Magnetic order in Ce0.95Nd0.05CoIn5: the Q-phase at zero magnetic field
S. Raymond, S. M. Ramos, D. Aoki, G. Knebel, V. Mineev, G. Lapertot
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Magnetic order in Ce . Nd . CoIn : the Q-phase at zero magnetic field S. Raymond, S. M. Ramos, D. Aoki, G. Knebel, V. Mineev and G. Lapertot SPSMS, UMR-E 9001, CEA-INAC/UJF-Grenoble 1, 38054 Grenoble, France (Dated: July 26, 2018)We report neutron scattering experiment results revealing the nature of the magnetic order occur-ring in the heavy fermion superconductor Ce . Nd . CoIn , a case for which an antiferromagneticstate is stabilized at a temperature below the superconducting transition one. We evidence anincommensurate order and its propagation vector is found to be identical to that of the magneticfield induced antiferromagnetic order occurring in the stoichiometric superconductor CeCoIn , theso-called Q-phase. The commonality between these two cases suggests that superconductivity is arequirement for the formation of this kind of magnetic order and the proposed mechanism is theenhancement of nesting condition by d -wave order parameter with nodes in the nesting area. PACS numbers:
The interplay between magnetism and superconductiv-ity is an essential topic whose investigation is common toseveral families of strongly correlated electron systems:cuprates, iron based superconductors and heavy fermionsystems. These systems share the common point thatthe antiferromagnetic (AFM) ground state can be tunedto a quantum critical point where the N´eel tempera-ture, T N , reaches zero as a function of pressure, chemicalsubstitution or magnetic field. At this quantum criti-cal point superconductivity often emerges but there isno paradigm: magnetism and superconductivity can co-exist or expel each other depending of each system. Inthis framework, many investigated systems have a N´eeltemperature higher than the superconducting transitiontemperature, T c . The opposite case T N < T c , knownfor rare earth transition metal borocarbide compoundsand Chevrel phases [1], is much less studied in stronglycorrelated electron systems especially for itinerant elec-tron ones where the same electrons participate to mag-netism and superconductivity. This situation arises cer-tainly from the lack of convenient experimental realiza-tion of this scenario. Paradoxically a case where it isnonetheless studied is a complex one: the one of mag-netic field induced AFM order starting from a super-conducting ground state. This case is common to thecuprate La − x Sr x CuO , showing both field induced orfield enhanced magnetism [2], and to the heavy fermioncompounds CeRhIn under pressure and CeCoIn at am-bient pressure [3]. This kind of cooperative effect betweenmagnetism and superconductivity reaches its pinnacle inCeCoIn where the field induced AFM phase disappearswhen superconductivity is suppressed at the upper criti-cal field H c .CeCoIn has the highest superconducting transitiontemperature among Ce heavy fermion compounds ( T c =2.3 K) [4]. It crystallizes in a tetragonal structure (spacegroup P4/mmm) and the superconducting gap symmetryis considered to be the singlet d x − y state [5]. A fieldinduced ordered phase (FIOP) occurs for a magnetic fieldapplied in the basal plane of the tetragonal structure, in a narrow range of temperature and magnetic field below300 mK and above 10.5 T, the upper critical field being11.4 T for this geometry. It was shown by Kenzelmannet al. that the FIOP is an AFM phase: the correspond-ing order is incommensurate with a propagation vector k IC =(0.45, 0.45, 0.5) and a magnetic moment of 0.15 µ B aligned along the c -axis of the tetragonal structure; theFIOP was thereafter named Q-phase [6]. Prior to thismicroscopic finding, the FIOP was thought to be therealization of a modulated superconducting phase, theso-called Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state[7]. Despite the finding of magnetic order, this possibilitycannot be excluded and a multicomponent order parame-ter may exist: the FIOP of CeCoIn might therefore be acoupling of superconducting and magnetic order param-eters. The uniqueness of the interpenetrated magneticand superconducting properties of CeCoIn turns out tobe a playground for advanced condensed matter physicsconcepts leading to many experimental and theoreticalworks.In the present study, we choose another route to reacha case T N < T c in a related situation achieved by Nd sub-stitution on CeCoIn . For 0.05 ≤ x ≤ − x Nd x CoIn with still high superconducting transi-tion temperature in the range 1-2 K [8]. For higher Ndsubstitution, superconductivity disappears for x > x > . Nd . CoIn ( T c ≈ T N ≈ . We suggest that thismagnetic order occurring with T N < T c is stimulated by d -wave nodal superconductivity.The neutron scattering measurements were carried outon the cold neutron three axis spectrometer (TAS) IN12located at ILL, Grenoble. The initial neutron beam isprovided by a double focusing pyrolitic graphite (PG) FIG. 1: Specific heat of Ce . Nd . CoIn divided by temper-ature as a function of temperature. The arrows indicate thesuperconducting ( T c ) and antiferromagnetic ( T N ) transitions. monochromator. Higher order contamination is removedbefore the monochromator by a velocity selector. Diffrac-tion measurements were carried out with the horizontallyfocusing PG analyzer used for reducing the background.The spectrometer was setup in long-chair configurationwith open-open-open collimations. The search for mag-netic Bragg peaks and the order parameter temperaturedependence measurement were performed using neutronsof wave-vector k i = k f = 1.3 ˚ A − while the Bragg peaksrocking curves were collected using k i = k f = 1.8 ˚ A − .The first configuration allows to reduce the incoherentbackground and the second one allows to reach higherscattering angle and also to reduce neutron absorption.The sample grown by the self-flux method [9] is a sin-gle crystal of approximate size 4*7*0.3 mm and a totalmass of 62 mg. It was mounted in a helium-3 cryostatwith the [1, -1, 0] axis vertical, the scattering plane be-ing thus defined by [1,1,0] and [0,0,1]. The whole sampleused for neutron scattering experiment was characterizedby EDX microanalysis which reveals a single homoge-neous composition. The specific heat, C , of a small partcut from this sample was measured in a standard PPMSapparatus. C/T is shown in Figure 1 as a function oftemperature. One can observe two transitions: the firstone at 1.84 K and, by further reducing the temperature,the onset of the second one at 0.9 K. The known phasediagram of Ce − x Nd x CoIn [8] allows (i) to ascribe thefirst transition to superconductivity and the second oneto antiferromagnetism and (ii) to check the good agree-ment between x , T N and T c for samples prepared by twodifferent groups.The aim of the present work is to investigate the char-acteristics of the AFM phase occurring inside the super-conducting one. In this paper, the scattering vector Q is decomposed into Q = τ + k , where τ is a Brillouin zonecenter and k is the propagation vector for a given mag-netic structure. The cartesian coordinates, H and L , ofthe scattering vector Q are expressed in reciprocal lattice FIG. 2: Q scans performed a) along ( H , H , 0.5) and b) (0.55,0.55, L ). Full (empty) circles are data obtained below (above) T N at 0.37 K (1.1 K). Lines are gaussian fit with linear back-ground. unit (r.l.u.) (( Q =( H , H , L )). The search for magneticsignal was performed at low temperature along the lines( H , H , 0.5) for 0.4 ≤ H ≤ L ) for 0 ≤ L ≤
1. All the reported propagation vectors in compounds re-lated to CeCoIn are located on these lines. A detail ofthe scan performed along ( H , H , 0.5) is shown in Fig.2a: for T =0.37 K (full circles), two peaks are observedat H =0.448 ± H =0.548 ± H =0.55 along the L directionis shown in Fig. 2b at low temperature. The intensityis maximum for L =0.5. No other magnetic peaks havebeen found; we conclude that the propagation vector ofthe antiferromagnetic phase investigated is k IC =(0.45,0.45, 0.5). The temperature variation of the maximumintensity measured at Q =(0.55, 0.55, 0.5)=(1,1,1)- k IC is shown in Figure 3. Only a small number of pointswere collected due to the weakness of the magnetic sig-nal. The N´eel temperature is located between 0.8 and0.9 K, in agreement with the data from specific heatmeasurements. To get insight into the magnetic struc-ture, rocking curves measurements were carried out forfive magnetic reflections (4 independent ones). Magneticform factor, Lorentz factor and absorption corrections FIG. 3: Temperature dependence of the neutron intensitymeasured at Q =(0.55, 0.55, 0.5). The line is a guide for theeyes. were taken into account. The two magnetic reflectionscollected at high scattering angle, (1.45, 1.45, 0.5) and(0.45, 0.45, 2.5), with dominant component of the scat-tering vector in the plane or respectively along the c -axisindicate that the ordered moment is neither solely alongthe c -axis nor confined to the plane (Such characteristicBragg reflections are often used to obtain the moment di-rection owing to the fact that neutron scattering probesonly magnetism perpendicular to Q ). The use of a coldTAS for performing diffraction experiments allows to de-tect a weak magnetic signal but does not allow for a fullstructure determination due to the low number of avail-able Bragg peaks in the scattering plane. Also only onemagnetic k -domain can be investigated in the scatteringplane normal to [1, -1, 0]: there is no access to Braggreflections corresponding to the second domain with thepropagation vector k ′ IC =(0.45, -0.45, 0.5). The two mag-netic Bragg peaks at Q =(0.55, 0.55, ± c -axis contributions of the magneticmoment. By normalizing their intensity to the weak in-tensity nuclear reflection (1,1,0) and the modest intensitynuclear reflection (1,1,1)[11], it is possible, without anyhypothesis on the moment direction, to deduce that theordered moment is bound in the range 0.04 - 0.08 µ B .Hence the higher boundary for the ordered moment inCe . Nd . CoIn corresponds to half the magnetic mo-ment found in the FIOP at 60 mK and 11 T [6].Among the different chemical substitutions leading tomagnetic order in CeCoIn , two cases were investigatedto our knowledge by neutron diffraction. Antiferromag-netism is observed in CeCo(In − x Cd x ) for x ≥ x =0.125. Neutrondiffraction was performed for x =0.1 ( T N ≈ T c ≈ x =0.075 ( T N ≈ T c ≈ k AF =(1/2, 1/2, 1/2) is found.In CeCo − x Rh x In , for x ≥ . x ≈ x =0.4 with T N ≈ T c ≈ k AF [13] while anothergroup reports in this concentration range the coexistenceof ordering with k AF and another incommensurate phasewith k ′ =(0.5, 0.5, 0.42) [14]. A likely reason for this dis-crepancy is a sample dependence in relation with slightchanges in impurities and defects [15]. For completeness,it should be mentioned that CeRhIn orders with a prop-agation vector (0.5, 0.5, 0.31) and that the c -axis incom-mensuration shifts to ≈ − x Rh x In and certainly to a different physics from that of the lowRh content. This distinction between the physics at lowand high Rh substitution is supported by the Fermi-surface reconstruction occurring for x ≈ toward a magnetic phase and superconductivity still ex-ists with T N > T c . In contrast, the magnetic orderingfound in the present study for Ce . Nd . CoIn is in-commensurate with incommensuration in the tetragonalbasal plane and surprisingly the propagation vector isthe one of the FIOP of pure CeCoIn . This finding hasstrong consequences on theoretical works describing theFIOP of CeCoIn since it shows that the propagationvector is not determined by the magnetic field itself butis related to an incipient magnetic instability revealedhere by Nd substitution. This magnetic order is uniqueamong 1-1-5 Ce compounds. The key point is certainlythat Ce . Nd . CoIn and the FIOP share the commonfeature that the AFM phase occurs inside the supercon-ducting phase ( T N < T c ).From this similarity and the fact that all other studiedCeCoIn alloys have commensurate AFM structure forlow substitution, we suggest that superconductivity is thekey ingredient to realize the incommensurate magneticground state with k IC . In order to pinpoint the possiblemechanism involved, it is useful to review the theories forthe magnetic field induced AFM phase of CeCoIn . Themost common propositions to explain the FIOP includesome of the following elements: (i) multicomponent or-der parameter with a coupling between spin density waveand among other possibilities FFLO superconductivity[22], π -wave superconductivity [23], pair density wave[24] (ii) the role played by the vortex lattice [25] (iii)the importance of Pauli limited superconductivity [26](iv) spin-exciton condensation [27] (v) the enhancementof nesting by superconductivity [28]. Our new result fa-vors the last mechanism since it is transposable to a sit-uation without magnetic field and hence to our findingsfor Ce . Nd . CoIn . The stimulation of antiferromag-netic instability by d -wave nodal superconductivity wasconsidered in two dimensions by Y. Kato, C. D. Batistaand I. Vekhter [28]. In this model, the nesting condi-tions are created by the magnetic field induced ellipticalFermi pockets of spin-polarized Bogoliubov quasiparti-cles. This mechanism does not work in the absence ofmagnetic field. However, the corresponding underlyingconcept transposable to zero magnetic field is that themagnetic ordering originates from the enhancement ofthe nesting condition by d -wave superconductivity withnode in the nesting area: the imperfect normal state nest-ing between convex and concave parts of the Fermi sur-face connected by the three dimensional wave-vector k IC is improved in the superconducting state having nodesconnected by k IC . In other words, the presence of nodesin the quasiparticle spectrum at the quasi-nesting wave-vector makes the regions of gapped Fermi surface near thequasi-nesting area more flat than in the normal state. Sofar, the existence of almost nested parts of the Fermi sur-face connected by k IC is not specifically pointed out inband structure calculation, dHvA and ARPES measure-ments [19–21] and this deserves further investigations.Since in pure CeCoIn , the superconducting state is notsufficient to stimulate the AFM phase, we can speculatethat the magnetic field provides further fine tuning. Itcannot be excluded that additional mechanisms are alsoinvolved as well.In summary, we evidence that the magnetic order oc-curring for slightly Nd doped CeCoIn has the same in-commensuate propagation vector as the magnetic fieldinduced AFM phase of pure CeCoIn . Since in bothcases T N < T c and since all the other related systemswith T c < T N have commensurate antiferromagnetic or-der, this suggests that superconductivity is required toreach this peculiar ground state. 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