Modification of magnetic fluctuations by interfacial interactions in artificially engineered heavy-fermion superlattices
Genki Nakamine, Takayoshi Yamanaka, Shunsaku Kitagawa, Masahiro Naritsuka, Tomohiro Ishii, Takasada Shibauchi, Takahito Terashima, Yuichi Kasahara, Yuji Matsuda, Kenji Ishida
aa r X i v : . [ c ond - m a t . s t r- e l ] F e b Modification of magnetic fluctuations by interfacial interactions in artificiallyengineered heavy-fermion superlattices
Genki Nakamine , Takayoshi Yamanaka , Shunsaku Kitagawa , Masahiro Naritsuka , TomohiroIshii , Takasada Shibauchi , Takahito Terashima , Yuichi Kasahara , Yuji Matsuda , and Kenji Ishida Department of Physics, Kyoto University, Kyoto 606-8502, Japan Department of Advanced Materials Science, The University of Tokyo, Kashiwa 277-8561, Japan (Dated: February 28, 2019)Recent progress in the fabrication techniques of superlattices (SLs) has made it possible tosandwich several-layer thick block layers (BLs) of heavy-fermion superconductor CeCoIn betweenconventional-metal YbCoIn BLs or spin-density-wave metal CeRhIn BLs of a similar thickness.However, the magnetic state in each BL, particularly at the interface, is not yet understood, asexperimental techniques applicable to the SL system are limited. Here, we report measurements of Co-nuclear magnetic resonance, which is a microscopic probe of the magnetic properties inside thetarget BLs. In the CeCoIn /YbCoIn SL, the low-temperature magnetic fluctuations of the CeCoIn BL are weakened as expected from the Rashba spin-orbit effect. However, in the CeCoIn /CeRhIn SL, the fluctuations show an anomalous enhancement below 6 K, highlighting the importance ofthe magnetic proximity effect occurring near a magnetic-ordering temperature T N ∼ BL. We suggest that the magnetic properties of the BLs can be altered by the interfacialinteraction, which is a new route to modify the magnetic properties.
Magnetic fluctuations in strongly correlated electronsystems have been intensively studied from experimen-tal and theoretical aspects. This is primarily relatedto the fact that most of unconventional superconduc-tors have been discovered in the verge of the mag-netic phase, and possess mainly strong antiferromagnetic(AFM) fluctuations[1–5]. The heavy-fermion (HF) su-perconductor CeCoIn is one such unconventional super-conductor. The superconducting (SC) transition tem-perature T c of CeCoIn is 2.3 K, which is the highest T c among Ce-based HF superconductors[6]. CeCoIn pos-sesses an extremely narrow conduction band with a rel-atively heavy effective mass and shares similarities withhigh- T c cuprates, including an unconventional SC gapwith d x − y symmetry and non Fermi-liquid behavior[7–9]. In addition, it has been considered that the supercon-ductivity is mediated by AFM fluctuations with quantumcritical characteristics[10, 11].Recently, the molecular beam epitaxy (MBE)technique was employed to synthesize arti-ficial Kondo superlattices (SLs) of alternat-ing layers of HF CeCoIn /conventional-metalYbCoIn [12] and CeCoIn /spin-density-wave (SDW)-metal CeRhIn [13, 14] with a few-unit-cell-layerthickness[15, 16]. These artificially engineered materialsprovide a new platform to study the two-dimensionalelectronic properties of HF superconductors, the inter-action between two different block layers (BLs), and themagnetic properties at the interfaces[17]. Particularly,interactions between superconductivity and bosonic ex-citations through an atomic interface have received muchattention since single-layer FeSe on a SrTiO substrateshows an extraordinarily high- T c due to the couplingwith the substrate[18–20]. Thus, it is important tostudy electronic and magnetic properties of BLs and the interfaces between two BLs. We consider that nuclearmagnetic resonance (NMR) and nuclear quadrupoleresonance (NQR) are among the best experimentalprobes for this purpose, as they can provide spatiallyresolved microscopic information about the target BLs.We have investigated the magnetic and SC properties inan epitaxial film of CeCoIn and the CeCoIn /YbCoIn SL from the
In NMR/NQR[21, 22]. We reported thatnuclear spin-lattice relaxation rate 1 /T on the epitaxialfilm is almost identical to 1 /T of the bulk single crystal,indicative of the high quality of the epitaxial film HFsample[21], and that 1 /T on the CeCoIn /YbCoIn SL revealed the strong suppression of the magneticfluctuations at the interface region[22].The interesting questions in such an SL system arewhether the magnetic and SC properties on the CeCoIn BL can be modified in the SL sample and, if so, whateffects and interactions are important, and how manylayers are affected in the BL. We have investigated theseissues from the Co ( I = 7/2)-NMR measurement ofthe CeCoIn /YbCoIn and CeCoIn /CeRhIn SL sam-ples. In this paper, we report the low-temperaturemagnetic fluctuations of the CeCoIn BL mainly in theCeCoIn /CeRhIn SL. The magnetic fluctuations of theCeCoIn BL in the CeCoIn /CeRhIn SL is almost un-changed with those of bulk CeCoIn down to 6 K, indicat-ing that the coupling between the CeCoIn and CeRhIn BLs is small. However, the magnetic fluctuations of theCeCoIn BL is enhanced below 6 K only at the one ortwo layers at the interface, indicating that the strongmagnetic fluctuations penetrate from the CeRhIn BLwith approaching to the magnetic ordering temperature T N ∼ BL. By taking into accountthe experimental results of the CeCoIn /YbCoIn thatthe magnetic fluctuations of the CeCoIn BL are weak- (c)(b)(a)(d) (CeCoIn ) Co FIG. 1. Field-sweep nuclear magnetic resonance (NMR) spec-tra at 4.2 K and 114.5 MHz on (a) 500-nm-thick CeCoIn film, (b) CeCoIn (5)/YbCoIn (5) superlattice (SL), (c)CeCoIn (5)/CeRhIn (5) SL and (d) 300-nm-thick CeRhIn film. The NMR signals in the film samples are identified, andthe NMR parameters are listed[ ? ]. ened by the Rashba interaction, we revealed that themagnetic properties are modified mainly at the interfaceregion, suggesting that the interfacial interaction is themost important interaction in the SL compounds.The SLs of CeCoIn (5)/YbCoIn (5) andCeCoIn (5)/CeRhIn (5), which were grown by theMBE technique, were stacked alternately along the c axis, where (5) indicates the number of unit-cell-layers of each BL. T c of the CeCoIn /YbCoIn , andCeCoIn /CeRhIn SLs is 1.2 and 1.4 K, respectively. Wealso prepared epitaxial-films of CeCoIn , YbCoIn , andCeRhIn , and performed NMR measurements on thesefilms and single-crystal CeCoIn for comparison withthe SL samples. Details of the synthesis process andsample characterization are shown in the reference[23 ? ]Figure 1 presents the Co and
In-NMR spectraof the (a) CeCoIn film, (b) CeCoIn /YbCoIn SL, (c)CeCoIn /CeRnIn SL, and (d) CeRhIn film, which weremeasured by sweeping the magnetic field parallel to the c -axis with f = 114.5 MHz at 4.2 K. In the CeCoIn filmsamples, the NMR signals arising from the Co site havea fine structure because of the presence of the electricfield gradient (EFG)[22]. The parameters of the Inand Co NMR spectra are listed in the table[ ? ]. The Co-NMR spectra of the SLs are observed around thefield range where the Co-NMR spectra of the film areobserved, but they become structureless mainly due to the inhomogeneity of the EFG at the Co site. In addi-tion, finite intensity was observed everywhere in the SLspectra, which arises from the In(1) and In(2) sites, sincethe EFG of these sites are much larger than that of theCo site and the inhomogeneity of the EFG makes thespectra extremely broader. The Co-NMR spectrum inthe CeCoIn /CeRnIn SL arises only from the CeCoIn BL, as no Co atoms exist in the CeRhIn BL.Nuclear spin-lattice relaxation rate 1 /T was measuredby the recovery of the nuclear magnetization m ( t ) ata time t after a saturation pulse. The relaxation of R ( t ) ≡ [ m ( ∞ ) − m ( t )] /m ( ∞ ) at the Co-NMR peakof the CeCoIn BL in two SLs, together with that of theCeCoIn film can be fit to a theoretical function f ( t ) fora spin 7/2 relaxation at the central transition[24], whichcan be expressed as R ( t ) ∝ f ( t ) = 0 .
012 exp (cid:18) − tT (cid:19) + 0 .
068 exp (cid:18) − tT (cid:19) +0 .
206 exp (cid:18) − tT (cid:19) + 0 .
714 exp (cid:18) − tT (cid:19) . (1)1 /T can be evaluated from the best fits. The experi-mental data and the fitting in the CeCoIn / YbCoIn SL are shown by the curves in Fig. S2 [ ? ].We also measured 1 /T at various fields at 4.2 K in twoSLs. In the measurement, 1 /T was estimated with thesame theoretical function of Eq. (1) to compare the 1 /T values, although the tail of the NMR peak arises from thenuclear-spin transitions other than the central transitionor even from the back-ground In signals. The 1 /T ob-tained with the above procedure is plotted in Figs. 1 (b)and (c), and they show a position dependence. It shouldbe noted that the NMR peak near the central transitionin the CeCoIn film has the largest 1 /T . This is becausethe coefficient of exp( − t/T ) in the theoretical functionis the largest at the central transition, thus 1 /T shouldbe the largest if the fitting for the evaluation of 1 /T wasperformed by the same theoretical function. We can de-termine the Co-NMR peak arising mainly from the cen-tral transition with the 1 /T measurement, even thoughthe NMR spectrum from the CeCoIn BL is so broadthat it is structureless. Temperature dependence of 1 /T of the BL was measured at the central-transition peak.The measurement of 1 /T at the CeCoIn BL is cruciallyimportant, as we are interested in the comparison be-tween the CeCoIn /YbCoIn SL and CeCoIn /CeRnIn SL. It is expected that the magnetic fluctuations at theCeCoIn BL will be different between the two SLs be-cause of the different adjacent BLs.A clear enhancement in the AFM fluctuations at theinterface region was observed in the CeCoIn /CeRhIn SL at low temperatures as discussed below. Figure 2 (a)and (b) show the relaxation of R ( t ) for the CeCoIn BLin the CeCoIn /CeRhIn SL and the CeCoIn film at 8and 1.77 K, respectively. Although R ( t ) for the CeCoIn Co-NMR f = 114.5 MHz 11.02 T (a) T = 8 K
CeCoIn film CeCoIn BL in CeCoIn /CeRhIn SL [ m ()- m ( t )] / m () t (ms) CeCoIn film CeCoIn BL in CeCoIn /CeRhIn SL (b) T = 1.77 K [ m ()- m ( t )] / m () t (ms) (f) T = 1.77 K(c) T = 8 K (d) T = 6 K [ m ()- m ( t )] / m () t (ms) (e) T = 5 K FIG. 2. Relaxations of R ( t ) of the CeCoIn BL in theCeCoIn /CeRhIn SL and R ( t ) of the CeCoIn film at (a)8 and (b) 1.77 K. (a) At 8 K, two R ( t ) can be fit with thetheoretical function with the almost same 1 /T over the fulltime range. (b) At 1.77 K, R ( t ) of the CeCoIn BL in theCeCoIn /CeRhIn SL has a larger 1 /T component at theshort time range, and a smaller 1 /T component can be fittedwith the same 1 /T component of the CeCoIn film in t > . ∗ f ( t ), and f ( t ) (the dotted line) isthe fitting curve of R ( t ) of the CeCoIn film. (c), (d), (e) and(f) are the R ( t ) in the time range between 0 and 2 msec at T = 8, 6, 5, and 1.77 K, respectively. The larger component of1 /T can be recognized below 6 K. BL in the CeCoIn /CeRhIn SL exhibits the same re-laxation behavior as that for the CeCoIn film at 8 K,the former R ( t ) has a larger component of 1 /T (shortercomponent of T ) than the latter R ( t ) at 1.77 K. Thelarger component of 1 /T can be recognized particularlyin the short time range less than 2 ms below 6 K as seenin Fig. 2 (c - f), but the smaller component of 1 /T (thelonger component of T ) is almost the same as 1 /T in theCeCoIn film, as the R ( t ) smaller than 1 /e can be fittedto the relaxation curve with the similar 1 /T of the filmwith the different initial value, as seen in the main panelof Fig. 2 (b). Thus, the larger component of 1 /T for theCeCoIn BL in the CeCoIn /CeRhIn SL was evaluatedbelow 5.5 K from the fit in the short time range where1 > R ( t ) > /e , as the larger component of 1 /T can beobserved only below 5.5 K, and the smaller componentof 1 /T was estimated from the time range where R ( t ) ofCeCoIn BL is smaller than 1 /e .Figure 3 shows the temperature dependence of 1 /T T for Co on the CeCoIn BL in the CeCoIn /CeRhIn and CeCoIn /YbCoIn SLs together with that of theCeCoIn and YbCoIn films and the bulk CeCoIn . As CeCoIn /CeRhIn YbCoIn filmCeCoIn /YbCoIn CeCoIn film CeCoIn bulk Co-NMR (cid:1) H ~ 11 T FIG. 3. Temperature dependence of 1 /T T for Co on theCeCoIn BL in the CeCoIn /YbCoIn and CeCoIn /CeRhIn SLs together with the CeCoIn and YbCoIn films. As for the1 /T T of the CeCoIn /CeRhIn SL, the larger (red open di-amonds) and smaller (red open triangles) 1 /T T componentsare plotted below 5.5 K. 1 /T T above 6K was evaluated fromthe single component shown by red closed diamond. The1 /T T of Co on the single-crystal CeCoIn is representedby a dotted line. for the 1 /T T of the CeCoIn /CeRhIn SL, the largerand smaller components of 1 /T ’s are plotted below 5.5K. 1 /T T for the CeCoIn BL in the CeCoIn /YbCoIn SL, which is smaller than 1 /T T of the CeCoIn film,indicates the suppression of the AFM fluctuations inthe CeCoIn BL. This result is consistent with ourprevious
In-NMR results for the CeCoIn /YbCoIn SL[22]. A stronger suppression of the AFM fluctuationsat the interface was shown by the site selective NMRmeasurements[22], with which we succeeded in identify-ing the
In-NMR signals arising from the interface andthe inner layers separately. However, such a local infor-mation could not be obtained from the Co-NMR mea-surement due to the smallness of the EFG at the Co site.In the absence of the local inversion symmetry of the Cecompounds with the strong correlations, the Rashba-typespin-orbit interaction is dominant and splits the Fermisurfaces into two sheets depending on spin structure. Animage of this effect is presented in Fig. 4 (a), and, asa result, the nesting condition is modified and the com-mensurate AFM fluctuations with Q = ( π/a, π/a, π/c ),which is dominant in CeCoIn , are markedly suppressed.In contrast, it should be noted that the 1 /T T for theCeCoIn BL in the CeCoIn /CeRhIn SL is nearly thesame as that in the bulk CeCoIn down to 6 K. Thisindicates that AFM fluctuations at the interface regionbetween the CeCoIn BL and CeRhIn BL are not sup- Ce Ce Yb Yb Ce YbCo Ce CoRh
CeCoIn /YbCoIn SL In(2) In(2)
CeCoIn /CeRhIn SLCeRhIn BL T N ~ 3 K (a) (b) ac - (cid:1) V FIG. 4. Arrangement of the atomic layers revealed witha high-resolution transmission electron microscope image in(a) CeCoIn /YbCoIn and (b) CeCoIn /CeRhIn BLs. Theatomic views on the (1, 0, 0) plane are shown. The interfacesof each BL layers are indicated by boxes, and the conceivableeffects are shown. pressed by the Rashba spin-orbit interaction, and thatthe coupling between the CeCoIn and CeRhIn BLs issmall, as magnetic fluctuations at the CeRhIn BL wouldbe larger than that of the CeCoIn BL. Below 6 K, 1 /T T has a larger component than that of the CeCoIn film,although the smaller component of 1 /T T is almost iden-tical to that of the CeCoIn film, as mentioned above.This indicates that the AFM fluctuations are enhancedbecause of the magnetic interaction between the two BLs.The larger component of 1 /T T in the CeCoIn BL con-tinues to increase down to 1.77 K, although a kink isobserved at about 2.5 K, which is slightly lower thanthe magnetic ordering temperature ( T N ∼ BL. The 1 /T T result indicates that the AFMfluctuations at the CeCoIn BL remain enhanced belowthe T N of the CeRhIn . The paramagnetic state of theCeCoIn BL below T N is also shown from the absenceof appreciable broadening of the Co-NMR spectrumby the internal field arising from the Ce ordered mo-ment as shown in Fig. S3[ ? ]. As the smaller com-ponent of 1 /T T for the CeCoIn BL is similar to that ofthe CeCoIn film and the fraction of this component isroughly estimated to be half of the total relaxation com-ponent, it is reasonable to conclude that the enhancementin the AFM fluctuations only occurs at the Ce layer sand-wiched by the Co and Rh atoms at the interface or the Ce layers next to this Ce layer as shown in Fig. 4 (b) sincethere remain the layers where the same AFM fluctuationsas those in the CeCoIn film persist. Our NMR resultsindicate that the Ce layers at the interface are not inthe ordered state, but would remain in the paramagneticstate and become the origin of strong AFM fluctuationsin the CeCoIn BL. This magnetic proximity might be re-garded as an injection of a strong AFM paramagnon intothe CeCoIn BL from the adjacent SDW-metal CeRhIn through the interface, although this injected region isconsidered to be only one or two lattices along the c -axisas discussed above.Up to now, we have not obtained the NMR results inthe SC state as our NMR measurement has been doneabove the upper critical field ( H c2 ), but we consider thatsuperconductivity of the CeCoIn /CeRhIn SL wouldbe in the stronger coupling nature than that of bulkCeCoIn from the recent result of the ratio of H c2 /T c ,although T c of the SL is lower[23]. This is suggestedby the result that superconductivity in the CeCoIn BLspossess an extremely strong coupling nature when AFMorder in the CeRhIn BLs vanishes[23]. We suggestthat the AFM paramagnons injected through the inter-face from the CeRhIn BLs would work to strengthenthe pairing interactions. This picture is similar to thesuggested mechanism of the higher- T c in the mono-layerFeSe, where pronounced oxygen optical phonons in thesubstrate couple with the mono-layer FeSe electrons andenhance the superconductivity[25].In conclusion, from NMR studies on two SLs, wedemonstrate that the dominant interaction working atthe interface region strongly depends on the characteris-tics of the adjacent BLs and that the magnetic propertiesof the CeCoIn BL are modified by the penetration ofthe interfacial magnetic properties into the inner layers.We suggest that the interfacial interaction is a key factorto tune the magnetic characteristics of the BL and willbecome a new method to control the magnetic proper-ties. To prove our suggestion, the spectroscopic exper-iments which can investigate the thickness dependenceof magnetic fluctuations are highly desired. We antici-pate that AFM-fluctuation-mediated superconductivity,which is realized only in the interface region, might be in-duced in an SL consisting of the conventional-metal andSDW-metal BLs.The authors acknowledge H. Ikeda and Y. Yanasefor fruitful discussions. This work was partiallysupported by Kyoto Univ. LTM center, Grant-in-Aid from the Ministry of Education, Culture, Sports,Science, Technology(MEXT) of Japan, Grants-in-Aidfor Scientific Research (KAKENHI) from the JapanSociety for the Promotion of Science (JSPS), the“J-Physics” (No. JP15H05882, No. JP15H05884, andNo. JP15K21732) and “Topological Quantum Phenom-ena” (No. JP25103713) Grant-in-Aid for Scientific Re-search on Innovative Areas from the MEXT of Japan,and by Grant-in-Aids for Scientific Research (Grants No.JP25220710, and No. JP15H05745). [1] N. D. Mathur, F. M. Grosche, S. R. Julian, I. R. Walker,D. M. Freye, R. K. W. Haselwimmer, and G. G. Lon-zarich, Nature , 39 (1998).[2] T. Moriya and K. Ueda, Rev. Prog. 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