Coupling of localized moments and itinerant electrons in EuFe2As2 single crystals studied by Electron Spin Resonance
E. Dengler, J. Deisenhofer, H.-A. Krug von Nidda, Seunghyun Khim, J. S. Kim, Kee Hoon Kim, F. Casper, C. Felser, A. Loidl
aa r X i v : . [ c ond - m a t . s up r- c on ] S e p Coupling of localized moments and itinerant electrons in EuFe As single crystalsstudied by Electron Spin Resonance E. Dengler, J. Deisenhofer, ∗ H.-A. Krug von Nidda, Seunghyun Khim, J. S. Kim, Kee Hoon Kim, F. Casper, C. Felser, and A. Loidl Experimentalphysik V, Center for Electronic Correlations and Magnetism,Institute for Physics, Augsburg University, D-86135 Augsburg, Germany FPRD, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea Departement of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea Institute for Inorganic and Analytic Chemistry,Johannes Gutenberg-Universit¨at, D-55099 Mainz, Germany (Dated: May 29, 2018)Electron spin resonance measurements in EuFe As single crystals revealed an absorption spec-trum of a single resonance with Dysonian lineshape. Above the spin-density wave transition at T SDW = 190 K the spectra are isotropic and the spin relaxation is strongly coupled to the CEs resultingin a Korringa-like increase of the linewidth. Below T SDW , a distinct anisotropy develops and therelaxation behavior of the Eu spins changes drastically into one with characteristic properties of amagnetic insulating system, where dipolar and crystal-field interactions dominate. This indicates aspatial confinement of the CEs to the FeAs layers in the SDW state.
PACS numbers: 76.30.-v,75.30.Fv,75.20.Hr,71.70.Ch
The discovery of superconductivity in Fe-based pnic-tides and chalcogenides has released an avalanche of sci-entific studies in condensed-matter physics and chem-istry. Three main material classes are currently spurringthe field: the R FeAsO compounds with R =La-Gd(1111-systems) [1, 2], the ternary A Fe As class with A =Ba,Sr,Ca,Eu (122-systems) [3, 4], and the binarychalcogenide systems such as FeSe [5, 6, 7]. The par-ent compounds of the 1111 and 122 systems exhibit aspin density wave (SDW) anomaly which is accompaniedby a structural distortion [8, 9, 10]. Upon doping the di-valent A -site ions in the 122 compounds by monovalentions like K the SDW anomaly becomes suppressed and asuperconducting ground state appears.Here we focus on EuFe As which exhibits a SDWanomaly at T SDW = 190 K [11, 12, 13]. The Eu ionswith spin S = 7/2 order antiferromagnetically at T N =19 K [12, 13, 23]. The system reportedly becomes super-conducting upon substituting Eu by K [4], As by P [14],or applying external pressure of about 26 kbar [15, 16].In contrast to the other 122 systems, where the substitu-tion of Fe by Co also leads to superconductivity [17, 18],the Eu compounds exhibit the onset of a superconductingtransition but seem to be hindered to reach zero resistiv-ity [19]. It has been suggested that there is a strongcoupling between the localized Eu spins and the con-duction electrons (CEs) from the two-dimensional (2D)FeAs layers as evidenced by magnetization and magneto-resistance measurements in the parent compound [20].To elucidate this coupling we investigated single crys-talline EuFe As by electron spin resonance (ESR) spec-troscopy. ESR has been shown to be a highly sensitivetool to study the spin fluctuations and magnetic interac-tions in cuprate superconductors and their parent com- pounds (see e.g. Ref. 22 and references therein). Ourresults show that above T SDW the relaxation time of theEu spins is dominated by the interaction with the CEs,while the Eu system shows a relaxation behavior remi-niscent of a magnetic insulator below T SDW .Polycrystalline EuFe As was prepared following theprocedure described in [21] and characterized by X-ray powder diffraction using Mo-K α radiation ( λ =0.7093165 nm; Bruker, AXS D8). High-quality EuFe As single crystals were grown using flux technique with start-ing composition of Eu:Fe:As:Sn = 1:2:2:19, where Sn wasremoved by centrifugation after crystal growth. The goodquality of the single crystals was confirmed by Laue x-ray diffraction as well as scanning electron microscopyequipped with energy dispersive x-ray analysis. The in-plane resistivity was measured using a standard 4-probemethod. For magnetization measurements we used aSQUID magnetometer MPMS5 (Quantum Design). ESRmeasurements were performed in a Bruker ELEXSYSE500 CW-spectrometer at X-band frequencies ( ν ≈ . < T <
300 K. ESR detectsthe power P absorbed by the sample from the transversemagnetic microwave field as a function of the static mag-netic field H . The signal-to-noise ratio of the spectra isimproved by recording the derivative dP/dH using lock-in technique with field modulation.Figure 1 shows ESR spectra of EuFe As for differenttemperatures and orientations of the single crystal. In allcases one observes a single exchange-narrowed resonanceline which is well described by a Dyson shape [24] P ( H ) ∝ ∆ H + α ( H − H res )( H − H res ) + ∆ H , (1) = 9.36 GHz H || c
H || ab
T = 50 K
EuFe As T = 100 K
H (kOe)H (kOe) ES R S i gna l ( a r b . un i t s ) T = 200 K
FIG. 1: (Color online) ESR spectra of an EuFe As singlecrystal taken at different temperatures for the magnetic fieldapplied parallel (left) and perpendicular (right) to the c axis. i.e. a Lorentz line at resonance field H res with half widthat half maximum ∆ H and a contribution 0 ≤ α ≤ α depends on sample size, geometry, andskin depth. If the skin depth is small compared to thesample size, α approaches 1. As ∆ H is of the same orderof magnitude as H res , the counter resonance at − H res was included in the fitting process as well [25].The T -dependence of the inverse double-integrated sig-nal intensity I ESR is illustrated in Fig. 2 for both promi-nent orientations of the single crystal as well as for apowder sample. Below 50 K and above 200 K, the inverseintensity 1/ I ESR follows a Curie-Weiss(CW)-like behav-ior with a CW temperature Θ ≈
19 K in agreement withthe static susceptibility. In the intermediate range oneobserves distinct deviations from linearity, which is re-lated to the changes of the D/A ratio and the electricalresistivity shown in the inset of Fig. 2. The skin depth δ ∝ p ρ/ν and, hence, the partial volume of the sampleprobed by the microwave field decreases with decreasingtemperature. These deviations are apparently reducedin the powder sample, because the microwave field pen-etrates nearly all sample volume due to the small grainsize. After correction of the single-crystal data with re-spect to the skin depth, we recover the CW law in theentire temperature range (solid line in Fig. 2).The T -dependences of H res and ∆ H are depicted inFig. 3 for H k c and H k ab and compared to the cor- T (K) D / A r a t i o ESR , /I ESR , H || c , H || ab powder T N T SDW / I ES R , / / I ES R ( a r b . un i t s ) SQUID: H = 1 kOe
EuFe As / ( m o l / e m u ) T (K) ab ( m c m ) FIG. 2: (Color online) T -dependence of the inverse static sus-ceptibility (left ordinate) of an EuFe As single crystal mea-sured with H = 1000 Oe aligned in the ab plane, the inverseESR intensity 1 /I ESR (right ordinate) for a single crystal anda powdered sample, and the skin-depth corrected values forthe single crystal data. Inset: T -dependenc of the D/A -ratioand the in-plane resistivity of the single crystal. responding data obtained in a powder sample. At hightemperature the ESR spectra are approximately isotropicat a resonance field H res ≈ . g value of 1.96(2), the linewidth increases linearly withtemperature with a slope of approximately 8 Oe/K. Be-low T SDW a pronounced anisotropy shows up in H res and∆ H , which is illustrated in detail in the inset of Fig. 3.While a strong angular dependence with 180 ◦ periodic-ity appears, when rotating the field from the c axis intothe ab plane, only a weak 90 ◦ modulation is observed,when rotating the field within the ab plane. The formercan be ascribed to the dominant uniaxial crystal-electricfield (CF) contribution, which will be determined below.The latter indicates the higher-order CF terms visible inthe ab plane, which will not be further discussed here.On decreasing temperature the anisotropy first tends toa kind of saturation (see Fig. 4), but below 50 K it fur-ther diverges accompanied by a strong inhomogeneousbroadening towards T N due to the onset of magnetic fluc-tuations. In the following we will restrict the discussionto temperatures T > T N . Metallic regime for
T > T
SDW : The ESR of local mo-ments in metals is characterized by a shift of the g value∆ g = J (0) N ( E F ) from its value in insulators and a linearincrease of the linewidth ∆ H ∝ h J ( q ) i N ( E F ) T whichboth depend only on the conduction-electron density of T N H ( k O e ) T (K) T SDW
34 H ll c H ll abpowder H r e s ( k O e ) EuFe As g=2 = 9.36 GHz angle (deg) H ( k O e ) T=150K3.33.43.5 H r e s ( k O e ) in plane - out of plane rotation in plane FIG. 3: (Color online) Temperature dependence of the res-onance field H res (upper frame) and linewidth ∆ H (lowerframe) of the ESR line in EuFe As obtained for single crystaland powder sample. The insets illustrate the anisotropies of H res and ∆ H for rotation of the magnetic field within the ab plane as well as from the ab plane to the c direction. Solidlines ∝ cos θ ,sin θ are to guide the eyes, the dotted line islinear fit, and the dashed line is a fit using Eq. 2. states N ( E F ) at the Fermi energy E F and the exchangeconstant J . The g shift results from the homogenous po-larization of the CEs in the external field (Pauli suscepti-bility), thus J is taken at zero wave vector. The linewidthis determined by the spin-flip scattering of CEs at the lo-cal moments (Korringa relaxation) and, therefore, J isaveraged over all possible scattering vectors q . Above T SDW the observed increase of the linewidth by 8 Oe/Kis a typical value for S-state 4 f local moments in metals[24, 26, 27] and, therefore, is ascribed to a pure Korringarelaxation in a three-dimensional (3D) environment.The negative g shift ∆ g ≈ − .
04 is unusual, but itsorder of magnitude is typical for metals. The negativesign indicates peculiarities of the 4 f -3 d coupling whichhas been reported early in Gd doped Laves phases [27].It is remarkable that inspite of the tetragonal symmetryof the crystal structure of EuFe As resonance field andlinewidth are isotropic within experimental accuracy, i.e.the CEs completely screen the ligand fields at the Eu site. SDW state for
T < T
SDW : Below T SDW the Korringarelaxation immediately disappears, although the resistiv-ity even decreases more strongly with decreasing temper-ature. Concomitantly, the shift of the g value due to thepolarization of the CEs diminishes and the averaged g T N T SDW H c / H ab T(K) g EuFe As / g c + / g ab FIG. 4: (Color online) Temperature dependence of the rel-ative anisotropy of the resonance linewidth ∆ H c / ∆ H ab (leftordinate, closed symbols) and the averaged g value (open sym-bols, right ordinate) of an EuFe As single crystal. value g = g c / g ab / T SDW corresponds to thetypical value g = 2 . in an insulating system.This is a first indication that the formation of the SDWleads to a spatial confinement of the CEs to the FeAslayers. Moreover, a pronounced anisotropy shows up inthe SDW state which reflects the symmetry of the ligandfields. In this temperature regime, if not too close to T N ,the T -dependence of the linewidth can be well describedin terms of Eu spin-spin relaxation typical for magneticinsulators. As pointed out by Huber et al. , in exchangecoupled spin systems the linewidth∆ H ( T ) = χ χ ( T ) ∆ H ∞ (2)is determined by the ratio of single-ion susceptibility χ ∝ /T and the experimental susceptibility χ ( T ) of in-teracting spins multiplied by the high-temperature limitof the linewidth ∆ H ∞ [28, 29]. This high temperaturelimit can be estimated following the theory of exchangenarrowing of Anderson and Weiss [30] as∆ H ∞ = hgµ B h ν i ν ex (3)where h ν i denotes the second moment of the resonance-frequency distribution due to any anisotropic interactionlike dipolar, hyperfine or crystal-electric field and ν ex isthe exchange frequency between the Eu spins.The dipolar contribution to the second moment reads h ν i = g µ S ( S + 1)2 h X j = i Θ ij r ij (4)where r ij and Θ ij denote the distance between spin i and j and the polar angle of the external magnetic field withrespect to the direction of r ij [31]. The main contributionresults from the four nearest Eu neighbors at r ij = a =3 .
907 ˚A[12]. With g = 2 and S = 7 / h ν i (Θ) = 36 GHz (2 + sin Θ) . (5)Here the polar angle Θ is measured between the di-rection of the external field and the crystallographic c axis. The exchange constant J between the Eu ionsis determined from the CW temperature Θ CW = 19 Kusing the Weiss molecular field equations 3 k B Θ CW = JzS ( S + 1) with z = 4 exchange coupled nearest neigh-bors in the ab plane as J/k B ≈ . hν ex ) ≈ zS ( S + 1) J resulting in ν ex ≈
150 GHz. Thusthe linewidth due to dipolar broadening is determined as∆ H ∞ ≈ .
085 kOe (2 + sin Θ). This explains about 25%of the experimental linewidth, but exhibits an oppositeanisotropy in comparison with the experimental data.The hyperfine interaction in
Eu ( A = 103 MHz)and Eu ( A = 46 MHz) [31] is at least one orderof magnitude smaller than the dipolar interaction, andhence can be neglected for the line broadening. There-fore, only the tetragonal CF can account for the observedanisotropy and magnitude of the linewidth.The second moment of the leading uniaxial term of theCF is given by h ν i (Θ) = 4 S ( S + 1) − D (1 + cos Θ) (6)with the polar angle Θ measured between external fieldand crystallographic c axis [29]. This provides the properanisotropy. The uniaxial zero-field splitting parameter D can be estimated from the experimentally observedasymptotic anisotropy of the linewidth at intermediatetemperatures (dashed line in Fig. 4)∆ H c ∆ H ab = h ν i (0 ◦ ) + h ν i (0 ◦ ) h ν i (90 ◦ ) + h ν i (90 ◦ ) ≈ . . (7)where h ν i = h ν i + h ν i was assumed. InsertingEqs. 5 and 6 yields D ≈ . H ∞ (0 ◦ ) ≈ . As showdistinct differences between the high-temperature phaseand the SDW state below 190 K. Although the systemremains metallic for all temperatures, the ESR linewidthand g value of the Eu ions change from a typical be-havior in a metallic environment with, e.g., a pure Kor-ringa relaxation to characteristic anisotropic features asusually observed in insulators (e.g. spin-spin relaxationvia dipolar and crystal fields). We ascribe this abruptchange to a local reduction of the 3D spin scattering dueto a reduced concentration of CEs at the Eu site andtheir spatial confinement to the 2D FeAs layers in theSDW state. Note . While finalizing this paper we became aware ofan ESR study of Co doped EuFe As for temperatures above 110 K, which shows a Korringa relaxation in agree-ment with our measurements [33].We thank Anna Pimenov for the SQUID measure-ments. We acknowledge partial support by the DeutscheForschungsgemeinschaft (DFG) via the Collaborative Re-search Center SFB 484 (Augsburg). The work at SNUwas supported by NRL (Grant No. M10600000238) pro-gram. ∗ Electronic address: [email protected][1] Y. Kamihara et al. , J. Am. Chem. Soc. , 3296 (2008).[2] X. H. Chen et al., Nature , 761(2008).[3] M. Rotter et al. , Phys. Rev. Lett. , 107006 (2008).[4] H. S. Jeevan et al. , Phys. Rev. B , 092406 (2008).[5] F.-C. Hsu et al. , Proceedings of the National Academyof Sciences USA , 14263 (2008).[6] Y. Mizuguchi et al. , Appl. Phys. Lett. , 152505 (2008).[7] S. Medvedev et al. , Nature Mater. , 630 (2009)[8] J. Dong et al., Europhys. Lett. , 27 006 (2008).[9] M. Rotter et al. , Phys. Rev. B et al. , New J. Phys. , 025014 (2009).[11] H. Raffius et al. , J. Phys. Chem. Solids , 135 .[12] H. S. Jeevan et al. , Phys. Rev. B , 052502 (2008).[13] D. Wu et al. , Phys. Rev. B , 155103 (2009).[14] Z. Ren et al., Phys. Rev. Lett. , 137002 (2009).[15] C. F. Miclea et al. , Phys. Rev. B , 212509 (2009)[16] T. Terashima et al. , J. Phys. Soc. Jap. , 083701 (2009).[17] A.S. Sefat et al. , Phys. Rev. Lett. , 117004 (2008).[18] A. Leithe-Jasper et al. , Phys. Rev. Lett. , 207004(2008).[19] Q. J. Zheng et al. , arXiv:0907.5547 (2009).[20] S. Jiang et al. , New J. Phys. , 025007 (2009).[21] M. Pfisterer and G. Nagorsen, Z. Naturforsch. , 811(1983).[22] B. Elschner and A. Loidl: in: Handbook on the Physicsand Chemistry of Rare Earth , ed. by K. A. Gschneidner(Jr.), L. Eyring, and M.B. Maple, Elsevier Science B. V.,Amsterdam, Vol. , 375 (2000).[23] Z. Ren et al. , Phys. Rev. B , 052501 (2008).[24] S. E. Barnes, Adv. Phys. , 801 (1981).[25] J.P. Joshi and S.V. Bhat, J. Mag. Res. , 284 (2004).[26] R.H. Taylor, Adv. Phys. , 681 (1975).[27] B. Elschner and A. Loidl: in: Handbook on the Physicsand Chemistry of Rare Earth , ed. by K. A. Gschneidner(Jr.), L. Eyring, Elsevier Science B. V., Amsterdam, Vol. , 221 (1997).[28] R. Kubo and K. Tomita, J. Phys. Soc. Jpn. , 888 (1954).[29] D. L. Huber et al. , Phys. Rev. B , 12155 (1999).[30] P. W. Anderson and P. R. Weiss, Rev. Mod. Phys. ,269 (1953).[31] A. Abragam and B. Bleaney, Electron ParamagneticResonance of Transition Ions , Clarendon Press, Oxford(1970).[32] H.-A. Krug von Nidda et al. , Phys. Rev. B , 14344(1998).[33] J. J. Ying et al.et al.