Magnetism of the Fe 2+ and Ce 3+ sublattices in Ce 2 O 2 FeSe 2 : a combined neutron powder diffraction, inelastic neutron scattering and density functional study
E. E. McCabe, C. Stock, J. L. Bettis Jr., M.-H. Whangbo, J. S. O. Evans
MMagnetism of the Fe and Ce sublattices in Ce O FeSe : a combined neutronpowder diffraction, inelastic neutron scattering and density functional study E. E. McCabe,
1, 2
C. Stock, J. L. Bettis Jr., M.-H. Whangbo, and J. S. O. Evans School of Physical Sciences, University of Kent, Canterbury, CT2 7NH, UK Department of Chemistry, Durham University, Durham, DH1 3LE, UK School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, UK Department of Chemistry, North Carolina State University, Raleigh, North Carolina, 27695-8204, USA (Dated: September 26, 2018)The discovery of superconductivity in the 122 iron selenide materials above 30 K necessitates anunderstanding of the underlying magnetic interactions. We present a combined experimental andtheoretical investigation of magnetic and semiconducting Ce O FeSe composed of chains of edge-linked iron selenide tetrahedra. The combined neutron diffraction and inelastic scattering studyand density functional calculations confirm the ferromagnetic nature of nearest-neighbour Fe – Se– Fe interactions in the ZrCuSiAs-related iron oxyselenide Ce O FeSe . Inelastic measurementsprovide an estimate of the strength of nearest-neighbor Fe – Fe and Fe – Ce interactions. These areconsistent with density functional theory calculations, which reveal that correlations in the Fe–Sesheets of Ce O FeSe are weak. The Fe on-site repulsion U Fe is comparable to that reported foroxyarsenides and K − x Fe − y Se , which are parents to iron-based superconductors.
1. INTRODUCTION
The discovery of iron-based superconductivity [1–4]with transition temperatures as high as 55 K [5] hasprompted efforts to understand both the electronic struc-ture and magnetism of these materials, which are interre-lated with superconductivity [6–8]. The first class of iron-based superconductors reported, the 1111 family, derivefrom Ln FeAsO ( Ln = trivalent lanthanide). They adoptthe ZrCuSiAs structure [9], composed of layers of edge-sharing O Ln tetrahedra alternating with layers of edge-sharing FeAs tetrahedra. A second class, 122 materials,derive from A Fe As ( A = Ca, Ba) with the ThCr Si structure [10], which again contains layers of edge-sharingFeAs tetrahedra. The metallic parent phases in bothclasses undergo structural phase transitions from tetrag-onal to orthorhombic symmetry just above an antifer-romagnetic (AFM) ordering temperature ( T N = 137 Kfor LaOFeAs [11] and 172 K for CaFe As [12]) withsmall ordered moments on the Fe sites in the ab plane.Superconductivity has also been observed in the binaryiron chalcogenide systems: the properties of Fe x Te arevery sensitive to the iron content [13] and superconduc-tivity can be induced by S or Se doping [14]; α -FeSe doesnot order magnetically and undergoes a transition to asuperconducting state at 8 K at ambient pressure [15],or 37 K at 7 GPa [16]. Recently, attention has turned tothe potassium-iron-selenide phase diagram, in particular,K . Fe . Se , which adopts a vacancy-ordered ThCr Si structure. This material is semiconducting [17–23] andorders antiferromagnetically below 559 K. Interestingly,the ordered Fe moments are large (3.31 µ B ) and areoriented perpendicular to the layer, in contrast to the1111 and 122 materials [24].The magnetism of the iron sublattice in these materialshas been the focus of much study in recent years. Initial studies on the 1111 and 122 materials suggested that theobserved stripe magnetic ordering (ferromagnetic stripesalong [010] in the orthorhombic unit cell) [25, 26] arisesfrom the competing nearest-neighbor (nn) and next-nearest-neighbor (nnn) AFM interactions [27, 28]. Sub-sequent work has highlighted the roles of other factorswhich lead to the complexity of the magnetic phase dia-gram for these materials [6, 29].In Ln FeAsO and Ln MnAsO materials, the Ln ionshave a significant role not only in tuning the super-conducting transition temperature in the doped phases(e.g. T c = 26 K for LaFeAsO − x F x [1], and 55 K forSmFeAsO − x F x [5]), but also in influencing the mag-netism in the undoped parent phases. For example, theFe moments of CeFeAsO order antiferromagneticallyin the ab plane at T N , Fe = 140 K [25] while the Ce moments couple strongly with the Fe moments at rel-atively high temperatures [30], before developing a longrange order below ∼ ab plane [25]. Recent studies suggested some re-orientation of the Fe moments within the ab plane atthe onset of the long range order of the Ce moments [31].The Ce ions influence the iron magnetic sublattice, andcan also induce exotic properties such as Kondo screen-ing of the local moment in closely-related CeFePO [32]and CeRuPO [33].The synthesis and crystal/magnetic structures of theiron oxyselenide Ce O FeSe were reported in 2011 [34].It adopts a ZrCuSiAs-related structurein which the tran-sition metal sites are half occupied by Fe cations in astripe ordered structure (Fig.1 a ). The magnetic struc-ture of Ce O FeSe (Fig.1 b ) determined from neutronpowder diffraction (NPD) data reported rather surpris-ing observations [34]. It undergoes an AFM ordering be-low T N = 171 K in which the Fe spins have a ferromag-netic (FM) order within each chain of edge-sharing FeSe a r X i v : . [ c ond - m a t . s t r- e l ] D ec c) a) b) d) Fe Se O Fe c b a b a a b c J b a c Fe Se O Ce Ce Ce Fe FIG. 1. [color online] (a) Orthorhombic nuclear unit cell and(b) monoclinic magnetic unit cell of Ce O FeSe (Ce = green,Fe = blue, O = red, and Se = yellow spheres). (c) An isolatedsheet of edge-sharing chains of FeSe tetrahedra present inCe O FeSe . (d) Zoomed-in view of the magnetic orderingin the Fe and Ce sublattices of Ce O FeSe . For convenienceof discussion, the directions of the orthorhombic unit cell areused to describe the magnetic structure in (c) and (d); theFM chains of edge-sharing FeSe tetrahedra lie in the ab -planewith the FM chains running along the a -direction. tetrahedra despite the Fe-Se-Fe angle (71.94 ◦ ) deviatingstrongly from 90 ◦ (Fig.1 b ), so one would have expected anAFM ordering according to the Goodenough-Kanamorirule [35–37]. In the present work we re-examine the mag-netic ordering in Ce O FeSe to confirm these unusualobservations on the basis of NPD and inelastic neutronscattering (INS) experiments as well as density functionaltheory (DFT) calculations. The paper is divided into fivesections including this introduction; experimental andcalculation descriptions; experimental and theoretical re-sults;and finally a discussion and conclusion.
2. EXPERIMENTAL DETAILS Ce O FeSe was prepared as a black, polycrystallinesample (2.48 g) as described previously [34]. Prelim-inary characterisation was carried out using a BrukerD8 X-ray diffractometer (reflection mode, Cu K α /K α radiation, Lynxeye Si strip position sensitive detector,step size 0.02 ◦ with variable slits) equipped with an Ox-ford Cryosystems PheniX cryostat. NPD data were col-lected on the high-flux D20 diffractometer at InstitutLaue Langevin (Grenoble, France) with neutron wave- length 2.41 ˚A. The sample was placed in a 6 mm cylin-drical vanadium can (to a height of ∼ θ range of 5-130 ◦ at2 K intervals on warming to 200 K. Powder diffractiondata were analyzed by the Rietveld method [38] using theTOPAS Academic software suite [39, 40] controlled by lo-cal routines. The diffractometer zero point and neutronwavelength were initially refined using data collected at12 K with lattice parameters fixed at values determinedpreviously [34]. The zero point and wavelength were thenfixed in all subsequent refinements. Typically, the back-ground was refined for each data set as well as the unitcell parameters and a Caglioti description of the peakshape. Structural characterization using data collectedon the HRPD diffractometer at ISIS revealed no struc-tural changes in this temperature range (4 – 218 K) [34],so the atomic coordinates were fixed and this work fo-cuses on the magnetic ordering. The web-based ISODIS-TORT software [41] was used to obtain a magnetic sym-metry mode description of the magnetic structure; mag-netic symmetry mode amplitudes were then refined todetermine the magnetic structures.The same polycrystalline sample was used for INS mea-surements. The sample was packed into an Al foil enve-lope and placed in an Al can. Two experiments wereperformed using the MARI direct geometry chopper in-strument at ISIS. The sample was cooled to 5 K in aclosed-cycle cryostat. The energy of the incident beam, E i , was selected using a Gd Fermi chopper spinning at150 Hz (for E i = 40 meV) or 400 Hz (for E i = 150 meV).In addition, a t chopper was used to block fast neu-trons and a thick disk chopper (spinning at 50 Hz) wasused to improve background from neutrons above theGd absorption edge. The cold triple-axis spectrometerSPINS at NIST Center for Neutron Research (Gaithers-burg, USA) was used to investigate the temperature de-pendence of the crystal fields. A pyrolytic graphite (PG)monochromator (004 reflection) was used on the incidentbeam to give good resolution at high energy transfers anda PG(002) analyzer (horizontally focused over 11 ◦ ) wastuned to select a fixed final energy of E f = 5.0 meV. ABe filter was used on the scattered side.In our DFT electronic structure calculations forCe O FeSe , we employed the projected augmented-wave (PAW) method encoded in the Vienna ab initiosimulation package [42–44], and the generalized gradientapproximation (GGA) of Perdew, Burke and Ernzerhof[45] for the exchange-correlation corrections, the planewave cutoff energy of 500 eV, and the threshold of self-consistent-field (SCF) energy convergence of 10 − eV. Weextract four spin exchange parameters by employing fiveordered spin states defined on a ( a , 2 b , c ) supercell (seebelow). The irreducible Brillouin zone was sampled with4 × × k -points. To describe the electron correlationassociated with the 3d states of Fe and the 4f states ofCe, the DFT plus on-site repulsion U (DFT+U) [46] cal-culations were carried out with effective U eff = U - J (seebelow).
3. RESULTS
In this section we outline the experimental and com-putational results of this paper. We first discuss the neu-tron diffraction results probing the magnetic structurefollowed by a section discussing inelastic neutron resultsfrom which exchange constants between the Fe ions andthe Ce ions are derived. Finally, these are compared withdensity functional calculations.
A. Neutron powder diffraction
Rietveld analysis of NPD data collected at 250 Kare consistent with the Fe-ordered, orthorhombic crys-tal structure described above. Additional reflections ob-served below T N are consistent with the magnetic or-dering (and propagation vector (cid:126)k = (0
12 12 )) reportedpreviously [34] and were indexed using an a n × b n × c n supercell (where the subscript n refers to the nuclearunit cell); hkl indices given subsequently for magnetic re-flections refer to this magnetic unit cell. The intensity ofthese reflections increases smoothly on cooling to ∼ ∼
170 K can be fitted bythe nuclear structure and a magnetic phase composed ofFM chains of edge-sharing FeSe tetrahedra, with AFMcoupling between adjacent FM chains (Fig.1 b ). Attemptsto fit the data with models containing AFM chains werenot successful. The “symmetry adapted ordering mode”approach [41] was used here to describe the magneticallyordered structure. Mode inclusion analysis (describedelsewhere, [47]) was used to confirm that this arrange-ment of Fe moments gives the best fit to the data anddoes not change below T N . Other models, including thosewith AFM chains, gave significantly worse fits. Whilstthis FM-chain model gives magnetic Bragg peaks in theobserved positions, the fit to the peak intensities wasnot perfect. Mode inclusion analyses were carried out atlower temperatures (80 K, 4 K) and confirmed that thearrangement of Fe moments does not change on cool-ing. Given the large ordered moment on the Fe sites inCe O FeSe , we would expect our refinements to be sen-sitive to slight reorientations of the Fe moments, butthere is no indication that reorientation of the Fe mo-ments occurs. This is in contrast to the related PrFeAsOin which the Fe moments cant slightly along c at theonset of Pr ordering [48]. I n t e n s i t y ( a r b i t r a r y un i t s ) Temperature (K) sum_mag a) c) d) e) I n t e n s i t y ( a r b i t r a r y un i t s ) Temperature (K) 011 -100102030405060 0 50 100 150 200 I n t e n s i t y ( a r b i t r a r y un i t s ) Temperature (K) 015 b) -20-10010 I n t e n s i t y ( a r b i t r a r y un i t s ) Temperature (K) 113 -1001020 I n t e n s i t y ( a r b i t r a r y un i t s ) Temperature (K) 013 -0.50.00.51.01.52.02.53.0 0 25 50 75 100 125 150 175 200 M a g n e t i c m o m e n t ( μ B ) Temperature (K) f) FIG. 2. [color online] Temperature-dependence of the mag-netic Bragg reflections: (a) Sum of the intensity of the 17strongest magnetic reflections. (b-e) The intensity of the (0 11), (0 1 3), (0 1 5) and (1 1 3) reflections ( hkl indices refer tothe a n × b n × c n magnetic unit cell) from the sequential re-finements using a Pawley phase to fit the magnetic reflections.(f) Evolution of the Fe (blue, solid) and Ce (green, open)magnetic moments on cooling from Rietveld refinements. Thesolid black line shows fit to the function M T = M (1 − ( TT N )) β for the Fe data between 100 - 171 K with M ,Fe = 3.40(4) µ B , T N = 175.5(8) K and β = 0.28(1). Whilst the FM-chain model gives a better fit thanAFM-chain models,further analysis indicated that in-cluding the Ce magnetic ordering modes improves thefit significantly ( R wp decreases from 5.49% to 4.37% at80 K, and from 7.19% to 4.61% at 4 K for one addi-tional parameter). Refinements are very sensitive to therelative signs of the Fe and Ce magnetic orderingmode amplitudes. For example, as measured by R wp , asurface plot showing fit for different amplitudes of theCe and Fe magnetic ordering modes indicates that thebest fit is obtained when both modes have the same sign,corresponding to a FM coupling between nn Fe and Cesites (see Supplementary Material). Refinement profilesand details are shown in Fig.3. If canting of the Ce mo-ments is included in the model, the Ce moments becomeoriented at ∼ ◦ to the ab plane (i.e., a z componentof 0.25(5) µ B ) and R wp is reduced by 0.04 %, but thisimprovement cannot be regarded as significant from ourdata.Analysis using ISODISTORT [41] suggests that themagnetic structure of Ce O FeSe can be described bythe C -centered space group C c /c [BNS: 15.9 with basis(0, -1, 1), (-1, 0, 0), (0, 2, 0) and origin at (0, 0, 0)] shown
2θ (°) I n t e n s i t y ( a r b i t r a r y un i t s ) Ce2O2FeSe2 59.97 %Ce2O2Se 1.71 %magnetic 38.32 %
Ce2O2FeSe2 59.97 %Ce2O2Se 1.71 %magnetic 38.32 % I n t e n s i t y ( a r b i t r a r y un i t s )
2θ (°) S S S S S S S S S S S S S S S S M M M M M M M M M M M observed calculated (total) calculated (magnetic) difference a n ×2 b n ×2 c n : C c /c: M M - M M - - M M - M M M M M - * * * * FIG. 3. [color online] Rietveld refinement profiles of the 4 K data for Ce O FeSe showing the observed (blue), calculated(red) and difference (grey) profiles. Both nuclear and magnetic-only phases were included in the refinement and scatteringfrom the magnetic phase is highlighted by the solid green line. The tick marks for the nuclear structure (black, top), and theCe O Se impurity ( <
2% by weight, marked by ∗ ) (blue, central) and magnetic (green, bottom) structure are shown below. Therefinement was carried out for the nuclear structure using space group Imcb , a = 5.6788(8) ˚A, b = 5.7087 (9) ˚A, c = 17.290(2)˚A, and for the magnetic structure using space group C c c , a = 18.208(2) ˚A, b = 5.6788(8) ˚A, c = 11.417, β = 108.272(3) ◦ .Moments of 3.14(8) µ B and 1.14(4) µ B were obtained for the Fe and Ce sites, respectively, with R wp = 4.34% and R p = 3.23%. hkl values for nuclear reflections are given in upper panel in black; hkl indices for magnetic reflections are given in lower panelin green (those for the a n × b n × c n magnetic unit cell above in bold; those for the C c c cell below italicised). in Figure1 b and refinement using 4 K data gives momentsof 3.14(8) µ B and 1.14(4) µ B for Fe and Ce sites, re-spectively. The ordered Fe moment in Ce O FeSe iscomparable with that reported for the Mott insulatingoxyselenides (e.g., La O Fe OSe (3.50(2) µ B ) [49] andthe parent phase to superconducting K . Fe . Se (3.31 µ B ) [24]), and is consistent with a high-spin d configu-ration for Fe sites. It is significantly larger than thatobserved in Ln FeAsO materials with poor metallic be-havior (e.g. 0.94(3) µ B for CeFeAsO at 1.7 K [25]).The sequential Rietveld refinements using NPD datacollected on cooling show that the Ce moment increasesalmost linearly at low temperatures. The Fe moment canbe fitted well by the critical behavior with β = 0.28(1)and T N = 175.8(8) K (Fig.2f) for 100 K < T <
171 K.This Fe moment ordering is similar to that observedfor CeFeAsO at T N = 137 K, which can be describedby critical behavior with β = 0.24(1) [30]. These val-ues for β are larger than those reported for 2D-Ising likesystems (including undoped BaFe As ( β =0.125 [50])and La O Fe OSe ( β =0.122 [49])), but smaller thanthose predicted for three-dimensional critical fluctuations( β =0.326, 0.367 and 0.345 for 3D Ising, 3D Heisenbergand 3D XY systems, respectively) [51]. The crossover be- tween 2D and 3D universality classes has been suggestedto originate from a coupling to an orbital degree of free-dom [52] or the prroximity of a Lifshitz point (see, forexample, Fe x Te [53] and BaFe As [54]).The unusual change in the relative intensities of thedifferent magnetic Bragg reflections observed on coolingCe O FeSe (Fig.2) can be rationalised in terms of thecontribution of the Ce and Fe moments to peak intensi-ties. The magnetic modes that describe the ordering ofboth the Fe and Ce moments have the same basis vec-tor (cid:126)k = (0
12 12 ). As a consequence, the ordering onthese two sublattices contributes to mostly the same re-flections. Based on the magnetic unit cell a n × b n × c n ,the hkl reflections with h = 2n, k, l (cid:54) = 2n and h + k + l = 2n(i.e., (0 1 1), (0 1 3), (0 1 5)) have contributions from bothCe and Fe sublattices, whilst some weaker hkl reflectionswith h (cid:54) =2n, k, l (cid:54) =2n and h + k + l (cid:54) =2n have contributionsonly from the Ce ordering. The ordering of the Fe and Cesublattices adds constructively for some peak intensities(e.g., (0 1 1), (0 1 9)) and destructively for others (e.g.,(0 1 5), (0 1 7), (0 1 3)) (For this latter (0 1 3) reflec-tion the Ce contribution is small and so the intensity isdominated by Fe ordering). The non-monotonic temper-ature dependence of the magnetic reflection intensitiesobserved for Ce O FeSe is similar to those reported for Ln CuO ( Ln = Pr, Nd, T N , Cu = 250-325 K) [55] andfor CeVO ( T N = 124-136 K) [56, 57]. B. Inelastic neutron scattering
INS was used to obtain experimental estimates for themagnetic exchange interactions. Low-energy fluctuationswere studied to probe directly the Fe-Fe exchange alongthe chains. Ce crystal electric field (CEF) excitationswere then investigated to determine the Fe-Ce exchange.Before discussing the scattering response from mag-netic ions, we first describe how the background was sub-tracted from the powder averaged data. The measuredneutron scattering intensity I meas is proportional to thestructure factor S ( Q, E ) but also includes a temperature-independent background contribution due to instrumenteffects and sample environment. Using the principleof detailed balance, we employ data collected at dif-ferent temperatures to account for the temperature-independent background. This allows us to isolate theinelastic scattering (Appendix A), which has both mag-netic and lattice (phonon) contributions. To extract thepurely magnetic scattering, we assume that the 300 Kscattering is dominated by phonons, which is a reason-able approximation. Scaling by the Bose factor andassuming a harmonic response (Appendix 1), we esti-mate the phonon cross section at each temperature andsubtract it from the background-corrected data. Us-ing this method we extract the purely magnetic scat-tering at a given temperature, as has been used previ-ously to study the hydrogen-containing polymeric mag-net Cu(quinoxaline)Br [58] and the low-energy magneticdynamics of Fe − x Te − y Se y [59].The purely magnetic contributions to the inelasticscattering are shown in Figure 4 for E i = 40 meV. Astrong, sharp excitation, independent of Q , is observedat E ∼
11 meV, which is ascribed to the Ce CEF exci-tations. At slightly lower energies, a gapped excitation isobserved near Q = 0. The gap value is similar to that ob-served in other parent Fe based superconductors suchas Fe x Te [60] and La O Fe OSe [49] and in 122 sys-tems including BaFe As [61]. Unlike the crystal fieldexcitation, this scattering is well-defined in momentumand decays quickly with momentum transfer, bearing astrong resemblance to the magnetic excitation observedin powder averaged measurements of La O Fe OSe [49].The temperature-dependence of this excitation is also dif-ferent from that of the Ce CEF excitation: at 4 K, ithas a gap of ∼ b, c ). Basedon these observations, we conclude that the low energy,low- Q scattering originates from the Fe magnetic sub-lattice.To separate the Ce CEF excitations from the Fe magnetic excitations, the CEF contribution was esti-mated by taking a cut over the momentum transfer rangeof Q = 2.8 - 3.5 ˚A − , and then scaling by the Ce formfactor [62] to estimate the momentum dependence. Thissubtraction takes advantage of the fact that the crystalfield excitations are dispersionless and flat in momentumtransfer, particularly in comparison with the strong mo-mentum dependence of the scattering associated with theFe sites (as observed for La O Fe OSe [49] for exam-ple). This analysis leaves only the strongly momentumvarying component near Q = 0 (Fig.4 d ), from which themagnetic exchange interactions between Fe sites canbe estimated.The single-mode approximation [63] can be used tocompare possible magnetic structures with different signs(AFM J <
0, FM J >
0) and magnitudes for the nninteraction J (illustrated in Figure 6). Using the singlemode approximation the structure factor S ( (cid:126)Q, E ) can bewritten in terms of a momentum-dependent term S ( (cid:126)Q )and a single Dirac delta function in energy: S ( (cid:126)Q, E ) = S ( (cid:126)Q ) δ [ E − (cid:15) ( (cid:126)Q )] . (1)where (cid:15) ( (cid:126)Q ) is the dispersion. We approximate δ ( E ) asa Lorentzian term with full-width equal to the calcu-lated resolution width in energy. The first moment sumrule [64] relates S ( (cid:126)Q ) to the dispersion: S ( (cid:126)Q ) = −
23 1 (cid:15) ( (cid:126)Q ) (cid:88) (cid:126)d J (cid:104) (cid:126)S · (cid:126)S (cid:126)d (cid:105) [1 − cos( (cid:126)Q · (cid:126)d )] . (2)where (cid:126)d is the bond vector connecting nn spins with anexchange interaction J . Making the assumption thatthis intrachain interaction dominates, we use the disper-sion relation for the one-dimensional (1D) chain system: (cid:15) ( (cid:126)Q ) = 4 S [∆ + J [1 − cos( πH )] ] . (3)where ∆ is the gap value determined by anisotropy and J is the nn intrachain exchange interaction.Representative calculations using the AFM and FMchain models are summarized in Figure 4. The AFMmodel gives correlations at finite Q , whereas the FMmodel gives magnetic scattering only at lowest measur-able wave vectors (near Q = 0). From the temperaturedependence (Figure 4 a − c ) and the subtracted data (Fig-ure 4 d ), the strongly temperature dependent magneticscattering is present near Q = 0. This is more consis-tent with a dominant FM J interaction (simulated inFigure 4 f ) than an AFM interaction where the scatter-ing is peaked at finite Q . Based on this comparison, weconclude that the exchange mechanism is predominatelyferromagnetic ( J > f − h shows results of sin-gle mode calculations for this FM chain model for various FIG. 4. [color online] MARI scan with E i = 40 meV showing Ce CEF excitation and magnetic excitation from the Fe sublatticeat (a) 4 K, (b) 75 K and (c) 115 K. (d) MARI scan with E i = 40 meV with scattering due to Ce CEF subtracted (seetext) showing only magnetic excitation from the Fe sublattice. Powder averaged single mode analysis spin wave calculationswith (e) AFM and (f) FM chains along [100]. An intrachain exchange interaction J = 10 meV (positive sign denotes FMinteractions) was used in these spin-wave calculations. (g), (h) show single mode calculations for different magnitudes of theFM J interaction. (The white regions at lowest momentum transfer are masked by the beam stop, and the curvature withincreasing energy transfer of this inaccessible region is due to the fixed incident energy kinematics imposed by the instrumentgeometry.) values of J . It is difficult to give an accurate value forthis exchange interaction given the scattering is concen-trated near Q = 0, but our calculations indicate that J ∼ CEF excitations observed in the INSdata at ∼
11 meV and ∼
37 meV (Fig.5) with the goalof extracting the coupling between Fe and Ce sites. Themagnetic nature of the peak around 11 meV is confirmedby the temperature dependence shown in Figure 5. Thesoftening of the first crystal field excitation (Fig. 5d-f)with increasing temperature could be the result of ther-mal expansion or of a change in the ground state [65]. Wenote that the softening observed can be reproduced bypoint charge calculations and is consistent with thermalexpansion. To obtain an estimate of Fe – Ce exchange, it is important to have a heuristic model for the Ce crystalfields from which eigenfunctions and transition energiescan be derived. Ce (4f , J = ) is a Kramers ion (Fig.5), and each level remains doubly degenerate for all crys-talline electric fields unless a magnetic field is applied.Magnetic ordering on the iron sublattice can give rise toa molecular field at the Ce sites if there is coupling be-tween Fe and Ce ions. In the oxyarsenide CeFeAsO,the degeneracy of Ce CEF states is lifted below T N,F e suggesting some Fe - Ce coupling [66], which is consistentwith muon spin rotation spectroscopy studies [30]. Inthe vacancy-ordered Ce O FeSe structure (space group Imcb ), the Ce atoms are on 8 j sites with local point sym-metry C . The resulting crystal field Hamiltonian can beexpressed in Stevens operators formalism which requiresfive nonzero terms to describe the monoclinic symmetryof the Ce site [67]: I n t en s i t y ( A r b i t r a r y U n i t s ) E ( m e V ) E (meV) I n t en s i t y ( C oun t s / m i n ) a) Ce J=5/2 |1>|0>|2> c) T=5 KE i =40 meVb) T=5 K,MARIE i =150 meV d) T=2 K,SPINSe) T=50 Kf) T=125 K FIG. 5. Mari and SPINS data for Ce O FeSe showing CEFlevels for Ce site as a function of temperature. The solidcurves are fits to a Gaussian function. H C = B O + B O + B O + B O + B O . (4)Ideally, these five terms would be determined by fittingto the experimental data but they cannot be uniquely andunambiguously determined with only two CEF energiesand intensities and the ordered moment from the NPDanalysis (which depends on the Ce ground state wave-function determined from the eigenvectors of Eqn. 4).Therefore, a simplified model for the crystal field schemehas been investigated. With no vacancy ordering on theiron sublattice (Fig.1), the symmetry of the Ce siteswould be tetragonal and the Hamiltonan for this schemecontains only three non-zero terms: H tetrag = B O + B O + B O . (5)using the two CEF energies and intensities and the or-dered moment from NPD (giving five experimental “datapoints”), the three coefficients are determined as B =1.5(2) meV, B = -0.03(1) meV B = -0.43(7) meV. Theambiguity regarding the sign of these coefficients wasresolved with the results from a “cluster” point chargecalculation integrating over 40 unit cells to ensure con-vergence of the Stevens coefficients (see appendices fordetails of this calculation). We now use this heuristic model of the crystal fieldsto derive an exchange coupling between the Fe – Ce ionsbased upon the broadening of the crystal field levels inthe magnetically ordered low temperature phase. Be-cause of Kramer’s theorem, the crystal field excitationsare doubly degenerate and only split in the presence of atime reversal violating magnetic field. This splitting canbe calculated by adding the following Zeeman term tothe crystal field Hamiltonian above for eigenstates i and j : H Zeeman ( i,j ) = µ µ B H (cid:104) i | J z | j (cid:105) (6)where µ B and µ are the Bohr magneton and perme-ability of free space, respectively, H is the effective mag-netic field, J z is an angular momentum operator along z , and (cid:104) i | J z | j (cid:105) is the angular momentum matrix elementfrom the ground state to the excited state. To accountfor the powder averaging, all three directions ( x , y , and z ) were averaged. The molecular field on the Ce siteis induced by magnetic ordering on the Fe sublattice(Fig.1 d ). In the absence of a molecular field at the Cesites, any splitting/broadening of the Kramers doubletsshould arise from the Fe – Ce coupling [66] and is con-sistent with muon spin relaxation studies, which indicatea strong non-Heisenberg anisotropic Fe – Ce exchangewell above T N , Ce in CeFeAsO [30]. In the Fe-orderedcrystal structure of Ce O FeSe (Fig.1 c ), the FM chainsof edge-shared FeSe tetrahedra alternate with vacantstripes along [010] and each Ce site is coupled to two Fesites within a single FM chain (Fig.1 d )) and there are nocompeting Fe – Ce interactions. The molecular field onthe Ce site due to the Fe magnetic sublattice is equal to2 SJ where J is the Fe – Ce exchange coupling. Thisprovides an opportunity to probe the Fe – Ce coupling bymeasuring the broadening of the crystal field excitations.The CEF levels observed for Ce O FeSe are broad-ened (Fig.5 d − f ) considerably beyond the instrumentalresolution (represented by the horizontal bar in Fig.5 e ),but it is difficult to determine the splitting of the Kramersdoublets (Fig.5) in contrast to the case of CeAsFeO. Toprovide an estimate for the Fe – Ce exchange coupling,we have fitted the low temperature excitation to a singleGaussian to obtain a full-width of 2.0(4) meV, giving amaximum value for any splitting of ∼ J of ∼ J interaction discussed above. C. Spin exchange and electronic structure
Summarizing the experimental results above, we ob-serve ferromagnetic Fe – Fe and weaker ferromagnetic
FM (-1, -1, -2, -4)
AF1 (-1, -1, -2, +4) AF2 (-1, +1, +2, -4) AF3 (+1, -1, +2, 0) AF4 (+1, +1, -2, 0) b c J J (along [110]) J Fe Ce (a) (b) (c) (d) (e) (f) J (along [010]) FIG. 6. [color online] (a) Four spin exchange paths ofCe O FeSe . (b-f) Five ordered spin arrangements FM andAF1 - AF4 employed to extract J – J by energy mappinganalysis. The numbers in the parentheses in the first row referto the relative energies in meV/FU, and the bracketed num-bers represent the numbers n , n , n and n of Eq. 8. AF2 isthe structure observed experimentally from diffraction with aweak J exchange expected from neutron inelastic scattering. Fe – Ce exchange. This is based on both magnetic neu-tron diffraction and inelastic scattering results. In thissection, we provide electronic structure calculations withthe goal of understanding these results and comparingthem with previous calculations.Figure 6 a shows the four spin exchanges of Ce O FeSe we investigate, namely, the intrachain exchange, J , andthe interchain exchanges, J and J , between Fe ions aswell as the exchange J between Fe and Ce ions. Toextract the values of J – J by energy-mapping analysis[68–70], we consider five ordered spin states FM and AF1– AF4 presented in Figure 6 b − f . The FM, AF1 and AF2states contain FM chains. The coupling between adjacentFM chains is FM in the FM and AF1 states, but AFMin the AF2 state. The coupling between the Fe andCe ions is FM in the FM and AF2 states, but AFM inthe AF1 state. The AF3 and AF4 states consist of AFMchains so that the net spin exchange between the Fe and Ce ions vanishes. The coupling between adjacentAFM chains is FM in the AF3 state, but AFM in theAF4 state. The AF2 state is closest to that observedexperimentally. The total spin exchange energies of theFM and AF1 – AF4 states can be expressed in terms ofthe spin Hamiltonian, H = − (cid:88) i
21 meV, is comparable in magni-tude to the experimental value of about 10 – 20 meV fromINS. Furthermore, the calculated value for the Fe – Ceexchange, J = 0.2 meV, is in good agreement with theexperimental value of about 0.15 meV. Similar energy-mapping analyses were carried out with other values of U F e and U Ce , as shown in Table II. These calculationsshow that J is strongly FM and that J is weakly FMfor the U F e = 2 eV and U Ce = 12 eV combination (allother combinations give J weakly AFM). TABLE II. Values of J – J (in meV) from energy-mappinganalyses based on various U Fe and U Ce values (in eV). J J J J U Fe = 2, U Ce = 12 +21.3 -1.4 -1.4 +0.2 U Fe = 2, U Ce = 10 +20.7 +1.8 -1.5 -0.6 U Fe = 0, U Ce = 12 +23.2 -2.1 -1.1 +0.0 U Fe = 0, U Ce = 10 +27.9 -0.1 -0.3 0.0 Figure 7 shows plots of the projected density of states(PDOS) obtained for the Ce 4f, Ce 5d, Fe 3d and Se4p states of Ce O FeSe from the DFT+U calculationswith U F e = 2 eV and U Ce = 6, 8, 10 and 12 eV. It showsa band gap of about 1 eV which is consistent with thesemiconducting behavior of Ce O FeSe observed exper-imentally (with band gap of 0.64 eV) [34].We note from Figure 7 that the Fe 3d states overlapwith the Se 4p states througout the filled energy region,which indicates that the interaction between Fe 3d andSe 4p orbitals takes place throughout this energy range.The Ce 5d states contribute to the filled region of theFe 3d and Se 4p states, and these contributions are notstrongly affected by the change in U Ce . However, on in-creasing U Ce from 6 eV to 12 eV, the Ce 4f states aregradually lowered in energy such that they overlap withthe filled Fe 3d and Se 4p states when U Ce <
12 eV,but do not when U Ce ≥
12 eV. Likewise, the filled Ce 4fstates overlap with the Ce 5d states when U Ce <
12 eVbut do not when U Ce ≥
12 eV. The ferromagnetic Fe –Se – Ce spin exchange J (and increased stability of theexperimentally observed AF2 spin arrangement) is foundwhen the Ce 5d states do not overlap in energy with theFe 3d and Se 4p states in the energy region within 2 eVbelow the Fermi level. This is understandable because anantiferromagnetic Fe-Se-Ce spin exchange would involvethe Fe 3d, Se 4p and Ce 5d orbitals. That the electronicstructure of Ce O FeSe is described by using a smallvalue of U F e (2 eV) suggests a weakly correlated natureof the iron-selenide sheets in Ce O FeSe . This is similarto that found for parent materials to iron-based super-conductors ( U F e ∼ As [74] and ∼ . Fe . Se [75]. The need for a large on-siterepulsion U Ce for Ce (12 eV) is comparable to the trendestablished for CeFeAsO where U Ce = 9 eV was required [76].
4. DISCUSSION
In the low-temperature magnetic structure ofCe O FeSe , both Ce and Fe moments lie withinthe ab plane, similar to the structure reported for Ce-FeAsO [25]. The observation of in-plane Ce momentsis consistent with the easy-axis along x proposed forCe sites in orthorhombic CeFeAsO [77]. The orderedCe moment of Ce O FeSe at 4 K (1.14(4) µ B ) isslightly larger than that reported for CeFeAsO (0.83(2) µ B at 1.7 K) [25], and is close to that expected fora Ce doublet ground state (1 µ B ) [66]. The highordering temperature for the Ce moments implied byour NPD data is surprising; other systems known tohave high Ce ordering temperatures include CeRh B (115 K) in which Ce ion is the only magnetic ion [78]and CeVO (50 K) in which Ce ordering is thought toarise from FM exchange between Ce and V ions[56, 57]. The high Ce moment ordering temperaturein Ce O FeSe is most probably due to the FM spinexchange between adjacent Ce and Fe ions, thatis, the long range magnetic order of the Fe sublatticeinduces that of the Ce ions. In CeFeAsO, each Cesite is coupled to two FM chains of edge-sharing FeAs tetrahedra with opposite spin orientations [25], leadingto frustration of any Ce – Fe exchange interactions[79]. This is expected to give a negligible field on theCe site (consistent with the low Ce moment orderingtemperature). The very small CEF splitting ( ∼ O FeSe is similar to that described forthe parasitic ordering of Ce moments in CeMnAsO[80].The nn Fe – Fe magnetic exchange interactions, J ,determined here experimentally are in good agreementwith our DFT calculations. They are similar in magni-tude to those reported for CeFeAsO [81] but of oppositesign. They are significantly larger than those reportedfor La O Fe OSe , in which the Fe cations are coor-dinated by both oxide and selenide anions, which maygive rise to more strongly correlated behavior [49]. Wenote that the nn J interactions in Ce O FeSe are FM,which may reflect some orbital ordering on Fe sites, asproposed for the pnictides [52].
5. CONCLUSIONS
In conclusion, the FM nature of Fe – Se – Fe nn inter-actions J has been confirmed by NPD and INS measure-ments. INS work indicates that this exchange is ∼
10 – 20meV. This is consistent with DFT + U calculations for U F e ≤ . Se sheets in Ce O FeSe are weakly correlated, sim-0 a) c) b) d) Ce f-state: ― Energy (eV) Energy (eV) Energy (eV) Energy (eV) S t a t e s ( e V / a t o m ) S t a t e s ( e V / a t o m ) S t a t e s ( e V / a t o m ) S t a t e s ( e V / a t o m ) Ce d-state: ― Fe d-state: ― Se p-state: ― U Ce = 6 eV U Ce = 8 eV U Ce = 10 eV U Ce = 12 eV FIG. 7. [color online] PDOS plots obtained for the Ce 4f, Ce 5d, Fe 3d and Se 4p states of Ce O FeSe from the DFT+Ucalculations with U Fe = 2 eV and U Ce = 6, 8, 10 and 12 eV. The vertical axis represents the density of states, and the horizontalaxis the energy in eV. ilar to the FeAs sheets in SmFeAsO and BaFe As . WeakFM Fe – Se – Ce interactions of 0.15 - 0.20 meV (repro-duced by DFT + U calculations for U F e = 2 eV) are notfrustrated in this cation-ordered ZrCuSiAs-related struc-ture. Therefore ”parasitic” ordering of Ce +3 might beinduced by magnetic ordering of the Fe sublattice, withCe moments parallel to adjacent Fe moments.See Supplemental Material at [URL will be inserted bypublisher] for details of analysis of NPD data includingrelative intensity of magnetic reflections on cooling aswell as surface plots for magetic refinements.We acknowledge STFC, EPSRC (EP/J011533/1),Royal Society of Edinbugh, and the NSF (DMR-0944772)for funding. We thank Emma Suard (ILL), Ross Stewart(ISIS) for assistance and Mark Green (Kent) and EfrainRodriguez (Maryland) for helpful discussions. APPENDIX A: INS DATA ANALYSIS
The principle of detailed balance can be used to es-timate the temperature-independent background contri-bution to the scattering. We can approximate that for a fixed wave vector and energy transfer, the neutron energygain (negative energy transfer, ( −| E | )) and neutron en-ergy loss (positive energy transfer, (+ | E | )) are related bythe following expression from the detailed balance prin-ciple: I meas (+ | E | , T ) = B ( | E | ) + S ( | E | , T ) (A1) I meas ( | E | , T ) = B ( | E | ) + S ( | E | , T ) exp [ − Ek B T ] (A2)where B and B are temperature-independent back-ground points, S ( | E | , T ) is the scattered intensity (withboth magnetic and phonon contributions) and exp [ − Ek B T ]is the Boltzmann factor. We assume that the resolutionof the inelastic scattering does not change over the en-ergy range investigated. With data collected at two ormore temperatures, B and B can be determined. For E i = 40 meV, data were collected at six temperatures (4K, 75 K, 115 K, 150 K, 200 K and 300 K). These datagive us experimental data points in both the energy gainand energy loss spectra (giving 12 data points in total)1with which the two background points B and B andthe six values for S ( | E | , Q, T ) can be determined.This detailed balance allows us to isolate the inelas-tic scattering but this has contributions from both mag-netic and phonon scattering. The measured intensity I meas is proportional to the structure factor S ( Q, E )which is related to the imaginary part of the suscepti-bility χ (cid:48)(cid:48) ( Q, E ): I meas ∝ S ( Q, E ) = 1 π [ n ( E ) + 1] χ (cid:48)(cid:48) ( Q, E ) (A3)where n(E) is the Bose factor. The scattering at 300 K isdominated by phonons and so the phonon contribution χ (cid:48)(cid:48) phonon ( Q, E ) can be written: χ (cid:48)(cid:48) phonon ( Q, E ) = S K ( Q, E )[ n ( E ) K + 1] (A4)The phonon contribution at each temperature was thenestimated using equation A3 and subtracted to obtain thepurely magnetic scattering at each temperature. APPENDIX B: POINT CHARGE CLUSTERMODEL CALCULATION
To guide the CEF analysis, we used a point charge“cluster” model (integrated over 40 unit cells to ensureconvergence of the Stevens coefficients) which gave theresults shown in Table B1.
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