Soft striped magnetic fluctuations competing with superconductivity in Fe_{1+x}Te
C. Stock, E. E. Rodriguez, O. Sobolev, J. A. Rodriguez-Rivera, R. A. Ewings, J. W. Taylor, A. D. Christianson, M. A. Green
aa r X i v : . [ c ond - m a t . s t r- e l ] S e p Soft striped magnetic fluctuations competing with superconductivity in Fe x Te C. Stock, E. E. Rodriguez, O. Sobolev, J. A. Rodriguez-Rivera,
R.A. Ewings, J.W. Taylor, A. D. Christianson, and M. A. Green School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK Department of Chemistry of Biochemistry, University of Maryland, College Park, MD, 20742, U.S.A. Forschungs-Neutronenquelle Heinz Maier-Leibnitz, FRM2 Garching, 85747, Germany NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, MD 20889 Department of Materials Science, University of Maryland, College Park, MD 20742 ISIS Facility, Rutherford Appleton Laboratory, Didcot, OX11 0QX, U.K. Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA School of Physical Sciences, University of Kent, Canterbury, CT2 7NH, UK (Dated: October 13, 2018)Neutron spectroscopy is used to investigate the magnetic fluctuations in Fe x Te - a parentcompound of chalcogenide superconductors. Incommensurate “stripe-like” excitations soften withincreased interstitial iron concentration. The energy crossover from incommensurate to stripy fluc-tuations defines an apparent hour-glass dispersion. Application of sum rules of neutron scatteringfind that the integrated intensity is inconsistent with an S =1 Fe ground state and significantlyless than S =2 predicted from weak crystal field arguments pointing towards the Fe being in asuperposition of orbital states. The results suggest that a highly anisotropic order competes withsuperconductivity in chalcogenide systems. Pnictide and chalcogenide superconductors have al-tered the view of what provides the basis for high temper-ature superconductivity. While the cuprate superconduc-tors universally derive from Mott insulators which can, atleast qualitatively, be understood in terms of a single elec-tronic band, the parent phase of iron based superconduc-tors has been less clear: Fe-based parent phases are eitherpoorly metallic or semimetallic resulting in a debate overwhether a localized or itinerant/spin density wave pictureis more appropriate. [1, 2] Towards this goal, it is im-portant to understand the magnetic excitation spectrumin starting materials as superconducting variants consistof fluctuating versions of this ground state. [3] Here westudy Fe x Te which is arguably the structurally sim-plest of the iron superconductors based upon single layersof tetrahedrally coordinated Fe ions. [4, 5] While theiron superconductors have been shown to display both lo-calized [6, 7] and itinerant properties [8, 9], Fe x Te hostsone of the most localized responses of all iron based su-perconductors evidenced by large ordered magnetic mo-ments and calculated heavy band masses. [10]In this study, we combine neutron scattering data fromspectrometers with overlapping dynamic ranges on twosamples of Fe x Te to understand the magnetic fluctua-tions. We report a one dimensional incommensurate ex-citation that softens with increased charge doping withinterstitial iron and hence competes with unconventionalchalcogenide superconductivity. We apply sum rulesof neutron scattering to evaluate the spin and orbitalground state of the iron cations. The results representa dynamical signature of a highly anisotropic striped or-der which competes with superconductivity in the chalco-genides.Superconductivity in Fe x Te − y Ch y (where Ch is a chalcogenide ion) has been most commonly achievedthrough anion substitution on the Te site y with eithersulfur or selenium. [11, 12] However, the cation concen-tration (interstitial iron x ) in Fe x Te − y Ch y is directlycorrelated with the anion concentration ( y ) and chemicaltechniques have been developed to independently tune x and y . [13] Several studies have found that changing theconcentration of interstitial iron has analogous effects toanion doping for a fixed selenium concentration. [14–16]The structural and magnetic properties of Fe x Te as afunction of x have been reported by several groups givinggenerally consistent results. [17–21] A neutron diffractionstudy found a phase diagram with two distinct phases asa function of interstitial iron. [22] For low concentrationsof x < x > x ∼
11% whereshort-range incommensurate spin-density wave order isobserved. Resistivity measurements found the collinear x <
11% values to be metallic at low temperatures whilelarger x >
11% are “semi” (or poorly) metallic and scat-tering from incommensurate spin fluctuations was impli-cated as the origin of the enhanced resistivity. [23] There-fore, based upon the fixed selenium studies [15, 16] andthese magnetic and structural results, metallicity and su-perconductivity are favored for smaller values of intersti-tial iron.Doping charge through interstitial iron therefore re-mains an independent means of controlling the electri-cal properties of the chalcogenides. We present neutroninelastic data taken from steady state reactor sources(MACS, PUMA, and HB1) and time of flight instruments −1 −0.5 0 0.5 12468−1 −0.5 0 0.5 12468 (H,0,−3/2) (r.l.u.) E ( m e V ) −1−0.500.51 −1−0.500.51 −1−0.500.51 ( , K ) (r . l . u . ) −1−0.500.51 (H,0) (r.l.u.)
12 130.20.4 0.40.80.510.40.8 Fe TeFe
Tee) 70 ± ± ± ± ± ± FIG. 1. Neutron inelastic scattering comparing commensu-rate Fe . Te with incommensurate Fe . Te. a − b )Constant-Q slices of the low-energy data taken on MACS(E f =2.6 meV). c − h ) Constant energy slices from MAPStaken with incident energies of 75, 150, and 350 meV. (MAPS) based at pulsed spallation sources. Further ex-perimental and sample details are given in the supple-mentary information (see also Ref. 24) and also detailson phonon contamination and how these were disentan-gled (see also Ref. 25).We first describe the dispersion of the spin excitationsin momentum. Representative constant energy and mo-mentum slices are displayed in Fig. 1 for both interstitialiron concentrations. Panels a − b ) show high energy res-olution constant- Q slices illustrating the gapped natureof the excitations for collinearly ordered x =0.057(7) andthe gapless low-energy incommensurate fluctuations for x =0.141(5) in the spiral magnetic phase. [26] Higher en-ergy excitations are displayed in panels c − h ) through a I n t en s i t y ( A r b . U n i t s ) −1 −0.5 0 0.5 101 (H,0) (r.l.u.) −1 −0.5 0 0.5 10100200 Fe Te (H,0,1.5) (r.l.u.) Fe Te −1 −0.5 0 0.5 1050100 (H,0,1.5) (r.l.u.) −1 −0.5 0 0.5 100.511.5 (H,0) (r.l.u.) b) 34 ± ± ± FIG. 2. Cuts along the (H, 0) direction for commensurate x =0.057(7) ( a − c ) and incommensurate x =0.141(5) ( d − f )crystals. The data is taken from thermal triple-axis and spal-lation source data. Open circles are symmetrized data anddisplayed for visual comparison. series of constant energy slices at 35, 70 and 113 meV.The data do not show clean circular spin-wave cones, butrather excitations broad in momentum and dispersing tothe zone boundary.Constant energy cuts for both commensurate and in-commensurate crystals are presented in Fig. 2. The solidlines are fits to a gaussian lineshape multiplied by theisotropic Fe form factor squared [27] from which a peakposition and integrated intensity were derived. The opensymbols are symmetrized data around ~Q =0. The verticaldashed lines emphasize the fact that as the energy trans-fer is increased, the peak position in momentum dispersesinward and then outward at higher energies.Based upon fits (Fig. 2) we construct a dispersioncurve (Fig. 3) along the [1 ,
0] direction comparing thecommensurate and incommensurate crystals. For thecommensurate x =0.057(7) sample, the excitations aregapped (Fig. 1) and then disperse inwards to a wave vec-tor H ≤ ∼
100 meV. Interestingly, the excitationsare nearly vertical as they extend to higher energies in-dicative of strong dampening at the zone boundary. This −0.6 −0.4 −0.2 0 0.2 0.4 0.6010203040 (q,0) (r.l.u.) E ( m e V ) −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1020406080100120140160 (q, 0) (r.l.u.) E ( m e V ) Fe Te, T=5 K
MAPS, E i =300 meVMAPS, E i =150 meVMAPS, E i =75 meVPUMA/HB1, E f =13.5 meVMACS, E f =3.6 meV a) Fe Te b) Fe Te c) x=0.057(7) d) x=0.141(5) FIG. 3. The dispersion of the magnetic excitations in Fe x Tewith x = 0 . a ) and x = 0 . c ) and d ) show the low-energy portion of themagnetic dispersion. The data is a compilation of triple-axisand spallation data. The inward dispersion described in thetext is highlighted by the arrows. marks a clear distinction from predictions based upon alocalized Heisenberg exchange. [28] A strong zone bound-ary dampening has been reported in superconductingiron based variants [29], in cuprates and associated withthe onset of the electronic pseudogap [30], and predictedto exist in Cr metal. [31] Our results however mark a cleardifference between parent cuprates (and even cupratesclose to the charged doped boundary of superconductiv-ity) [32, 33] and iron based systems as we do not seelocalized spin-waves which can be interpreted in terms ofa localized Heisenberg model on a Mott insulating groundstate.The fluctuations in incommensurate x =0.141(5) aredifferent. The low-energy fluctuations are gapless anddisperse inwards until ∼
20 meV and then disperse out-wards until the highest energy transfers studied. How-ever, in contrast to the commensurate x =0.057(7) mate-rial the excitations do not reach the zone boundary butdisperse up to the highest energies studied. There aretherefore two effects of doping with interstitial iron - first,to decrease or soften the inward dispersing minimum in the magnetic excitations, and second, to increase the topof the excitation band. A common feature from both in-terstitial iron concentrations is the inward (or nearly ver-tical) dispersion at low energies. This dispersion neverreaches the commensurate Q =0 positions, but dispersestowards an incommensurate position that softens in en-ergy with increased interstitial iron concentration.The energy inward dispersion in Fig. 3 also representsa cross over from two-dimensional excitations to stronglyone-dimensional where the momentum dependence is welldefined in H, however broad along both L and K. Thisis illustrated in Fig. 1 f that show the magnetic fluctu-ations form stripes at high energy. To characterize this,we have fit the K dependence at each energy transferto I ( K ) ∝ (1 + 2 α cos( ~Q · ~b )), where α represents thestrength of correlations between stripes aligned along a .The results are shown in Fig. 4 c − d ) for both interstitialiron concentrations. The parameter α falls, within error,to zero at energies above the inward dispersion indicatingone dimensional stripy fluctuations - a feature absent insuperconducting chalcogenides [29] and pnictides [34–36].The highly one-dimensional nature of the fluctuations in-dicate that a highly anisotropic order is proximate inthe chalcogenide superconductors. The anisotropy ex-ceeds that observed in superconducting LaFeAsO [37]and CaFe As in the paramagnetic phase [38]. While thethe results may indicate stripe-like fluctuations, as dis-cussed in the context of the cuprates, [39, 40] it may alsoreflect an underlying anisotropy associated with the or-bital ground state. It is difficult to interpret the results interms of anisotropic localized exchange (as recently donefor the low energy fluctuations K . Fe . Se [41] andSrCo As [42]) given the lack of spin-wave cones and theintegrated intensity discussed below. Highly anisotropicorders such as quadruopolar order, discussed in termsof triangular S =1 magnets originating from biquadraticexchange (term “spin nematic”), [43, 44] or “nematic”order connected with the underlying Fermi surface topol-ogy may be the origin. [45–48] We note that all of theseproposals predict a director where, in analogy to liquidcrystals, there is some form of orientational order.To understand the underlying ground state, we nowdiscuss the integrated intensites. The ~q integrated inten-sity for the commensurate and incommensurate samplesare shown in Fig. 4. The calibration method is dis-cussed in the supplementary information (see also Ref.49–53). The integrated intensity shows a peak near wherethe momentum dispersion (Fig. 3) shows a minimum inwavevector reflecting a van-Hove type singularity wherethe group velocity of the magnetic mode reaches zero.For both interstitial concentrations at large energy trans-fers above the peak in the local susceptibility, the inte-grated intensity is nearly constant. The average value atthese energy transfers is similar to the normalized val-ues reported for pnictide systems such as CaFe As [35]indicating a strong similarity in the physics between the ( / π ) ∫ d q [ n ( E ) + ] χ ’’ ( q , E ) ( µ B / e V ) α a) Fe Te c) x=0.141(5)d) x=0.057(7)
MAPS, E i =300 meVMAPS, E i =150 meVMAPS, E i =75 meVPUMA/HB1, E f =13.5 meV b) Fe Te FIG. 4. Momentum integrated intensity in absolute units as afunction of energy transfer for a ) incommensurate x =0.141(5)and b ) commensurate x =0.057(7) samples. The “stripe” cor-relation parameter α is plotted for both concentrations in c − d ). pnictides and the chalcogenides.The combined inward dispersion and peak in the lo-cal susceptibility indicate an hour-glass like dispersion.While similar to La − x Sr x CuO , the momentum depen-dence in Fe x Te differs to YBa Cu O x where the twobranches meet at the commensurate ( π , π ) point. [54–57] Similar structures have also been observed in morelocalized La / Sr / CoO [58] and single-layered man-ganites [59]. Interestingly, the hour-glass dispersion isabsent in the superconducting state Fe x Te . Se . . [60]An analogous “U” type dispersion was observed to be sta-bilized by Ni/Cu doping [61] which suppressed supercon-ductivity and incommensurate order has been observednear the superconducting phase in BaFe − x Ni x As andFe x Se y Te − y . [62, 63] These results indicate that thesoft incommensurate mode is detrimental to supercon-ductivity and, given the presence in both localized andmetallic magnets, that the hour-glass dispersion is notdirectly tied to an electronic origin. Our results wouldpoint towards the hour-glass point marking a cross overfrom two dimensional to one dimensional fluctuations asdiscussed above.Based on the available magnetic and crystal field data,it is not clear how to understand the single-ion proper- ties of the tetrahedrally coordinated Fe ion in Fe x Te.Hence the neutron scattering cross section, which is typ-ically fixed by the value of S , is uncertain. In a localizedmodel, there are two possible scenarios for populating the3d electron configuration. [6, 64] In the the first case,termed the weak or intermediate crystal field limit, theHund’s energy scale dominates and the low-energy dou-bly degenerate | e i and higher energy triply degenerate | t i states are populated giving S =2. The other extreme,referred to as the large crystal field limit, the energy split-ting between | e i and | t i dominates and this results in anorbital triplet state with S =1. [65] An interplay betweenthese two energy scales has been suggested to cause apossible spin-state transition in pnictides. [66] Fe x Tehas been argued to be in this strong crystal field S =1limit. [67, 68] This also seems to corroborated by a se-ries of neutron diffraction results in the chalcogenide andpnictide systems where small ordered (proportional gS ,where g is the Lande factor) moments are reported.The neutron scattering cross section is governed byseveral sum rules and in particular the zeroeth momentsum rule which can be written as R dE R d q π [ n ( E ) +1] χ ′′ ( q, E ) = g µ B S ( S + 1) (further details provided inthe supplementary information). The integral includesboth elastic and inelastic scattering contributions andis independent of broadening due to itinerant effects asthe integral is performed over all momentum and en-ergy. Some estimates on the value for S have beenmade based upon purely localized spin-wave models asin CaFe As [35] and BaFe As [69]. These have beensummarized for other 122 systems and are typically inthe range from S ∼ µ B with no dynam-ics reported. [71] These small values are consistent witha strong crystal field picture fixing S =1. However, wealso note that neutron inelastic scattering results on Mottinsulating La O Fe OSe have been consistent with theweak crystal field picture with S =2 [72–74] and the largeordered moments in K x Fe − y Se variants. [75]Through the use of the total moment sum rule we canestimate S in Fe x Te. As we have noted, while our re-sults which extend up to energy transfers of 175 meVdo not capture all of the magnetic cross section, an in-tegral over this energy range gives a lower limit on thetotal spectral weight and hence an effective S . Combin-ing both static and dynamic contributions gives 3.4 ± µ B and 3.7 ± µ B for x =0.141(5) and 0.057(7)respectively. For S =1 and 2 we would expect a totalintegral of 2.67 and 8 µ B respectively. Entropic argu-ments based upon high temperature heat capacity mea-surements would suggest that S eff = is more appro-priate and this would give a predicted integral of 5 µ B ,closer to our measurements given that even at 175 meVthe top of the band has not been reached. While ourresults are consistent with earlier low-energy measure-ments on Fe . Te [76], we find significant spectral weightextending up to high energies giving the apparent low-temperature discrepancy. More discussion on this pointis provided in the supplementary information. The inte-grated intensities are difficult to understand in terms ofa purely localized model with S =1 or 2 discussed above,therefore suggesting the importance of itinerant effects.Such effects maybe captured by considering orbital tran-sitions [77] or an orbitally entangled ground state whichcan also account for the highly anisotropic nature sug-gested by the high energy spin dynamics. [78] We havesearched for high energy orbital transitions without suc-cess and this is discussed in the supplementary informa-tion (see also Ref. 79–83).In summary, our work finds three results based uponour study the spin fluctuations in parent Fe x Te. First,we observe the presence of a soft incommensurate stripyexcitations. Second, by applying sum rules, we find theintegrated intensity to be inconsistent with a S =1 groundstate expected in the presence of a strong crystalline elec-tric field. Third, our results produce an apparent hour-glass structure which defines a cross over point from twodimensional fluctuations to one dimensional. The resultspoint to the parent Fe ground state of chalcogenide su-perconductors being highly anisotropic and also in an in-termediate state between strong ( S =2) and weak ( S =1)orbital ground states.We are grateful for funding from the RSE, the CarnegieTrust, STFC, and through the NSF (DMR-09447720). [1] D. C. Johnston, Adv. Phys. , 803 (2010).[2] R. J. Birgeneau, C. Stock, J. M. Tranquada, and K. Ya-mada, J. Phys. Soc. Jpn. , 111003 (2006).[3] P. A. Lee, N. Nagaosa, and X. G. Wen, Rev. Mod. Phys. , 17 (2006).[4] D. Fruchart, P. Convert, P. Wolfers, R. Madar, J. P. Sen-ateur, and R. Fruchart, Mat. Res. Bull. , 169 (1975).[5] F. C. Hsu, J. Y. Luo, K. W. Yeh, T. K. Chen, T. W.Huang, P. M. Wu, Y. C. Lee, Y.-L. Huang, Y. Y. Chu,D. C. Yan, and M. K. Wu, PNAS , 14262 (2008).[6] Q. Si and E. Abrahams, Phys. Rev. Lett. , 076401(2008).[7] D. X. Yao and E. W. Carlson, Phys. Rev. B , 052507(2008).[8] I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du,Phys. Rev. Lett. , 057003 (2008).[9] K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka,H. Kontani, and H. Aoki, Phys. Rev. Lett. , 087004(2008).[10] Z. P. Yin, K. Haule, and G. Kotliar, Nat. Mat. , 932(2011).[11] B. C. Sales, A. S. Sefat, M. A. McGuire, R. Y. Jin,D. Mandrus, and Y. Mozharivskyj, Phys. Rev. B ,094521 (2009).[12] Y. Mizuguchi, F. Tomioka, S. Tsuda, T. Yamaguchi, andY. Takano, Appl. Phys. Lett. , 012503 (2009).[13] E. E. Rodriguez, Z. Zavalij, P. Y. Hsieh, and M. A. Green, J. Amer. Chem. Soc. , 10006 (2010).[14] N. Tsyrulin, R. Viennois, E. Gianini, M. Boehm,M. Jimenez-Ruiz, A. A. Omrani, B. D. Piazza, and H. M.Ronnow, New. J. Phys. , 073025 (2012).[15] E. E. Rodriguez, C. Stock, P. Y. Hsieh, N. P. Butch,J. Paglione, and M. A. Green, Chem. Sci. , 1782 (2011).[16] C. Stock, E. E. Rodriguez, and M. A. Green, Phys. Rev.B , 094507 (2012).[17] E. E. Rodriguez, C. Stock, P. Zajdel, K. L. Krycka, C. F.Majkrzak, P. Zavalij, and M. A. Green, Phys. Rev. B , 064403 (2011).[18] C. Koz, S. Rossler, A. A. Tsirlin, S. Wirth, andU. Schwarz, Phys. Rev. B , 094509 (2013).[19] S. Rossler, D. Cherian, W. Lorenz, M. Doerr, C. Koz,C. Curfs, Y. Prots, U. K. Rossler, U. Schwarz, S. Eliza-beth, and S. Wirth, Phys. Rev. B , 174506 (2011).[20] Y. Mizuguchi, K. Hamada, K. Goto, H. Takatsu, H. Kad-owaki, and O. Miura, Sol. State Commun. , 1047(2012).[21] I. A. Zaliznyak, Z. J. Xu, J. S. Wen, J. M. Tranquada,G. D. Gu, V. Solovyov, V. N. Glazkov, A. I. Zheludev,V. O. Garlea, and M. B. Stone, Phys. Rev. B , 085105(2012).[22] E. E. Rodriguez, D. A. Sokolov, C. Stock, M. A. Green,O. Sobolev, J. A. Rodriguez-Rivera, H. Cao, andA. Daoud-Aladine, Phys. Rev. B , 165110 (2013).[23] G. F. Chen, Z. G. Chen, J. Dong, W. Z. Hu, G. Li, X. D.Zhang, P. Zheng, J. L. Luo, and N. L. Wang, Phys. Rev.B , 140509 (2009).[24] J. A. Rodriguez, D. M. Adler, P. C. Brand, C. Broholm,J. C. Cook, C. Brocker, R. Hammond, Z. Huang, P. Hun-dertmakr, J. W. Lynn, N. C. Maliszewskyj, J. Moyer,J. Orndorff, D. Pierce, T. D. Pike, G. Scharfstein, S. A.Smee, and R. Vilaseca, Meas. Sci. Technol. , 034023(2008).[25] H. F. Fong, B. Keimer, D. Reznik, D. L. Milius, andI. A. Aksay, Phys. Rev. B , 6708 (1996).[26] C. Stock, E. E. Rodriguez, M. A. Green, P. Zavalij, andJ. A. Rodriguez-Rivera, Phys. Rev. B , 045124 (2011).[27] P. J. Brown, International Tables of Crystallography, VolC (Kluwer, Dordrecht, 2006).[28] O. J. Lipscombe, G. F. Chen, C. F. an T. G. Per-ring, D. L. Abernathy, A. D. Christianson, T. Egami,N. Wang, J. Hu, and P. Dai, Phys. Rev. Lett. ,057004 (2011).[29] M. D. Lumsden, A. D. Christianson, E. A. Goremychkin,S. E. Nagler, H. A. Mook, M. B. Stone, D. L. Abernathy,T. Guidi, G. J. Macdougall, C. Cruz, A. S. Sefat, M. A.Mcguire, B. C. Sales, and D. Mandrus, Nat. Phys. ,182 (2010).[30] C. Stock, R. A. Cowley, W. J. L. Buyers, C. D. Frost,J. W. Taylor, D. Peets, R. Liang, D. Bonn, and W. N.Hardy, Phys. Rev. B , 174505 (2010).[31] K. Sugimoto, Z. Li, E. Kaneshita, K. Tsutsui, and T. To-hyama, Phys. Rev. B , 134418 (2013).[32] R. Coldea, S. M. Hayden, G. Aeppli, T. G. Perring, C. D.Frost, T. E. Mason, S. W. Cheong, and Z. Fisk, Phys.Rev. Lett. , 5377 (2001).[33] C. Stock, R. A. Cowley, W. J. L. Buyers, R. Coldea,C. L. Broholm, C. D. Frost, R. J. Birgeneau, R. Liang,D. A. Bonn, and W. N. Hardy, Phys. Rev. B , 172510(2007).[34] S. O. Diallo, V. P. Antropov, T. G. Perring, C. Bro-holm, J. J. Pulikkotil, N. Ni, S. L. Budko, P. C. Canfield, A. Kreyssig, A. I. Goldman, and R. J. McQueeney, Phys.Rev. Lett. , 187206 (2009).[35] J. Zhao, D. T. Adroja, D. X. Yao, R. I. Bewley, S. Li,X. F. Wang, G. Wu, X. H. Chen, J. Hu, and P. Dai, Nat.Phys. , 555 (2009).[36] C. Lester, J. H. Chu, J. G. Analytis, T. G. Perring, I. R.Fisher, and S. M. Hayden, Phys. Rev. B , 064505(2010).[37] M. Ramazanoglu, J. Lamsal, G. S. Tucker, J. Q. Yan,S. Calder, T. Guidi, T. Perring, R. W. McCallum, T. A.Lograsso, A. Kreyssig, A. I. Goldman, and R. J. Mc-Queeney, Phys. Rev. B , 140509 (2013).[38] S. O. Diallo, D. K. Pratt, R. M. Fernandes, W. Tian, J. L.Zarestky, M. Lumsden, T. G. Perring, C. L. Broholm,N. Ni, S. L. Bud’ko, P. C. Canfield, H. F. Li, D. Vaknin,A. Kreyssig, A. I. Goldman, and R. J. McQueeney, Phys.Rev. B , 214407 (2010).[39] G. S. Uhrig, K. P. Schmidt, and M. Gruninger, Phys.Rev. Lett. , 267003 (2004).[40] E. W. Carlson, D. X. Yao, and D. K. Campbell, Phys.Rev. B , 064505 (2004).[41] J. Zhao, Y. Shen, R. J. Birgeneau, M. Gao, Z. Y. Lu,D. H. Lee, X. Z. Lu, H. J. Xiang, D. L. Abernathy, andY. Zhao, Phys. Rev. Lett. , 177002 (2014).[42] W. Jayasekara, Y. Lee, A. Pandey, G. S. Tucker, A. Sap-kota, J. Lamsal, S. Calder, D. L. Abernathy, J. L.Niedziela, B. N. Harmon, A. Kreyssig, D. Vaknin, D. C.Johnston, A. I. Goldman, and R. J. McQueeney, Phys.Rev. Lett. , 157001 (2013).[43] H. Tsunetsugu and M. Arikawa, J. Phys. Soc. Jpn. ,083701 (2006).[44] A. Lauchli, F. Mila, and K. Penc, Phys. Rev. Lett. ,087205 (2006).[45] B. A. Ivanov and A. K. Kolezhuk, Phys. Rev. B ,052401 (2003).[46] R. M. Fernandes, A. V. Chubukov, and J. Schmalian,Nature Physics , 97 (2014).[47] M. Tsuchiizu, Y. Ohno, S. Onari, and H. Kontani, Phys.Rev. Lett. , 057003 (2013).[48] Y. Ohno, M. Tsuchiizu, S. Onari, and H. Kontani, J.Phys. Soc. Jpn. , 013707 (2013).[49] C. Stock, W. J. L. Buyers, D. Peets, R. Liang, D. A.Bonn, W. N. Hardy, and R. J. Birgeneau, Phys. Rev. B , 014502 (2004).[50] G. Shirane, S. M. Shapiro, and J. M. Tranquada, Neu-tron Scattering with a Triple Axis Spectrometer (Cam-bridge University Press, Cambridge, UK, 2002).[51] H. F. Fong, P. Bourges, Y. Sidis, L. P. Regnault, J. Bossy,A. Ivanov, D. L. Milius, I. A. Aksay, and B. Keimer,Phys. Rev. B , 14773 (2000).[52] P. Dai, H. A. Mook, R. D. Hung, and F. Dogan, Phys.Rev. B , 054524 (2001).[53] G. Xu, Z. Xu, and J. M. Tranquada, Rev. Sci. Instrum. , 083906 (2013).[54] N. B. Christensen, D. F. McMorrow, H. M. Ronnow,B. Lake, S. M. Hayden, G. Aeppli, T. G. Perring,M. Mangkorntong, M. Nohara, and H. Tagaki, Phys.Rev. Lett. , 147002 (2004).[55] J. M. Tranquada, H. Woo, T. G. Perring, H. Goka, G. D.Gu, G. Xu, M. Fujita, and K. Yamada, Nature , 534(2004).[56] D. Reznik, J. P. Ismer, I. Eremin, L. Pintschovius,T. Wolf, M. Arai, Y. Endoh, T. Masui, and S. Tajima,Phys. Rev. B , 132503 (2008). [57] C. Stock, R. A. Cowley, W. J. L. Buyers, P. S. Clegg,R. Coldea, C. Frost, R. Liang, D. Peets, D. A. Bonn,W. N. Hardy, and R. J. Birgeneau, Phys. Rev. B ,024522 (2005).[58] A. T. Boothroyd, P. Babkevich, D. Prabhakaran, andP. G. Freeman, Nature , 341 (2011).[59] H. Ulbrich, P. Steffens, D. Lamago, Y. Sidis, andM. Braden, Phys. Rev. Lett. , 247209 (2012).[60] S. Chi, J. A. Rodriguez-Rivera, J. W. Lynn, C. Zhang,D. Phelan, D. K. Singh, R. Paul, and P. Dai, Phys. Rev.B , 214407 (2011).[61] Z. Xu, J. Wen, Y. Zhao, M. Matsuda, W. Ku, X. Liu,G. Gu, D. H. Lee, R. J. Birgeneau, J. M. Tranquada,and G. Xu, Phys. Rev. Lett. , 227002 (2012).[62] H. Luo, R. Zhang, M. Laver, Z. Yamani, M. Wang, X. Lu,M. Wang, Y. Chen, S. Li, S. Chang, J. W. Lynn, andP. Dai, Phys. Rev. Lett. , 247002 (2012).[63] R. Khasanov, M. Bendele, A. Amato, P. Babkevich, A. T.Boothroyd, A. Cervellino, K. Conder, S. N. Gvasaliya,H. Keller, H. H. Klauss, H. Luetkens, V. Pomjakushin,E. Pomjakushina, and B. Roessli, Phys. Rev. B ,140511 (2009).[64] C. Cao, P. J. Hirschfeld, and H. P. Cheng, Phys. Rev. B , 220506 (2008).[65] F. Kr¨uger, S. Kumar, J. Zaanen, and J. van den Brink,Phys. Rev. B , 054504 (2009).[66] H. Gretarsson, S. R. Saha, T. Drye, J. Paglione, J.Kim,D. Casa, T. Gog, W. Wu, S. R. Julian, and Y. J. Kim,Phys. Rev. Lett. , 047003 (2013).[67] A. M. Turner, F. Wang, and A. Vishwanath, Phys. Rev.B , 224504 (2009).[68] K. Haule and G. Kotliar, New J. Phys. , 025021 (2009).[69] R. A. Ewings, T. G. Perring, R. I. Bewley, T. Guidi,M. J. Pitcher, D. R. Parker, S. J. Clarke, and A. T.Boothroyd, Phys. Rev. B , 220501 (2008).[70] B. Schmidt, M. Siahatgar, and P. Thalmeier, Phys. Rev.B , 165101 (2010).[71] E. E. Rodriguez, C. Stock, K. L. Krycka, C. F. Majkrzak,P. Zajdel, K. Kirshenbaum, N. P. Butch, S. R. Saha,J. Paglione, and M. A. Green, Phys. Rev. B , 134438(2011).[72] D. G. Free and J. S. O. Evans, Phys. Rev. B , 214433(2010).[73] J. X. Zhu, R. Yu, H. Wang, L. L. Zhao, M. D. Jones,J. Dai, E. Abrahams, E. Morosan, M. Fang, and Q. Si,Phys. Rev. Lett. , 216405 (2010).[74] E. E. McCabe, C. Stock, E. E. Rodriguez, A. S. Wills,J. W. Taylor, and J. S. O. Evans, Phys. Rev. B ,100402(R) (2014).[75] J. Zhao, H. Cao, E. Bourret-Courchesne, D. H. Lee, andR. J. Birgeneau, Phys. Rev. Lett. , 267003 (2012).[76] I. A. Zaliznyak, Z. Xu, J. M. Tranquada, G. Gu, A. M.Tsvelik, and M. B. Stone, Phys. Rev. Lett. , 216403(2011).[77] Z. P. Yin, K. Haule, and G. Kotliar, arXiv:1311.1188.[78] J. Chaloupka and G. Khaliullin, Phys. Rev. Lett ,207205 (2013).[79] Y. J. Kim, A. P. Sorini, C. Stock, T. G. Perring,J. van den Brink, and T. P. Devereaux, Phys. Rev. B , 085132 (2011).[80] R. A. Cowley, W. J. L. Buyers, C. Stock, Z. Yamani,C. Forst, J. W. Taylor, and D. Prabhakaran, Phys. Rev.B , 205117 (2013).[81] J. P. Hill, G. Blumberg, Y.-J. Kim, D. S. Ellis, S. Waki- moto, R. J. Birgeneau, S. Komiya, Y. Ando, B. Liang,R. L. Greene, D. Casa, and T. Gog, Phys. Rev. Lett. , 097001 (2008).[82] J. D. Perkins, R. J. Birgeneau, J. M. Graybeal, M. A. Kastner, and D. S. Kleinberg, Phys. Rev. B , 9390(1998).[83] C. Stock, R. A. Cowley, J. W. Taylor, and S. M. Ben-nington, Phys. Rev. B , 024303 (2010). r X i v : . [ c ond - m a t . s t r- e l ] S e p Supplementary information for “Soft striped magnetic fluctuations competing withsuperconductivity in Fe x Te”
C. Stock, E. E. Rodriguez, O. Sobolev, J. A. Rodriguez-Rivera,
R.A. Ewings, J.W. Taylor, A. D. Christianson, and M. A. Green School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK Department of Chemistry of Biochemistry, University of Maryland, College Park, MD, 20742, U.S.A. Forschungs-Neutronenquelle Heinz Maier-Leibnitz, FRM2 Garching, 85747, Germany NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, MD 20889 Department of Materials Science, University of Maryland, College Park, MD 20742 ISIS Facility, Rutherford Appleton Laboratory, Didcot, OX11 0QX, U.K. Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA School of Physical Sciences, University of Kent, Canterbury, CT2 7NH, UK (Dated: October 13, 2018)We present supplementary information regarding the experimental details, “spurious” phononscattering, and the formalism used to derive absolute units for the neutron scattering intensities.In particular, we discuss the zeroeth moment sum rule presented in the main text of the paper andhow we compared our data against this constraint on neutron scattering. More discussion regardingthe comparison with other neutron inelastic scattering experiments is also expanded. We thendiscuss low-energy phonons which potentially overlap measurements of the magnetic excitations -particularly at low energies below ∼
30 meV. By combining spallation time-of-flight and reactortriple-axis we have checked for consistency and taken steps to ensure such phonon contamination isabsent in the data presented in the main text.
I. SAMPLE DETAILS
The electronic and magnetic properties inFe x Te − y Ch y can be tuned through either anionor cation substitution and has been the topic of severaldetailed studies. The results are generally consistentfor the specific case of interstitial iron doping throughtuning the variable x . Two extremes of the phase dia-gram are reported with a critical concentration of x ∼ and in Refs. 8 and 9 but with largervalues of interstitial iron concentrations. Diffractionstudies discussing the critical properties near this criticalconcentration of interstitial iron have been reported inRef. 3 and 4. The current study reported in the maintext discusses the spin fluctuations in both of theseextremes and finds strong differences across the entiredispersion band.The sample preparation and details for single crystalsused in this study have been discussed in detail in severalprevious studies. Both ∼ II. EXPERIMENTAL DETAILS
The magnetic response in Fe x Te possesses a highlythree-dimensional line shape in momentum at low en-ergies which crosses over to a more two-dimensional lineshape at higher energies. To track the momentum depen-dence, we have used a combination of three-axis measure-ments performed at reactor based sources combined withspallation source data taken at higher energies. Whilethe momentum transfer of all measurements performedwith a three-axis spectrometer was tuned to a particu-lar value with all three components of the momentumtransfer vector fixed, the spallation data was taken withthe c -axis component (or the L direction) being an im-plicit variable coupled, and hence varying, with energytransfer and in-plane momentum. This technique worksfor purely two-dimensional or one-dimensional systems,but care needs to be taken for three dimensional exci-tations. Three different sets of experiments were per-formed on each of the two interstitial iron concentrations x discussed in the main text. We outline the detailedexperimental setups used here. A. Cold triple-axis measurements - MACS
Low energy (E <
10 meV) measurements were per-formed using the MACS (Multi Axis Crystal Spectrome-ter located on the NG0 guide position) at the NIST Cen-ter for Neutron research. Constant energy planes wereconstructed by fixing the final energy to E f =3.6 meV us-ing the 20 double-bounce PG(002) analyzing crystals anddetectors and varying the incident energy by a double-focused PG(002) monochromator. Each detector channelwas collimated using 90 ′ Soller slits before the analyzingcrystal. Further details of the instrument design can befound in Ref. 13. Full maps of the spin excitations in the(H0L) scattering plane, as a function of energy transfer,were then constructed by measuring a series of constantenergy planes. Warm Beryllium filters were used on thescattered side to filter out higher order neutrons. All ofthe data has been corrected for the λ/ B. Thermal triple-axis measurements - HB1(ORNL) and PUMA (FRM2)
Medium energy transfers (E=5-20 meV) were per-formed using thermal triple-axis spectrometers at OakRidge National Labs (HB1) and the FRM2 reactor(PUMA). On PUMA, a vertically focussing and horizon-tally flat PG(002) monochromator was used with a hor-izontally flat PG(002) analyzer. Soller slit collimatorswere used and the sequence were fixed at 40 ′ -mono-40 ′ - S -open-analyzer-open. The experiments used a fixed fi-nal energy of 13.5 meV and a PG filter was placed on thescattered side to remove higher-order contamination fromthe monochromator. The choice was made to not usehorizontal focussing on the monochromator and analyzerdue to the presence of the close proximity of phononswhich were found to easily mimic magnon dispersion andcontaminate the results - particularly above ∼
20 meV.Further discussion is given below. On HB1, a verticallyfocussed and horizontally flat PG(002) monochromatorwas used with a horizontally and vertically flat PG(002)analyzer. The final energy was fixed at E f =13.5 meVand a graphite filter was used on the scattered side toremove higher order neutrons from the monochromator.Soller slit collimation of 80 ′ was used before and after thesample position. All data from these thermal triple-axisexperiments have been corrected for contamination of theincident beam monitor using calculations described in theappendix of Ref. 14 and in Ref. 15. For the PUMA andmost of the HB1 measurements the sample was alignedin the (H0L) scattering plane and some measurements,described below, were done in the (HHL) scattering onHB1. C. Spallation time-of-flight measurements - MAPS
Higher energy transfers overlapping with the dynamicranges discussed above were performed using the MAPSchopper spectrometer at the ISIS Facility. The samplewas aligned such that Bragg positions of the form (H0L)lay within the horizontal scattering plane and cooled witha bottom loading closed cycle refrigerator to tempera- tures of 10 K. The c axis was aligned parallel to the inci-dent beam ( ~k i ). The t chopper was spun at a frequencyof 50 Hz and phased to remove high energy neutronsfrom the target. A “sloppy” Fermi chopper was used tomonochromate the incident beam. To cover a wider dy-namic range, we used three different incident energies ofE i =75, 150, and 300 meV with the Fermi chopper spun atfrequencies of 200, 250, 350 Hz respectively. The energyresolution at the elastic ( E =0) position was 4.0, 9.0, and18.1 meV for E i =75, 150, and 300 meV configurationsrespectively. The detectors consisted of an array of posi-tion sensitive detectors allowing good angular resolutionboth within and vertical to the scattering plane. D. Spallation time-of-flight measurements - MARI
Searches for high-energy crystal field excitations,which may result from an orbital degree of freedom, wereperformed on the MARI direct geometry spectrometer.The experiments used a t chopper spun at 50 Hz to re-move high energy neutrons in parallel with a “relaxed”Fermi chopper spun at 600 Hz. The sample was cooled ina closed cycle cryostat to temperatures between 3 K and400 K and the incident beam was aligned parallel to the c axis. The configuration was used assuming single-iontype excitations which have no strong dispersion in mo-mentum. The results from this experiment are describedbelow. III. NEUTRON CROSS SECTIONS, ABSOLUTENORMALIZATION, AND SUM RULES
In this section we outline the cross sections and normal-ization methods used to obtain the data in the main textof the paper. We note that similar analyses have beenperformed and discussed for the cuprates.
While sev-eral papers outline the formalism and the methods forthis we largely follow the formulae and methods usedRef. 14.
A. Cross sections and absolute intensities
For completeness, we outline the cross sections usedin this section for obtaining the integrated intensitiesquoted in the main text. We have performed this analysisso that our results can be compared with other systemsand with theory. We outline the formulae for the case oftriple-axis as the spallation data taken on MAPS was di-rectly normalized using a vanadium standard. In the caseof a triple-axis spectrometer measured with an incidentbeam monitor, the measured intensity from phonon ormagnetic scattering is directly proportional to the mag-netic or phonon cross section. We note that a detaileddiscussion of this process is described in Ref. 18. I ph,mag ( ~Q, E ) ∝ S ph,mag ( ~Q, E ) . (1)The constant of proportionality ( A ) can be determinedfrom the measured integrated intensity of a phonon or us-ing a known vanadium standard. In the case of a phonon,the cross section is I ph ( ~Q ) = A (cid:18) ¯ h (cid:19) [1 + n ( E )] | F N | ... (2) × Q cos ( β ) M e − W where M is the mass of the unit cell, the Debye-Wallerfactor e − W ∼
1, [1 + n ( E )] is the Bose factor, | F N | isthe static structure factor of the nearby Bragg reflection,Ω is the phonon frequency, and β is the angle between ~Q and the phonon eigenvector. Measuring the energy inte-grated intensity I ph ( ~Q ) = R dEI ph ( ~Q, E ) of the acousticphonon therefore affords a measurement of the calibra-tion constant A .For the magnetic scattering, the magnetic correlationfunction is related to magnetic S mag ( ~Q, E ) by the follow-ing, S mag ( ~Q, E ) = g f ( ~Q ) ... (3) × X αβ (cid:16) δ αβ − ˆ Q α ˆ Q β (cid:17) S αβ ( ~Q, E ) . The correlation function is related by the fluctuation dis-sipation theorem to the imaginary part of the spin sus-ceptibility χ ( ~Q, E ) by S αβ ( ~Q, E ) = π − [ n ( E ) + 1] χ ′′ ( ~Q, E ) g µ B . (4)In our analysis, we assumed that the paramagnetic scat-tering is isotropic in spin, therefore, χ ′′ = χ ′′ xx = χ ′′ yy = χ ′′ zz . Putting this all together, we can then write thefollowing for the magnetic cross section. I mag ( ~Q, E ) = A ( γr ) f ( Q ) e − W [1 + n ( E )] πµ B ... (5) × (2 χ ′′ ) , where ( γr ) is 73 mbarns sr − and f ( Q ) is the isotropicmagnetic form factor for Fe . We emphasize here thatwe have assumed isotropic or paramagnetic scattering tofix the form of the spin susceptibility χ ′′ . While it islikely that this approximation holds for our high-energydata where the energy transfer is much larger than theanisotropy gap, this assumption could potentially intro-duce errors into the spectral weight at low energies near the ∼ ∼
20 meV)we have used a vanadium standard. For this calibrationwe have taken a cut through the elastic line assuming adominant incoherent cross section of the vanadium stan-dard. When compared with the phonon calibration de-scribed above at lower energy transfers, both methodsagreed within error.
B. Zeroeth moment sum rule
The intensity integrated overall energies and momen-tum transfer is constrained by the zeroeth moment sumrule. This rum rule depends on the underlying value ofthe spin magnitude S and therefore provides a meansof understanding the ground state properties. Here wewrite the equations used in the analysis discussed in themain text.Integrating S ( ~Q, E ) over all energies and momentumtransfers is constrained by the following equation, Z dE Z d QS mag ( ~Q, E ) = 23 g S ( S + 1) . (6)Substituting in the cross section for paramagnetic scat-tering discussed above, we get the following,˜ I = π − Z dE Z d Q [ n ( E ) + 1] χ ′′ ( Q, E ) = ... (7)13 g µ B S ( S + 1)The integral is overall energy transfers including elas-tic ( E = 0) and inelastic contributions. In our exper-iments, we were able to obtain reliable data up to 175meV and therefore we have cut the integral arbitrarily atthis value. A breakdown of the total integrated spectralweight listing our measured dynamic (inelastic), static(elastic), and total values is provided in Table I. TABLE I. Absolute intensitiesx ˜ I dynamic ( µ B ) ˜ I static ( µ B ) ˜ I total ( µ B )0.057(7) 0.49 1.8 3.70.141(5) 0.83 1.6 3.4 Based on this analysis, we observe a significant amountof the low-temperature spectral weight is present in theinelastic channel. For comparison, a similar analysis over I n t en s i t y ( C oun s / m i n ) E (meV) E ( m e V ) (0.5,0,L) (r.l.u.) a) Fe Te, PUMAE f =13.5 meV, T= 4 K b) Q=(0.5,0,0.5)c) Q=(0.5,0,0.6) FIG. S1. a ) The c -axis dispersion taken from a series ofconstant- Q scans examples of which are illustrated in b ) and c ). The data illustrate a weak dispersion of the excitationsalong the c . a similar energy range in the cuprates (with S = ) gavea total integral of ∼ µ B in ortho-II YBa Cu O . . We obtain consist results with Ref. 20 when only in-tegrating the data up to ∼
30 meV - the same energyrange probed in that experiment. However, we observesignificant spectral weight at higher energies up to 175meV, not investigated in previous works. We thereforedo not find the low temperature results can be inter-preted in terms of a S=1 strong crystal field frameworkas discussed in the main text.
IV. WEAK DISPERSION ALONG THE c -AXIS As noted above, the magnetic excitations at low-energies are three-dimensional in the sense that theyare peaked in momentum along all three directions.While the lower energy data was obtained using cold andthermal triple-axis spectrometers where the momentumtransfer could be tuned to a particular position, the spal-lation source data depend on the excitations being twodimensional and therefore the value of L on MAPS varieswith energy transfer (see discussion in Ref. 19).To check this and over which energy range this approx-imation is valid, we have measured the c -axis dispersionin detail on the commensurate Fe . Te crystal usingthe PUMA thermal triple-axis spectrometer. The results are illustrated in Fig. S1 taken at 4 K for momentumpositions along ~Q =( ,0,0.5) to ( ,0,1.0). Panel a ) showsthe results of gaussian fits plotting the peak position asa function of momentum transfer. The data show a veryweak dispersion from ∼ ∼
10 meV consis-tent with results presented previously in Ref. 5. Exam-ple scans are presented in panels b ) and c ). The verticaldashed line illustrates the comparatively small changein the frequency as the momentum transfer is changedalong L . Based on this result of a weak c -axis dispersionwe consider the approximation of two-dimensional spinexcitations to be valid over the energy range probed inour spallation source data. V. STRIPE CORRELATIONS AND ONEDIMENSIONAL SCATTERING
As noted based on the two-dimensional slices presentedin Fig. 1 of the main text, the inward dispersion or “hour-glass” dispersion marks the cross over from two dimen-sional excitations to one dimensional. This was quan-tified as a function of energy for both interstitial ironconcentrations by fitting the K dependence to the form F ( K ) ∝ (1 + 2 α cos( ~Q · ~b )) multiplied by the iron fac-tor squared as discussed above to capture the fact thatL is changing as a function of K. Sample fits are shownin Fig. S2 illustrated weak correlations along K at lowenergies (panel a where E=15 ± b where E=30 ± VI. PHONON CONTAMINATION OF THEMAGNETIC SIGNAL
In this section we discuss the possibility for phononcontamination of the magnetic signal in Fe x Te andsteps we have taken to avoid and check for this in ourdata.
A. Low-energy phonons and possible magneticcontamination giving H =0 scattering During the course of the experiments reported in themain text, we discovered several spurious excitations nearthe dynamic magnetic scattering which later turned outto be due to phonons. In this section, we report on sev-eral low-energy phonons up to 30 meV energy transferthat potentially contaminate the magnetic results. Wehave checked that the scattering and in particular thedispersion relation in the main text is magnetic by com-paring several different Brillouin zones. Because of thelow-energy phonons, we found spallation data was themost reliable between the energy ranges of 15- 30 meVand this was cross checked with thermal triple-axis mea-surements. Fe Te, MAPS, E I =75 meV, T=5 K I n t en s i t y ( A r b . U n i t s ) −1 −0.5 0 0.5 10246810 (0.5 ± a) E=15 ± ± FIG. S2. The momentum dependence along K for Fe . Teat a ) 15 ± b ) 30 ± Fe x Te is a highly two dimensional material with lay-ers weakly held together by van der Waals forces. This isevidenced by the weak magnetic interactions along the c -axis discussed and characterized in the previous section.One phonon branch which gave the appearance of com-mensurate (H=0) scattering in our experiments was alow-energy acoustic branch propagating along c . This isillustrated in Fig. S3 taken on MACS with E f =3.6 meV.Panel a ) illustrates a constant- Q slice taken along the ( ± . Tesample illustrating an acoustic phonon mode with a topof the band at L=1.5 and 0.5 of ∼ . Te at 70 K (panel b ) shows thesame phonon mode with possibly a slightly lower maxi-mum energy. The top of the band in the acoustic phonon −3 −2 −10246810 (0 ± E ( m e V ) −1 0 10246810 MACS, E f =3.6 meV, Fe Te (H,0,−1.50 ± −1 −0.5 0 0.5 10246810 (H,0,−2.50 ± a) x=0.141(5), T=2 Kb) x=0.057(7), T=70 K d) x=0.057(7), T=2 K magnetic phonon c) x=0.057(7), T=2 K FIG. S3. A summary of the low-energy c -axis propagatingphonons based upon cold triple-axis data taken on MACSwith E f =3.6 meV. a ) Illustrates a constant energy slice takenalong the ( ± . Te crystal. b )Illustrates a similar slice taken for commensurate (collinearmagnetic structure) Fe . Te. is very similar to the energy of the gap in the commen-surate Fe . Te sample shown in Fig. 1 in the maintext and appears at L equal to half integer positions.The problem in terms of measuring magnetic scatter-ing is further illustrated in Fig. S3 panels c ) and d ) whichshows constant Q slices for L=-1.5 and -2.5. The growthin intensity near H=0 with increasing | Q | supports thefact that the commensurate H=0 scattering originatesfrom phonons and not magnetism. B. Phonons at 20-30 meV and possible magneticcontamination giving strong dispersion
The energy range extending from ∼ L and H were requiredto close the scattering triangle. Similar to the situa-tion above, we found there were several phonon brancheswhich crossed the nuclear zone boundary giving the ap-pearance of a strong dispersion in the magnetic scatter- MAPS, E i =75 meV, Fe Te, T=10 K (H,0 ± E ( m e V ) FIG. S4. A T=10 K constant- Q slice illustrating a phononbranch highlighted by the dashed line. ing. The problem is demonstrated in Fig. S4 where weshow a constant- Q slice from our MAPS data set onFe . Te. In this particular experiment, the c axiswas aligned along the incident beam k i . Note that whileboth in-plane momentum transfer components, H and K , are well defined, the out of plane component L varieswith energy transfer. An excitation branch crossing themagnetic scattering can be seen extending from ∼ . Te in the (HHL) scat-tering plane. The data show well defined phonons witha minimum of 20 meV and extending up to ∼
30 meVwhere they cross the nuclear zone boundary but the mag-netic zone centre. These phonons contaminated severalattempts both on PUMA and HB1 to extend the thermaltriple-axis data into this range. We therefore relied onspallation source data over this energy range to extractthe magnetic dispersion reported in the main text.
C. Hydrogen related modes contaminating resultsat high energies giving apparent crystal field levels
Given the speculation and the large discussion aroundthe issue whether Fe is in a S=1 or 2 ground state,we performed a search for higher energy orbital excita- (H, H, 0) (r.l.u.) E ( m e V ) Fe TeHB1, E f =13.5 meVT=10 K FIG. S5. A constant-Q slice compiled from a series of constantenergy scans on HB1 thermal triple-axis spectrometer (OakRidge). A clear phonon branch extending in the range of20-30 meV can be seen. tions in the range below ∼
750 meV using the MARIdirect geometry spectrometer at ISIS (configuration dis-cussed above). These searches were motivated by thepossibility of spin-orbit transitions and the observationof similar orbital transitions using neutrons reported re-cently for Mott insulating NiO and CoO where a groundstate orbital degeneracy exists.
There has also beenthe observation of similar high energy modes in super-conducting YBa Cu O x which seemed to overlap withpeaks observed using infrared and possibly inelastic reso-nant x-ray measurements. The origin of these peaksin the cuprates is still unclear and as noted in Ref. 12,there are other scattering possibilities involving hydro-gen related modes that occur over the same energy range.Therefore checks need to be performed to determine theabsence of hydrogen scattering and one test which canbe performed on a wide-angle spectrometer like MARI isto search for a hydrogen recoil line as studied in detailedand demonstrated on polyethylene. We have performed such a test and the results areshown in Fig. S6. Panels a ) and b ) show that peaksare observed at low momentum transfer. Panel c ) showsa representative constant- Q slice showing the presenceof an excitation at ∼
370 meV. The solid black lineshows the predicted position of the hydrogen recoil line( E recoil = ¯ h (2 M p ) Q assuming the impulse approxima-tion). There are two problems with interpreting this ex-citation, and indeed the ones at ∼
170 meV, as magneticcrystal field or orbital excitations. First, the intensity ofthe excitations initially increases with momentum trans-
FIG. S6. High-incident energy scattering performed onMARI. a ) and b ) illustrated one-dimensional cuts integrat-ing over Q =[0,10] ˚A − . The results show several peaks at ∼
170 meV and ∼
370 meV. c ) illustrates a constant- Q slicetaken with E i =750 meV. The solid curve shows the positionof the expected hydrogen recoil line and the presence of in-tensity along this line indicates that the sample has absorbedhydrogen in some form. fer and peaks at around the recoil line in momentum.Second, as evidenced by intensity around the expectedrecoil position there is absorption of hydrogen into thesample. Based on these two points we conclude that thesharp excitations represented in Fig. S6 a ) and b ) aredue to hydrogen modes and not due to orbital transi-tions. The width of these excitations was found not to respond to the structural and magnetic transition tem-peratures in this compound, but was observed to broadenat high temperatures near room temperature.Therefore, in summary, we conclude that the high-energy excitations observed are spurious and due to hy-drogen absorbed into the sample. The exact chemicalorigin of this remains unclear and we note that heatingthe sample at 400 K, while pumping, did not decreasethe hydrogen recoil scattering implying that it originatesbeyond the surface of the sample and is not due to simplywater absorption. D. Conclusion from “spurious” phonon scattering
The first conclusion we draw from this analysis is thatthere is no measurable low-energy H =0 magnetic scatter-ing in Fe x Te. There is a low-energy c -axis propagatingphonon mode which has a maximum energy position sim-ilar to the energy scale of the low-energy magnetic fluc-tuations. The magnetic scattering is therefore confinednear the ( π ,0) position except at high energies where itdisperse to the zone boundary as discussed in the mainpart of the text. This phonon contamination needs to beaccounted for and removed when considering the totalmoment and in particular the temperature dependenceof the integrated intensity.The second conclusion is that the phonon scatteringin the range near 20-30 meV crosses the magnetic zonecentre and mimics a dispersion over this energy range.We have avoided this problem by cross checking severaldifferent Brillouin zones and performing scattering ex-periments at the lowest Brillouin zones possible usingchopper spectrometers at spallation sources. We notethat a similar problem was reported in the cuprates andwas raised as a particular concern for triple-axis mea-surements. In those cases detailed calculations wereemployed to check the data. The development of newchopper spectrometers which can be used with high inci-dent energies and small scattering angles allows a directmeasurement of this.The third conclusion is that the sharp excitations athigh energies are the result of modes involving hydro-gen scattering. Again, the use of wide scattering anglechopper instruments with high incident energies allows adirect test for hydrogen in the sample. E. E. Rodriguez, Z. Zavalij, P. Y. Hsieh, and M. A. Green,J. Amer. Chem. Soc. , 10006 (2010). E. E. Rodriguez, C. Stock, P. Y. Hsieh, N. P. Butch,J. Paglione, and M. A. Green, Chem. Sci. , 1782 (2011). E. E. Rodriguez, C. Stock, P. Zajdel, K. L. Krycka, C. F.Majkrzak, P. Zavalij, and M. A. Green, Phys. Rev. B ,064403 (2011). E. E. Rodriguez, D. A. Sokolov, C. Stock, M. A. Green,O. Sobolev, J. A. Rodriguez-Rivera, H. Cao, andA. Daoud-Aladine, Phys. Rev. B , 165110 (2013). C. Stock, E. E. Rodriguez, M. A. Green, P. Zavalij, and J. A. Rodriguez-Rivera, Phys. Rev. B , 045124 (2011). C. Stock, E. E. Rodriguez, and M. A. Green, Phys. Rev.B , 094507 (2012). B. C. Sales, A. S. Sefat, M. A. McGuire, R. Y. Jin, D. Man-drus, and Y. Mozharivskyj, Phys. Rev. B , 094521(2009). S. Rossler, D. Cherian, W. Lorenz, M. Doerr, C. Koz,C. Curfs, Y. Prots, U. K. Rossler, U. Schwarz, S. Eliza-beth, and S. Wirth, Phys. Rev. B , 174506 (2011). C. Koz, S. Rossler, A. A. Tsirlin, S. Wirth, andU. Schwarz, Phys. Rev. B , 094509 (2013). I. A. Zaliznyak, Z. J. Xu, J. S. Wen, J. M. Tranquada,G. D. Gu, V. Solovyov, V. N. Glazkov, A. I. Zheludev,V. O. Garlea, and M. B. Stone, Phys. Rev. B , 085105(2012). Y. Mizuguchi, K. Hamada, K. Goto, H. Takatsu, H. Kad-owaki, and O. Miura, Sol. State Commun. , 1047(2012). C. Stock, R. A. Cowley, W. J. L. Buyers, C. D. Frost, J. W.Taylor, D. Peets, R. Liang, D. Bonn, and W. N. Hardy,Phys. Rev. B , 174505 (2010). J. A. Rodriguez, D. M. Adler, P. C. Brand, C. Broholm,J. C. Cook, C. Brocker, R. Hammond, Z. Huang, P. Hun-dertmakr, J. W. Lynn, N. C. Maliszewskyj, J. Moyer,J. Orndorff, D. Pierce, T. D. Pike, G. Scharfstein, S. A.Smee, and R. Vilaseca, Meas. Sci. Technol. , 034023(2008). C. Stock, W. J. L. Buyers, D. Peets, R. Liang, D. A. Bonn,W. N. Hardy, and R. J. Birgeneau, Phys. Rev. B ,014502 (2004). G. Shirane, S. M. Shapiro, and J. M. Tranquada,
NeutronScattering with a Triple Axis Spectrometer (CambridgeUniversity Press, Cambridge, UK, 2002). H. F. Fong, P. Bourges, Y. Sidis, L. P. Regnault, J. Bossy,A. Ivanov, D. L. Milius, I. A. Aksay, and B. Keimer, Phys.Rev. B , 14773 (2000). P. Dai, H. A. Mook, R. D. Hung, and F. Dogan, Phys. Rev. B , 054524 (2001). G. Xu, Z. Xu, and J. M. Tranquada, Rev. Sci. Instrum. , 083906 (2013). C. Stock, R. A. Cowley, W. J. L. Buyers, P. S. Clegg,R. Coldea, C. Frost, R. Liang, D. Peets, D. A. Bonn, W. N.Hardy, and R. J. Birgeneau, Phys. Rev. B , 024522(2005). I. A. Zaliznyak, Z. Xu, J. M. Tranquada, G. Gu, A. M.Tsvelik, and M. B. Stone, Phys. Rev. Lett. , 216403(2011). Y. J. Kim, A. P. Sorini, C. Stock, T. G. Perring, J. van denBrink, and T. P. Devereaux, Phys. Rev. B , 085132(2011). R. A. Cowley, W. J. L. Buyers, C. Stock, Z. Yamani,C. Forst, J. W. Taylor, and D. Prabhakaran, Phys. Rev.B , 205117 (2013). J. P. Hill, G. Blumberg, Y.-J. Kim, D. S. Ellis, S. Waki-moto, R. J. Birgeneau, S. Komiya, Y. Ando, B. Liang,R. L. Greene, D. Casa, and T. Gog, Phys. Rev. Lett. ,097001 (2008). J. D. Perkins, R. J. Birgeneau, J. M. Graybeal, M. A. Kast-ner, and D. S. Kleinberg, Phys. Rev. B , 9390 (1998). C. Stock, R. A. Cowley, J. W. Taylor, and S. M. Benning-ton, Phys. Rev. B , 024303 (2010). H. F. Fong, B. Keimer, D. Reznik, D. L. Milius, and I. A.Aksay, Phys. Rev. B54