Cyclotron resonance and mass enhancement by electron correlation in KFe 2 As 2
Motoi Kimata, Taichi Terashima, Nobuyuki Kurita, Hidetaka Satsukawa, Atsushi Harada, Kouta Kodama, Kanji Takehana, Yasutaka Imanaka, Tadashi Takamasu, Kunihiro Kihou, Chul-Ho Lee, Hijiri Kito, Hiroshi Eisaki, Akira Iyo, Hideto Fukazawa, Yoh Kohori, Hisatomo Harima, Shinya Uji
CCyclotron resonance and mass enhancement by electron correlation in KFe As Motoi Kimata , † , Taichi Terashima , , Nobuyuki Kurita , , Hidetaka Satsukawa , Atsushi Harada ,Kouta Kodama ∗ , Kanji Takehana , Yasutaka Imanaka , Tadashi Takamasu ,Kunihiro Kihou , , Chul-Ho Lee , , Hijiri Kito , , Hiroshi Eisaki , , Akira Iyo , ,Hideto Fukazawa , , Yoh Kohori , , Hisatomo Harima , , and Shinya Uji , ∗ National Institute for Materials Science (NIMS), Ibaraki 305-0003, Japan JST, Transformative Research-Project on Iron Pnictides (TRIP), Tokyo 102-0075, Japan. National Institute of Advanced Industrial Science and Technology (AIST), Ibaraki 305-8568, Japan. Department of Physics, Chiba University, Chiba 263-8522, Japan. and Department of Physics, Graduate School of Science, Kobe University, Hyogo 657-8501, Japan.
Cyclotron resonance (CR) measurements for the Fe-based superconductor KFe As are performed.One signal for CR is observed, and is attributed to the two-dimensional α Fermi surface at the Γpoint. We found a large discrepancy in the effective masses of CR [(3.4 ± m e ( m e is the freeelectron mass)] and de-Haas van Alphen (dHvA) results, a direct evidence of mass enhancementdue to electronic correlation. A comparison of the CR and dHvA results shows that both intra- andinterband electronic correlations contribute to the mass enhancement in KFe As . PACS numbers: 71.18.+y, 71.38.Cn, 74.70.Xa, 76.40.+b
Recently discovered Fe-based superconductors [1] haveattracted much attention because of their high transi-tion temperatures ( T c ). The maximum T c exceeds 54 −
56K [2–4]. For Fe-based superconductors, substantial evi-dence points to the occurrence of unconventional super-conductivity (extended s -wave and nodal gap structures)both experimentally and theoretically [5, 6]. In uncon-ventional superconductivity, it is believed that a strongelectronic correlation exists, which renormalizes the massof the conduction electrons, and that it is closely re-lated to the superconducting mechanism. Because ef-fective mass is an excellent measure of electronic cor-relation for a conductor, the effective masses as wellas the Fermi surface (FS) structures provide valuableinformation on the superconducting mechanism. Thusfar, the FS structures and effective masses ( m ∗ ) for Fe-based superconductors have been reported in various ex-periments, such as those involving de-Haas van Alphen(dHvA) oscillations, optical spectroscopy, angle-resolvedphotoemission spectroscopy (ARPES) [5, 6], and angle-dependent magnetoresistance oscillations (AMROs) mea-surements [7]. Recently, systematic dHvA measurementsfor BaFe [As (2 − x) P x ] revealed critical-like increase of themass enhancement factor toward the antiferromagnetic(AF) phase boundary [8], which is another importantaspect needed for understanding the superconductingmechanism.KFe As is an end member of the [Ba (1 − x) K x ]Fe As family. This material has a relatively low T c ( ≈ ∗ Also at the Graduate School of Pure and Applied Sciences, Uni-versity of Tsukuba. † Present address: Institute for Solid State Physics, University ofTokyo, Kashiwa, Chiba 277-8581, Japan. ture is closely related to the superconducting mechanism.This is in a sharp contrast to the other end memberBaFe As , in which a magnetic transition associated withstructural change takes place at around 140 K [11], andreconstructed small FSs are observed at low temperatures[12]. The specific heat, thermal conductivity, microwavepenetration depth, and small-angle neutron scatteringmeasurements for KFe As indicate the presence of anodal superconducting gap structure [13–16]. However,the detailed gap structure is still under debate: d -wavesymmetry with vertical line nodes or extended s-wavesymmetry with horizontal nodes is proposed [15, 16].Because the optimally doped material of this family (x ≈ .
4) is considered as a fully gapped superconduc-tor, the study of the FS structure and effective mass ofKFe As has a significant meaning for the understandingof the superconducting mechanism in [Ba (1 − x) K x ]Fe As family. According to the ARPES measurements [17, 18],there are large FSs ( α , ζ , and β ) centered at the Γ pointand small (cid:15) FSs near the corners of the first Brillouin zone(FBZ), although there are discrepancies in their sizes.In the dHvA measurement [19], three different FSs ( α , ζ , and (cid:15) ) are found, whose effective masses are 6.0 and6.5 m e ( α ), 8.5 and 18 m e ( ζ ), and 6.0 and 7.2 m e ( (cid:15) ) forthe minimal and maximal cross sections of the quasi-two-dimensional (Q2D) FS ( m e is the free electron mass), re-spectively. The corresponding mass enhancement factors(= m ∗ dHvA /m band , where m band is the calculated bandmass) are reported to be: 4.3 and 2.7 ( α ), 3.9 and 6.9( ζ ), and 20 and 24 ( (cid:15) ), respectively. The AMRO mea-surements reveal two series of oscillations: strong oscilla-tions associated with α and a weak one associated with ζ [7]. For the α FS, the averaged mass enhancement factorfrom the dHvA measurements (=3.5) is reasonably con-sistent with the recently reported ARPES measurementsresult, where m ∗ ARPES /m band ≈ a r X i v : . [ c ond - m a t . m t r l - s c i ] N ov C a v i t y t r an s m i ss i on ( a r b . un i t ) θ = -5º , 0.6 K 62.0 GHz (b) Raw dataSingle crystal sample θ B c Oscillatory magnetic fieldInduced current (a)
Teflon pillar Cavity B Coupling holesCavity plate
FIG. 1: (color online). (a) Schematic of the sample and cavityconfiguration. The induced ac current is coupled with thecyclotron motion of electrons. (b) Magnetic field dependenceof the cavity transmission for ν = 62.0 GHz and T = 0.6 K.The lower (red) and upper (blue) curves show the raw dataand the background-subtracted data, respectively (see text fordetails). The sharp absorption at around 2 T is attributed tothe ESR of some impurities or contaminations, and the broadabsorption (indicated by the arrow) corresponds to CR. ( m ∗ dHvA /m band ≈
2) [20]. Such a large mass enhance-ment is likely due to the strong electron-electron (e-e)interaction in KFe As . The electron-phonon (e-p) cou-pling in iron-pnictides is generally thought to be weakas suggested by theoretical estimations of the couplingconstants for LaOFeAs and BaFe As [21–23]. However,there still exist some inconsistencies in the FS structuresfor different experiments, which renders the argumentsexplaining mass enhancement less reliable.Here, we report the cyclotron resonance (CR) experi-ments for KFe As . Single crystals of KFe As are ob-tained from the same batch as that used for our previousdHvA and AMRO measurements. Although CR mea-surements are a powerful method to directly obtain theeffective mass of a conductor, they cannot determine thesize of the cross sectional area and the position of the FSin the k -space, leading to some ambiguity in assignmentof the CR signal for multi FS systems. In this study, wehave compared the CR results with our previous AMROand dHvA measurements, which allows the unambigu-ous assignment of the CR signal. A comparison of theeffective mass determined from CR measurements ( m ∗ CR )with m ∗ dHvA further enables us to determine the contribu-tion of e-e interaction to mass enhancement [24–28]. Weobtain the e-e coupling constants corresponding to theintra- and interband e-e interactions separately, whichare closely related to the superconducting mechanism.Single crystals of KFe As are synthesized by aflux method [29]. The residual resistivity ratios(= ρ (300K)/ ρ (5K)) of the crystals amount to approxi-mately 600. The plate-like crystals with typical dimen-sions of 1 × × < (0.1) mm are used for the measure- ments. The interlayer direction ( c -axis) is perpendicularto the basal plane of the crystal [Fig. 1(a)]. The CRexperiments are performed in the range from 55 GHz to82 GHz by a cavity perturbation technique [28, 30]. Thesample, which is mounted on a small Teflon pillar witha small amount of grease, can be rotated in a He cryo-stat [31, 32], and a dc magnetic field of up to 15 T isapplied by a superconducting solenoid [Fig. 1(a)]. TheTE n ( n = 1 −
3) modes are used, consequently, the acmagnetic field is applied parallel to the long axis of thesample at any field angle [Fig. 1(a)]. The resistivity ofthe present sample at 5 K along the ab -plane ( ≈ µ Ωcm)and the c -axis ( ≈ µ Ωcm) gives the microwave pene-tration depths for ν = 60 GHz as δ ab ≈ µ m and δ c ≈ µ m, respectively. They are much smaller than thesample dimensions: the measurements are done in theskin-depth regime.The lower (red) curve in Fig. 1(b) shows the mag-netic field dependence of the cavity transmission for ν = 62.0 GHz (TE mode) at 0.6 K. The upper criticalfield at low temperatures ( T < k B T < ∼ hν , and they become more prominent as thetemperature is lowered. The resonance field is almost in-dependent of the temperature. The transmission dropsrather abruptly above 12 T at low temperatures. Thereason for this is not clear.Figure 3(a) shows the field dependence of the trans-mission at various field angles θ . The resonance fieldsare determined by fitting the resonance curves to Eq.(8) in Ref. [35]. The resonance shifts to a higher fieldas θ increases, following a 1/cos θ dependence [Fig. 3(b)].This clearly shows that the observed CR signals originatefrom the 2D FS of KFe As . The resonance also shiftsto a higher field as the frequency ν increases [Fig. 4(a)].The linear fit of the ν dependence gives the effective massof (3.4 ± . m e [Fig. 4(b)]. C a v i t y t r an s m i ss i on ( a r b . un i t ) θ = -5º, 62.0 GHz FIG. 2: (color online). Field dependence of the cavity trans-mission at various temperatures. +50º+45º+40º+35º+30º+25º+15º+5º-5º-15º-25º-35º-45º-50º C a v i t y t r an s m i ss i on ( a r b . un i t ) (a) R e s onan c e fi e l d ( T ) (b) ! (degree) FIG. 3: (color online). (a) Field dependence of the transmis-sion spectra at 0.6 K and ν = 62.0 GHz. The dashed curvesindicate the fitting results obtained by Eq. (8) in Ref. [35].(b) θ dependence of the resonance field. The dashed curverepresents the B res / cos θ with B res = 7.4 T. Although the multiple Q2D FSs have been observed inrecent dHvA and AMRO measurements on KFe As , wehave found only one series of resonances in the presentCR measurement. Essentially the CR signal correspondsto the electrical conductivity under the high-frequencyelectric field. Therefore, the CR data are directly com-pared with the AMRO data, which are related to the F r equen cy ( G H z ) C a v i t y t r an s m i ss i on ( a r b . un i t ) (a) m*= 3.4m e Resonance field (T)0 2 4 6 8 10 12 (b) m*/m e C a v i t y t r an s m i ss i on ( a r b . un i t ) (c) 3.4m e FIG. 4: (color online). (a) Transmission for several microwavefrequencies at 0.6 K. (b) Frequency vs resonance field plot ob-tained from the data in (a). The dashed straight line givesthe cyclotron effective mass of (3.4 ± . m e . (c) Transmis-sion for ν = 55.4 and 62.0 GHz as a function of m ∗ /m e . Bothspectra show only single resonance at 3.4 m e . electrical conductivity in the dc limit. In AMRO mea-surements, the α oscillation is well resolved and its am-plitude is much stronger than that of ζ . Therefore, theCR signal is likely ascribable to the α FS. Indeed, thescattering times obtained from the CR line width, τ CR ≈ − × − s ( ω c τ ≈ α FS obtained during the dHvA measurements, τ dHvA ≈ − × − s. On the other hand, the ζ FS has a relatively three-dimensional shape (large energydispersion along the c -axis) and the masses correspondingto the maximal and minimal cross sections are 8.5 and18 m e , respectively [19]. Therefore, the CR signal fromthe ζ FS is possibly broadened by the mass distributionand is consequently difficult to observe.The harmonic resonances of the fundamental CR areoccasionally observed in some Q2D systems [26, 27, 36,37]. The resonance fields of the harmonic CRs are givenby B /n , where B and n are the resonance field of thefundamental CR and integers ( n = 2 , , , ... ), respec-tively. The origin of high-order harmonic CRs is relatedto the periodic motion of the electrons on the Q2D FSwith higher order corrugations [38–40]. The transmissionspectra for ν = 55 . m ∗ / m e ,clearly show that only the fundamental CR is present butthat no high harmonic CRs, e.g., no signals exist at 1.7or 6.8 m e .Here, we discuss the difference in the mass renormal-ization effects between the dHvA oscillation and CRmeasurements; m ∗ dHvA = 6 . m e on an average, and m ∗ CR = 3 . m e for the α FS. It is well known that m ∗ dHvA is renormalized by both e-p and e-e interactions. On theother hand, according to Kohn’s theorem [24], a long-wavelength radiation can couple only to the center-of-mass motion of electrons, which is not affected by e-einteractions. In this situation, corresponding to the CRmeasurements in single-band systems, m ∗ CR is renormal-ized only by the e-p interaction (not by the e-e interac-tion). However, this is not the case for CR measurementsin multi-band systems. In multi-band systems such asKFe As , m ∗ CR can be renormalized by the interband(not intraband) e-e interaction [28, 41, 42]. Based onthe above discussion, we assume the effective mass inKFe As as m ∗ dHvA = (1 + λ ep )(1 + λ intraee + λ interee ) m band and m ∗ CR = (1 + λ ep )(1 + λ interee ) m band [43], where λ ep , λ intraee , and λ interee are the e-p, intraband e-e, and inter-band e-e coupling constants, respectively. For the α FS,we obtain λ intraee / (1 + λ interee ) = 0 . m ∗ dHvA /m e = 6 . m ∗ CR /m e = 3.4. If we use the theoreti-cal value for the related materials, i.e., λ ep ≈ . λ intraee = 1 . λ interee = 0 .
5. This leads us toconclude that both the intra- and the interband e-e inter-actions enhance the effective mass of KFe As althoughthe λ ep and m band values remain rather ambiguous.In Fe-based superconductors, a possible superconduct-ing mechanism is the AF fluctuation between differentFS pockets, as discussed in the literatures [44, 45]. InKFe As , the main Q2D FSs are located at the Γ point[17, 18], and a nodal gap structure has been proposed [13–16]. These might suggest that the superconductivity inKFe As is mainly mediated by the intraband AF fluctu-ation [15]. However, the present CR study shows the exis-tence of appreciable interband e-e interaction in KFe As despite the absence of nesting between electron and holeFSs. This may be consistent with a recent inelastic neu- tron scattering measurement, which suggests significantinterband scattering between the bands around the Γ and X points [46]. At present, it is still controversial whichAF fluctuation is the dominant superconducting mecha-nism for KFe As .In the compensated Fe based superconductors,BaFe [As (2 − x) P x ], and LaFePO, significant discrepanciesbetween the dHvA results and the band calculations arereported [8, 20]. The origin has been discussed in termsof the energy band shifts due to strong interband e-einteraction between the hole and electron FSs [47]. InKFe As , the strong interband and/or intraband e-e cor-relation evidenced by the CR measurements might alsobe the origin of the discrepancies between the dHvA re-sults and the band calculation [19].In summary, a single CR signal is observed in KFe As ,which is ascribed to the α FS centered at the Γ point. Theobtained m ∗ CR of (3.4 ± m e is significantly smallerthan the m ∗ dHvA of the α FS, i.e., 6.3 m e on an average.This directly indicates the presence of the strong massenhancement on account of the e-e interaction. A com-parison between the dHvA and CR analyses results alsosuggests that the effective mass of KFe As is enhancedby both the intra- and the interband e-e interactions.This work was supported by grant-in-aid for Scien-tific Research on Innovative Areas, (No. 20102005) fromJSPS, Japan. K.K. thanks NIMS for providing the juniorresearch assistantship. [1] Y. Kamihara et al. , J. Am. Chem. Soc. , 3296 (2008).[2] H. Kito, H. Eisaki, and A. Iyo, J. Phys. Soc. Jpn. ,063707 (2008).[3] Z.-A. Ren et al. , Chin. Phys. Lett. , 2215 (2008).[4] C. Wang et al. , Europhys. Lett. , 67006 (2008).[5] K. Ishida, Y. Nakai, and H. Hosono, J. Phys. Soc. Jpn. , 062001 (2009).[6] D. C. Johnston, Adv. Phys. , 803 (2010).[7] M. Kimata et al. , Phys. Rev. Lett., , 246403 (2010).[8] H. Shishido et al. , Phys. Rev. Lett. , 057008 (2010).[9] M. Rotter, M. Tegel, and D. Johrendt, Phys. Rev. Lett. , 107006 (2008).[10] H. Chen et al. , Europhys. Lett. , 17006 (2009).[11] M. Rotter et al. , Phys. Rev. B , 020503 (2008).[12] T. Terashima et al. , arXiv: 1103.3329.[13] H. Fukazawa et al. , J. Phys. Soc. Jpn. , 083712 (2009).[14] J. K. Dong et al. , Phys. Rev. Lett. , 087005 (2010).[15] K. Hashimoto et al. , Phys. Rev. B , 014526 (2010).[16] H. Kawano-Furukawa et al. , Phys. Rev. B , 024507(2011).[17] T. Sato et al. , Phys. Rev. Lett. , 047002 (2009).[18] T. Yoshida et al. , arXiv: 1007.2698.[19] T. Terashima et al. , J. Phys. Soc. Jpn. , 053702 (2010).[20] A. I. Coldea et al. , Phys. Rev. Lett. , 216402 (2008).[21] L. Boeri, O. V. Dolgov, and A. A. Golubov, Phys. Rev.Lett. , 026403 (2008).[22] T. Yildirim, Phys. Rev. Lett. , 037003 (2009).[23] L. Boeri et al. , Phys. Rev. B , 020506(R) (2010). [24] W. Kohn, Phys. Rev. , 1242 (1961).[25] K. Kanki and K. Yamada, J. Phys. Soc. Jpn. , 1103(1997).[26] S. Hill et al. , Phys. Rev. Lett., , 3374 (2000).[27] A. Ardavan et al. , Physica B , 379 (2001).[28] M. Yoshida et al. , Phys. Rev. B , 075102 (2005).[29] K. Kihou et al. , J. Phys. Soc. Jpn. , 124713 (2010).[30] M. Mola et al. , Rev. Sci. Instrum. , 186 (2000).[31] M. Kimata et al. , Jpn. J. Appl. Phys. , (2005) 4930.[32] S. Takahashi and S. Hill, Rev. Sci. Instrum. , 023114(2005).[33] T. Terashima et al. , Phys. Rev. Lett. , 259701 (2010).[34] J. S. Kim et al. , Phys. Rev. B , 172502 (2011).[35] G. Dresselhaus, A. F. Kip, and C. Kittel, Phys. Rev. ,(1955) 368.[36] Y. Oshima et al. , J. Phys. Soc. Jpn. , 1031 (2002).[37] M. Kimata et al. , Phys. Rev. B , 045126 (2007).[38] S. Hill, Phys. Rev. B , 4931 (1997).[39] R. H. McKenzie and P. Moses, Phys. Rev. B. , R11241(1999).[40] S. J. Blundell, A. Ardavan, and J. Singleton, Phys. Rev.B , R6129 (1997).[41] H. Kublbeck and J. P. Kotthaus, Phys. Rev. Lett., ,1019 (1975).[42] Y. Takada and T. Ando, J. Phys. Soc. Jpn. , 905(1978).[43] R. E. Prange and A. Sachs, Phys. Rev. , 672 (1967).[44] I. I. Mazin et al. , Phys. Rev. Lett. , 057003 (2008). [45] K. Kuroki et al. , Phys. Rev. Lett. , 087004 (2008).[46] C. H. Lee et al. , Phys. Rev. Lett. , 067003 (2011). [47] Ortenzi et al. , Phys. Rev. Lett.103