High-energy spin fluctuation in low- T c iron-based superconductor LaFePO 0.9
Motoyuki Ishikado, Shin-ichi Shamoto, Katsuaki Kodama, Ryoichi Kajimoto, Mitsutaka Nakamura, Tao Hong, Hannu Mutka
aa r X i v : . [ c ond - m a t . s up r- c on ] A p r High-energy spin fluctuationin low- T c iron-based superconductor LaFePO . Motoyuki Ishikado , Shin-ichi Shamoto , Katsuaki Kodama , Ryoichi Kajimoto ,Mitsutaka Nakamura , Tao Hong , and Hannu Mutka Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society(CROSS), Tokai, Naka, Ibaraki 319-1106, Japan Advanced Science Research Center, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science and Technology(AIST), Tsukuba, Ibaraki 305-8562, Japan Materials Sciences Research Center, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan J-PARC Center, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan Neutron Scattering Division, Oak Ridge National Laboratory (ORNL), Oak Ridge, Tennessee 37831, USA Institut Laue-Langevin (ILL), 71 avenue des Martyrs, CS 20156, F - 38042 Grenoble Cedex 9, France * m [email protected] + [email protected] ABSTRACT
Spin fluctuations are widely believed to play an important role in the superconducting mechanisms of unconventional high-temperature superconductors. Spin fluctuations have been observed including iron-based superconductors. However, insome iron-based superconductors such as LaFePO . , they have not been observed by inelastic neutron scattering (INS).LaFePO . is an iron-based superconductor with a low superconducting transition temperature ( T c = 5 K), where line nodesare observed in the superconducting gap function. The line-node symmetry typically originates from sign reversal of theorder parameter in spin-fluctuation-mediated superconductivity. This contradiction has been a long-standing mystery of thissuperconductor. Herein, spin fluctuations were found at high energies such as 30 −
50 meV with comparable intensities to anoptimally doped LaFeAs(O,F). Based on this finding, the line-node symmetry can be explained naturally as spin-fluctuation-mediated superconductivity.
Introduction
In iron-based superconductors, superconductivity appears in the vicinity of an antiferromagnetic (AF) phase and a structuralphase transition from tetragonal to orthorhombic phases. Therefore, spin and multi-orbital dynamics are believed to play animportant role in the superconducting mechanisms . The spin dynamics have been studied intensively by inelastic neutronscattering (INS) . In the superconducting states, magnetic resonance modes have been observed in the INS spectra of iron-based superconductors . Based on the doping dependence, the magnetic resonance energies are closely correlated with thesuperconducting gap energies . The low-energy spin dynamics are well explained by the Fermi surface nesting model .On the other hand, neither the magnetic resonance mode nor the spin fluctuation itself have been observed in the low su-perconducting transition temperature ( T c ) iron-based superconductor LaFePO − y . LaFePO − y is the first superconductordiscovered among the iron-based pnictogen compounds . Low-energy spin dynamics have also been studied by nuclear mag-netic resonance, suggesting that there are no AF spin fluctuations . The spin fluctuations are also strongly suppressed onhighly-doped LaFeAs(O,F) and Ba(Fe,Co) As . The suppression of low-energy spin fluctuations in both LaFeAs(O,F)and Ba(Fe,Co) As is explained by the poor nesting condition between Fermi surfaces (FSs) at Γ and M points caused by thedisappearance of hole FSs with increased electron doping . After the disappearance of hole FSs, the spin fluctuation energiesare expected to increase due to the necessary energy for electron-hole excitation between the two bands . A theoretical cal-culation based on a combination of density functional theory (DFT) and dynamical mean field theory (DMFT) successfullyreproduced the effective band width of magnetic excitations of NaFeAs in a wide energy range . According to theoreticalcalculation, spin fluctuations are expected to exist only above 30 meV for LaFePO . The pnictogen height ( h Pn ) of LaFePOis relatively low (1.14 ˚A) compared to that of BaFe As (1.37 ˚A), resulting in a wide band width of the magnetic excitationsin LaFePO. This is expected to result in a weak INS intensity at high energies .The parent stoichiometric material LaFePO . exhibits no superconductivity, long range magnetic order, or structural phase1ransition . Nevertheless, electron-doped LaFePO − y shows line-node symmetry revealed by the temperature dependence ofthe magnetic penetration depth and thermal conductivity measurements . The line-node symmetry of the sign-reversingorder parameter reminds us of the intervention of the magnetic fluctuation. Therefore, it is intriguing that there is no magneticorder in the parent material of LaFePO . in contrast to LaFeAsO . . Consequently, it is quite important to obtain dynamicalinformation on the spin fluctuations of LaFePO . in a wide energy range to examine the effects of the spin fluctuation on thesuperconductivity with line-node gap symmetry.Inelastic neutron scattering measurements have been performed on powder samples of LaFePO . with T c = 5 K andoptimally doped LaFeAsO . F . (LaFeAsOF) with T c = 29 K as a reference. They were characterized by magnetic suscep-tibility and X-ray diffraction measurements as shown in Fig. 1. In this paper, we demonstrate that spin fluctuation has beenclearly observed in low- T c LaFePO . ( T c = 5 K) in the range of 30 −
50 meV with similar intensities to the optimally dopedLaFeAsO . F . at the normal state (non-superconducting state), suggesting the universality of the correlation betweenline-node symmetry and spin fluctuations. Results
The constant-energy ( E ) cuts of the dynamical structure factor S ( Q , E ) at each momentum and energy transfer ( Q and E ) forLaFePO . and the optimally doped LaFeAsOF at 30 K are shown in Fig. 2. The low- Q region is limited by a kinematiccondition with the incident and final wave vectors. For low-energies ranging from 9 to 15 meV, the spin fluctuation is clearlyobserved only for the optimally doped LaFeAsOF as a peak at about 1.1 ˚A − , corresponding to the Q = ( π , 0) position inthe reduced tetragonal unit cell with a ∼ . The 2-dimensionalspin fluctuation is expected to appear as a magnetic rod in the Q -space. The magnetic rod intensity rapidly decreases withincreasing Q due to the magnetic form factor of Fe + . Although the magnetic rod signal has a small tail at a higher Q position after averaging the Debye ring, the signal can be approximated as a single Gaussian peak due to the broad width.For LaFePO . , the peak is strongly suppressed compared to that of LaFeAsO . F . . The magnetic resonance mode isexpected to be at 2.4 meV in LaFePO . based on the simple linear dependence of the energy on T c10–12 .Even at energies below 3 meV, spin fluctuations and the magnetic resonance mode in LaFePO . were not observed inDisk chopper time-of-flight spectrometer, IN5, and Cold Neutron Triple-Axis Spectrometer, CTAX, (See the Supplementaryinformation). These results are consistent with a previous report for LaFePO .At high energies, however, a spin fluctuation in LaFePO . was found as shown in Fig. 3. One may doubt that the signalmay be originated by phonons. However, the difference between phonon and magnetic signals can be distinguished by the Q and T dependences of the intensity. For the Q dependence, 2-dimensional spin fluctuations are expected to appear as magneticrods at various Q positions such as ( π , 0), ( π , 2 π ), (3 π , 0), (3 π , 2 π ), etc., due to the periodicity of Brillouin zone . As shownin Fig. 3, the first peak of Q = ( π , 2 π ) appeared at Q =2.6 ˚A − , whereas the second peak of Q = (3 π , 0) appeared at Q =3.4˚A − . The intensity depends on the multiplicity and the magnetic form factor of Fe + . In the case of LaFePO . , the intensityratio of ( π , 2 π ) to (3 π , 0) becomes about 4. The expected small peaks were observed at around 3.4 ˚A − in Fig.3 includingLaFeAsO . F . . The intensity ratio and the peak width were fixed in the fits in Fig. 3. In addition, the magnetic inelasticsignals are usually observed along the transverse directions (e.g. K direction at (1,0)) to the in-plane scattering vector . Thishas been attributed to the strong inter-band scattering along the longitudinal direction . Because of the present powder dataaveraging along the Debye ring, peak broadening due to the dispersion was mainly observed at Q = 2.6 ˚A − in Fig.3 . Thefitted intensities of the constant- E cuts of Fig. 2 at Q ∼ − , and Fig. 3(a), (c) at Q ∼ − were converted to χ ” ( E ) by using Bose factor, multiplicity, and magnetic form factor of Fe + , as shown in Fig. 4.For the temperature dependence, magnetic signals usually become weak at high temperatures mainly due to the shorteningof lifetime. On the other hand, phonon intensity simply increases with increasing temperature based on the Bose factor.Figure 3 shows the spin fluctuations in LaFePO . measured at T = 30 and 300 K. Based on the Bose factors in the E -range,the intensities at T = 300 K should increase by factors ranging from 1.11 to 1.46 compared to those at T = 30 K. Contrarily,all the intensities decreased with increasing temperature by factors ranging from 0.00 to 0.82. In addition to the two peaksin the INS pattern, this opposite temperature dependence strongly supports that the observed signals are originated from spinfluctuations. Discussion
Any strong AF spin fluctuations have not been observed previously for both LaFePO . and the optimally doped LaFeAsOF inthe nuclear spin relaxation rate 1/ T T of nuclear magnetic resonance (NMR) measurements . Here, by using INS, theywere observed at high energies. For LaFePO . , there is a large energy gap greater than 12 meV in the χ ” ( E ) . This energydependence is consistent with a theoretical calculation by DFT+DMFT , in addition to there being no enhancement of thenuclear spin relaxation rate 1/ T T of NMR measurements. This can also be explained by the wide effective band width of the agnetic excitations from the relatively low pnictogen height in LaFePO . . The observed intensity of χ ” ( E ) in LaFePO . at30-50 meV is greater than that of the optimally doped LaFeAsO . F . . These strong spin fluctuations are consistent withline-node symmetry in spin-fluctuation-mediated superconductors .On the other hand, the spin fluctuations in the optimally doped LaFeAsOF have a much lower energy component, as shownin Fig. 4. It is intriguing to point out that the absolute value of χ ” ( E ) at about 20 meV ( ∼ µ eV − Fe − ) for LaFeAsOF isalso very similar to the value ∼ µ eV − Cu − of La . Sr . CuO (in addition to having similar T c value) although theirelectronic structures, i.e., single and multi-orbitals, are very different. This similarity can be a hint for these unconventionalsuperconductivity from the spin fluctuation point of view.The existence of low-energy spin fluctuations may be related to the proximity to the AF parent compound with a structuralphase transition. For the LaFeAsOF system, the low-temperature enhancement of 1/ T T is observed only in the vicinity ofthe AF ordered phase. Upon electron doping, the enhancement is rapidly suppressed, suggesting an energy gap in χ ” ( E ) atlow energies . The AF spin fluctuations, however, are found here to persist at high energies in this work. The low- E spinfluctuation below 10 meV seems to disappear depending on the material parameter, U / W (electron-electron correlation energy, U , and electronic band width, W ) by increasing the doping or W . The detailed structure of χ ” ( E ) has some discrepanciesfrom DFT+DMFT calculation. For example, the observed peak structure at 30-50 meV in LaFePO . (Fig. 4) does not appearin the calculation. In addition, according to the calculation, the intensity for LaFePO is one order of magnitude smaller thanthat of LaFeAsO. Therefore, it is necessary to study in details how the energy dependence of the spin fluctuations depends onthe material parameters experimentally . Methods
Polycrystalline samples of LaFePO . , and LaFeAsO . F . were prepared by a solid-state reaction method. LaP, LaAs,Fe O , Fe, and FeF powders were used as the starting materials. LaP(As) was obtained by reacting La powders and P(As) grains in an evacuated quartz tube at 500 ◦ C for 5 h and then 700 ◦ C (850 ◦ C) for 10 h. The starting materials wereground with the nominal compositions LaFePO . and LaFeAs(O . F . ) . using agate mortar and then were pressed intopellets. Note that the molar ratio of (O − x F x ) . is lower than the stoichiometry because of partial oxidation of the precursor.They were then sintered for 10 h in an evacuated quartz tube at a sintering temperature 1250 ◦ C for LaFePO . and 1100 ◦ C forLaFeAsO − x F x . The heating rate was kept below 50 ◦ C/h to prevent the explosion of the quartz tube due to the sudden increaseof the P(As) vapor pressure. All the processes were performed in a glove box filled with nitrogen or helium gas. The actualfluorine content of LaFeAsO − x F x was determined by Secondary Ion Mass Spectrometry to be 0.082. X-ray diffractionpatterns were measured using Cu K α radiation (Rigaku RINT 1100), and the observed peaks were indexed to the tetragonalZrCuSiAs-type (so-called 1111-type) structure with space group of P / nmm and the lattice parameters were a = 3.955 ˚A and c = 8.504 ˚A for LaFePO . and a = 4.026 ˚A and c = 8.724 ˚A for LaFeAsO . F . as shown in Fig. 1(b). The dc magneticsusceptibility was measured using a SQUID magnetometer (MPMS, Quantum Design Inc.) under a magnetic field of 5 Oe.As shown in Fig. 1 (a), the T c values were determined to be 5 K for LaFePO . and 29 K for LaFeAsO . F . . Among threesamples of LaFePO − y with different initial oxygen contents ( y =0.0, 0.1, 0.2), the largest superconducting shielding volumefraction of ∼ y =0.1. On the other hand, the stoichiometric compound, LaFePO − y ( y =0.0) showed nosuperconductivity, which is consistent with a previous report .INS measurements were carried out using three spectrometers for high- and low- energy region complementally. High-energy measurements were performed using a Fermi chopper spectrometer at 4D Space Access Neutron Spectrometer (4SEA-SONS), BL01, in Japan Proton Accelerator Research Complex (J-PARC) Materials and Life Science Experimental Facility(MLF). The incident energies of E i =45.5 and 150 meV were employed with the multi- E i method . The energy resolu-tions are 3.2 and 18.0 meV for E i =45.5 and 150 meV at around E =0 meV, respectively. These values were obtained byestimating the full width at half maximum (FWHM) of the incoherent scattering around zero-neutron energy transfer. Themeasurement time and the sample weight are 11.5 h - and 25 g, respectively, for LaFePO . and 22 h - and 25 g, respectively,for LaFeAsO . F . at a beam power of 280 kW. To access the low- E region corresponding to the expected magneticresonance energy of about 2 meV of LaFePO . , a cold triple-axis spectrometer (CTAX) at High Flux Isotope Reactor (HFIR)in ORNL and chopper spectrometer IN5 in ILL were used. The measured transferred energy ranged from 1.0 to 3.0 meVfrom the CTAX and the neutron wavelength was λ =4.5 ˚A at IN5. The same 34 g sample was split into 14 g and 20 g for eachspectrometer. For both measurements, orange cryostats were used to access low temperatures down to 1.5 K.The constant- E plot was fit by Gaussian functions with constant, linear and quadratic functions as backgrounds. Theabsolute value of dynamical structure factor, S ( Q , E ) , is normalized by the Bragg peak intensity at (002). We also confirmedthat the absolute value of the S ( Q , E ) coincided within 10% by using another method of vanadium normalization. Thedynamical spin susceptibility is estimated as an isotropic spin fluctuation . U TSUSEMI software was used for data analysisof the data sets obtained at 4SEASONS . cknowledgements The authors thanks to Prof. M. Arai, Drs. Y. Inamura, S. Wakimoto, A. Iyo, H. Eisaki, F. Esaka and Mr. F. Mizunofor their helpful discussions. Magnetic susceptibility measurements were performed by using the SQUID magnetometer(MPMS,Quantum Design Inc.) at the CROSS user laboratory (B402). INS experiments at J-PARC MLF were carried outunder project numbers 2009A0087, 2014A0114 and 2017I0001. The experiment at ILL was conducted under the experimentnumber DIR-97 as a support program (Director’s Discretion Time (DIR)) to the earthquake damage of Japanese neutron facil-ities. This work was supported by JST, Transformative Research-Project on Iron Pnictides (TRIP), Grant-in-Aid for SpeciallyPromoted Research, Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan (No. 17001001), andJSPS KAKENHI Grant Number JP15K17712. A portion of this research used resources at the High Flux Isotope Reactor, aDOE Office of Science User Facility operated by the Oak Ridge National Laboratory, and was partly supported by the US-Japan Collaborative Program on Neutron Scattering.
Author contributions statement
M.I., S.S., K.K., R.K., M.N., T.H. and H.M. conducted the inelastic neutron scattering measurements. M.I. synthesized andcharacterized the powder samples. S.S. designed and coordinated the experiments. S.S. and M.I. mainly contributed to themanuscript with help from the others. All authors reviewed the manuscript and the comments were taken into consideration.
Additional information
Competing financial interests: The authors declare no competing interests.
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20 30 40 50 600100020003000400050006000 I n t e n s it y ( a r b . un it s ) q (degrees) LaFePO LaFeAsO F ( ) ( )( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )( )( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) Figure 1.
Magnetic susceptibilities (a) and X-ray diffraction patterns (b) of measured powder samples of LaFePO . andLaFeAsO . F . . Zero field cooling (ZFC) and field cooling (FC) processes are shown in (a) by arrows with solid andbroken lines, respectively. The diffraction pattern of LaFePO . is vertically shifted for clarity. (Å -1 ) (b)
15 meV12 meV9 meV (a) S ( Q , E ) ( m b s r - m e V - F e - ) Q (Å -1 ) Figure 2.
Constant- E cuts of the dynamical structure factor S ( Q , E ) at T = 30 K for (a) LaFePO . and (b)LaFeAsO . F . . The peak width, full width at half maximum (FWHM), for each fit is fixed to be 0.35 ˚A − . The Q -resolution at Q ∼ − is less than 0.12 ˚A − , which is much smaller than the observed widths. Scattering patterns arevertically shifted for clarity. (c)30 K Q (Å -1 ) S ( Q , E ) ( m b s r - m e V - F e - ) Q (Å -1 ) Q (Å -1 )(a) 30 K (b) 300 K
40 meV60 meV30 meV50 meV
Figure 3.
Constant- E cuts of the dynamical structure factor S ( Q , E ) in the energy range from 30 to 60 meV for (a)LaFePO . at T = 30 K, (b) LaFePO . at T = 300 K, and (c) LaFeAsO . F . at T = 30 K. The solid lines are fits with fixedintensity ratios. The FWHMs are fixed to be 0.5 ˚A − at ( π , 2 π ) and 0.35 ˚A − at (3 π , 0). The latter width is fixed based onthe width at ( π , 0). The Q -resolution at Q ∼ − is less than 0.25 ˚A − and that at Q ∼ − is less than 0.18 ˚A − ,which is much smaller than the observed widths. Scattering patterns are vertically shifted for clarity. c " ( E ) ( m B / e V / F e ) Energy (meV)
Figure 4.
Momentum-integrated dynamical spin susceptibility χ ” ( E ) for LaFePO . (red filled circles) andLaFeAsO . F . (blue filled circles). All the points were measured at the normal state of T = 30 K. The solid and brokenlines are guides for the eye.= 30 K. The solid and brokenlines are guides for the eye.