Lack of coupling between superconductivity and orthorhombic distortion in stoichiometric single-crystalline FeSe
A. E. Böhmer, F. Hardy, F. Eilers, D. Ernst, P. Adelmann, P. Schweiss, T. Wolf, C. Meingast
LLack of coupling between superconductivity and orthorhombic distortion instoichiometric single-crystalline FeSe
A. E. Böhmer,
1, 2
F. Hardy, F. Eilers,
1, 2
D. Ernst, P. Adelmann, P. Schweiss, T. Wolf, and C. Meingast Institut für Festkörperphysik, Karlsruhe Institute for Technology, 76021 Karlsruhe, Germany Fakultät für Physik, Karlsruhe Institute for Technology, 76131 Karlsruhe, Germany (Dated: September 24, 2018)The coupling between superconductivity and othorhombic distortion is studied in vapor-grownFeSe single crystals using high-resolution thermal-expansion measurements. In contrast to theBa122-based (Ba122) superconductors, we find that superconductivity does not reduce the or-thorhombicity below T c . Instead we find that superconductivity couples strongly to the in-planearea, which explains the large hydrostatic pressure effects. We discuss our results in light of the spin-nematic scenario and argue that FeSe has many features quite different from the typical Fe-basedsuperconductors. PACS numbers: 74.70.Xa, 74.25.Bt, 74.62.Fj
The interplay of structure, magnetism and supercon-ductivity has been a recurrent theme in the study of iron-based superconductors[1]. Among these systems, PbO-type β -FeSe has the simplest crystallographic structureand a rich phase diagram[1]. It undergoes a structuralphase transition, similar to that of many parent com-pounds of the 1111 and 122 iron-based systems, at ∼ K. In these later materials, structural and magnetic or-der track each other closely, which has led to the sugges-tion of a magnetic (spin-nematic) origin of the structuraldistortion[2]. In FeSe, however, no static magnetism isfound at ambient pressure[3, 4] and spin-fluctuations arefound to be enhanced only at low temperatures[5], whichraises the question of the origin of the structural transi-tion. FeSe becomes superconducting at a modest T c = 8 K[6], yet the onset of superconductivity rises dramati-cally to ∼ K under hydrostatic pressure[7, 8], whichalso induces static magnetic order[9]. Recently, super-conductivity even up to over 50 K was demonstrated instrained epitaxial thin films[10]. With its huge sensitiv-ity of T c to external pressure and the large separationbetween structurally distorted and magnetically orderedphase, FeSe is an intriguing system to study the phaseinterplay using pressure as a tuning parameter. Uniax-ial pressure effects, as can be studied by thermal expan-sion, are of special interest, because they are usuallyvery anisotropic in the iron-based systems due to thelayered crystal structures[11, 12]. Further, these typesof measurements provide a sensitive probe of the cou-pling between superconducting and orthorhombic orderparameters[13, 14].Single-crystal growth of β -FeSe, on the other hand, iscomplicated by the rich constitutional binary phase dia-gram of Fe and Se, where the tetragonal, superconducting β -FeSe phase is located deep below the solidus line[15]. Inconsequence, crystal growth experiments from the meltor self flux result in hexagonal δ -FeSe, which undergoesa series of structural transformations and decompositionreactions on cooling to room temperature[15]. Only if the initial Se content is low enough, can tetragonal β -FeSe be obtained, however, only in the form of a plateletof hexagonal morphology which contains both, tetragonal β -FeSe and magnetic Fe Se [15].In this Letter, we report on high-resolution thermal-expansion of vapor-grown single-crystalline β -FeSe.Growth directly in the tetragonal structure results in highquality single-crystals, which are well suited to studythe anisotropy of pressure effects; a necessary comple-ment to hydrostatic-pressure studies in any non-cubicmaterial. We show that the dramatic increase of T c under hydrostatic pressure arises from a reduction ofthe in-plane area, while T c is five times less sensitiveto the c -axis length. Further, we demonstrate non-Fermi-liquid behavior in the low-temperature in-planethermal-expansion coefficients, which slightly reduces theorthorhombic distortion and presumably arises from low-temperature spin-fluctuations. Surprisingly, orthorhom-bic distortion and superconductivity do not compete inFeSe, in contrast to underdoped 122 pnictides, which sug-gests that the structural transition may not be of mag-netic origin.Fe and Se powders were mixed in an atomic ratio 1.1:1and sealed in an evacuated SiO ampoule together witha eutectic mixture af KCl and AlCl . The ampoule washeated to ◦ C on one end while the other end was keptat ◦ C. After 28.5 days isometric FeSe crystals withtetragonal morphology were extracted at the colder end(Fig. 1 (a,b)). At such low temperatures, samples formdirectly in the tetragonal state and do not undergo struc-tural transformations or decomposition reactions. Wave-length dispersive x-ray spectroscopy reveals an impuritylevel below 500 ppm, in particular there is no evidencefor Cl, Si, K or Al impurities.x-ray powder diffraction confirms the tetragonal struc-ture with lattice constants a = 3 . Å and c = 5 . Å. Structural refinement with a 4-circlediffractometer using Mo-radiation yields a compositionof Fe:Se=0.995(4):1 ( i. e. stoichiometric within the error a r X i v : . [ c ond - m a t . s up r- c on ] M a r p M/H
H | | a b2 0 0 O eF CZ F C T c c (10-4 emu mol-1 Oe-1) T ( K )H | | a b1 T ( a )( b ) ( c ) T s FIG. 1. (color online) (a,b) Photographs of tetragonal β -FeSegrown using a low-temperature vapor-transport technique.(c) Temperature dependence of the magnetic susceptibilityin a field of 1 T, applied parallel to the ab plane. The in-set shows the low-temperature data in a field of 20 mT. Thescreening is larger than − because of the demagnetizationeffect. bar) and a structural z parameter of z = 0 . . Noindications for interstitial atoms were found. Fig. 1 (c)shows the temperature dependence of the magnetic sus-ceptibility with field applied parallel to the ab plane mea-sured in a vibrating sample magnetometer. A small butsharp kink, which we associate with the structural tran-sition, is observed at 87 K. The superconducting transi-tion has a sharp onset at 8 K and is broadened by therelatively high applied field. High-resolution thermal ex-pansion was measured in a capacitance dilatometer[16],in which the sample is pressed against one plate of aplate-type capacitor with a force of ∼ . N, directedalong the measured sample length. As for underdopedBaFe As [13, 14], this force can be used to in-situ detwinsamples of FeSe below their tetragonal-to-orthorhombicphase transition (from space group P4/nmm to Cmma).In particular, if the thermal expansion along [110] T (tetragonal notation) is measured, samples are detwinnedby the applied force and the (shorter) orthorhombic a axis is measured[17]. Measuring thermal expansion alongthe tetragonal [100] T direction yields, ideally, the aver-age of a and b axis. Under this assumption, the thermalexpansion of the orthorhombic b axis can be inferred[14].Fig. 2 shows the thus obtained relative sample-lengthchanges ∆ L i L i, = L i ( T ) − L i (300 K ) L i (300 K ) and uniaxial thermal-expansion coefficients α i = L i dL i dT , where the index i stands for the direction. The ∆ L i L i, data are in goodagreement with previous x-ray studies[18] and show clearevidence for a second-order tetragonal-to-orthorhombicphase transition at T s = 87 K. We note that the c -axis anomaly at T s is unusually small when com-pared to underdoped Ba(Fe,Co) As (Co-Ba122)[13] orBaFe (As,P) (P-Ba122)[14]. The very small anomaly inthe volume average of the thermal expansion indicates [ 1 0 0 ] T ( t w i n n e d i n - p l a n e a v e . )[ 1 1 0 ] T ( d e t w i n n e d , a a x i s ) b a x i s ( i n f e r r e d ) T ( K ) a i (10-6K-1) [ 0 0 1 ] T ( c a x i s )V o l u m e / 3 ( i n f e r r e d ) ( e )( e ) ( b )( c ) c a x i s D L/L0 (10-3) b a x i s a a x i st w i n n e d ( a ) D L / L = 1 x 1 0 - 6 a a x i s t w i n n e d D L / L = 1 x 1 0 - 6 b a x i s T c D L / L = 2 x 1 0 - 6 FIG. 2. (color online) (a) Relative length changes along thethree measured directions (orthorhombic a axis, in-plane aver-age and c axis) and inferred b -axis length change (continuouslines). For comparison, the corresponding data from x-raydiffraction[18] are given (circles). (b), (c) and (d) show the b -axis, in-plane average and a -axis length change close to T c ,respectively, on a magnified scale. (e) Uniaxial thermal ex-pansion coefficients of FeSe along three measured directions,with the thermal-expansion along the b axis and the volumeaverage inferred from the measurements. The inset shows thedata close to T c on a magnified scale. that T s does not couple strongly to hydrostatic pressure.No distinct second, potentially magnetic, phase transi-tion is observed below T s . At T c = 7 . K, the dis-continuity in the in-plane thermal-expansion coefficients ∆ α i (kink in ∆ L i ( T ) ) clearly confirms a sharp, bulk su-perconducting transition. ∆ α i is related to the uniaxialpressure derivative of T c via the Ehrenfest relationship dT c dp i = V m ∆ α i ∆ C p /T c . (1) V m = 23 . cm /mol is the molar volume and ∆ C p /T c =9 . mJ mol − K − is the specific heat jump, whichwe take from Reference 19. We thus obtain dT c dp twin =2 . K/GPa for the in-plane average, dT c dp a = 2 . K/GPa, dT c dp b = 3 . . K/GPa and dT c dp c = 0(0 . K/GPa.The hydrostatic pressure derivative of T c is simply givenby the sum of the uniaxial components dT c dp v = dT c dp a + dT c dp b + dT c dp c = 5 . . K GPa − and is in good agreementwith the initial slope of direct measurements, which yield dT c dp v = 6 − K GPa − [9, 20]. It is clear from our resultsthat the comparatively large dT c dp v in FeSe arises not fromparticularly large uniaxial components but from lack oftheir cancellation. The in-plane derivatives are compara-ble in size to slightly overdoped Co-Ba122[11, 12]. How-ever, in Co-Ba122, in-plane and c -axis pressure deriva-tives have opposite signs and largely cancel in the hydro-static average (with the negative p c derivative slightlyprevailing)[11, 13], while the p c derivative is approxi-mately zero in FeSe. The structural tuning parameter ofthe 122-systems is the c/a ratio[12–14]. In FeSe instead,the in-plane distance alone appears to be the tuning pa-rameter, which couples strongly to hydrostatic pressure.Basically the same picture emerges when consideringthe uniaxial strain derivatives of T c , dT c dε j = (cid:80) i c ij dT c dp i ,which can be calculated if the set of elastic constants c ij ( i, j = 1 − is known. For tetragonal FeSe, these con-stants have been calculated using DFT[21] to c = 95 . GPa, c = 48 . GPa, c = 13 . GPa and c = 39 . GPa[22]. Using the above c ij values (allowing for an er-ror of 10%) we find dT c dε a = − K, dT c dε b = − K and dT c dε c = − K. It is evident that T c dependssensitively on the in-plane lengths. The correspondinguniaxial Grüneisen parameter is d ln T c dε ab = − , i. e. shrinking ( a + b ) / by 1% increases T c by ∼ . Notethat a and b decrease by ∼ . % between ambient pres-sure and 7 GPa, where the highest T c is reached[8]. T c is five times less sensitive to changes of the c -axis length( d ln T c dε c = − ). It is striking that the c -axis length hassuch a small effect on T c , especially since the Se height(i.e. the c -axis length times the internal z -parameter) wasfound to correlate closely with T c [23]. The z -parameterhowever, may depend in a complicated manner both onin-plane and c -axis lengths. For a detailed investigationof its relation to uniaxial pressure effects, this dependencewould have to be established.Fig. 3 presents our results concerning the interplay be-tween orthorhombicity, magnetic fluctuations and super-conductivity in FeSe. Fig. 3 (a) shows the orthorhombicorder parameter δ = | a − b | / ( a + b ) ≈ | a − b | / a of FeSe,undoped Ba122 and underdoped Co-Ba122 (4.5% Co-content), all computed from our thermal-expansion mea-surements. Although no magnetic transition is found, δ ( T = 0) of FeSe is of similar magnitude as in the 122-systems. While δ ( T ) is reduced below T c in the 4.5%Co-Ba122, there is no discernable feature in δ ( T ) of FeSe at T c (Fig. 3 (b,c)). Curiously, however, δ ( T ) has a weakmaximum at ∼ K, which we will discuss before weaddress the response of δ ( T ) at T c in more detail.The maximum of δ ( T ) is caused by the sign change of - 404 - 101 ( e )( d ) ( f )( c )( b ) T ( K ) d (10-3) F e S e ( T c = 7 . 7 5 K )4 . 5 % C o - B a 1 2 2( T c = 1 3 . 5 K ) ( a ) B a F e A s T c T ( K ) - 5
F e S e - 6 T c T / T c d d /dT (10-6K-1) T ( K ) a i/T (10-6K-2) F e S e a a x i sF e S e b a x i s2 0 % P - B a 1 2 2 a a x i s F e S e d d /dT (10-6K-1) FIG. 3. (color online) (a) Orthorhombic order parameter δ = | b − a | / a of FeSe (orange line), undoped Ba122 (dashed blackline) and underdoped Co-Ba122 (black line) computed fromthermal-expansion measurements. (b) and (c) show δ ( T ) ofFeSe and Co-Ba122, respectively, below 20 K on a magnifiedscale. Note that the scale in (b) is ten times smaller thanin (c). (d) α a,b /T of FeSe (red and purple lines) and α a /T of underdoped P-Ba122 (dark green line). For clarity, databelow T c are shown in a lighter color. The arrow points atthe crossing of the normal-state in-plane thermal-expansioncoefficients of FeSe. (e) and (f) show dδdT of FeSe and Co-Ba122, respectively, close to T c . both α a ( T ) and α b ( T ) at ∼ K (see inset Fig. 2(e)),which points to an additional low-temperature contribu-tion to the thermal expansion. This contribution, whichappears to be diverging down to T c , becomes evident ina plot of α a,b T (Fig. 3 (d)). For a Fermi-liquid, one ex-pects a constant αT -term at low temperatures, which isdirectly related to the uniaxial pressure derivative of theSommerfeld coefficient, as seen for P-Ba122 with 20%P-content[14] (Fig. 3(d)). The non-Fermi-liquid charac-ter of the thermal-expansion of FeSe becomes apparentin this comparison. A new energy scale with a negative(positive) contribution to α a T ( α b T ) emerges below ∼ Kand causes these coefficients to diverge. Note that nei-ther the Knight-shift, nor specific heat have previouslyshown indications of non-Fermi-liquid behavior [5, 19].However, thermal-expansion is expected to be an espe-cially sensitive probe for locating such non-Fermi-liquidbehavior[24] and enhanced low-temperature spin fluctu-ations have reavealed that FeSe is on the brink of a mag-netic phase transition near T = 0 [5]. Our observationof non-Fermi-liquid behavior is probably related to thisquantum critical point and the new energy scale maybe linked to the low-temperature spin fluctuations. Itis then, however, curious that these fluctuations cause areduction of the orthorhombic order parameter of FeSe.In the 122-pnictides, in contrast, the onset of magnetismenhances δ ( T ) [25], suggesting that the relation betweenmagnetism and orthorhombicity may be different in FeSe.The very small ab -plane anisotropy of ∆ α i of FeSe at T c implies that δ ( T ) has no more than a tiny anomaly at T c , as can indeed be seen in Fig. 3 (b). Only a small kinkin the temperature derivative dδdT (Fig. 3(d)) is observed,which is such that δ will have a tendency to be somewhatlarger in the superconducting state than in the normalstate. In particular, there is no indication of competitionbetween orthorhombicity and superconductivity in FeSe.Such a competitive coupling was clearly observed in un-derdoped Co-Ba122 (see Fig. 3(c) and Ref. 26) and otherdoped Ba122-compounds[27] and results in a reduction of δ below T c , or equivalently in a positive anomaly in dδdT (see Fig. 3(f)). This coupling was proposed to arise, ul-timately, from the competition between magnetism andsuperconductivity[26]. In this scenario, magnetic spinfluctuations, which give rise to “nematic” order that, inturn, induces an orthorhombic distortion via magneto-elastic coupling, are weakened by the onset of supercon-ductivity. It is an important question which part of thisscenario is not valid for FeSe. Our results suggest thateither superconductivity does not interact strongly withspin fluctuations or that the structural transition has anon-magnetic origin.In conclusion, high-resolution thermal-expansion mea-surements of vapor-grown β -FeSe have revealed a numberof unusual properties, which suggest that FeSe is not atypical iron-based superconductor. The structural tun-ing parameter of FeSe is the in-plane area, compared tothe c/a ratio in 122-systems, which explains why T c cou-ples so strongly to hydrostatic pressure. In underdoped122 pnictides, magnetism and orthorhombicity are coop-erative and compete with superconductivity. In FeSe, onthe other hand, T c and magnetism both increase underhydrostatic pressure, suggesting that they act coopera-tively. Further, superconductivity does not compete withorthorhombicity, which raises the question of the origin ofthe orthorhombic phase transition. Also, we show that anew energy scale, presumably associated with spin fluctu-ations, emerges at low temperature and slightly reducesthe orthorhombic distortion below 12 K. Further stud-ies on the nature of these different phases, which exhibitsuch an unusual interplay, will be of great interest.We wish to thank J. Schmalian and R. M. Fernandesfor discussions. This work was supported by the DFGunder the priority program SPP1458. [1] G. R. Stewart, Rev. Mod. Phys. , 1589 (2011).[2] R. M. Fernandes and J. Schmalian, Supercond. Sci. Tech-nol. , 084005 (2012).[3] M. Bendele, A. Amato, K. Conder, M. Elender, H. Keller,H.-H. Klaus, H. Luetkens, E. Pomjakushina, A. Raselli,and R. Khasanov, Phys. Rev. Lett. , 087003 (2010).[4] T. M. McQueen, A. J. Williams, P. W. Stephens, J. Tao,Y. Zhu, V. Ksenofontov, F. Casper, C. Felser, and R. J.Cava, Phys. Rev. Lett. , 057002 (2009).[5] T. Imai, K. Ahilan, F. L. Ning, T. M. McQueen, andR. J. Cava, Phys. Rev. Lett. , 177005 (2009).[6] F.-C. Hsu, J.-Y. Luo, K.-W. Yeh, T.-K. Chen, T.-W.Huang, P. M. Wu, Y.-C. Lee, Y.-L. Huang, Y.-Y. Chu,D.-C. Yan, and M.-K. Wu, Proc. Natl. Acad. Sciences , 14262 (2008).[7] S. Medvedev, T. M. McQueen, I. A. Troyan, T. Palasyuk,M. I. Eremets, R. J. Cava, S. Naghavi, F. Casper,V. Ksenofontov, G.Wortmann, and C. Felser, NatureMat. , 630 (2009).[8] S. Margadonna, Y. Takabayashi, Y. Ohishi,Y. Mizuguchi, Y. Takano, T. Kagayama, T. Naka-gawa, M. Takata, and K. Prassides, Phys. Rev. B ,064506 (2009).[9] M. Bendele, A. Ichsanow, Y. Pashkevich, L. Keller,T. Strässle, A. Gusev, E. Pomjakushina, K. Conder,R. Khasanov, and H. Keller, Phys. Rev. B , 064517(2012).[10] Q.-Y. Wang, Z. Li, W.-H. Zhang, Z.-C. Zhang, J.-S.Zhang, W. Li, H. Ding, Y.-B. OU, P. Deng, K. Chang,J. Wen, C.-L. Song, K. He, J.-F. Jia, S.-H. Ji, Y.-Y.Wang, L.-L. Wang, X. Chen, X.-C. Ma, and Q.-K. Xue,Chin. Phys. Lett. , 037402 (2012).[11] S. L. Bud’ko, N. Ni, S. Nandi, G. M. Schmiedeshoff, andP. C. Canfield, Phys. Rev. B , 054525 (2009).[12] F. Hardy, P. Adelmann, T. Wolf, H. v. Löhneysen, andC. Meingast, Phys. Rev. Lett. , 187004 (2009).[13] C. Meingast, F. Hardy, R. Heid, P. Adelmann, A. Böh-mer, P. Burger, D. Ernst, R. Fromknecht, P. Schweiss,and T. Wolf, Phys. Rev. Lett. , 177004 (2012).[14] A. E. Böhmer, P. Burger, F. Hardy, T. Wolf, P. Schweiss,R. Fromknecht, H. v. Löhneysen, C. Meingast, H. K.Mak, R. Lortz, S. Kasahara, T. Terashima, T. Shibauchi,and Y. Matsuda, Phys. Rev. B , 094521 (2012).[15] H. Okamoto, Journal of Phase Equilibria , 383 (1991).[16] C. Meingast, B. Blank, H. Bürkle, B. Obst, T. Wolf,H. Wühl, V. Selvamanickam, and K. Salama, Phys. Rev.B , 11299 (1990).[17] Following conventions, we call the shorter orthorhombicin-plane axis a , opposed to the prevailing custom in 122-pnictides.[18] R. Khasanov, M. Bendele, K. Conder, H. Keller, E. Pom-jakushina, and V. Pomjakushin, New J. Phys. , 073024(2010).[19] J.-Y. Lin, Y. S. Hsieh, D. A. Chareev, A. N. Vasiliev,Y. Parsons, and H. D. Yang, Phys. Rev. B , 220507(R)(2011).[20] S. Masaki, H. Kotegawa, Y. Hara, H. Tou, K. Murata,Y. Mizuguchi, and Y. Takano, J. Phys. Soc. Jpn. ,063704 (2009).[21] S. Chandra and A. K. M. A. Islam, Physica C , 2072(2010). [22] c agrees within 8% with the experimental low-temperature value of 42.7 GPa[28] reported from a mea-surement on thin films. Using the calculated c ij val-ues, the linear compressibilites K a = − a dadp = K b =4 . × − GPa − and K c = 17 . × − GPa − are ob-tained, which are also in relatively good agreement withthe experiment ( K a = 6 . × − GPa − , K b = 6 . × − GPa − and K c = 17 . × − GPa − [29]). Addition-ally, the elastic properties show relatively little ab -planeanisotropy.[23] Y. Mizuguchi, Y. Hara, K. Deguchi, S. Tsuda, T. Yam-aguchi, K. Takeda, H. Kotegawa, H. Tou, and Y. Takano,Supercond. Sci. Technol. , 054013 (2010).[24] M. Garst and A. Rosch, Phys. Rev. B , 205129 (1995).[25] M. G. Kim, R. M. Fernandes, A. Kreyssig, J. W. Kim,A. Thaler, S. L. Bud’ko, P. C. Canfield, R. J. McQueeney, J. Schmalian, and A. I. Goldman, Phys. Rev. B ,134522 (2011).[26] S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes,D. K. Pratt, A. Thaler, N. Ni, S. L. Bud’ko, P. C. Can-field, J. Schmalian, R. J. McQueeney, and A. I. Gold-man, Phys. Rev. Lett. , 057006 (2010).[27] S. Avci, O. Chmaissem, E. A. Goremychkin,S. Rosenkranz, J.-P. Castellan, D. Y. Chung, I. S.Todorov, J. A. Schlueter, H. Claus, M. G. Kanatzidis,A. Daoud-Aladine, D. Khalyavin, and R. Osborn, Phys.Rev. B , 172503 (2011).[28] Y.-C. Wen, Y.-C. Liao, H.-H. Chang, B.-H. Mok, Y.-C.Lee, T.-W. Huang, K.-W. Yeh, J.-Y. Luo, M.-J. Wang,C.-K. Sun, and M.-K. Wu, Journal of Applied Physics , 073505 (2011).[29] J. N. Millican, D. Phelan, E. L. Thomas, J. B. Leão, andE. Carpenter, Solid State Commun.149