Competition between unconventional superconductivity and incommensurate antiferromagnetic order in CeRh1-xCoxIn5
S. Ohira-Kawamura, H. Shishido, A. Yoshida, R. Okazaki, H. Kawano-Furukawa, T. Shibauchi, H. Harima, Y. Matsuda
aa r X i v : . [ c ond - m a t . s t r- e l ] A p r Competition between unconventional superconductivity and incommensurateantiferromagnetic order in CeRh − x Co x In S. Ohira-Kawamura , ∗ H. Shishido , † A. Yoshida , R. Okazaki ,H. Kawano-Furukawa , T. Shibauchi , H. Harima , and Y. Matsuda , Academic and Information Board, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan Department of Physics, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan Department of Physics, Kobe University, Kobe 657-8501, Japan Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan (Dated: November 12, 2018)Elastic neutron diffraction measurements were performed on the quasi-two dimensional heavyfermion system CeRh − x Co x In , ranging from an incommensurate antiferromagnet for low x toan unconventional superconductor on the Co-rich end of the phase diagram. We found that thesuperconductivity competes with the incommensurate antiferromagnetic (AFM) order characterizedby q I = ( , , δ ) with δ = 0 . q c =( , , ). This is in sharp contrast to the CeRh − x Ir x In system, where both the commensurateand incommensurate magnetic orders coexist with the superconductivity. These results reveal thatparticular areas on the Fermi surface nested by q I play an active role in forming the superconductingstate in CeCoIn . PACS numbers: 74.70.Tx, 74.25.Dw, 75.25.+z
The unconventional superconducting (SC) pairingstate realized in strongly correlated electron systems, in-cluding heavy fermion and high- T c cuprates, often de-velops, to varying extents, in the proximity of a mag-netically ordered state. Therefore, it is widely believedthat the magnetic fluctuations play important roles forthe Cooper pairing. In fact, strong coupling between themagnetic excitation spectra and SC order parameter hasbeen reported in high- T c cuprates [1] and a heavy fermioncompound [2]. To obtain further insights into the micro-scopic mechanism of unconventional superconductivity,more detailed information of the electronic structure, es-pecially the position on the Fermi surface which playsan active role for the pairing formation, is strongly re-quired. In the case of high- T c cuprates with a simple two-dimensional (2D) Fermi surface, the hot spots, at whichthe scattering rate is dramatically enhanced, appear atcertain parts of the Fermi surface, as a consequence of thestrong 2D antiferromagnetic (AFM) fluctuations due tothe nesting of the Fermi surface [3]. On the other hand,such information is still lacking in heavy fermion systemsto date, mainly because the complicated 3D Fermi sur-face often makes it difficult to specify the actual activeposition on the Fermi surface.A new heavy fermion family of Ce M In , where M canbe either Ir, Co or Rh, has attracted much interest on ac-count of the relationship between the superconductivityand magnetism [4, 5]. CeCoIn and CeIrIn are super-conductors with the SC transition temperatures of T c =2 . [6, 7]. This, together with the d -wave(presumably d x − y ) gap symmetry [8], indicates impor- tance of the AFM fluctuations for the superconductivityof CeCoIn . On the other hand, in another compoundCeRhIn , the superconductivity is highly suppressed, andan AFM order appears below T N = 3 . q I = ( , , δ ), δ = 0 . q c = ( , , )has been found in CeRh − x Ir x In [10], and then the su-perconductivity coexists with the two distinct magneticorders in a wide composition range (0 . ≤ x ≤ . . Co . In [11].Such an unusual coexistence of three different types ofcooperative ordered states is quite unique among the un-conventional superconductors. Then, it is important tounderstand their magnetic properties for elucidating themechanism of the unconventional superconductivity inthe Ce M In systems.We here report the results of the elastic neutron diffrac-tion measurements on CeRh − x Co x In , ranging from theAFM metallic to the unconventional SC states. We foundthat, in sharp contrast to CeRh − x Ir x In , the super-conductivity is strongly suppressed by the incommen-surate AFM order characterized by q I = ( , , . q c = ( , , ). These results provide important infor-mation of the positions on the Fermi surface which areresponsible for the unconventional superconductivity inCeRh − x Co x In . This is the first report to provide suchinformation in the heavy fermion compounds. We willalso discuss a difference in the SC states of CeCoIn andCeIrIn , based on the different types of the coexistenceof the magnetism and superconductivity. x = 0.3 x = 0.3 x = 0.4 x = 0.6 x = 0.4 x = 0.6(b)(c) (f)(e)(d)0.3 0.4 1.5 (1/2, 1/2, l ) T (K) I n t e n s it y ( c oun t s / s ec ) I n t e g r a t e d i n t e n s it y ( c oun t s / s ec ) FIG. 1: Neutron diffraction profiles for CeRh − x Co x In for(a) x = 0 .
3, (b) 0.4 and (c) 0.6 for Q = ( , , l ). For x = 0 . . ≤ l ≤ .
55 is shown instead of0 . ≤ l ≤ .
55, because mosaic peaks are observed at thelatter position. Open and closed circles respectively show theresults at 1.5 K and 5 K. Temperature dependences of theintegrated intensities for the Bragg peaks at q c = ( , , )(circles) and q I = ( , , . x = 0 .
3, (e) 0.4 and (f) 0.6.
Single crystals of CeRh − x Co x In for x = 0, 0.2, 0.3,0.4, 0.6, 0.7, 0.75 and 1 were prepared by the self-flux method [12]. Elastic neutron diffraction experi-ments were carried out on the x = 0 .
3, 0.4, 0.6, 0.7and 0.75 samples at the triple-axis spectrometer GPTAS(4G) installed at the JRR-3 reactor in Japan AtomicEnergy Agency. The samples with the typical size of ∼ × × . were set with ( h h l ) scattering plane,and were cooled down to 0.7 K. The neutrons with mo-mentum of k = 3 .
814 ˚A − or 2.67 ˚A − were used forthe measurements. The 40’-40’-40’-80’ collimators andtwo pyrolytic graphite filters, which eliminate the higher-order reflections, were used. To check the sample quality,we have also measured the specific heat and resistivity ofthe samples with the same compositions as those used forthe neutron diffraction measurements (the same batch)and the x = 0, 0.2 and 1 samples.Figures 1(a), (b) and (c) respectively show the neutrondiffraction profiles along the l direction ( Q = ( , , l )) forCeRh − x Co x In with x = 0 .
3, 0.4 and 0.6 at T = 1 . T < T N ) and 5 K ( T > T N ). Magnetic Bragg peaksare observed at 1.5 K at q c = ( , , ) for x = 0 .
3, 0.4and 0.6, indicating appearance of commensurate AFMorders, while such a peak is not observed for x ≥ . x = 0 .
3, in addi-tion to the commensurate AFM peak, another magneticBragg peak is observed at q I = ( , , . C m a g / T ( J / K • m o l )
420 T (K)CeRh Co x In x = 01 0.40.6 0.2 FIG. 2: Specific heat divided by temperature, C mag /T , ofCeRh − x Co x In as a function of temperature. The solid ar-rows indicate the SC transition, and the dotted ones the AFMtransition. incommensurate AFM peak is observed in CeRhIn .Temperature dependences of the integrated intensitiesof the Bragg peaks for x = 0 .
3, 0.4 and 0.6 are depictedin Figs. 1(d), (e) and (f), respectively. The commen-surate AFM Bragg peaks (filled circles) develop below3.0 K, 3.1 K, and 2.8 K for x = 0 .
3, 0.4, and 0.6. The in-commensurate AFM Bragg peak with q I = ( , , . x = 0 . M c for the commensurateAFM order and M I for the incommensurate one are eval-uated to be M c = 0 . µ B /Ce and M I ∼ . µ B /Cefor x = 0 . M c = 0 . µ B /Ce for x = 0 . M c =0 . µ B /Ce for x = 0 .
6. For evaluating the moments,we assumed the spins lying on the basal plane, similarto the helical AFM moments in CeRhIn [9]. These val-ues are close to those reported in CeRh − x Ir x In [10]. Itshould be emphasized here, however, that there is a cru-cial difference that the incommensurate AFM peak is notobserved for x ≥ .
4, within the experimental accuracy.A further support of the absence of the incommen-surate AFM order at x ≥ . C mag /T , for x = 0, 0.2, 0.4, 0.6 and 1. Here C mag /T isobtained by subtracting nonmagnetic contributions esti-mated by C/T of LaRhIn . In x = 0 .
4, two anomaliesof the specific heat associated with the commensurateAFM and SC transitions are observed at T = 2 . x - T phase diagram for CeRh − x Co x In deter-mined by the present neutron diffraction, specific heatand resistivity measurements is depicted in Fig. 3(a).The incommensurate AFM order, which is observed inthe pure CeRhIn system, appears below x = 0 . T ( K ) CeRh Ir x In IC (b) SC T ( K ) IC CeRh Co x In (a) C SC
IC + C
FIG. 3: (a) x - T phase diagram for CeRh − x Co x In from theneutron diffraction ( (cid:13) ), specific heat ( (cid:3) , ⋄ ) and resistivitymeasurements ( ▽ , △ ). At x =0.2 (solid arrow) and x =0.7(dotted arrow), the superconductivity and the AFM orderwere not observed down to T =0.7 K, respectively. (b) x - T phase diagram for CeRh − x Ir x In reported in refs. 10 and 16is illustrated schematically. is absent at x ≥ .
4. The SC state is not observeddown to 0.7 K at x = 0 .
2, while it suddenly appearsat x ∼ .
3. The commensurate AFM order simulta-neously appears here, and stays on the intermediate x region (0 . ≤ x ≤ . − x Co x In reported previously. The compo-sition ( x ) dependence of T c is consistent with the resultsreported in ref. 15, but the x dependence of the magnetictransition temperature shows a clear difference. Namely,the present results show step-like behavior in contrast toa smooth curve from x = 0 to the QCP ( x ∼ .
75) inref. 15. At the present stage, we do not know the ori-gin of this difference. Judging from the disappearance ofboth the superconductivity and the commensurate AFMorder at x = 0 . T N , however,we conclude that the phase boundary between the in-commensurate and commensurate AFM phases is of firstorder, and then the coexistence of the commensurate andincommensurate AFM orders observed at x = 0 . x = 0 . x = 0 . − x Ir x In re-ported in refs. 10 and 16, in Fig. 3(b). The two phasediagrams shown in Fig. 3 bear some resemblance; First,simultaneous appearance of the superconductivity and commensurate AFM order is observed at low x regime.Second, the superconductivity coexists with the commen-surate AFM order in the intermediate x regime. How-ever, a significant difference also exists there. Namely,while the incommensurate AFM order coexists with thesuperconductivity in CeRh − x Ir x In , there is no intrinsiccoexistence of the incommensurate AFM order with thecommensurate AFM order and the superconductivity inCeRh − x Co x In , implying that the superconductivity isstrongly suppressed by the incommensurate AFM orderin the latter system. A possible origin for this will bediscussed later.It may also be meaningful to compare the present re-sults to some other experimental results on CeRhIn un-der pressure. Recently, specific heat measurements underhydrostatic pressure revealed that the incommensurateAFM order suddenly disappears above a critical pressure p ∗ c ∼ T c steeply increasesabove it [17]. Therefore, the absence of the coexistingphase of the incommensurate AFM order and the su-perconductivity seems to be a common feature in theCeRh − x Co x In system and CeRhIn under pressure.The present result that, in CeRh − x Co x In , the super-conductivity competes with the incommensurate AFMorder but coexists with the commensurate one can pro-vide an important insights for the mechanism of the un-conventional superconductivity in this system. Namely,the area of the Fermi surface which disappears by the gapformation due to the incommensurate AFM order playsan active role for the superconductivity. However, thearea which disappears at the commensurate AFM ordermay not be important for the superconductivity, becausethe superconductivity coexists with the commensurateAFM order.Then it is tempting to discuss which area on the Fermisurface is connected by the q I - and q c - wave numbers.According to the de Haas-van Alphen experiments, the14th band has the heaviest mass [18]. We therefore as-sume that the 14th band is the main band for the super-conductivity. It is necessary to search all nesting posi-tions connected by q I and q c in the 3D Fermi surface,but we discuss here the area symmetric about the Γ-point for simplicity. Figures 4(a), (b), and (c) illustratethe cross section of the 14th band perpendicular to k z at k z =0.149, 0.351 and , respectively. The distances be-tween the pairs of these sections inverted with respect tothe Γ-point equal to the z -components of q I , (0 0 1) − q I ,and q c , respectively. The blue dotted lines represent theboundaries of the Brillouin zone when the AFM ordersset in. Thus the positions of the Fermi surface whichintersect the blue lines are supposed to be strongly influ-enced by the AFM orders. At a first glance, the area at FIG. 4: (a)-(c) The cross section of the 14th Fermi surfaceperpendicular to k z , at (a) k z = 0 . .The blue dotted lines represent the boundary of the AFMBrillouin zone. (d) The 3D figure of the cylindrical part of14th Fermi surface. The red hatched regions represent thearea which connected by q I = ( , , . − q I vector. The red area is suggested to playan active role for the SC pairing formation. the corrugation on the cylindrical Fermi surface paintedin red in Fig. 4(b) appears to be strongly nested throughthe (0 0 1) − q I vector. Taking into account the fact thatthe disappearance of the superconductivity is concomi-tant with the appearance of the incommensurate AFMorder, it is natural to interpret that this area of the Fermisurface plays active roles for the occurrence of both thesuperconductivity and the incommensurate AFM order,and so that the gap formation accompanied with the in-commensurate AFM order strongly suppresses the su-perconductivity. On the other hand, such a large nestingarea is absent at k z = 0 .
25, as shown in Fig. 4(c). Thisseems to be relevant to the fact that the superconductiv-ity is insensitive to the commensurate AFM order. Fig-ure 4(d) illustrates the cylindrical part of the 14th band.The red area connected by (0 0 1) − q I (blue arrow) playsan active role for the superconductivity.We finally discuss the difference between CeCoIn and CeIrIn inferred from the present study. Themost remarkable difference is that the incommensurateAFM order strongly suppresses the superconductivity inCeRh − x Co x In , while they coexist in CeRh − x Ir x In .This implies that the active area on the Fermi surfacefor the superconductivity is different in these two sys-tems. Interestingly, a possible difference of the SC gapsymmetry in these two systems has been suggested veryrecently by the thermal conductivity measurements: theline nodes are located perpendicular to the ab -plane inCeCoIn , while parallel to the ab -plane in CeIrIn [19]. In summary, the neutron diffraction measurementsreveal that, in CeRh − x Co x In , the superconductivitycompetes with the incommensurate AFM order, while itcoexists with the commensurate one. This is in sharpcontrast to CeRh − x Ir x In system, in which both thecommensurate and incommensurate magnetic orders co-exist with superconductivity. Based on these results, it issuggested that particular positions on the Fermi surfacenested by (0 0 1) − q I may play an active role in formingthe SC state in CeCoIn . The present results further im-ply that the incommensurate spin fluctuation originatingfrom the nesting characterized by (0 0 1) − q I plays an im-portant role for the pairing interaction. To confirm this,the neutron quasi- and in-elastic scattering experimentsthrough the SC transition is strongly desired.We thank H. Amitsuka, N. Furukawa, H. Ikeda,H. Kontani, S. Onari, M. Sigrist and M. Yashima forvaluable discussion, and M. Azuma, Y. Onuki, R. Settaiand Y. Shimakawa for assistance in some of the measure-ments. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Educa-tion, Culture, Sports, Science and Technology. H. S. wassupported by the Research Fellowships of the Japan So-ciety for the Promotion of Science for Young Scientists. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] H. F. Fong et al ., Phys. Rev. Lett. , 316 (1995).[2] N. K. Sato et al ., Nature , 340 (2001).[3] A. Damascelli, Z. Hussain and Z. X. Shen, Rev. Mod.Phys. , 473 (2003).[4] H. Hegger et al ., Phys. Rev. Lett. , 4986 (2000).[5] C. Petrovic et al ., Europhys. Lett. , 354 (2001); J.Phys, Condens. Matter , L337 (2001).[6] Y. Kohori et al ., Phys. Rev. B , 134526 (2001).[7] M. Yashima et al ., J. Phys. Soc. Jpn. , 2073 (2004).[8] K. Izawa et al ., Phys. Rev. Lett. , 057002 (2001).[9] W. Bao et al , Phys. Rev. B , R14621 (2000); Phys.Rev. B , 099903(E) (2003).[10] A. D. Christianson et al ., Phys. Rev. Lett. , 217002(2005).[11] M. Yokoyama et al ., J. Phys. Soc. Jpn. , 103703 (2006).[12] H. Shishido et al ., J. Phys. Soc. Jpn. , 162 (2002).[13] T. Park et al ., Nature , 65 (2006).[14] G. Knebel, D. Aoki, D. Braithwaite, B. Salce, and J.Flouquet, Phys. Rev. B , 020501(R) (2006).[15] J. R. Jeffries et al ., Phys. Rev. B , 024551 (2005).[16] S. Kawasaki et al ., Phys. Rev. Lett. et al ., J. Phys.: Condens. Matter13