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Magnetic structure of Cd-doped CeIrIn$_5$

Magnetic structure of Cd-doped CeIrIn$_5$ Magnetic structure of Cd-doped CeIrIn 1 1 2 3 3 K. Beauvois, N. Qureshi, R. Tsunoda, Y. Hirose, R. Settai, 4 5, 6 7 8, ∗ D. Aoki, P. Rodi`ere, A. McCollam, and I. Sheikin Institut Laue Langevin, CS 20156, 38042, Grenoble Cedex 9, France Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan Department of Physics, Niigata University, Niigata 950-2181, Japan Institute for Materials Research, Tohoku University, Oarai, Ibaraki, 311-1313, Japan Institut N´eel, Universit´e Grenoble Alpes, F-38000 Grenoble, France CNRS, Institut N´eel, F-38000 Grenoble, France High Field Magnet Laboratory (HFML-EMFL), Radboud University, 6525 ED Nijmegen, The Netherlands Laboratoire National des Champs Magn´etiques Intenses (LNCMI-EMFL), CNRS, UGA, F-38042 Grenoble, France (Dated: May 26, 2020) We report the magnetic structure of nominally 10% Cd-doped CeIrIn5, CeIr(In0.9Cd0.1)5, deter- mined by elastic neutron scattering. Magnetic intensity was observed only at the ordering wave vector Q = (1/2, 1/2, 1/2), commensurate with the crystal lattice. A staggered moment of AF 0.47(3)μ at 1.8 K resides on the Ce ion. The magnetic moments are found to be aligned along the crystallographic c axis. This is further confirmed by magnetic susceptibility data, which suggest the c axis to be the easy magnetic axis. The determined magnetic structure is strikingly different from the incommensurate antiferromagnetic ordering of the closely related compound CeRhIn , in which the magnetic moments are antiferromagnetically aligned within the tetragonal basal plane. I. INTRODUCTION the delocalization of Ce f-electrons was observed at x ≃ 0.4 where the magnetic order changes from incommen- surate to commensurate and superconductivity suddenly The interplay between antiferromagnetism and uncon- emerges . It was also argued that particular areas on the ventional superconductivity remains one of the key ques- Fermi surface nested by the incommensurate wave vector tions in Ce-based heavy-fermion compounds. For over a of CeRhIn Q = (1/2, 1/2, 0.297) play an important 5 AF decade, the CeMIn (M = Co, Rh, Ir) heavy-fermion role in forming the superconducting state in CeCoIn . materials have served as prototypes for exploring this Furthermore, in Sn-doped CeRhIn , a drastic change in issue. These compounds crystallize in the tetragonal the magnetic order and a commensurate antiferromag- HoCoGa structure (space group P 4/mmm). CeIrIn 5 5 netism was observed in the proximity of the quantum and CeCoIn show superconductivity at ambient pres- 1 2 critical point , where superconductivity is expected, but sure below T = 0.4 K and 2.3 K , respectively. In has not been observed so far. On the other hand, several CeRhIn , which is an antiferromagnet with T = 3.8 K 5 N neutron diffraction experiments performed in CeRhIn at ambient pressure, superconductivity with a maximum under pressure up to 1.7 GPa did not reveal the presence T of 2.1 K occurs in the vicinity of a pressure-induced 13–15 of a commensurate antiferromagnetic order . This quantum critical point at the critical pressure P ≃ 2.4 3,4 pressure, however, is considerably lower than the critical GPa . value, P ≃ 2.4 GPa, although a pressure-induced bulk In all three materials, superconductivity is likely to superconductivity is observed above about 1.5 GPa . be induced by magnetic quantum fluctuations, which are In non-magnetic CeCoIn and CeIrIn , a quantum crit- 5 5 strongly enhanced in the vicinity of a quantum critical ical point can be induced by doping, e.g. by Cd sub- point . It was shown theoretically that d-wave supercon- stitution into In sites . Temperature-doping phase di- ductivity can be indeed induced by such magnetic fluctu- agrams obtained from specific heat measurements are ations, but only if they are near commensurate wave vec- shown in Fig. 1. Here, x is the nominal concentration tors . This idea is supported by neutron scattering mea- of Cd, while the real concentration is about 10 times surements of CeCoIn , which have demonstrated a strong smaller . As shown in Fig. 1 (a), introduction of Cd coupling between commensurate magnetic fluctuations into CeCoIn creates initially a two phase region above and superconductivity . It is now widely believed that nominal x = 0.075, where T > T , followed by only N c a commensurate magnetic order is favorable for the for- antiferromagnetism for x > 0.12. The phase diagram of mation of superconductivity around a quantum critical CeIr(In Cd ) (Fig. 1 (b)) is strikingly different. Only 1−x x 5 point in this family of materials. Indeed, a commensurate a magnetic ground state is observed beyond the disap- magnetic order was observed to either coexist or com- pearance of superconductivity in the composition range pete with incommensurate ordering in CeRhIn doped 8 9,10 slightly above nominal CeIr(In Cd ) , for which the 0.95 0.05 5 with either Ir or Co . Remarkably, in these com- superconducting critical temperature is already reduced pounds, commensurate antiferromagnetism emerges in to about 0.1 K, as shown in the inset of Fig. 1 (b). the vicinity of a quantum critical point where supercon- ductivity also appears. Interestingly, in CeRh Co In The magnetic structure of Cd-doped CeCoIn was 1−x x 5 5 a drastic change of the Fermi surface corresponding to previously investigated by elastic neutron scattering for arXiv:2005.11782v1 [cond-mat.str-el] 24 May 2020 2 nominal Cd concentrations of 6% (T ≈ T ≈ 2 K) , NQR spectrum below T exhibits no clear splitting, but N c N 7.5% (T ≈ 2.4 K, T ≈ 1.7 K) , and 10% (T ≈ a large broadening at its tail, suggesting an inhomoge- N c N 3 K, T ≈ 1.3 K) . In all studies, magnetic in- neous antiferromagnetic order with a large distribution tensity was observed only at the ordering wave vector of magnetic moments . The NQR measurements in Cd- Q = (1/2, 1/2, 1/2) commensurate with the crystal doped CeIrIn thus did not shed any light on its magnetic AF 5 lattice. This is in line with the above-mentioned hy- structure, which remains an open question. Therefore, a pothesis that a commensurate magnetic order is favorable neutron diffraction experiment is necessary to address for heavy-fermion superconductivity, at least in CeMIn this issue. compounds. It would be instructive to further test this In this paper, we present neutron diffraction and mag- hypothesis in Cd-doped CeIrIn , for which the magnetic netic susceptibility data on CeIr(In Cd ) single crys- 1−x x 5 structure is currently unknown. tals with x = 0.1, where x represents the nominal con- centration, for which the system orders magnetically at T ≈ 3 K. (a) CeCo(In Cd ) 1-x x 5 c II. EXPERIMENTAL DETAILS 3 Single crystals of CeIr(In Cd ) were grown using a 0.9 0.1 5 standard In-flux technique with a nominal concentration AFM of 10% Cd in the indium flux . Previous microprobe measurements performed on a series of CeCo(In Cd ) 1−x x 5 samples grown by the same technique suggest that the SC actual Cd concentration is only 10% of the nominal flux 17,20 concentration . Although microprobe examination of 0 the CeIr(In Cd ) crystals has not been done, it can 1−x x 5 (b) be assumed that the Cd concentration in these samples is also approximately 10% of that in the flux from which CeIr(In Cd ) 1-x x 5 they were grown. Therefore, the actual Cd concentration AFM in our sample is likely to be about 1%. Neutron diffraction experiment was performed on the D10 beamline of the Institut Laue-Langevin (ILL) of 5% Cd 1.0 Grenoble (France). For this experiment, we prepared a plateletlike sample with the dimensions 6× 5× 0.5 mm , 0.5 mm being the thickness along the tetragonal a axis, 10T 2 with the other a and c axis being in the plane. The in- 0.5 strument was used in a four-circle configuration with an T (K) SC 80×80 mm two-dimensional microstrip detector. A ver- 0 1 2 3 4 tically focusing pyrolytic graphite monochromator was 0 5 10 15 20 25 30 employed, fixing the wavelength of the incoming neutrons Nominal x% Cd to 2.36 A. A pyrolytic graphite filter was used in order −4 to suppress higher-order contaminations to 10 of the FIG. 1. Doping x dependence of antiferromagnetic (AFM) primary beam intensity. To reach temperatures down to and superconducting (SC) transition temperatures in (a) 1.8 K, we used a closed-cycle cryostat equipped with a CeCo(In Cd ) and (b) CeIr(In Cd ) . All the data are 1−x x 5 1−x x 5 17 Joule-Thompson stage in the four-circle geometry. from ref. , except for the point for CeIr(In Cd ) , which 0.95 0.05 5 The crystal structure was refined using 230 nuclear is from our own specific heat measurements shown in the in- Bragg peaks. For all peaks, the measured neutron Bragg set. Here x is the nominal Cd content of crystals. Arrows indicate Cd concentrations, for which the magnetic structure intensity was corrected for extinction, absorption, and was determined by neutron diffraction in previous studies for Lorentz factor. For the absorption correction, we accu- 18–20 CeCo(In Cd ) and in this work for CeIr(In Cd ) . 1−x x 5 1−x x 5 rately modeled the sample shape using the Mag2Pol pro- gram . The obtained lattice parameters at T = 10 K ˚ ˚ The above results of the neutron diffraction in single are a = 4.6491(3) A and c = 7.4926(9) A. Regarding crystals of CeCo(In Cd ) are in good agreement with the actual Cd concentration and its distribution between 1−x x 5 the nuclear-quadrupole-resonance (NQR) measurements the two In sites, it is difficult to obtain a reliable result in a powder sample of CeCo(In Cd ) . Upon cool- directly from the refinement using these as adjustable 0.9 0.1 5 ing the sample below T , the NQR line splits into two, in- parameters since the scattering lengths of Cd and In are dicating a homogenous commensurate antiferromagnetic very close to each other. To overcome this issue, we per- state with a uniform magnetic moment over the whole formed the absorption correction with subsequent crystal sample. On the other hand, in CeIr(In Cd ) , the structure refinement for several Cd concentrations rang- 0.925 0.075 5 T (K) T (K) C/T (J/K mol) ing from 1% to 4% and assuming equal Cd occupation peak disappears at T = 5 K, which is above T . In of the two In sites. The best result was obtained for order to search for additional peaks with an incommen- 3% Cd concentration. To check the self-consistency of surate magnetic wave vector, we performed a complete this value, we then used the 3% Cd absorption corrected Q scan in the direction corresponding to the line (1/2, data for a refinement with Cd concentration as an ad- 1/2, L) for 0 ≤ L ≤ 1 of the reciprocal space at T = justable parameter. This yielded the concentration of 1.8 K, as shown in Fig. 2(b). The latter Q scan con- 0.02(2), consistent with 3% obtained from the previous firmed the presence of a temperature-dependent Bragg iteration. The 3% Cd concentration estimated in this way peak at Q = (1/2, 1/2, 1/2). However, we did not ob- in our sample agrees reasonably well with the assumption serve any additional magnetic Bragg peaks corresponding based on the analogy between In-flux grown samples of to an incommensurate magnetic wave vector. In particu- CeIr(In Cd ) and CeCo(In Cd ) discussed above. lar, there are no peaks around Q = (1/2, 1/2, 0.3) char- 1−x x 5 1−x x 5 acteristic of pure CeRhIn at ambient pressure or Q = 10,12 (1/2, 1/2, 0.4) observed in either doped or pressur- 13,15 III. RESULTS AND DISCUSSION ized CeRhIn . An increased neutron intensity was observed at Q = (1/2, 1/2, 1). However, the intensity is temperature-independent, suggesting a λ/2 contamina- tion from the very strong structural Bragg peak reflection (a) (1, 1, 2) as its origin. 400 1.8 K CeIr(In Cd ) 5 K 0.9 0.1 5 Q = (H, H, H) (a) (1/2, -1/2, 3/2) T = 1.8 K 100 4 0.40 0.45 0.50 0.55 0.60 H (r.l.u.) (b) 1.8 K (b) Q = (1/2, 1/2, L) 6 K (1, 0, 1) T = 10 K 200 2 0.0 0.2 0.4 0.6 0.8 1.0 L (r.l.u.) 16.5 17.0 17.5 18.0 (deg.) FIG. 2. Elastic scans in CeIr(In Cd ) along the [111] (a) 0.9 0.1 5 and [001] (b) directions performed below and above the N´eel FIG. 3. Ω scans through the magnetic Bragg peak (1/2, -1/2, temperature. Reciprocal lattice units (r.l.u.) are used as coor- 3/2) at T = 1.8 K (a) and the nuclear Bragg peak (1, 0, 1) dinates of the reciprocal space. The intensity is in number of at T = 10 K (b). The intensities are in number of counts per 5 4 counts per 5×10 monitor counts, which corresponds roughly 5 × 10 and 3.5 × 10 monitor counts for the magnetic and to 50 s. The solid lines are Gaussian fits of the peaks. nuclear peaks respectively. Solid lines are Gaussian fits of the peaks. Note that the full width at half maximum (FWHM), indicated by arrows, is the same for the two peaks. Figure 2(a) shows the Q scan performed along the [111] direction both below (1.8 K) and above (5 K) the N´eel temperature, T . A clear peak is observed at Q = (1/2, The artificial peak at Q = (1/2, 1/2, 1) is apparently 1/2, 1/2) at T = 1.8 K, corresponding to a commensu- narrower than the magnetic Bragg peak at Q = (1/2, rate magnetic wave vector Q = (1/2, 1/2, 1/2). The 1/2, 1/2). In general, broadening of this magnetic peak AF Neutron intensity (counts) Neutron intensity (counts) I (1 0 co u n ts) I (1 0 co u n ts) might be an indication of a slight incommensurability latter value is consistent with T determined from previ- 17 22 with Q = (1/2, 1/2, 1/2±δ) or of a reduced correlation ous specific heat and resistivity measurements. It is AF length. However, direct comparison of the widths of two also in agreement with the magnetic susceptibility data peaks even from the same Q scan is misleading because shown in Fig. 5(b). of different resolution conditions at different values of Q. The proper way to assess the width of a magnetic peak is (a) to compare Ω scans through both magnetic and a nuclear 4 Bragg peak located at a close 2θ position. Unfortunately, CeIr(In Cd ) 0.9 0.1 5 such a comparison is not possible for the magnetic peak Q = (1/2, 1/2, 1/2) at Q = (1/2, 1/2, 1/2), as there are no nuclear peaks nearby. On the other hand, this can be conveniently done for the magnetic (1/2, -1/2, 3/2) peak (2θ = 34.4 ) and the nuclear (1, 0, 1) peak (2θ = 34.6 ). The Ω scans through these two peaks are shown in Fig. 3(a) and (b) ◦ 1 respectively. The FWHM is 0.23(1) for the magnetic peak and 0.228(3) for the nuclear one, i.e. the two peaks have the same width within the error bar. Therefore, our data do not reveal any indication for an incommensurate magnetic order or a reduced correlation length. 0.020 (b) H = 1 T H || c 1.8 K 0.018 CeIr(In Cd ) 0.9 0.1 5 2.2 K 2.6 K 6 K 0.010 H || a 0.009 0 1 2 3 4 5 6 7 8 9 10 T (K) 0.40 0.45 0.50 0.55 0.60 (1/2, 1/2, L) FIG. 5. (a) Temperature dependence of the (1/2, 1/2, 1/2) magnetic Bragg peak intensity after subtracting the back- ground. The intensity is in number of counts per 4.5 × 10 FIG. 4. Q scans performed along the [001] direction at dif- monitor counts, which corresponds roughly to 8 min. The line ferent temperatures. The intensity is in number of counts per is a phenomenological fit as explained in the text. (b) Mag- 1 × 10 monitor counts, which corresponds roughly to 100 s. netic susceptibility measured in magnetic field of 1 T applied The lines are Gaussian fits of the peaks. both along the c and a axis as a function of temperature. Figure 4 shows elastic scans along the [001] direction across Q = (1/2, 1/2, 1/2) at different temperatures. In order to refine the magnetic structure, a data set of The magnetic Bragg peak at Q = (1/2, 1/2, 1/2) does 13 magnetic Bragg reflections was collected at T = 1.8 K. not shift with temperature; only its intensity decreases As the magnetic peaks are rather weak, they were inte- with increasing temperature. Since the position of the grated using the RPlot program for a small detector magnetic propagation vector in reciprocal space does not area around its center to reduce the background noise. change with temperature, the temperature dependence of The same mask on the detector was used for the inte- the neutron diffraction intensity at the center of the mag- gration of nuclear peaks. For all magnetic peaks, the netic Bragg peak Q was recorded (Fig. 5(a)). This inten- correction for extinction, absorption, and Lorentz fac- sity, I, is proportional to the square of the ordered mag- tor was performed the same way as for nuclear peaks netic moment. To determine the N´eel temperature, the described above. The resulting intensities are shown in data were fitted by a phenomenological function I/I = Table I. The refinement was then performed using the α 23 1−(T/T ) , with α a free parameter. This function was Mag2Pol program . Only two arrangements of the mag- successfully used to fit the temperature dependence of netic moments are allowed by the group theory: they can the magnetic Bragg peak intensity in other heavy fermion be either aligned in the basal plane or along the c axis. 25,26 12 compounds, such as CePd Si , Sn-doped CeRhIn , For both structures, the calculated intensities are also 2 2 5 18 27 Cd-doped CeRhIn , and CePt In . The best fit is shown in Table I. A much better result is obtained for 5 2 7 obtained with α = 2.0 ± 0.5 and T = 3.0 ± 0.1 K. The the c axis configuration, i.e. magnetic moments antifer- Neutron intensity (counts) M/H (emu/mol) Neutron intensity (10 counts) romagnetically aligned along the c axis. This structure ing to perform NQR measurements on a single crystal of is consistent with the magnetic susceptibility data shown CeIr(In Cd ) . 0.9 0.1 5 in Fig. 5(b), which suggest the c axis to be the easy mag- The antiferromagnetic arrangement of the magnetic netic axis. The staggered magnetic moment is found to moments, which are aligned along the c axis in be M = 0.47(3)μ per Ce atom at T = 1.8 K. It is obvi- CeIr(In Cd ) , is different from both pure and doped 0.9 0.1 5 ous, however, that the magnetic intensity does not satu- CeRhIn . Indeed, the ordered moments were found to rate at T = 1.8 K (Fig. 5(a)). The extrapolation of I(T ) lie in the tetragonal basal plane in the incommensurate to T = 0 yields the magnetic moment M ≈ 0.6μ /Ce 24,32–34 phase of CeRhIn , and both in the incommensu- at the zero temperature limit. This value is similar to rate and commensurate states of CeRh Ir In . On 1−x x 5 M ∼ 0.7μ /Ce estimated in CeCo(In Cd ) from B 0.9 0.1 5 the other hand, the same antiferromagnetic arrangement NQR measurements . Remarkably, both CeIrIn and of the ordered moments along the c axis occurs in U- CeCoIn doped with 10% Cd undergo an antiferromag- based 115 compounds, such as UNiGa and, most prob- netic transition at about the same temperature, T ≈ 3 ably, URhIn . K (Fig. 1). The commensurate magnetic order with Q = AF (1/2, 1/2, 1/2) determined here for CeIr(In Cd ) is 0.9 0.1 5 TABLE I. Magnetic refinement for the two possible magnetic also strikingly different from that in pure CeRhIn , c ab structures, as discussed in the text. I and I are the calc calc in which an incommensurate magnetic structure with calculated intensities for magnetic moments aligned along the 24,32–34 Q = (1/2, 1/2, 0.297) was reported . On the AF c axis and in the basal plane respectively. (Note: R = 18.7, other hand, the same commensurate magnetic ordering R = 48.1). ab 18–20 wave vector was observed in Cd-doped CeCoIn , in c ab which superconductivity coexists with magnetic order Q I I I obs calc calc over a wide range of Cd concentrations (Fig. 1(a)). Fur- (1/2, -1/2, 1/2) 1024(49) 504 205 thermore, the same commensurate magnetic structure (1/2, -1/2, 3/2) 294(27) 167 178 with ordering wave vector (1/2, 1/2, 1/2) develops in the (1/2, -1/2, 5/2) 87(10) 57 131 8 9,10 doping series CeRh Ir In and CeRh Co In at 1−x x 5 1−x x 5 (3/2, -1/2, -1/2) 286(42) 343 133 low temperatures over the doping range, for which super- (3/2, -1/2, 3/2) 208(15) 226 116 conductivity coexists with antiferromagnetism. At first (3/2, -3/2, -1/2) 193(20) 236 91 glance, this appears surprising given that superconduc- (3/2, -3/2, 3/2) 190(15) 175 79 tivity does not coexist with antiferromagnetic order in Cd-doped CeIrIn (Fig. 1(b)). A possible clue to this (1/2, -1/2, 7/2) 32(5) 20 84 5 puzzle is offered by In-NQR measurements in Cd-doped (5/2, 1/2, 1/2) 137(17) 164 35 CeIrIn . These measurements suggest that supercon- (5/2, 3/2, 1/2) 115(25) 116 10 ductivity in pure and Cd-doped CeIrIn is likely mediated (1/2, 5/2, 3/2) 111(15) 128 13 by valence fluctuations, and not spin fluctuations, as in (5/2, 3/2, 3/2) 166(25) 93 11 other CeMIn compounds. (5/2, 5/2, 1/2) 190(77) 60 1 At first glance, it is surprising why the commensurate magnetic order with such a strong staggered magnetic moment was not observed in NQR measurements in Cd- IV. CONCLUSIONS doped CeIrIn . These measurements, however, were performed on a sample with nominal Cd concentration of 7.5%, in which the magnetic moment is likely to be In summary, we carried out elastic neutron scattering reduced with respect to CeIr(In Cd ) studied here. experiments on CeIr(In Cd ) . At low temperatures, 0.9 0.1 5 0.9 0.1 5 Furthermore, in CeIr(In Cd ) the antiferromag- we found magnetic intensity at the commensurate wave 0.925 0.075 5 netic transition temperature is lower than 2 K . This vector Q = (1/2, 1/2, 1/2). The magnetic intensity AF implies that the NQR measurements, performed at 1.5 K, is building up below T ≈ 3 K, with T being in good N N 17 22 were done barely below the N´eel temperature, where the agreement with specific heat , resistivity , and mag- ordered moment is presumably very small. Finally, the netic susceptibility data. No indication for additional in- NQR measurements were carried out on a powder sam- tensity was observed at incommensurate positions, such ple, which alone might strongly affect the result. For as (1/2, 1/2, 0.297), where CeRhIn , the related antifer- example, NQR measurements performed on a powder romagnetic member of the CeMIn family, orders. A mag- sample of CeRhIn under pressure revealed a change of netic moment of 0.47(3)μ at 1.8 K resides on the Ce ion, 5 B magnetic structure from incommensurate to commen- and the moments are antiferromagnetically aligned along surate , while no such change was observed in either the c axis. This is again in contrast to CeRhIn , in which 13–15 neutron diffraction or single-crystal NQR measure- magnetic moments are antiferromagnetically aligned in ments . From this point of view, it would be interest- the basal plane. 6 ACKNOWLEDGMENTS We thank E. Ressouche, B. Ouladdiaf, and C. Simon for fruitful discussions. 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Magnetic structure of Cd-doped CeIrIn$_5$

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Abstract

Magnetic structure of Cd-doped CeIrIn 1 1 2 3 3 K. Beauvois, N. Qureshi, R. Tsunoda, Y. Hirose, R. Settai, 4 5, 6 7 8, ∗ D. Aoki, P. Rodi`ere, A. McCollam, and I. Sheikin Institut Laue Langevin, CS 20156, 38042, Grenoble Cedex 9, France Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan Department of Physics, Niigata University, Niigata 950-2181, Japan Institute for Materials Research, Tohoku University, Oarai, Ibaraki, 311-1313, Japan Institut N´eel, Universit´e Grenoble Alpes, F-38000 Grenoble, France CNRS, Institut N´eel, F-38000 Grenoble, France High Field Magnet Laboratory (HFML-EMFL), Radboud University, 6525 ED Nijmegen, The Netherlands Laboratoire National des Champs Magn´etiques Intenses (LNCMI-EMFL), CNRS, UGA, F-38042 Grenoble, France (Dated: May 26, 2020) We report the magnetic structure of nominally 10% Cd-doped CeIrIn5, CeIr(In0.9Cd0.1)5, deter- mined by elastic neutron scattering. Magnetic intensity was observed only at the ordering wave vector Q = (1/2, 1/2, 1/2), commensurate with the crystal lattice. A staggered moment of AF 0.47(3)μ at 1.8 K resides on the Ce ion. The magnetic moments are found to be aligned along the crystallographic c axis. This is further confirmed by magnetic susceptibility data, which suggest the c axis to be the easy magnetic axis. The determined magnetic structure is strikingly different from the incommensurate antiferromagnetic ordering of the closely related compound CeRhIn , in which the magnetic moments are antiferromagnetically aligned within the tetragonal basal plane. I. INTRODUCTION the delocalization of Ce f-electrons was observed at x ≃ 0.4 where the magnetic order changes from incommen- surate to commensurate and superconductivity suddenly The interplay between antiferromagnetism and uncon- emerges . It was also argued that particular areas on the ventional superconductivity remains one of the key ques- Fermi surface nested by the incommensurate wave vector tions in Ce-based heavy-fermion compounds. For over a of CeRhIn Q = (1/2, 1/2, 0.297) play an important 5 AF decade, the CeMIn (M = Co, Rh, Ir) heavy-fermion role in forming the superconducting state in CeCoIn . materials have served as prototypes for exploring this Furthermore, in Sn-doped CeRhIn , a drastic change in issue. These compounds crystallize in the tetragonal the magnetic order and a commensurate antiferromag- HoCoGa structure (space group P 4/mmm). CeIrIn 5 5 netism was observed in the proximity of the quantum and CeCoIn show superconductivity at ambient pres- 1 2 critical point , where superconductivity is expected, but sure below T = 0.4 K and 2.3 K , respectively. In has not been observed so far. On the other hand, several CeRhIn , which is an antiferromagnet with T = 3.8 K 5 N neutron diffraction experiments performed in CeRhIn at ambient pressure, superconductivity with a maximum under pressure up to 1.7 GPa did not reveal the presence T of 2.1 K occurs in the vicinity of a pressure-induced 13–15 of a commensurate antiferromagnetic order . This quantum critical point at the critical pressure P ≃ 2.4 3,4 pressure, however, is considerably lower than the critical GPa . value, P ≃ 2.4 GPa, although a pressure-induced bulk In all three materials, superconductivity is likely to superconductivity is observed above about 1.5 GPa . be induced by magnetic quantum fluctuations, which are In non-magnetic CeCoIn and CeIrIn , a quantum crit- 5 5 strongly enhanced in the vicinity of a quantum critical ical point can be induced by doping, e.g. by Cd sub- point . It was shown theoretically that d-wave supercon- stitution into In sites . Temperature-doping phase di- ductivity can be indeed induced by such magnetic fluctu- agrams obtained from specific heat measurements are ations, but only if they are near commensurate wave vec- shown in Fig. 1. Here, x is the nominal concentration tors . This idea is supported by neutron scattering mea- of Cd, while the real concentration is about 10 times surements of CeCoIn , which have demonstrated a strong smaller . As shown in Fig. 1 (a), introduction of Cd coupling between commensurate magnetic fluctuations into CeCoIn creates initially a two phase region above and superconductivity . It is now widely believed that nominal x = 0.075, where T > T , followed by only N c a commensurate magnetic order is favorable for the for- antiferromagnetism for x > 0.12. The phase diagram of mation of superconductivity around a quantum critical CeIr(In Cd ) (Fig. 1 (b)) is strikingly different. Only 1−x x 5 point in this family of materials. Indeed, a commensurate a magnetic ground state is observed beyond the disap- magnetic order was observed to either coexist or com- pearance of superconductivity in the composition range pete with incommensurate ordering in CeRhIn doped 8 9,10 slightly above nominal CeIr(In Cd ) , for which the 0.95 0.05 5 with either Ir or Co . Remarkably, in these com- superconducting critical temperature is already reduced pounds, commensurate antiferromagnetism emerges in to about 0.1 K, as shown in the inset of Fig. 1 (b). the vicinity of a quantum critical point where supercon- ductivity also appears. Interestingly, in CeRh Co In The magnetic structure of Cd-doped CeCoIn was 1−x x 5 5 a drastic change of the Fermi surface corresponding to previously investigated by elastic neutron scattering for arXiv:2005.11782v1 [cond-mat.str-el] 24 May 2020 2 nominal Cd concentrations of 6% (T ≈ T ≈ 2 K) , NQR spectrum below T exhibits no clear splitting, but N c N 7.5% (T ≈ 2.4 K, T ≈ 1.7 K) , and 10% (T ≈ a large broadening at its tail, suggesting an inhomoge- N c N 3 K, T ≈ 1.3 K) . In all studies, magnetic in- neous antiferromagnetic order with a large distribution tensity was observed only at the ordering wave vector of magnetic moments . The NQR measurements in Cd- Q = (1/2, 1/2, 1/2) commensurate with the crystal doped CeIrIn thus did not shed any light on its magnetic AF 5 lattice. This is in line with the above-mentioned hy- structure, which remains an open question. Therefore, a pothesis that a commensurate magnetic order is favorable neutron diffraction experiment is necessary to address for heavy-fermion superconductivity, at least in CeMIn this issue. compounds. It would be instructive to further test this In this paper, we present neutron diffraction and mag- hypothesis in Cd-doped CeIrIn , for which the magnetic netic susceptibility data on CeIr(In Cd ) single crys- 1−x x 5 structure is currently unknown. tals with x = 0.1, where x represents the nominal con- centration, for which the system orders magnetically at T ≈ 3 K. (a) CeCo(In Cd ) 1-x x 5 c II. EXPERIMENTAL DETAILS 3 Single crystals of CeIr(In Cd ) were grown using a 0.9 0.1 5 standard In-flux technique with a nominal concentration AFM of 10% Cd in the indium flux . Previous microprobe measurements performed on a series of CeCo(In Cd ) 1−x x 5 samples grown by the same technique suggest that the SC actual Cd concentration is only 10% of the nominal flux 17,20 concentration . Although microprobe examination of 0 the CeIr(In Cd ) crystals has not been done, it can 1−x x 5 (b) be assumed that the Cd concentration in these samples is also approximately 10% of that in the flux from which CeIr(In Cd ) 1-x x 5 they were grown. Therefore, the actual Cd concentration AFM in our sample is likely to be about 1%. Neutron diffraction experiment was performed on the D10 beamline of the Institut Laue-Langevin (ILL) of 5% Cd 1.0 Grenoble (France). For this experiment, we prepared a plateletlike sample with the dimensions 6× 5× 0.5 mm , 0.5 mm being the thickness along the tetragonal a axis, 10T 2 with the other a and c axis being in the plane. The in- 0.5 strument was used in a four-circle configuration with an T (K) SC 80×80 mm two-dimensional microstrip detector. A ver- 0 1 2 3 4 tically focusing pyrolytic graphite monochromator was 0 5 10 15 20 25 30 employed, fixing the wavelength of the incoming neutrons Nominal x% Cd to 2.36 A. A pyrolytic graphite filter was used in order −4 to suppress higher-order contaminations to 10 of the FIG. 1. Doping x dependence of antiferromagnetic (AFM) primary beam intensity. To reach temperatures down to and superconducting (SC) transition temperatures in (a) 1.8 K, we used a closed-cycle cryostat equipped with a CeCo(In Cd ) and (b) CeIr(In Cd ) . All the data are 1−x x 5 1−x x 5 17 Joule-Thompson stage in the four-circle geometry. from ref. , except for the point for CeIr(In Cd ) , which 0.95 0.05 5 The crystal structure was refined using 230 nuclear is from our own specific heat measurements shown in the in- Bragg peaks. For all peaks, the measured neutron Bragg set. Here x is the nominal Cd content of crystals. Arrows indicate Cd concentrations, for which the magnetic structure intensity was corrected for extinction, absorption, and was determined by neutron diffraction in previous studies for Lorentz factor. For the absorption correction, we accu- 18–20 CeCo(In Cd ) and in this work for CeIr(In Cd ) . 1−x x 5 1−x x 5 rately modeled the sample shape using the Mag2Pol pro- gram . The obtained lattice parameters at T = 10 K ˚ ˚ The above results of the neutron diffraction in single are a = 4.6491(3) A and c = 7.4926(9) A. Regarding crystals of CeCo(In Cd ) are in good agreement with the actual Cd concentration and its distribution between 1−x x 5 the nuclear-quadrupole-resonance (NQR) measurements the two In sites, it is difficult to obtain a reliable result in a powder sample of CeCo(In Cd ) . Upon cool- directly from the refinement using these as adjustable 0.9 0.1 5 ing the sample below T , the NQR line splits into two, in- parameters since the scattering lengths of Cd and In are dicating a homogenous commensurate antiferromagnetic very close to each other. To overcome this issue, we per- state with a uniform magnetic moment over the whole formed the absorption correction with subsequent crystal sample. On the other hand, in CeIr(In Cd ) , the structure refinement for several Cd concentrations rang- 0.925 0.075 5 T (K) T (K) C/T (J/K mol) ing from 1% to 4% and assuming equal Cd occupation peak disappears at T = 5 K, which is above T . In of the two In sites. The best result was obtained for order to search for additional peaks with an incommen- 3% Cd concentration. To check the self-consistency of surate magnetic wave vector, we performed a complete this value, we then used the 3% Cd absorption corrected Q scan in the direction corresponding to the line (1/2, data for a refinement with Cd concentration as an ad- 1/2, L) for 0 ≤ L ≤ 1 of the reciprocal space at T = justable parameter. This yielded the concentration of 1.8 K, as shown in Fig. 2(b). The latter Q scan con- 0.02(2), consistent with 3% obtained from the previous firmed the presence of a temperature-dependent Bragg iteration. The 3% Cd concentration estimated in this way peak at Q = (1/2, 1/2, 1/2). However, we did not ob- in our sample agrees reasonably well with the assumption serve any additional magnetic Bragg peaks corresponding based on the analogy between In-flux grown samples of to an incommensurate magnetic wave vector. In particu- CeIr(In Cd ) and CeCo(In Cd ) discussed above. lar, there are no peaks around Q = (1/2, 1/2, 0.3) char- 1−x x 5 1−x x 5 acteristic of pure CeRhIn at ambient pressure or Q = 10,12 (1/2, 1/2, 0.4) observed in either doped or pressur- 13,15 III. RESULTS AND DISCUSSION ized CeRhIn . An increased neutron intensity was observed at Q = (1/2, 1/2, 1). However, the intensity is temperature-independent, suggesting a λ/2 contamina- tion from the very strong structural Bragg peak reflection (a) (1, 1, 2) as its origin. 400 1.8 K CeIr(In Cd ) 5 K 0.9 0.1 5 Q = (H, H, H) (a) (1/2, -1/2, 3/2) T = 1.8 K 100 4 0.40 0.45 0.50 0.55 0.60 H (r.l.u.) (b) 1.8 K (b) Q = (1/2, 1/2, L) 6 K (1, 0, 1) T = 10 K 200 2 0.0 0.2 0.4 0.6 0.8 1.0 L (r.l.u.) 16.5 17.0 17.5 18.0 (deg.) FIG. 2. Elastic scans in CeIr(In Cd ) along the [111] (a) 0.9 0.1 5 and [001] (b) directions performed below and above the N´eel FIG. 3. Ω scans through the magnetic Bragg peak (1/2, -1/2, temperature. Reciprocal lattice units (r.l.u.) are used as coor- 3/2) at T = 1.8 K (a) and the nuclear Bragg peak (1, 0, 1) dinates of the reciprocal space. The intensity is in number of at T = 10 K (b). The intensities are in number of counts per 5 4 counts per 5×10 monitor counts, which corresponds roughly 5 × 10 and 3.5 × 10 monitor counts for the magnetic and to 50 s. The solid lines are Gaussian fits of the peaks. nuclear peaks respectively. Solid lines are Gaussian fits of the peaks. Note that the full width at half maximum (FWHM), indicated by arrows, is the same for the two peaks. Figure 2(a) shows the Q scan performed along the [111] direction both below (1.8 K) and above (5 K) the N´eel temperature, T . A clear peak is observed at Q = (1/2, The artificial peak at Q = (1/2, 1/2, 1) is apparently 1/2, 1/2) at T = 1.8 K, corresponding to a commensu- narrower than the magnetic Bragg peak at Q = (1/2, rate magnetic wave vector Q = (1/2, 1/2, 1/2). The 1/2, 1/2). In general, broadening of this magnetic peak AF Neutron intensity (counts) Neutron intensity (counts) I (1 0 co u n ts) I (1 0 co u n ts) might be an indication of a slight incommensurability latter value is consistent with T determined from previ- 17 22 with Q = (1/2, 1/2, 1/2±δ) or of a reduced correlation ous specific heat and resistivity measurements. It is AF length. However, direct comparison of the widths of two also in agreement with the magnetic susceptibility data peaks even from the same Q scan is misleading because shown in Fig. 5(b). of different resolution conditions at different values of Q. The proper way to assess the width of a magnetic peak is (a) to compare Ω scans through both magnetic and a nuclear 4 Bragg peak located at a close 2θ position. Unfortunately, CeIr(In Cd ) 0.9 0.1 5 such a comparison is not possible for the magnetic peak Q = (1/2, 1/2, 1/2) at Q = (1/2, 1/2, 1/2), as there are no nuclear peaks nearby. On the other hand, this can be conveniently done for the magnetic (1/2, -1/2, 3/2) peak (2θ = 34.4 ) and the nuclear (1, 0, 1) peak (2θ = 34.6 ). The Ω scans through these two peaks are shown in Fig. 3(a) and (b) ◦ 1 respectively. The FWHM is 0.23(1) for the magnetic peak and 0.228(3) for the nuclear one, i.e. the two peaks have the same width within the error bar. Therefore, our data do not reveal any indication for an incommensurate magnetic order or a reduced correlation length. 0.020 (b) H = 1 T H || c 1.8 K 0.018 CeIr(In Cd ) 0.9 0.1 5 2.2 K 2.6 K 6 K 0.010 H || a 0.009 0 1 2 3 4 5 6 7 8 9 10 T (K) 0.40 0.45 0.50 0.55 0.60 (1/2, 1/2, L) FIG. 5. (a) Temperature dependence of the (1/2, 1/2, 1/2) magnetic Bragg peak intensity after subtracting the back- ground. The intensity is in number of counts per 4.5 × 10 FIG. 4. Q scans performed along the [001] direction at dif- monitor counts, which corresponds roughly to 8 min. The line ferent temperatures. The intensity is in number of counts per is a phenomenological fit as explained in the text. (b) Mag- 1 × 10 monitor counts, which corresponds roughly to 100 s. netic susceptibility measured in magnetic field of 1 T applied The lines are Gaussian fits of the peaks. both along the c and a axis as a function of temperature. Figure 4 shows elastic scans along the [001] direction across Q = (1/2, 1/2, 1/2) at different temperatures. In order to refine the magnetic structure, a data set of The magnetic Bragg peak at Q = (1/2, 1/2, 1/2) does 13 magnetic Bragg reflections was collected at T = 1.8 K. not shift with temperature; only its intensity decreases As the magnetic peaks are rather weak, they were inte- with increasing temperature. Since the position of the grated using the RPlot program for a small detector magnetic propagation vector in reciprocal space does not area around its center to reduce the background noise. change with temperature, the temperature dependence of The same mask on the detector was used for the inte- the neutron diffraction intensity at the center of the mag- gration of nuclear peaks. For all magnetic peaks, the netic Bragg peak Q was recorded (Fig. 5(a)). This inten- correction for extinction, absorption, and Lorentz fac- sity, I, is proportional to the square of the ordered mag- tor was performed the same way as for nuclear peaks netic moment. To determine the N´eel temperature, the described above. The resulting intensities are shown in data were fitted by a phenomenological function I/I = Table I. The refinement was then performed using the α 23 1−(T/T ) , with α a free parameter. This function was Mag2Pol program . Only two arrangements of the mag- successfully used to fit the temperature dependence of netic moments are allowed by the group theory: they can the magnetic Bragg peak intensity in other heavy fermion be either aligned in the basal plane or along the c axis. 25,26 12 compounds, such as CePd Si , Sn-doped CeRhIn , For both structures, the calculated intensities are also 2 2 5 18 27 Cd-doped CeRhIn , and CePt In . The best fit is shown in Table I. A much better result is obtained for 5 2 7 obtained with α = 2.0 ± 0.5 and T = 3.0 ± 0.1 K. The the c axis configuration, i.e. magnetic moments antifer- Neutron intensity (counts) M/H (emu/mol) Neutron intensity (10 counts) romagnetically aligned along the c axis. This structure ing to perform NQR measurements on a single crystal of is consistent with the magnetic susceptibility data shown CeIr(In Cd ) . 0.9 0.1 5 in Fig. 5(b), which suggest the c axis to be the easy mag- The antiferromagnetic arrangement of the magnetic netic axis. The staggered magnetic moment is found to moments, which are aligned along the c axis in be M = 0.47(3)μ per Ce atom at T = 1.8 K. It is obvi- CeIr(In Cd ) , is different from both pure and doped 0.9 0.1 5 ous, however, that the magnetic intensity does not satu- CeRhIn . Indeed, the ordered moments were found to rate at T = 1.8 K (Fig. 5(a)). The extrapolation of I(T ) lie in the tetragonal basal plane in the incommensurate to T = 0 yields the magnetic moment M ≈ 0.6μ /Ce 24,32–34 phase of CeRhIn , and both in the incommensu- at the zero temperature limit. This value is similar to rate and commensurate states of CeRh Ir In . On 1−x x 5 M ∼ 0.7μ /Ce estimated in CeCo(In Cd ) from B 0.9 0.1 5 the other hand, the same antiferromagnetic arrangement NQR measurements . Remarkably, both CeIrIn and of the ordered moments along the c axis occurs in U- CeCoIn doped with 10% Cd undergo an antiferromag- based 115 compounds, such as UNiGa and, most prob- netic transition at about the same temperature, T ≈ 3 ably, URhIn . K (Fig. 1). The commensurate magnetic order with Q = AF (1/2, 1/2, 1/2) determined here for CeIr(In Cd ) is 0.9 0.1 5 TABLE I. Magnetic refinement for the two possible magnetic also strikingly different from that in pure CeRhIn , c ab structures, as discussed in the text. I and I are the calc calc in which an incommensurate magnetic structure with calculated intensities for magnetic moments aligned along the 24,32–34 Q = (1/2, 1/2, 0.297) was reported . On the AF c axis and in the basal plane respectively. (Note: R = 18.7, other hand, the same commensurate magnetic ordering R = 48.1). ab 18–20 wave vector was observed in Cd-doped CeCoIn , in c ab which superconductivity coexists with magnetic order Q I I I obs calc calc over a wide range of Cd concentrations (Fig. 1(a)). Fur- (1/2, -1/2, 1/2) 1024(49) 504 205 thermore, the same commensurate magnetic structure (1/2, -1/2, 3/2) 294(27) 167 178 with ordering wave vector (1/2, 1/2, 1/2) develops in the (1/2, -1/2, 5/2) 87(10) 57 131 8 9,10 doping series CeRh Ir In and CeRh Co In at 1−x x 5 1−x x 5 (3/2, -1/2, -1/2) 286(42) 343 133 low temperatures over the doping range, for which super- (3/2, -1/2, 3/2) 208(15) 226 116 conductivity coexists with antiferromagnetism. At first (3/2, -3/2, -1/2) 193(20) 236 91 glance, this appears surprising given that superconduc- (3/2, -3/2, 3/2) 190(15) 175 79 tivity does not coexist with antiferromagnetic order in Cd-doped CeIrIn (Fig. 1(b)). A possible clue to this (1/2, -1/2, 7/2) 32(5) 20 84 5 puzzle is offered by In-NQR measurements in Cd-doped (5/2, 1/2, 1/2) 137(17) 164 35 CeIrIn . These measurements suggest that supercon- (5/2, 3/2, 1/2) 115(25) 116 10 ductivity in pure and Cd-doped CeIrIn is likely mediated (1/2, 5/2, 3/2) 111(15) 128 13 by valence fluctuations, and not spin fluctuations, as in (5/2, 3/2, 3/2) 166(25) 93 11 other CeMIn compounds. (5/2, 5/2, 1/2) 190(77) 60 1 At first glance, it is surprising why the commensurate magnetic order with such a strong staggered magnetic moment was not observed in NQR measurements in Cd- IV. CONCLUSIONS doped CeIrIn . These measurements, however, were performed on a sample with nominal Cd concentration of 7.5%, in which the magnetic moment is likely to be In summary, we carried out elastic neutron scattering reduced with respect to CeIr(In Cd ) studied here. experiments on CeIr(In Cd ) . At low temperatures, 0.9 0.1 5 0.9 0.1 5 Furthermore, in CeIr(In Cd ) the antiferromag- we found magnetic intensity at the commensurate wave 0.925 0.075 5 netic transition temperature is lower than 2 K . This vector Q = (1/2, 1/2, 1/2). The magnetic intensity AF implies that the NQR measurements, performed at 1.5 K, is building up below T ≈ 3 K, with T being in good N N 17 22 were done barely below the N´eel temperature, where the agreement with specific heat , resistivity , and mag- ordered moment is presumably very small. Finally, the netic susceptibility data. No indication for additional in- NQR measurements were carried out on a powder sam- tensity was observed at incommensurate positions, such ple, which alone might strongly affect the result. For as (1/2, 1/2, 0.297), where CeRhIn , the related antifer- example, NQR measurements performed on a powder romagnetic member of the CeMIn family, orders. A mag- sample of CeRhIn under pressure revealed a change of netic moment of 0.47(3)μ at 1.8 K resides on the Ce ion, 5 B magnetic structure from incommensurate to commen- and the moments are antiferromagnetically aligned along surate , while no such change was observed in either the c axis. This is again in contrast to CeRhIn , in which 13–15 neutron diffraction or single-crystal NQR measure- magnetic moments are antiferromagnetically aligned in ments . From this point of view, it would be interest- the basal plane. 6 ACKNOWLEDGMENTS We thank E. Ressouche, B. Ouladdiaf, and C. Simon for fruitful discussions. 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Published: May 24, 2020

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