure 3(a) and 3(b) shows transverse rocking curve scans through and , respectively, at the sharp resonance energy meV above and below . While there is slightly more magnetic scattering at the AF ordering wave vector compared with that at in both the normal and superconducting states xylu14s (), the superconductivity induced intensity changes shown in Fig. 3(c) and 3(d), defined as the resonance Eschrig (), at these two wave vectors are indistinguishable within the statistics of our measurement.
Figures 4(a-d) summarize wave vector scans at the energy of the broad resonance meV around and . Similar to data at meV, we find that the superconductivity-induced intensity gain of the broad resonance is almost indistinguishable at these wave vectors, again confirming the notion that the resonance is not sensitive to the twinning state of the system.
In electron doped NaFeCoAs, the dominant orbital character of the electron pockets would be at and at in the Brillouin zone [Fig. 1(c)] qqge (); Liu_arpes (); thirupathaiah (). The orbital character of the hole pocket is . If the superconducting pairing amplitudes are highly orbital dependent,i.e., , the superconducting gap can be anisotropic along the electron pocket and this gap anisotropy gives rise to a splitting of the resonance peak RYu14 (). Such an orbital-selective pairing scenario is consistent with both ARPES measurements qqge () and INS results in twinned samples CLZhang13 ().
In the uniaxial strain detwinned sample, the degeneracy of the and orbitals is lifted and, correspondingly, the Fermi surface is distorted qqge (). To investigate whether the double resonances in the orbital-selective pairing scenario still exist in the presence of a splitting between the and orbitals, we calculated the imaginary part of the spin susceptibility in the superconducting state from a multiorbital model with an orbital splitting term RYu14 (). Our result for a strong orbital selectivity is presented in Fig. 5. We find two resonance peaks at each of the wave vectors and for a nonzero splitting . The intensities of the counterpart peaks at and are comparable. At each resonance peak, there is a relative shift of the resonance energy between the and resonances. This shift is proportional to the splitting . The calculated double-resonances feature at both and is qualitatively consistent with the experimental observation in the detwinned sample. The experiment can not resolve a relative shift of the resonance energy. This could be because either the splitting is small in the detwinned underdoped compound, or the coupling between the superconductivity and the splitting is rather weak. Further comparison between theory and experiments is needed to fully settle the issue.
In conclusion, our INS experiments on partially detwinned NaFeCoAs reveal the presence of two resonances at each of the wave vectors and . This is different from the scenario where the two resonances are due to the coexisting AF order with superconductivity knolle11 (); WCLv14 (). Instead, the data are qualitatively consistent with the proposal that the double resonances originate from an orbital dependence of the superconducting pairing. Our results provide further evidence that orbital selectivity plays an important role in understanding not only the normal state but also the superconducting pairing of the multiorbital electrons in the iron pnictides.
We thank Z. C. Sims for his help in single crystal growth efforts. 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.). Part of the work is also supported by the Robert A. Welch foundation grant numbers C-1893 (P.D.) and C-1411 (Q.S.). Q.S. is also supported by US NSF DMR-1309531. R.Y. was supported by the NSFC grant No. 11374361, and the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China.
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