Spin-wave excitations and superconducting resonant mode in Cs{}_{x}Fe{}_{2-y}Se{}_{2}

Spin-wave excitations and superconducting resonant mode in CsFeSe

A. E. Taylor a.taylor1@physics.ox.ac.uk Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom    R. A. Ewings ISIS Facility, Rutherford Appleton Laboratory, STFC, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom    T. G. Perring ISIS Facility, Rutherford Appleton Laboratory, STFC, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom    J. S. White Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Laboratory for Quantum Magnetism, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland    P. Babkevich Laboratory for Quantum Magnetism, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland    A. Krzton-Maziopa Laboratory for Developments and Methods, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Faculty of Chemistry, Warsaw University of Technology, PL-00664 Warsaw, Poland    E. Pomjakushina Laboratory for Developments and Methods, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    K. Conder Laboratory for Developments and Methods, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland    A. T. Boothroyd a.boothroyd@physics.ox.ac.uk Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom

We report neutron inelastic scattering measurements on the normal and superconducting states of single-crystalline CsFeSe. Consistent with previous measurements on RbFeSe, we observe two distinct spin excitation signals: (i) spin-wave excitations characteristic of the block antiferromagnetic order found in insulating FeSe compounds, and (ii) a resonance-like magnetic peak localized in energy at 11 meV and at an in-plane wave vector of . The resonance peak increases below K, and has a similar absolute intensity to the resonance peaks observed in other Fe-based superconductors. The existence of a magnetic resonance in the spectrum of RbFeSe and now of CsFeSe suggests that this is a common feature of superconductivity in this family. The low energy spin-wave excitations in CsFeSe show no measurable response to superconductivity, consistent with the notion of spatially separate magnetic and superconducting phases.

74.25.Ha, 74.70.Xa, 78.70.Nx, 75.30.Ds

I Introduction

The FeSe compounds ( = K, Rb, Cs and Tl) present an interesting new twist in the field of iron-based superconductors. The discovery of superconductivity with transition temperatures K in this series,Guo et al. (2010); Wang et al. (2011a); Krzton-Maziopa et al. (2011); Fang et al. (2011) in conjunction with antiferromagnetism with an unusually high ordering temperature of up to 559K and large ordered moment of about 3.3 per Fe,Bao et al. (2011) naturally raises the question: can superconductivity coexist microscopically with such a robust magnetic state? Although there are regions in the phase diagrams of the iron pnictide superconductors in which magnetism and superconductivity are believed to coexist microscopically, the highest s and bulk superconductivity are found when the magnetic state has been suppressed.Johnston (2010); Stewart (2011); Lumsden and Christianson (2010) Another distinct feature of the FeSe systems is their band structure.Zhang et al. (2011a); Qian et al. (2011) The Fermi surface lacks the large hole pocket at the zone center that features prominently in theories of superconductivity and magnetism in other iron-based superconductors.

The magnetic structure observed in superconducting FeSe samples consists of blocks of four ferromagnetically aligned Fe spins, with antiferromagetic alignment between these blocks. This magnetic state forms on a superstructure of ordered Fe vacancies that has optimal composition FeSe.Pomjakushin et al. (2011a); Bao et al. (2011); Pomjakushin et al. (2011b); Wang et al. (2011b); Ye et al. (2011) A ordered phase has also been observed in some samples and is thought to be closely related to the superconducting phase.Wang et al. (2011b); Ricci et al. (2011a); Li et al. (2012)

Initial experimental investigations of FeSe supported a picture of microscopic coexistence of the superconducting and antiferromagnetic states.Guo et al. (2010); Krzton-Maziopa et al. (2011); Shermadini et al. (2011); Torchetti et al. (2011); Yu et al. (2011); Ma et al. (2011); Kotegawa et al. (2011); Bao et al. (2011) These studies were backed up by calculations based on the antiferromagnetic state.Das and Balatsky (2011); Yan et al. (2011); Cao and Dai (2011); Zhang et al. (2011b) Further work, however, has found evidence for a spatial separation of superconducting (metallic) and antiferromagnetic (insulating or semiconducting) phases.Li et al. (2011); Charnukha et al. (2012a); Ricci et al. (2011b); Chen et al. (2011); Wang et al. (2011b); Ksenofontov et al. (2011) The most recent results, from NMR,Texier et al. (2012) scanning electron microscopy (SEM),Speller et al. (2012) optical spectroscopy,Yuan et al. (2012) Raman scattering and optical microscopy,Zhang et al. (2012) and low energy muon spin rotationCharnukha et al. (2012b) may help to explain the apparent discrepancies in the earlier work. They indicate that phase separation occurs with a complex plate-like morphology on a sub-micron scale. Proximity effects between nanodomains could therefore allow an interplay between superconducting and magnetic regions, and may explain the apparent bulk superconductivity despite estimates of a genuine superconducting phase fraction of only 5–10%.

The interplay between superconductivity and static magnetic order remains a key issue in the FeSe family. Another important property is the magnetic dynamics, which are widely thought to play a role in mediating superconductivity in the iron-based superconductors.Johnston (2010); Stewart (2011); Lumsden and Christianson (2010) Up to now, investigations of the magnetic dynamics have focussed on RbFeSe. The spin-wave spectrum of the insulating parent antiferromagnetic phase has been measured by inelastic neutron scattering and the results were successfully modelled in terms of a local moment Heisenberg Hamiltonian.Wang et al. (2011c) Superconducting samples of RbFeSe have also been studied, and a spin resonance has been discovered.Park et al. (2011) The resonance is quasi-two-dimensional and characterized by an increase in scattering intensity below at an energy of approximately 14 meV and at the wave vector and equivalent positions, which corresponds to in square lattice notation.Park et al. (2010) This wave vector is not the same as the usual resonance wave vector of the iron based superconductors, which is etc. In Ref. Park et al., 2011 it was suggested that the position of the resonance in RbFeSe can be traced to the nesting of electron-like Fermi surface pockets together with a -wave superconducting pairing state based on the theory of Maier et al.,Maier et al. (2011) unlike the pairing generally thought to be present in other iron-based superconductors. In another study of RbFeSe, a magnetic signal was reported close to in addition to spin-wave excitations from the block antiferromagnetic order and the magnetic resonance at .Wang et al. (2012)

In this work we studied the spin excitations in superconducting CsFeSe, with particular focus on the low energy magnetic features and their response to superconductivity. We find that the spin excitations associated with the block antiferromagnetic order have a very similar spectrum to those observed in non-superconducting RbFeSe up to the highest energy probed ( 150 meV). To within experimental error, we find no influence of superconductivity on the low energy magnetic excitations from the block antiferromagnetic order, in contrast to the response of the magnetic Bragg peak and a two-magnon Raman peak which both show a small anomaly in intensity on cooling below .Bao et al. (2011); Zhang et al. (2012) Finally, we observe a spin resonance below at , establishing that this feature is not confined to RbFeSe but is present in other members of the FeSe family. The results suggest that the sample consists of distinct magnetically ordered and superconducting phases.

Ii Experimental Methods

The CsFeSe single crystals were grown by the Bridgman process as decribed in Ref. Krzton-Maziopa et al., 2011. The nominal composition of the crystals used in this study is CsFeSe, and their superconducting and magnetic properties have been reported previouslyKrzton-Maziopa et al. (2011); Shermadini et al. (2011); Pomjakushin et al. (2011a). The crystals were coated in Cytop varnish before handling in air, and then checked for crystalline quality prior to the experiment. Magnetic susceptibility measurements shown in Fig. 1 established that the onset of bulk superconductivity occurs at K. By ‘bulk’ we mean that full flux exclusion is achieved after cooling in zero field. However, this does not necessarily imply 100% superconducting volume fraction, since non-superconducting regions can be screened by surface currents in a zero-field-cooled measurement. A crystal from the neutron scattering sample was remeasured after the experiment and found to have an unchanged .

Figure 1: (Color online) Magnetic susceptibility of one of the CsFeSe single crystals used here, measured with a field of Oe applied along the axis after cooling in zero field. A susceptibility of corresponds to full Meissner flux exclusion, but as no demagnetization corrections have been applied is not a rigorous lower bound.

The inelastic neutron scattering experiments were performed on the MERLIN time-of-flight (TOF) chopper spectrometer at the ISIS Facility.Bewley et al. (2006) Three single crystals were co-aligned to give a sample of total mass 0.42 g, with a uniform mosaic of (full width at half maximum). The sample was mounted with the axis parallel to the incident neutron beam, and the axis horizontal. Spectra were recorded in the large position-sensitive detector array with neutrons of incident energy and  meV at  K, and  meV at , 20, 34 and 44 K. For a fixed sample orientation only three of the four components are independent. We will use and the two in-plane wave vector components . This means that the out-of-plane wave vector component varies with . The scattering from a standard vanadium sample was used to normalize the spectra and place them on an absolute intensity scale, with units mb sr meV f.u., where 1 mb = 10 m and f.u. stands for formula unit of CsFeSe.

Iii Results

Figure 2: (Color online) (a) Map of two-dimensional reciprocal space for CsFeSe, showing positions of the magnetic ordering vectors and the magnetic resonance signals. Wave vectors are indexed with respect to the one-Fe unit cell (unfolded Brillouin zone). The open circles are reciprocal lattice points, and the dashed square is the first Brillouin zone for this unit cell. The two small tilted squares are the first Brillouin zones for the unit cells of the left-handed (LH) and right-handed (RH) magnetic domains.Bao et al. (2011) The paths along which cuts shown in later figures were taken are represented by thick solid lines. (b) Neutron scattering intensity map of CsFeSe in the same area of reciprocal space as shown in (a). The data were recorded with an incident neutron energy of 100 meV. The areas of missing data are due to the beam stop and masked detectors.

Figure 2(a) is a map of the plane in two-dimensional reciprocal space, showing the positions of the antiferromagnetic Bragg peaks and the magnetic resonance signal reported in Ref. Park et al., 2011. We index positions in reciprocal space with respect to the one-Fe sub-lattice, lattice parameters  Å. Figure 2(b) is a map of the neutron scattering intensity averaged over the energy range 10 to 20 meV and projected onto the same region of the plane as shown in Fig. 2(a). The strong scattering signal localized at and equivalent positions is due to magnetic fluctuations associated with the block antiferromagnetic order on the Fe vacancy superstructure. The eight-fold symmetry of the magnetic spectrum, which derives from the superposition of two four-fold patterns from left-handed and right-handed magnetic structures, respectively, is apparent from this figure. All spectra presented hereafter have been folded into one octant to improve statistics.

The magnetic spectrum is revealed in more detail in Fig. 3, which shows a strongly dispersive spin-wave band extending from below 20 meV up to 63 meV, and a second band between 85 and 120 meV. The existence of the latter is demonstrated in Fig. 3(a) via two energy scans recorded at fixed wavevectors of and . These positions were chosen after inspection of an intensity map like that in Fig. 2(b) but at an energy of 100 meV, which showed a regular pattern of diffuse magnetic scattering with maximum intensity at and minimum at .

Figure 3: (Color online) Spin-wave spectrum of CsFeSe. (a) Energy cuts showing the band of magnetic scattering around 100 meV. The data are from a run with incident neutron energy  meV at 4 K. The orange triangles were recorded at the wave vector , where there is a clear magnetic signal with maximum intensity near 105 meV. The green diamonds are a similar cut from the nearby position , which is away from any magnetic scattering. (b) Spin-wave dispersion of the low-energy band, measured at K. The method used to obtain the data points is described in the text. The different colored symbols indicate data obtained with different incident neutron energies, . The dashed lines mark the magnetic Brillouin zone boundaries. For energies below 60 meV, the vertical error bars represent the width of the cut in energy and the horizontal error bars represent the error in the fitted peak position. For the two points at 63 meV, the horizontal error bar is the width of the cut in wave vector and the vertical error bar is the error from the fit.

Figure 3(b) plots the in-plane dispersion of the lower spin-wave band. In constant-energy maps in the plane, the low-energy spin-wave scattering appears as a ring of intensity centered on the positions. The points in Fig. 3(b) were obtained as follows. Gaussian fits were made to peaks in constant-energy cuts along the line passing through the magnetic wavevectors and — see Fig. 2(a). Gaussian functions fitted to pairs of peaks symmetrically displaced either side of each were constrained to have the same area and width. The peak positions were corrected for the systematic shift caused by the curvature of the dispersion surface over the width of the cuts. Where appropriate, a non-magnetic background was estimated from cuts taken along nearby lines in reciprocal space. The points at the magnetic Brillioun zone (BZ) boundaries (marked in Fig. 3(b) by dashed lines) were obtained from a Gaussian fit to the peak in a background-corrected energy cut.

Figure 4: (Color online) (a) Constant-energy cuts through showing the temperature dependence of the spin-wave scattering averaged over the energy range 13 to 15 meV. Data were recorded with an incident energy  meV, giving an out-of-plane wave vector component . Successive cuts are displaced vertically by 40 units for clarity. Dashed lines are fits to Gaussian peaks on a linear background, as described in the main text. (b) The integrated intensity (in mbsrmeVf.u.) given by the area of the fitted Gaussian peaks as a function of temperature. The intensities have been normalized by the Bose factor .

The results shown in Figs. 3(a) and (b) bear a very close resemblance to the magnetic spectrum of non-superconducting RbFeSe reported in Ref. Wang et al., 2011c. Our data are not sufficient to determine the detailed dispersion in the out-of-plane direction , but the spectra measured with different to probe at different values are consistent with a minimum anisotropy gap of meV and a maximum of about 20 meV, somewhat lower than the maximum of 30 meV reportedWang et al. (2011c) for RbFeSe. In Ref. Wang et al., 2011c, a third spin-wave band was observed in RbFeSe, with a dispersion from 180 and 230 meV. Our data do not extend high enough in energy to confirm the existence of this band in CsFeSe.

In Fig. 4 we show the temperature dependence of the spin-wave peak at averaged over the energy range 13 to 15 meV. Figure 4(a) shows wave vector scans recorded at four different temperatures, two below and two above . The peaks show no discernible change within this temperature range. To check this quantitatively we fitted the data to a Gaussian function on a linear background, allowing the width, center and area of the Gaussian, and the slope and intercept of the background to vary. To correct for the increase in signal due to the thermal population of spin-waves we normalized the data by the Bose population factor. Figure 4(b) plots the areas of the fitted peaks as a function of temperature. To within the experimental error (about 3%) there is no change upon crossing the superconducting transition temperature.

Figure 5: (Color online) (a) Neutron scattering intensity map of CsFeSe averaged over energies between 9 and 13 meV. The data were recorded at K with an incident energy  meV. The inset shows the peak intensity as a function of energy, where the intensity is given as the imaginary part of the local susceptibility. (b) Constant-energy cuts through the map in (a) showing the temperature dependence of the magnetic signal at . The out-of-plane wave vector at the peak is . Successive cuts are displaced vertically by 5 units for clarity. The dotted line through the 4 K cut is a fit to a Gaussian peak on a linear background. The inset in (b) shows the integrated intensity of the 4 K Gaussian peak and of constrained Gaussian fits to the higher temperature data (see text) as a function of temperature. The integrated intensities (in mb srmeVf.u. Å) have been normalized by the Bose factor .

Finally, we consider the magnetic dynamics at wave vectors away from the points in reciprocal space. Figure 5(a) shows an intensity map recorded at 4 K and averaged over the energy range 9 to 13 meV. The data have been folded onto an octant of reciprocal space to improve statistics. To within the experimental error, there is no evidence for the excitations observed near and equivalent positions by Wang et al. in similar measurements on superconducting RbFeSe.Wang et al. (2012) However, our data do reveal a weak signal centered on with a maximum at an energy of about 11 meV (see inset to Fig. 5(a)). Wave vector cuts through this peak in the direction averaged over 9–13 meV are shown in Fig. 5(b) at a series of temperatures. The cut at 4 K, well below , shows a well defined peak which has been fitted with a Gaussian function on a linear background (dashed line). Above the peak is either strongly suppressed or absent. Fits were made to the cuts at higher temperatures with the width and center of the Gaussian fixed to the values found at K. The inset to Fig. 5(b) shows the integrated intensity of the fitted Gaussian peaks as a function of temperature. The signal clearly increases as the temperature decreases. To determine the absolute strength of the peak we have converted its integrated intensity into the -averaged or local susceptibility .Lester et al. (2010) We assumed the peak is two-dimensional and used the dipole form factor of Fe. The inset to Fig. 5(a) shows the energy dependence of at  K.

Iv Discussion

One of the goals of this work was to determine whether the spin dynamics of the block antiferromagnetic phase in superconducting samples of FeSe are different to those in insulating samples, and whether they respond to superconductivity. Figure 3 presents a clear demonstration that the antiferromagnetic spin-waves persist in superconducting CsFeSe and have a similar spectrum to that of insulating RbFeSe.Wang et al. (2011c) We find the top of the low energy acoustic spin-wave branch to be  meV, and the center of the medium energy band to be  meV, compared with  meV and  meV, respectively, found in RbFeSe.Wang et al. (2011c)

We find no evidence for a coupling between the low energy spin-waves and superconductivity. This is illustrated in Fig. 4 for an energy near 14 meV where the scattering is strongest. However, we also examined the data from 8 meV up to 27 meV and found no change in the spin-wave scattering on cooling through at any energy in this range. From our results we can rule out any superconductivity-induced change at low energies greater than 3–4%. By contrast, previous studies on superconducting KFeSe reported systematic reductions of 5% or more in the intensities of a magnetic Bragg peak and a two-magnon Raman peak at  meV on cooling below .Bao et al. (2011); Zhang et al. (2012) One possibility is that the size of the effect depends on the energy probed, however a more plausible explanation is based on the notion that these samples are phase-separated on a nanoscale into superconducting and magnetically ordered (non-superconducting) regions which only interact at the interfaces.Yuan et al. (2012); Texier et al. (2012); Speller et al. (2012) Below , the superconducting proximity effect could suppress magnetic order near the phase boundaries, so that samples with different interfacial surface areas would respond to superconductivity by different amounts.

Although we find no effect of superconductivity on the magnetic excitations associated with the block antiferromagnetic order, we do observe the magnetic resonance peak at previously reported in superconducting RbFeSe.Park et al. (2011); Friemel et al. (2012); Wang et al. (2012) As shown in Fig. 5, we find that the magnetic signal at increases in intensity on cooling below , and there is tentative evidence that the peak persists at temperatures above in agreement with the observations of Friemel et al.Friemel et al. (2012) The existence of resonance peaks in the iron pnictides has been explained in terms of nesting features in the Fermi surface enhanced by electronic correlations and superconducting coherence effects.Maier and Scalapino (2008) Within this framework, and with a realistic band structure model, Friemel et al.Friemel et al. (2012) were able to reproduce the position of the magnetic resonance in RbFeSe assuming a superconducting gap. Further theoretical work is needed to understand the magnetic resonance in detail, but our results at least establish that the resonance is present in another FeSe superconductor. This suggests that the resonance could be a characteristic feature of superconductivity in this family.

Finally, we make some remarks about the absolute intensities of the magnetic features. The scattering intensities in our measurements and those of Ref. Wang et al., 2012 are calibrated and given in absolute units of cross section. This allows us to compare the strengths of the magnetic signal from the sample of RbFeSe used in Ref. Wang et al., 2012 with those from the sample of CsFeSe used here. The amplitude of the spin-wave peak at 14 meV for CsFeSe (Fig. 4 above) is about 55 mb sr meV f.u., which is similar to the amplitude of 40 mb sr meV f.u. at 10 meV for RbFeSe (Fig. 5(b) of Ref. Wang et al., 2012). However, the amplitude of the resonance peak in CsFeSe, about 2.5 mb sr meV f.u., is about five times larger than that reported for RbFeSe — compare Fig. 5(b) above with Fig. 6 of Ref. Wang et al., 2012. One should of course be cautious when comparing peak amplitudes. Nevertheless, it does appear that the resonance peak is more prominent in CsFeSe than in RbFeSe. This could indicate that the crystal used here has a higher volume fraction of superconducting phase than that used in Ref. Wang et al., 2012.

It is also interesting to compare the strength of the resonance peak with that in other Fe-based superconductors. Results for have been reported previously for BaFeCoAs and BaFeNiAs.Lester et al. (2010); Liu et al. (2012) In both cases the resonance peak amplitudes (i.e. the increase on cooling below ) are 3–4  eV f.u. and the energy-integrated signal  f.u.. From the inset to Fig. 5(a) the corresponding values for CsFeSe are ()  eV f.u. and ()  f.u., remarkably similar to the values for the two arsenide superconductors. Since the latter were near optimal doping they are expected to be bulk superconductors with close to 100% superconducting volume fraction. It is tempting, therefore, to conclude that the resonance peak and hence superconductivity in CsFeSe is associated with most or all of the sample volume. However, there are many other factors that could control the size of the resonance peak, e.g. the degree of nesting, strength of magnetic correlations, etc. and these may differ from one material to another. We simply note that the resonance peak in CsFeSe is similar in strength to that in other Fe-based superconductors.

V Conclusions

The magnetic spectrum of CsFeSe studied in this work comprises two components: a low energy resonance-like excitation with wave vector which responds to superconductivity and is similar in strength to the corresponding feature found in other Fe-based superconductors, and spin-wave excitations of the block antiferromagnetic order with wave vector which do not respond to superconductivity to within the experimental sensitivity. The spin-wave component closely resembles that of non-superconducting (insulating) RbFeSe. Together with other recent studies, these results are consistent with a microstructure composed of spatially separate superconducting and non-superconducting domains, with the Fe vacancy superstructure and block antiferromagnetism confined to the non-superconducting phase. It remains a materials challenge to try to maximize the volume fraction of the superconducting phase.

This work was supported by the U.K. Engineering & Physical Sciences Research Council and the Science & Technology Facilities Council. Work in Switzerland was supported by the Swiss National Science Foundation and its NCCR programme MaNEP. We thank M. Kenzelmann, A. Podlesnyak, L.-P. Regnault and F. Bourdarot for help with the experimental work.


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