Magnetic ground state of FeSe

Abstract

Elucidating the nature of the magnetism of a high-temperature superconductor is crucial for establishing its pairing mechanism. The parent compounds of the cuprate and iron-pnictide superconductors exhibit Néel and stripe magnetic order, respectively. However, FeSe, the structurally simplest iron-based superconductor, shows nematic order (T_s =90 K), but not magnetic order in the parent phase, and its magnetic ground state is intensely debated. Here we report inelastic neutron-scattering experiments that reveal both stripe and Néel spin fluctuations over a wide energy range at 110 K. On entering the nematic phase, a substantial amount of spectral weight is transferred from the Néel to the stripe spin fluctuations. Moreover, the total fluctuating magnetic moment of FeSe is ∼60% larger than that in the iron pnictide BaFe₂ As₂ . Our results suggest that FeSe is a novel S=1 nematic quantum-disordered paramagnet interpolating between the Néel and stripe magnetic instabilities.

ARTICLE

Received 27 Jan 2016 | Accepted 8 Jun 2016 | Published 19 Jul 2016

Qisi Wang1,*, Yao Shen1,*, Bingying Pan1,*, Xiaowen Zhang1, K. Ikeuchi2, K. Iida2, A.D. Christianson3,4, H.C. Walker5, D.T. Adroja5, M. Abdel-Haez6,7, Xiaojia Chen6, D.A. Chareev8,9, A.N. Vasiliev9,10,11& Jun Zhao1,12

Elucidating the nature of the magnetism of a high-temperature superconductor is crucial for establishing its pairing mechanism. The parent compounds of the cuprate and iron-pnictide superconductors exhibit Nel and stripe magnetic order, respectively. However, FeSe, the structurally simplest iron-based superconductor, shows nematic order (Ts 90 K), but not

magnetic order in the parent phase, and its magnetic ground state is intensely debated. Here we report inelastic neutron-scattering experiments that reveal both stripe and Nel spin uctuations over a wide energy range at 110 K. On entering the nematic phase, a substantial amount of spectral weight is transferred from the Nel to the stripe spin uctuations. Moreover, the total uctuating magnetic moment of FeSe is B60% larger than that in the iron pnictide BaFe2As2. Our results suggest that FeSe is a novel S 1 nematic

quantum-disordered paramagnet interpolating between the Nel and stripe magnetic instabilities.

1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China. 2 Research Center for Neutron Science and Technology, Comprehensive Research Organization for Science and Society, Tokai, Ibaraki 319-1106, Japan. 3 Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA. 4 Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA.

5 ISIS Facility, Rutherford Appleton Laboratory, STFC, Chilton, Didcot OX11 0QX, United Kingdom. 6 Center for High Pressure Science and Technology Advanced Research, Shanghai, 201203, China. 7 Faculty of Science, Department of Physics, Fayoum University, 63514 Fayoum, Egypt. 8 Institute of Experimental Mineralogy, Russian Academy of Sciences, 142432 Chernogolovka, Russia. 9 Institute of Physics and Technology, Ural Federal University, 620002 Ekaterinburg, Russia. 10 Low Temperature Physics and Superconductivity Department, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia. 11 National University of Science and Technology MISiS, Moscow 119049, Russia. 12 Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to J.Z.(email: mailto:[email protected]

Web End [email protected] ).

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Magnetic ground state of FeSe

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12182

Recently, FeSe has attracted considerable interest because of its atypical magnetism16 and fascinating superconducting properties710. Although the superconducting transition

temperature Tc of bulk FeSe (TcE8 K) is low, it increases drastically under pressure (TcE37 K; ref. 7), by carrier doping (TcE4048 K; refs 8,9), or in the mono layer limit (TcB65-109 K, ref. 10). The unique superconducting properties of FeSe are presumably related to its magnetism, which has also been shown to be uncommon. FeSe displays nematic, but not stripe magnetic order1,11 that is unexpected because nematic order has been argued to be the consequence of stripe magnetic order, and both break the C4 lattice symmetry11. In iron pnictides, the stripe magnetic order invariably occurs at or immediately below the

nematic-(tetragonal-to-orthorhombic) ordering temperature11. Although previous works have shown that the nematic order could be driven by spin uctuations without the requirement of magnetic order24,12, the microscopic origin of the absence of the long-range stripe magnetic order in FeSe remains elusive.

Theoretical studies have suggested that the stripe magnetic order in FeSe is absent due to the development of other competing instabilities26. Several ground states have been proposed, including Nel order2, staggered dimer/trimers/ tetramers magnetic order3, pair-checkerboard order5, spin antiferroquadrupolar order4 and charge current-density wave order6. In experimental studies, neutron-scattering measurements showed substantial low-energy stripe spin uctuations in single

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Figure 1 | Momentum dependence of the spin uctuations in FeSe at 4 and 110 K. (a) Schematic representation of the stripe and Nel spin uctuations in the (H, K) plane. (bj) Constant-energy images acquired at 110 K at indicated energies. (ks) Constant-energy images obtained at 4 K at the same intensity scale as those acquired at 110 K. The measurements in (bd,km) and (ej,ns) were carried out on ARCS with the incident neutron energy of 79and 294 meV, respectively. The sample has two equally populated orthogonal twin domains in the ab plane at 4 K and the intensities near (1, 0) and (0, 1) are roughly the same. Symmetry equivalent data were pooled to enhance statistical accuracy. The |Q|-dependent background is subtracted for the data (bd,km) below the aluminium phonon cutoff energy of B 40 meV. Above 40 meV, raw data are presented (ej,ns). The colour bars indicate intensity in unit of mbar sr 1 meV 1 f.u. 1. The dashed ellipses and circles mark the stripe and Nel wavevectors, respectively.

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crystal12 and powder samples13. However, because of the limitations of the q-space information that can be obtained for powder measurements and the relatively narrow energy range probed previously, the precise nature of the magnetic ground state remains undetermined; this elucidation requires measurements of the momentum structure of the spin-uctuation spectrum from low energy to the zone boundary over the entire Brillouin zone.

In this paper, we used inelastic neutron scattering to map out the spin-uctuation spectra over the entire Brillouin zone in single-crystalline FeSe (Methods). Our data reveal the coexistence of the stripe and Nel spin uctuations, both of which are coupled with nematicity. In addition, although the spin-uctuation bandwidth is lower, the total uctuating magnetic moment ( m2

h i 5.19 m2B/Fe) of FeSe is B60% larger than that in the iron

pnictide BaFe2As2 (ref. 14). These ndings suggest that FeSe is an S 1 nematic quantum-disordered paramagnet, interpolating

between the Nel and stripe magnetic instabilities2.

ResultsMomentum and energy dependence of spin uctuations. Figure 1 shows the constant-energy images of spin uctuations in the (H, K) plane. Here, in the high-temperature tetragonal phase (110 K), the spin response is strongest at Q (1, 0)

(marked by dashed ellipse) at 15 meV (Fig. 1b), which is consistent with previous low-energy measurements12,13. With an increase in energy (Fig. 1cj), the spin uctuations show anisotropic dispersion and counter-propagate mainly along the K direction. This is analogous to the stripe spin uctuations detected in other iron-based superconductors11,14,15. Most notably, in addition to the stripe spin uctuations, comparatively weaker, but clear scattering appears near (1, 1) (Fig. 1b, dashed circle), which implies the presence of spin uctuations associated with the Nel magnetic instability (Methods); different from the anisotropic stripe spin uctuations, the Nel spin uctuations are nearly isotropic in the transverse and longitudinal directions (Fig. 1bg). With an increase in the energy up to B150 meV, the Nel and stripe spin uctuations overlap and cover a broad area centred at (1, 1) (Fig. 1j). On cooling to within the nematic phase (T 4 K), the

Nel spin-uctuation signal weakens considerably and is almost

undetectable o35 meV (Fig. 1k,l). On the other hand, the momentum structure of the stripe spin uctuation is essentially unchanged above and below Ts (Fig. 1ks).

To further elucidate the spin uctuations in EQ space, we projected the spin uctuations along the K direction near (1, 0) and (1, 1) (Fig. 2). Because the incident neutron beam was parallel to the c axis, the energy transfer was coupled with L. No L modulations were observed from the scattering near (1, 0, L) and (1, 1, L), which indicates a two-dimensional nature of the magnetism. As shown in Fig. 2a, the stripe spin uctuations stem from (1, 0), split into two branches at B35 meV and extend up to above B150 meV at 110 K. The steeply dispersive Nel spin uctuations are also visible (green arrowheads). As the temperature is lowered to 4 K, the Nel spin uctuation exhibits a B30 meV gap, while the stripe spin uctuations o70 meV are clearly enhanced (Fig. 2b).

To quantify the dispersions and intensities of the stripe and Nel spin uctuations, we made constant-energy cuts at distinct energies (Fig. 3). As Fig. 3di show, at T 110 K, the single peak centred at

(1, 0) at 15 meV evolves into a pair of peaks along the K direction at EZ35 meV. By contrast, the peak position of the Nel spin uctuation (see green arrowheads) shows little change; it only broadens gradually in wavevector with increasing energy. The Nel spin uctuation is more clearly visible along the transverse direction (Fig. 3mr) because of the comparatively weaker inuence of the stripe spin uctuations. Here, double peaks formed due to the dispersion are not seen o68 meV, because the Nel spin uctuations are commensurate and steeply dispersive (Fig. 3mr). At higher energies, the Nel and stripe spin-uctuation spectra merge with each other, and their dispersions cannot be determined unambiguously (Fig. 3ac,jl). The Nel spin uctuation becomes featureless at low energies (Fig. 3i,r) at 4 K, which agrees with the results shown in the constant-energy and EQ images (Figs 1k and 2b). We attempted to t both types of spectra concurrently using a linear spin-wave theory for the two-neighbour (J1(a/b)J2) or three-

neighbour (J1(a/b)J2J3) Heisenberg model, where J1(a/b), J2 and J3 are nearest neighbour (in the a/b direction), next-nearest neighbour and next next-nearest neighbour exchange coupling constants, respectively; but this was unsuccessful mainly because this theory cannot account for the observed strong low-energy spin excitations at both (1, 0) and (1, 1).

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Figure 2 | Dispersions of the stripe and Nel spin uctuations in FeSe at 4 and 110 K. Background-subtracted EK slice of the spin uctuations at various incident energies: (a) T 110 K; (b) T 4 K. The data at EZ40 and Er40 meV were collected on ARCS by using incident energy of 294 and 79 meV,

respectively. The isotropic Fe2 magnetic form factor is corrected for both sets of the data. The spectral weight transfer from the Nel (1, 1) to stripe (1, 0) wavevector below B70 meV on cooling to 4 K can be clearly seen. The open circles are dispersions obtained from the constant-energy cuts o68 meV in Fig. 3. The colour bar indicates intensity in unit of mbar sr 1 meV 1 f.u. 1. The vertical bars indicate the energy integration range. The horizontal bars at 15 meV indicate the full-width at half-maximum of the Gaussian ttings in Fig. 3i. The horizontal bars at other energies are the errors derived by least-square ttings. The dashed lines are a guide to the eye.

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E=15010 meV

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Figure 3 | Constant-energy cuts of the stripe and Nel spin uctuations in FeSe at 4 and 110 K. (ai) Constant-energy cuts through the stripe and Nel magnetic wavevectors along the K direction at 4 and 110 K. (jr) Constant-energy cuts through the Nel magnetic wavevector Q (1, 1) along the

transverse direction. The scan directions are marked by the arrows in the insets. The peak positions (dispersions) are determined by tting with Gaussian proles convoluted with the instrumental resolution, with the Fe2 magnetic form factor corrected. The tted dispersions are shown in Fig. 2. The error bars indicate 1 s.d.

Momentum integrated local susceptibility above and below Ts.

More insight into the nature of the underlying magnetic ground state and its interaction with the nematicity could be acquired by calculating in absolute units the energy dependence of the momentum integrated local susceptibility w00(o) above and below

Ts; as Fig. 4a,b show, at T 110 K, the Nel spin-uctuation

spectral weight is roughly 26% of that of the stripe spin uctuation o52 meV, where the two signals are well separated in q-space. Upon cooling to T 4 K, the spectral weight loss for the

Nel spin uctuations is approximately recovered by the enhanced stripe spin uctuations (red shaded areas), and thus the total local susceptibility w00(o) does not show a marked change across Ts (Fig. 4c). Moreover, the detailed temperature dependence of the stripe and Nel spin uctuations show that the spectral weight transfer is clearly coupled with the development of the nematic phase (Fig. 4d). At both 4 and 110 K, the total w00(o) exhibits a high maximum at B105 meV and extends up to 220 meV (Figs 2a,b and 4c). This bandwidth is considerably lower than that (B340 meV) of the stripe ordered BaFe2As2 (ref. 14), which is very likely due to the competition between the Nel and stripe magnetic instabilities. Clearly, this type of competition

also prevents the long-range magnetic order in FeSe. By integrating the spectral weight from low energy to the zone boundary, we determined that the total uctuating moment at 4 and 110 K are m2

h i gmB

5.190.32 and 5.120.27

m2B/Fe, respectively, which are larger than those in the superconducting BaFe1.9Ni0.1As2 ( m2h i 3.2 m2B/Fe) and stripe-

ordered BaFe2As2 ( m2

h i 3.17 m2B/Fe) (ref. 14). Accordingly, this

yields an effective spin of SE0.74 in FeSe, which likely corresponds to an S 1 ground state in the presence of

itinerant electrons.

DiscussionThe coexistence of the Nel and stripe spin uctuations is unexpected because FeSe contains only one type of magnetic ions. This differs from the Mn-doped nonsuperconducting iron-pnictide compound BaFe2 xMnxAs2, where the Nel magnetic

correlation is induced by the local moments of Mn, while the stripe magnetic correlation is induced by Fe, given that pure BaMn2As2 is a local-moment Nel type antiferromagnet16.

Although density functional theory and dynamical mean-eld

2S S 1

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a b d

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Figure 4 | Energy dependence of the local susceptibility v00(x) for FeSe at 4 and 110 K. (ac) Energy dependence of w00(o), at 4 and 110 K, calculated for (a) the Nel spin uctuations, (b) the stripe spin uctuations, and (c) the sum of the stripe and Nel spin uctuations. A resonance mode is clearly observed at B4 meV and 4 K, whose intensity is consistent with the previous low-energy measurements normalized with acoustic phonons12.

(d) Temperature dependence of the intensities of the stripe and Nel spin uctuations. The data in ac were collected on ARCS (incident energy Ei 294,

79, 40 meV) and 4SEASONS (Ei 21, 13.6 meV). The data in d were collected on MERLIN (Ei 123.4 meV). The horizontal and vertical bars indicate the

energy integration range, and the statistical errors of 1 s.d., respectively. The solid and dashed lines are a guide to the eye.

theory failed to reproduce the observed band structure of FeSe (refs 17,18), a random-phase approximation calculation with an engineered tight-binding band structure19 predicted the spin uctuations near (1, 0) and (1, q). However, in this phenomenological model19, the (1, q) spin uctuation is incommensurate and gapless below Ts, which is inconsistent with our data. The relatively small spin-uctuation bandwidth and large uctuating moment together with the low-carrier density17,18 indicate that the magnetic moments in FeSe are more localized than in iron pnictides.

In the more localized case, we can exclude the previously proposed competing staggered dimer/trimers/tetramers magnetic order3 and pair-checkerboard order5. Here, the competition between the Nel and stripe magnetic instabilities could be instead understood within the framework of a frustrated J1J2 model. In this model, for an S 1 system, the Nel order is stable

for J2/J1t0.525, whereas the stripe order is the ground state for0.555tJ2/J1 (refs 20,21). It was predicted that FeSe would be an S 1 nematic quantum paramagnet in the intermediate coupling

region (0.525tJ2/J1t0.555), which is characterized by gapped stripe and Nel spin uctuations2,21. This agrees with our data that the majority of the spectral weight is concentrated at relatively high energies (B100 meV) even in the presence of itinerant electrons (Figs 2a,b and 4c). Furthermore, in this

scenario, the nematic order is viewed as a vestigial order that is retained when the static stripe order is suppressed by quantum uctuations2. The nding that the stripe spin uctuation carries considerably more spectral weight than the Nel spin uctuation suggests that the system is indeed closer to stripe rather than to Nel order. On this basis, the temperature evolution of the spin uctuations that we observed can be explained. As the stripe magnetic order breaks the C4 lattice symmetry, while the Nel order preserves it, the orthorhombic-/nematic-phase transition might partially lift the magnetic frustration and drive the system towards the stripe-ordered phase. Thus, the stripe spin uctuations are enhanced, while the Nel spin uctuations are suppressed and gapped in the nematic phase. These considerations lead to a natural understanding of the paramagnetic nematic phase in FeSe.

We now discuss the evolution of the magnetism, nematicity and superconductivity in FeSe, and its derivatives. Since the Nel spin uctuation is gapped in the nematic phase, it is unlikely responsible for the electron pairing in bulk FeSe at ambient pressure. However, the competition between the Nel and stripe magnetic instabilities across Ts suggests that the magnetic ground state and superconductivity could be highly tunable. Indeed, it has been shown that high pressure not only enhances superconductivity, but also induces static magnetic order in FeSe

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(refs 22,23). This is surprising as superconductivity always competes with the static magnetic order in iron pnictides. Further neutron diffraction measurements under pressure are required to clarify the nature of this magnetic order. In addition, the proximity of the Nel magnetic instability of FeSe might also have implications for our understanding of the magnetism in the K dosed9,24, molecule intercalated25 and mono layer10,26 FeSe, because in these heavily electron-doped compounds, the nematic order and the hole pockets are absent, and the electron pockets at two adjacent zone edges are connected by the Nel wavevector Q (1, 1). Interestingly, this would be in analogy with the

cuprate superconductors in terms of the magnetism and Fermi surface topology27. To further elucidate the role of the Nel spin uctuations in iron-based superconductivity, a detailed study of the pressure-/electron-doping dependence of the spin correlations in FeSe would be desirable.

To conclude, we have reported the observation of the Nel spin uctuations over a wide energy range in an iron-based super-conductor. We show that the absence of the long-range magnetic order in FeSe is due to the competition between the Nel and stripe magnetic instabilities. This differs from the parent compounds of the cuprate and iron pnictide high-temperature superconductors, where only one type of magnetic order is observed. Our ndings agree with a theoretical prediction that FeSe is a novel S 1

nematic quantum-disordered paramagnet interpolating between the Nel and stripe magnetic instabilities2, which indicates a connection between the magnetism of the cuprate- and iron-based superconductors. The experimental determination of the nematic magnetic ground state of FeSe will be extremely valuable in identifying the microscopic mechanism of superconductivity in FeSe-based materials810,2426.

Methods

Sample growth and characterizations. Our FeSe single crystals were grown under a permanent gradient of temperature (B400330 C) in the KClAlCl3 ux28. The single-crystal X-ray and neutron diffraction renements on our samples indicated a stoichiometric chemical composition to within the error bars, and no interstitial atoms or impurity phases were observed (Supplementary Note 1; Supplementary Figs 13; Supplementary Table 1). The specic heat, magnetic susceptibility and resistivity measurements performed on randomly selected FeSe single crystals further demonstrate that our sample is a bulk superconductor without detectable impurities. (Supplementary Note 1; Supplementary Figs 4 and 5).

Neutron-scattering experiments. Our inelastic neutron-scattering measurements were carried out on the ARCS time-of-ight chopper spectrometer at the Spallation Neutron Source of Oak Ridge National Laboratory, USA, 4SEASONS chopper spectrometer at the Japan Proton Accelerator Research Complex and MERLIN chopper spectrometer at the Rutherford Appleton Laboratory, Didcot, UK. The large detector arrays on these instruments allowed us to measure spin excitations over a wide range of energy and momentum. The |Q|-dependent background is subtracted for the data below the aluminium phonon cutoff energy of B40 meV (Supplementary Note 2; Supplementary Fig. 7). To facilitate comparison with theory and previous measurements, our data were normalized into absolute units by using the elastic incoherent scattering of a standard vanadium sample. The absolute intensity of the resonance mode is consistent with previous low-energy data12 normalized with acoustic phonons (Supplementary Fig. 6). The incident neutron beam was aligned parallel to the c axis. The wavevector Q at (qx, qy, qz) is dened as (H, K, L) (qxa/2p, qyb/2p, qzc/2p) in the reciprocal lattice units in the

orthorhombic unit cell. In this unit cell, the magnetic wavevectors associated with the stripe and Nel magnetic order are Q (1, 0) and Q (1, 1), which correspond

to the ordering wavevectors of the parent compounds of the iron pnictides and the cuprates, respectively.

Data availability. All relevant data that support the ndings of this study are available from the corresponding author on request.

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Acknowledgements

We gratefully acknowledge H. Cao for the neutron diffraction experimental support, andQ. Si, R. Yu, A. Kreisel, P. Hirschfeld, B. M. Andersen and R. Valenti for discussions. This work was supported by the Ministry of Science and Technology of China (973 project: 2015CB921302), the National Natural Science Foundation of China (No. 11374059) and the Shanghai Pujiang Scholar Program (No. 13PJ1401100). Research at the Spallation Neutron Source of Oak Ridge National Laboratory was sponsored by the Scientic User Facilities Division, Ofce of Basic Energy Sciences, US Department of Energy. A.N.V. was supported in part by the Ministry of Education and Science of the Russian Federation in the framework of the Increase Competitiveness Program of NUST MISiS (No. 2-2014-036). D.A.C. and A.N.V. also acknowledge the support of the Russian Foundation for Basic Research through grants 13-02-00174, 14-02-92002, 14-02-92693 and Act 211 Government of the Russian Federation (No. 02.A03.21.0006).

Author contributions

J.Z. conceived the research. Q.W., X.Z., D.A.C. and A.N.V. synthesized the sample. Q.W., Y.S., B.P., M.A. and X.C. characterized the sample. Q.W., Y.S. and B.P. conducted the neutron experiments with experimental assistance from K. Ikeuchi, K. Iida, A.D.C.,

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How to cite this article: Wang, Q. et al. Magnetic ground state of FeSe. Nat. Commun. 7:12182 doi: 10.1038/ncomms12182 (2016).

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D.T.A. and H.C.W. J.Z., Q.W., Y.S. and B.P. analysed the data and wrote the paper. All authors provided comments for the paper.

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