Magnetic anisotropy in hole-doped superconducting Ba{}_{0.67}K{}_{0.33}Fe{}_{2}As{}_{2} probed by polarized inelastic neutron scattering

Magnetic anisotropy in hole-doped superconducting BaKFeAs probed by polarized inelastic neutron scattering

Chenglin Zhang Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Mengshu Liu Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Yixi Su Jülich Centre for Neutron Science JCNS-FRM II, Forschungszentrum Jülich GmbH, Outstation at FRM II, Lichtenbergstrasse 1, D-85747 Garching, Germany    Louis-Pierre Regnault Institut Laue-Langevin, 6, rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France    Meng Wang Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China    Guotai Tan Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Physics Department, Beijing Normal University, Beijing 100875, China    Th. Brckel Jlich Centre for Neutron Science JCNS and Peter Grnberg Institut PGI, JARA-FIT, Forschungszentrum Jlich GmbH, 52425 Jlich, Germany    Takeshi Egami Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Joint Institute of Neutron Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    Pengcheng Dai Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
July 15, 2019

We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-doped superconductor BaKFeAs ( K). In the normal state, the imaginary part of the dynamic susceptibility, , shows magnetic anisotropy for energies below 7 meV with -axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at 5 and 0.75 meV open at wave vectors and , respectively, with a broad neutron spin resonance at meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the -axis and in-plane polarized spin excitations, resulting resonance with different energy widths for the -axis and in-plane spin excitations. The observation of spin anisotropy in both opitmally electron and hole-doped BaFeAs is due to their proximity to the AF ordered BaFeAs where spin anisotropy exists below .

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Neutron polarization analysis has played an important role in determining the magnetic structure and excitations of solids moon (). For high-transition temperature (High-) copper oxide superconductors derived from hole or electron-doping from their antiferromagnetic (AF) parent compounds, neutron polarization analysis have conclusively shown that the collective magnetic excitation coupled to superconductivity at the AF wave vector of the parent compounds, termed neutron spin resonance mignod (), has a magnetic origin mook (); fong (); dai96 (); headings (); wilson (); jzhao11 (); eschrig (). Furthermore, by carrying out neutron polarization analysis with a spin-polarized incident neutron beam along the scattering wave vector (where and are the incident and final wave vectors of the neutron, respectively), ; perpendicular to but in the scattering plane, ; and perpendicular to and the scattering plane, , one can use neutron spin flip (SF) scattering cross sections and to determine the spatial anisotropy of spin excitations moon (). If the resonance is an isotropic triplet excitation of the singlet superconducting ground state, one expects that the degenerate triplet would be isotropic in space as pure paramagnetic scattering eschrig (). For optimally hole-doped copper oxide superconductor YBaCuO ( K), neutron polarization analysis reveals that spin excitations in the normal state are spatially isotropic and featureless for energies meV, consistent with pure paramagnetic scattering. Upon entering into the superconducting state, a quasi-isotropic spin resonance occurs at meV to within the precision of the measurements and a spin anisotropy develops in the lower energy meV, resulting in a clear spin gap below 22 meV for the -axis polarized dynamic susceptibility and in-plane for meV headings (). The low-energy spin anisotropy is likely due to spin-orbit coupling in the system. For optimally electron-doped copper oxide superconductor PrLaCeCuO, spin excitations are isotropic both above and below jzhao11 (). Therefore, the spin anisotropy in the superconducting state of hole-doped YBaCuO is unrelated to the normal state paramagnetic scattering.

Like copper oxide superconductors, superconductivity in iron pnictides also arises when electrons or holes are doped into their AF parent compounds Kamihara (); Rotter (); ljli (); Cruz (); dai (). Furthermore, unpolarized neutron scattering experiments have shown that both hole and electron-doped iron pnictides exhibits a neutron spin resonance similar to copper oxide superconductors Christianson (); clzhang (); lumsden (); chi (); inosov (); hqluo12 (). In the initial polarized neutron scattering experiment on optimally electron-doped superconductor BaFeNiAs ( K), was found to be much larger than for energies meV below , while the resonance at meV is only weakly anisotropic lipscombe10 (). In a subsequent polarized neutron scattering measurement on undoped AF parent compound BaFeAs qureshi12 (), isotropic paramagnetic scattering at low-energy ( meV) were found to become anisotropic spin waves below the Nel temperature with a much larger in-plane () spin gap than that of the out-of-plane gap (). These results indicate a strong single-ion anisotropy and spin-orbit coupling, suggesting that more energy is needed to rotate a spin within the orthorhombic - plane than rotating it to the -axis qureshi12 (). However, similar polarized neutron experiments on electron-overdoped BaFeNiAs ( K), which is far away from the AF ordered phase, reveal isotropic paramagnetic scattering both above and below msliu12 (). Very recently, Steffens et al. report evidence for two resonance-like excitations in the superconducting state of optimally electron-doped BaFeCoAs ( K). In addition to an isotropic resonance at meV with weak dispersion along the -axis, there is a resonance at meV polarized only along the -axis with strong intensity variation along the -axis steffens (). In the normal state, there are isotropic paramagnetic scattering at AF wave vectors with and weak anisotropic scattering with a larger -axis polarized intensity at steffens ().

Figure 1: (Color online) Neutron polarization analysis determined -axis () and in-plane () components of spin excitations in BaKFeAs from raw SF constant- scans at and and . To extract and , we use methods described in Ref. msliu12 () and assume in the tetragonal crystal. (a) Energy dependence of and at K. (b) Identical scans at K. (c) The solid and open circles show the temperature difference (2 K45 K) for and , respectively. (d) The sum of at 45 and 2 K. Since background scattering is not expected to change between these temperatures clzhang (), such a procedure will increase statistics of magnetic scattering. The black data points are collected at with Å, while the red data points are at with Å. The solid and dashed lines are guided to the eyes.
Figure 2: (Color online) Constant- scans at below and above . (a) Energy dependence of and at K and (b) at 2 K. The superconductivity-induced spin gaps are at and 7 meV for and , respectively. At resonance energy of meV, the scattering is isotropic. (c) The solid and open circles show the temperature difference (2 K45 K) for and , respectively. (d) The sum of at 45 and 2 K. The solid and dashed lines are guided to the eyes.

If the observed anisotropic magnetic scattering in the superconducting state of optimally electron-doped BaFeNiAs lipscombe10 () and BaFeCoAs steffens () are indeed associated with the anisotropic spin waves in BaFeAs qureshi12 (), one would expect similar anisotropic spin excitations in hole-doped materials not too far away from the parent compound. In this paper, we report neutron polarization analysis on spin excitations of the optimally hole-doped superconducting BaKFeAs. From the previous unpolarized INS work on the same sample, we know that spin excitations in the superconducting state have a resonance at meV, a small spin gap ( meV) at and a large gap ( meV) at clzhang (). In the normal state, spin excitations at both wave vectors are gapless and increase linearly with increasing energy clzhang (). Our polarized INS experiments reveal that the persistent low-energy spin excitations at the AF wave vector below are entirely -axis polarized. Although there is also superconductivity-induced spin anisotropy similar to optimally electron-doped BaFeNiAs lipscombe10 () and BaFeCoAs steffens (), the low-energy -axis polarized spin excitations do not change across and therefore cannot have the same microscopic origin as the spin isotropic resonance at meV. We suggest that the persistent -axis polarized spin excitations in the superconducting state of optimally hole and electron-doped iron pnictide superconductors is due to their proximity to the AF ordered parent compound. Their coupling to superconductivity may arise from different contributions of Fe 3 and 3 orbitals to superconductivity malaeb ().

Figure 3: (Color online) Energy dependence of spin anisotropy as determined by the difference between for temperatures (a) 45 K and (b) 2 K at wave vector and . Similar differences above (c) and below (d) at . The energy width is broader in (d) compared with (b). The solid and dashed lines are guided to the eyes.

Single crystals of BaKFeAs are grown by a self-flux method clzhang (). About 10 grams of single crystals are coaligned in the scattering plane (with mosaicity at full width half maximum) with a tetragonal unit cell for which Å, and Å. In this notation, the vector Q in three-dimensional reciprocal space in Å is defined as , where , , and are Miller indices and are reciprocal lattice vectors. Our polarized INS experiments were carried out on the IN22 triple-axis spectrometer with Cryopad capability at the Institut Laue-Langevin in Grenoble, France. The fixed final neutron wave vectors were set at Å and Å in order to close the scattering triangles. To compare with previous polarized INS results on iron pnictides lipscombe10 (); qureshi12 (); msliu12 (); steffens (), we converted the measured neutron SF scattering cross sections , , and into -axis () and in-plane () components of the magnetic scattering msliu12 ().

Figure 4: (Color online) Constant-energy scans along the and directions at an energy transfer of meV for different neutron polarization directions. (a) Neutron SF scattering cross sections , , and at 45 K along the direction. Similar scans along the direction at (b) 2 K and (c) 45 K. All data are obtained with . The solid lines are fit by Gaussian.

Figure 1 shows energy scans above and below at wave vectors and . We chose these two equivalent wave vectors with different fixed final neutron energies to satisfy the kinematic condition for the large covered energy range. Since the iron magnetic form factors, geometrical factors, and instrumental resolutions are different at these two wave vectors, we use left and right scales for and , respectively. In the normal state (45 K), spin anisotropy for energies below meV is clear with () larger than () [Fig. 1(a)]. For meV, spin excitations are nearly isotropic. This is different from electron-doped BaFeCoAs, where paramagnetic scattering at is isotropic above steffens (). In the superconducting state (2 K), and in BaKFeAs vanish below 5 meV, consistent with opening of a superconductivity-induced spin gap [Fig. 1(b)] clzhang (). From meV to the resonance energy at meV, both and increase with increasing energy, but with different slope resulting significant spin anisotropy () appearing near meV [Fig. 1(b)]. This is similar to the spin anisotropy in BaFeCoAs steffens (). Figure 1(c) shows the temperature difference of magnetic scattering, revealing net intensity gains for and only above 7 and 10 meV, respectively. Figure 1(d) shows the sum of the SF magnetic scattering intensities for three different neutron polarizations, which improve the statistics, above and below . Consistent with Fig. 1(c), the superconductivity-induced net magnetic intensity gain appears only above 7 meV, forming a resonance at meV.

Figure 2 summarizes the identical scans as that of Fig. 1 at the AF wave vector above and below . At K, we see clear spin anisotropy below meV with similar to the spin excitations at [Fig. 2(a)]. Upon cooling to 2 K, a large spin gap opens below meV in , but there is still magnetic scattering in extending to at least meV. Therefore, the low-energy signal above 1 meV at reported in the earlier unpolarized neutron measurements clzhang () are entirely -axis polarized magnetic scattering. The neutron spin resonance at is isotropic. The temperature difference plots between 2 and 45 K display a broad and narrow peak for and , respectively [Fig. 2(c)]. Fig. 2(d) shows the sum of SF magnetic scattering below and above . Consistent with unpolarized work clzhang (), we see net intensity gain of the resonance in the superconducting state for energies above meV, different from that of BaFeCoAs where the magnetic intensity starts to gain above meV in the superconducting state [Fig. 4(b) in steffens ()].

To further illustrate the effect of spin anisotropy, we plot in Figs. 3(a)-3(d) the differences of above and below at wave vectors and . In the normal state, we see clear magnetic anisotropy with for energies below 7 meV [Figs. 3(a) and 3(c)]. In the superconducting state, the differences reveal similar intensity peaks centered around 7 meV at and , but with a much broader width for [Figs. 3(b) and 3(d)]. Since there are essentially no intensity gain in across near 7 meV [Figs. 1(c) and 2(c)], the apparent peaks in arise from different responses of and across . While the intensity of across is suppressed below 7 meV and enhanced above it, similar cross over energy occurs around 10 meV in , thus resulting peaks near 7 meV in at 2 K [Figs. 3(b) and 3(d)]. Therefore, the differences in superconductivity-induced spin gaps in and at and are causing peaks in .

Finally, to confirm the low-energy spin anisotropy discussed in Figs. 1-3, we show in Figs. 4(a)-4(c) constant-energy scans with three different neutron polarizations at meV along the and directions. In the normal state, shows clear peaks at and [Figs. 4(a) and 4(c)]. In both cases, we also find , thus confirming the anisotropic nature of the magnetic scattering with . In the superconducting state, while and are peaked at , is featureless. These results again confirm the presence of a larger superconductivity-induced spin gap in than that in [Fig. 2(b)].

From Figs. 1-4, we see anisotropic spin susceptibility in both the normal and superconducting state of BaKFeAs, different from optimally electron-doped BaFeCoAs where the anisotropy is believed to emerge only with the opening of the superconducting gap steffens (). Furthermore, our data reveal that large differences in the superconductivity-induced spin gaps at and clzhang () arise from the differences in spin gaps of -axis polarized spin excitations. These results are similar to the previous work on electron-doped BaFeNiAs lipscombe10 () and BaFeCoAs steffens (), suggesting that the influence of a strong spin anisotropy in undoped parent compound BaFeAs qureshi12 () extends to both optimally electron and hole-doped iron pnictide superconductors. For comparison, we note that spin excitations in superconducting iron chalcogenides are different, having slightly anisotropic resonance with isotropic spin excitations below the resonance boothroyd (); prokes ().

In Ref. steffens (), it was suggested that the observed spin anisotropy in BaFeCoAs can be understood as a -axis polarized resonance whose intensity strongly varies with the -axis wave vector. This is not the case in BaKFeAs since we find much weaker -axis modulation of the magnetic intensity clzhang (). Therefore, the spin anisotropy seen in optimally electron and hole-doped superconductors is a consequence of these materials being close to the AF ordered parent compound BaFeAs, where spin-orbit coupling is expected to be strong kruger (); lee (); lv (), and is not fundamental to superconductivity of these materials. To understand how spin anisotropy in optimally hole and electron-doped iron pnictide superconductors might be coupled to superconductivity via spin-orbit interaction, we note that hole and electron-doped iron pnictides are multiband superconductors with different superconducting gaps for different orbitals. If -axis and in-plane spin excitations arise from quasiparticle excitations of different orbitals between hole and electron Fermi pockets jhzhang (), the large differences in superconducting gaps for Fermi surfaces of different orbital characters might induce the observed large spin anisotropy.

We are grateful to W. C. Lv for helpful discussions and H.F. Li, K. Schmalzl, and W. Schmidt for their assistance in the neutron scattering experiment. The work at UTK is supported by the US DOE BES No. DE-FG02-05ER46202. C.L.Z and T.E are partially supported by the US DOE BES through the EPSCoR grant, DE-FG02-08ER46528. Work at IOP is supported by the MOST of China 973 programs (2012CB821400).


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