Charge Dynamics of the Spin-Density-Wave State in Bafe2as2

Eur. Phys. J. B 67, 513–517 (2009) DOI: 10.1140/epjb/e2009-00062-2 THE EUROPEAN PHYSICAL JOURNAL B Regular Article

Charge dynamics of the spin-density-wave state in BaFe2As2

F. Pfuner1, J.G. Analytis2,J.-H.Chu2,I.R.Fisher2, and L. Degiorgi1,a 1 Laboratorium für Festkörperphysik, ETH - Zürich, 8093 Zürich, Switzerland 2 Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford, 94305-4045 California, USA

Received 28 November 2008 / Received in ﬁnal form 19 January 2009 Published online 21 February 2009 – c EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2009

Abstract. We report on a thorough optical investigation of BaFe2As2 over a broad spectral range and as a function of temperature, focusing our attention on its spin-density-wave (SDW) phase transition at TSDW = 135 K. While BaFe2As2 remains metallic at all temperatures, we observe a depletion in the far infrared energy interval of the optical conductivity below TSDW , ascribed to the formation of a pseudogap- like feature in the excitation spectrum. This is accompanied by the narrowing of the Drude term consistent with the dc transport results and suggestive of suppression of scattering channels in the SDW state. About 20% of the spectral weight in the far infrared energy interval is aﬀected by the SDW phase transition.

PACS. 75.30.Fv Spin-density waves – 78.20.-e Optical properties of bulk materials and thin ﬁlms

A new field in condensed matter research was recently ini- is also currently believed that the superconductivity in tiated by the discovery of superconductivity in doped iron these systems is intimately connected with magnetic fluc- oxyarsenides [1]. After the first report on LaFeAs(O1−xFx) tuations and a spin-density-wave (SDW) anomaly within with a critical temperature Tc of 26 K, even higher tran- the FeAs layers. This is obviously of interest, since a SDW sition temperatures up to 55 K were reached in fluorine phase may generally compete with other possible order- doped SmFeAs(O1−xFx)[1,2]. This novel family of com- ings and complicated phase diagrams are often drawn due pounds has generated a lot of interest, primarily because to their interplay. Undoped LaFeAsO as well as BaFe2As2 high-temperature superconductivity is possible in materi- undergo a SDW phase transition which is also associated als without CuO2 planes. Since these planes are essential with a reduction of the lattice symmetry from tetrago- for superconductivity in the copper oxides, its occurrence nal to orthorhombic [1,3]. The classical prerequisite for in the pnictides raises the tantalizing question of a differ- the formation of a SDW state is the (nearly) perfect nest- ent pairing mechanism. While the nature of such a pairing of the Fermi surface (FS), leading to the opening of ing mechanism is currently in dispute, it is evident that a gap. Density functional calculations of the electronic superconductivity in the oxypnictides emerges from spe- structure [6] reveal that the main effect of doping is to cific structural and electronic conditions in the (FeAs)δ− change the relative sizes of the electron and hole FS and layer. Therefore, it soon appears that other structure types therefore to lead to a reduction in the degree of nesting could serve as parent material. The recently discovered of the FS itself. Doping suppresses the SDW instability BaFe2As2 compound with the well-known ThCr2Si2-type and induces the superconductivity. Alternatively, it was structure is an excellent candidate [3]. This latter struc- also proposed that the metallic SDW state could be solely ture contains practically identical layers of edge-sharing induced by interactions of local magnetic moments (i.e., FeAs4/4 tetrahedra with the same band filling, but sepa- without invoking the opening of a gap), resembling the na- rated by barium atoms instead of LaO sheets. BaFe2As2 ture of antiferromagnetic order in the cuprate parent com- can serve as an alternative compound for oxygen-free iron pounds [7]. It is therefore of relevance to acquire deeper in- arsenide superconductors. Superconductivity was indeed sight into the SDW phase and to establish how this broken established at 38 K in K-doped [4] and at 22 K in Co- symmetry ground state affects the electronic properties of doped [5]BaFe2As2 through partial substitution of the these materials. Ba and Fe site, respectively. We focus here our attention on BaFe2As2,whichisa Superconductivity in suitably doped BaFe2As2 com- poor metal exhibiting Pauli paramagnetism and where the pounds conclusively proves that it originates only from the SDW phase transition at TSDW is accompanied by anoma- iron arsenide layers, regardless of the separating sheets. It lies in the specific heat, electrical resistance and magnetic susceptibility [3]. We provide a thorough investigation of a e-mail: degiorgi@solid.phys.ethz.ch the optical response over an extremely broad spectral 514 The European Physical Journal B range at temperatures both above and below TSDW .A self-consistent picture emerges in which below the SDW transition a reshuffle of states [8] occurs due to the opening of a SDW gap on a portion of the FS (i.e., pseudogap). We also observe a mobility increase of the charge carriers, which are not gapped by the SDW condensate, as a consequence of the reduction of electron-electron scattering in the SDW state.

BaFe2As2 single crystals were grown by a self flux method as described in references [9,10]. Ba and FeAs in the molar ration 1:4 were placed in an alumina crucible and sealed in quartz tube. The mixture was heated to 1190 ◦C, and held for 32 h, before it was slowly cooled to 1070 ◦C, at which temperature the furnace was powered off. After cooling to room temperature single crystals were mechanically separated from the solidified ingot. The large (∼2 × 2mm2) crystals have a platelet morphology, with the c-axis perpendicular to the plane of the platelet. Our specimens were characterized through dc transport inves- tigations (see inset of Fig. 3, below), obtaining equivalent results as reported in reference [3] and indicating a SDW transition at TSDW ∼ 135 K. We measured the optical reflectivity R(ω) of shiny surfaces from the far infrared (FIR) up to the ultraviolet (50–5 × 104 cm−1)attem- peratures from 300 K down to 10 K. Our specimen was placed inside an Oxford cryostat with appropriate optical windows. From the FIR up to the mid-infrared spectral range we made use of a Fourier-transformed inter- ferometer equipped with a He-cooled bolometer detector, while in the visible and ultraviolet energy intervals we employed a Perkin Elmer spectrometer. Measuring R(ω) over such a broad spectral range allows to perform reliable Kramers-Kronig (KK) transformation from where we ob- tain the phase of the complex reflectance and consequently all optical functions. Details pertaining to the experiment and the KK analysis can be found elsewhere [11,12]. Fig. 1. (Color online) (a) Optical reflectivity and (b) real part σ1(ω) of the optical conductivity as a function of temperature Figure 1a displays the optical reflectivity in the FIR −1 in the FIR spectral range. The insets in both panels show the energy interval (i.e., ω ≤ 600 cm ), emphasizing its tem- same quantities at 10 and 200 K from the far infrared up to perature dependence across the SDW phase transition. the ultraviolet spectral range with logarithmic energy scale. The inset of Figure 1a shows on the other hand R(ω) The open circles in panel (b) at 200 cm−1 mark the values of over the whole measured range at 10 and 200 K, represen- σ1 used for the calculation of the Λ quantity (see text). tative for the SDW and normal state, respectively. R(ω) of BaFe2As2 has an overall metallic behavior, characterized by a broad bump at about 5000 cm−1 and by the the narrowing of the effective (Drude) metallic component onset of the reflectivity plasma edge below 3000 cm−1 (in- of the optical conductivity. Apart from the already men- set Fig. 1a). Of interest is the temperature dependence of tioned broad excitation at 5000 cm−1, we did not observe R(ω), which first indicates a depletion of R(ω)withde- any additional mode in R(ω) below 3000 cm−1 and over- creasing temperature in the energy interval between 200 lapped to its plasma edge. This contrasts with previous −1 and 500 cm (from where all spectra were found to merge optical data [14,15] of the SDW phase of La(O1−xFx)FeAs together) and then a progressive enhancement of R(ω)be- and SmFeAs(O1−xFx), where several sharp modes in the low 200 cm−1 and towards zero frequency, so that all R(ω) infrared range were indeed detected. These features were spectra cross around 200 cm−1. The temperature depen- ascribed to the vibrational lattice modes of both the ab dence of R(ω)isevidentbelowTSDW , while from 150 K plane as well as of the orthogonal c axis. The presence up to 300 K all R(ω) spectra coincide almost perfectly of both polarizations is in agreement with the polycrys- over the whole investigated spectral range [13]. The en- talline nature of those samples [14,15], suggesting also that hancement of R(ω)atlowfrequencies(ω ≤ 200 cm−1) the main contribution to the optical properties of pellets with decreasing temperature can be already considered as comes from the more insulating c axis. The absence of a direct indication for the progressive decrease of the free (sharp) phonon peaks in our spectra indicates that we are charge carriers scattering rate, which will later manifest in addressing the conducting (ab) plane, where the phonon F. Pfuner et al.: Charge dynamics of the spin-density-wave state in BaFe2As2 515 modes are screened by the effective Drude component. In this regard, our R(ω) spectra share common features with the optical findings on K-doped BaFe2As2 [16]and LaFePO [17] single crystals in the normal phase. Further- more, it is worth mentioning that we did not find any polarization dependence of R(ω) within the platelets surface. Therefore, this reinforces the notion that we are addressing the isotropic (ab)planeofBaFe2As2. For the purpose of the KK transformation, the R(ω) spectra may be extended towards zero frequency with the well-known Hagen-Rubens extrapolation [11,12] R(ω)= 1 − 2 ω/σdc, making use of σdc values in fair agreement with the transport result (inset Fig. 3)[18]. At high frequencies R(ω) can be extrapolated as R(ω) ∼ ω−s (2

scattering rate parameter (ΓD) with decreasing temperature. Such a narrowing of the metallic contribution in σ1(ω) is the direct consequence of the progressive enhancement of the measured R(ω) in the energy interval between 50 and 200 cm−1 (Fig. 1a) with decreasing temperature. The inset of Figure 3 displays ΓD(T)/ΓD(200 K) from our Lorentz-Drude fit (Fig. 2a) [24] as a function of temperature together with dc resistivity data taken for samples prepared by the same technique. Both quantities are normalized at 200 K and follow the same trend in tempera- tureaboveaswellasbelowTSDW . We also calculate the static limit (ω → 0) of the scattering rate [24] within the generalized Drude model [19], thus incorporating the high frequency tail of the Drude term phenomenologically ac- counted for by the first h.o. As shown in the inset of Fig- ure 3, this alternative approach definitely supports our first crude analysis of the free charge carriers scattering rate, based on the simple Drude component only. The SDW transition reduces the possible scattering channels Fig. 3. (Color online) Temperature dependence of the quantity so that the resistivity and the Drude scattering rate de- −1 T Λ (see text) and of the pseudogap energy scale ωSP normal- crease rather abruptly below SDW . ized at 10 K. The inset shows the temperature dependence of Therefore, from the data as well as from their phe- the dc resistivity and of the scattering rate ΓD for the simple nomenological Lorentz-Drude analysis emerges a picture (full triangle) and generalized (open triangle) Drude model, in which at T>TSDW delocalized states (i.e., free charge normalized at 200 K [24]. The interpolation lines are meant as carriers close to the Fermi level), represented by the Drude guide to the eyes. term, coexist with more localized or low-mobility states, described in σ1(ω) by the three FIR Lorentz h.o.’s cover- ing the spectral range from 50 up to 700 cm−1 (Fig. 2a). T three FIR h.o.’s of Figure 2a, remains however constant When lowering the temperature below SDW , a pseudo- at all temperatures (Fig. 2b) [20]. gap develops and a rearrangement of states takes place in such a way that excitations pile up in the spectral range Such a redistribution of spectral weight governs the −1 −1 appearance of the depletion in σ1(ω) between 100 and around 420 cm as well as around 50 cm . These latter −1 400 cm below TSDW (Fig. 1b). Following a well excitations merge into the high frequency tail of the nar- σ ω established procedure [21], we thus define the characteris- row Drude term of 1( ). Comparing the removed spectral σ ω T tic average weighted energy scale: weight within the depletion of 1( )inFIRbelow SDW with the total spectral weight encountered in σ1(ω)upto −1 3 2 about 700 cm above TSDW , we estimate that approxi- j=2 ωjSj ωSP = . (1) mately 20% of the total weight is affected by the develop- 3 S2 j=2 j ment of the pseudogap. In conclusion, we have provided a comprehensive anal- The sum is over the second and third h.o. in our ysis of the excitation spectrum in BaFe2As2, with respect Lorentz-Drude fit (Fig. 2a), which account for the gap-like −1 to its SDW phase transition. Our data reveal the for- edge in σ1(ω) in the range between 200 and 500 cm . mation of a pseudogap excitation and the narrowing of ω The quantity SP , shown in Fig. 3, is then ascribed to the metallic contribution in σ1(ω)atTSDW ,whichtracks the representative (single particle, SP)energyscalefor the behavior of the dc transport properties. It remains to the pseudogap excitation, resulting below TSDW from the be seen how one can reconcile the pseudogap-like feature reshuffle of states at energies lower than the mobility edge. well established in the optical response with the apparent The ratio between ωSP at 10 K and kBTSDW (kB being absence of any gap excitation in the angle-resolved pho- the Boltzmann constant) is of about 4, somehow larger toemission spectroscopy [7]. This issue is intimately con- than the prediction within the weak-coupling limit of the nected to the more general and still open question whether mean-field BCS theory [22] but comparable to what has the reshuffle of states, leading to an optical signature com- been found in the SDW organic Bechgaard salts [23]. The patible with the pseudogap excitation, is the consequence increase of ωSP below TSDW is obvious. This goes hand of the SDW-driven structural phase transition and a FS in hand with the decrease of σ1(ω) in the energy interval nesting or is in fact due to a more exotic mechanism. around 200 cm−1 (open circles in Fig. 1b). We calculate −1 −1 the quantity Λ = σ1(200 cm ,T)/σ1(200 cm ,10K), Note added in proof. After we completed this work, −1 and find indeed that Λ scales with ωSP as a function of we learned of an independent work on the title compound temperature (Fig. 3). by Hu et al. [25]; at the SDW phase transition they ob- As far as the Drude term is concerned, its narrow- serve the formation of partial gaps, which are associated to ing (Fig. 1b) is well represented by the decrease of the two different energy scales and remove a large part of the F. Pfuner et al.: Charge dynamics of the spin-density-wave state in BaFe2As2 517

Drude term. The Drude scattering rate was also found to 13. The temperature independence of R(ω) above 150 K is decrease substantially at the onset of the SDW transition. consistent with the very weak temperature dependence of the dc transport properties above TSDW (inset Fig. 3 and Ref. [3]). The authors wish to thank M. Lavagnini for fruitful dis- 14. J. Dong et al., Europhys. Lett. 83, 27006 (2008) cussions. This work has been supported by the Swiss Na- 15. M. Tropeano et al., Supercond. Sci. Technol. 22, 034004 tional Foundation for the Scientific Research within the NCCR (2009) MaNEP pool. This work is also supported by the Department 16. G. Li et al., Phys. Rev. Lett. 101, 107004 (2008) of Energy, Office of Basic Energy Sciences under contract 17. M.M. Qazilbash et al., e-print arXiv:cond-mat/0808.3748 DE-AC02-76SF00515. 18. At T 70 K the Hagen-Rubens (HR) extrapolation was considered only for frequencies up to ω 20 cm−1;thus linearly interpolating R(ω) in the energy interval between References 20 and 50 cm−1 (i.e., the first measured frequency). This satisfies the condition for applicability (i.e., ω<ΓD, ΓD 1. Y. Kamihara et al., J. Am. Chem. Soc. 130, 3296 (2008) being the Drude scattering rate) of the HR extrapola- 2. X.H. Chen et al., Nature 453, 761 (2008) tion [11,12]. 3. M. Rotter et al., Phys. Rev. B 78, 020503(R) (2008) 19. D.N. Basov, T. Timusk, Rev. Mod. Phys. 77, 721 (2005), 4. M. Rotter et al., Phys. Rev. Lett. 101, 107006 (2008) and references therein 5. A.S. Sefat et al., Phys. Rev. Lett. 101, 117004 (2008) 20. The additional weight due to the temperature independent 6. D.J. Singh, Phys. Rev. B 78, 094511 (2008) contributions in σ1(ω) at high frequencies corresponds to 7. L.X. Yang et al., e-print arXiv:cond-mat/0806.2627,to an additive constant at all temperatures, which is no longer be published in Phys. Rev. Lett. considered here. 8. BaFe2As2 is a compensated metal and as such we con- 21. A. Sacchetti et al., Phys. Rev. B 74, 125115 (2006) sider all states within a many-band scenario effectively 22. M. Tinkham, Introduction to superconductivity 2nd edn. contributing to the transport properties. (McGraw-Hill, New York, 1996) 9. K. Kitagawa et al., J. Phys. Soc. Jpn 77, 114709 (2008) 23. V. Vescoli et al., Phys. Rev. B 60, 8019 (1999) −1 10. X.F. Wang et al., e-print arXiv:cond-mat/0806.2452 24. The Drude scattering rate at 200 K is 60.7 cm , while its 11. F. Wooten, Optical Properties of Solids (Academic Press, static limit evinced from the generalized Drude approach −1 New York, 1972) is 55.8 cm . 12. M. Dressel, G. Grüner, Electrodynamics of Solids 25. W.Z. Hu et al., Phys. Rev. Lett. 101, 257005 (2008) (Cambridge University Press, 2002)