Unusual Kondo-hole effect and crystal-field frustration in Nd-doped CeRhIn 5
P. F. S. Rosa, A. Oostra, J. D. Thompson, P. G. Pagliuso, Z. Fisk
UUnusual Kondo-hole effect and crystal-field frustration in Nd-doped CeRhIn P. F. S. Rosa , , A. Oostra , J. D. Thompson , P. G. Pagliuso , and Z. Fisk University of California, Irvine, California 92697-4574, U.S.A. Los Alamos National Laboratory, Los Alamos, New Mexico 87545, U.S.A. Instituto de F´ısica “Gleb Wataghin”, UNICAMP, Campinas-SP, 13083-859, Brazil. (Dated: September 25, 2018)We investigate single crystalline samples of Ce − x Nd x RhIn by means of X-ray diffraction, mi-croprobe, magnetic susceptibility, heat capacity, and electrical resistivity measurements. Our datareveal that the antiferromagnetic transition temperature of CeRhIn , T Ce N = 3 . x Nd , by virtue of the “Kondo hole” created by Nd substitution. The extrapolationof T Ce N to zero temperature, however, occurs at x c ∼ .
3, which is below the 2D percolation limitfound in Ce − x La x RhIn . This result strongly suggests the presence of crystal-field frustration ef-fects. Near x Nd ∼ .
2, the Ising AFM order from Nd ions is stabilized and T Nd N increases up to11 K in pure NdRhIn . Our results shed light on the effects of magnetic doping in heavy-fermionantiferromagnets and stimulate the study of such systems under applied pressure. I. INTRODUCTION
A remarkable variety of unexpected phenomena ariseswhen magnetic impurities are introduced in a metal. Oneof the most striking examples is that of Gold (Au) metal,which is, in its pure form, a good conductor displayingdecreasing electrical resistance with decreasing tempera-ture. A few parts per million (ppm) of magnetic Iron im-purities in Au, however, cause the resistance to rise log-arithmically at a material-specific Kondo impurity tem-perature T K [1]. This so-called single-ion Kondo effect re-flects the incoherent scattering of conduction electrons bythe magnetic impurities introduced into the host [2]. Inaddition to introducing only a few ppm of magnetic impu-rities, it is also possible to synthesize materials in whichthere is a periodic lattice of Kondo “impurities” coupledto the surrounding sea of itinerant electrons. At temper-atures well above T K , conduction electrons are scatteredincoherently by the periodic array of Kondo “impurities”,but at much lower temperatures, translational invarianceof the “impurities” requires that a strongly renormalizedBloch state develop in which scattering is coherent [3].A good example of these behaviors is found when Lais replaced systematically by magnetic (Kondo) Ce ionsin the non-magnetic host LaCoIn [4]. In the Kondo-lattice limit CeCoIn , the low temperature resistivity isvery small, and the compound hosts unconventional su-perconductivity in which the effective mass of electronsin the renormalized conduction bands is large [5]. If asmall number of Ce atoms in CeCoIn now is replacedby non-magnetic La ions, a Kondo-impurity effect de-velops on the La ions. The absence of a Ce ion in theperiodic Kondo lattice creates a “Kondo-hole” such thatLa acts as a Kondo impurity and incoherently scatterselectrons in the renormalized heavy conduction bands [6]In the series Ce − x La x CoIn , the system evolves at lowtemperatures as a function of x from a coherent Kondolattice ( x = 0) to a a collection of incoherently scatteringKondo impurities at x ∼ .
4. Interestingly, this cross-over coincides with the percolation limit of a 2D squarelattice on which the La/Ce ions sit. Magnetic doping has not been extensively studied inCeCoIn or other members within the Ce m M n In m +2 n ( M = transition metals Co, Rh, Ir, Pd, Pt; n = 0 , , m = 1 , ,
3) family of which it is a part. Recently, how-ever, Nd-doping in CeCoIn at concentrations 5 − . Nd . CoIn are identical to those observed in the field-induced mag-netically ordered phase in pure CeCoIn ( Q -phase) [8, 9].These results indicate that the Nd ions are fundamentallychanging the electronic system and not acting simply asa Kondo hole. To our knowledge, there is no report onthe effects of magnetic doping in the antiferromagnetic(AFM) member CeRhIn up to date. In the following weaddress the open questions: (i) how will Nd interact withthe AFM order of CeRhIn ? (ii) will there be a “Kondo-hole” effect? We note that “Kondo-hole” behavior hasbeen observed in Ce − x La x RhIn where AFM order de-creases linearly with La. In the limit T N →
0, the criticalLa concentration, x c ∼ by means of X-ray diffraction, mi-croprobe, magnetization, heat capacity, and electrical re-sistivity measurements. Our data show that the AFM or-dering temperature of CeRhIn ( T Ce N = 3 . x Nd , and extrapolates tozero at a critical Nd concentration of x c ∼ x c is below the percolationlimit indicates that there is another mechanism frustrat-ing the magnetic order of the Ce sublattice. We arguethat this mechanism is the crystal-field frustration dueto the different spin configurations of CeRhIn (easy c -axis magnetization but with ordered moments in-plane)and NdRhIn (Ising spins along c-axis). In fact, around x Nd ∼ .
2, the Ising AFM order of the Nd sublattice isstabilized and T Nd N increases up to 11 K in pure NdRhIn . a r X i v : . [ c ond - m a t . s t r- e l ] A p r II. EXPERIMENTAL DETAILS
Single crystalline samples of Ce − x Nd x RhIn ( x = 0 , . , . , . , . , . , . , . , . ,
1) weregrown by the In-flux technique. The crystallographicstructure was verified by X-ray powder diffraction atroom temperature. In addition, several samples werecharacterized by elemental analysis using a commercialEnergy Dispersive Spectroscopy (EDS) microprobe.Magnetization measurements were performed using acommercial superconducting quantum interference de-vice (SQUID). The specific heat was measured using acommercial small mass calorimeter that employs a quasi-adiabatic thermal relaxation technique. The in-planeelectrical resistivity was obtained using a low-frequencyac resistance bridge and a four-contact configuration.
III. RESULTS
Figure 1a shows the actual Nd concentration obtainedby EDS ( x EDS ) as a function of the nominal Nd concen-tration x nominal . The smooth and monotonic relationshipbetween the x EDS and x nominal indicates that Nd is beingincorporated in the lattice. Further, the small error bars,∆ x , point to a rather homogeneous distribution of Nd.In the extremes of the series, x EDS has an error bar of∆ x ∼ .
02. For Nd concentrations around 50%, a largervariation of ∆ x = 0 .
05 is observed, which is expectedfor concentrations in the middle of the series. We note,however, that ∆ x is the standard deviation accountingfor different samples from the same batch and not for asingle sample. On average, the variation within a singlecrystal ( ∼ .
01) is smaller than the standard deviation.These results indicate that Nd substitutes Ce homoge-neously instead of producing an intergrown of NdRhIn .Herein, we will refer to the actual EDS concentration. b ) xEDS x n o m i n a l a ) x E D S a (Å) c (Å)
FIG. 1. a) Actual concentration measured by EDS, x EDS ,as a function of nominal concentration, x nominal in the seriesCe − x Nd x RhIn . b) Tetragonal lattice parameters as a func-tion of x EDS along the series Ce − x Nd x RhIn . Figure 1b shows the lattice parameters obtained bypowder X-ray diffraction as a function of Nd concentra-tion. The X-ray powder patterns show that all membersof the series crystallize in the tetragonal HoCoGa struc-ture and no additional peaks are observed. A smoothdecrease is found in both lattice parameters a and c , inagreement with Vegard’s law. This result implies thatthe volume of the unit cell is decreasing with Nd con-centration, suggesting that Nd doping produces positivechemical pressure. Using the bulk modulus of CeRhIn ,we estimate that a rigid shift of the lattice parame-ters from CeRhIn to Ce . Nd . RhIn corresponds to∆ P = 0 .
25 GPa of applied pressure. From the phasediagram of CeRhIn under pressure [11], this ∆ P wouldcorrespond to an increase of T N by 0 . . Nd . RhIn , indicating that chemical pressure isnot the main tuning parameter determining T N .Figures 2a and b show the T -dependence of the mag-netic susceptibility, χ ( T ), for a field of 1 kOe appliedalong the c -axis and ab -plane, respectively. For low Ndconcentrations ( x Nd = 0 . , . T N in the χ c ( T ) data, i.e., when H || c -axis. This resultis somewhat unexpected because AFM order is observedby a clear peak in heat capacity measurements of bothCeRhIn and Ce − x Nd x RhIn . Instead of an expectedpeak in χ ( T ), we observe a low- T Curie-tail, suggestingthat the Nd ions are free paramagnetic impurities embed-ded in the Kondo lattice. When H || ab -plane, however, χ ab ( T ) displays a very similar behavior when comparedto pure CeRhIn : there is a maximum in χ ( T ) followedby a kink at T Ce N . We attribute this difference to the factthat the spins in NdRhIn point along the c -axis andthe magnetic susceptibility along this direction is muchlarger than the in-plane susceptibility. Thus, χ ab ( T ) datareveals a linear decrease of T Ce N = 3 . x Nd up to x Nd = 0 .
14. Between x Nd = 0 .
14 and x Nd = 0 .
23, thetransition temperature starts to increase again, suggest-ing that the AFM order due to Nd ions starts to de-velop at T Nd N . Though not obvious in these data, χ ab ( T )reaches a maximum at T max χ > T Ce N in CeRhIn andlightly Nd-doped samples. The temperature T max χ alsodecreases with x Nd , from ∼ . to ∼ . x Nd = 0 .
23. Evidence for T max χ , however,is lost for x Nd > .
23 due to the dominant contributionfrom the Nd AFM order. We will return to this analysiswhen discussing the phase diagram of Fig. 5. Finally, forhigher Nd concentrations, both χ c ( T ) and χ ab ( T ) showAFM behavior of a typical local moment system.From fits of the polycrystalline average of the data(inset of Fig. 2a) to a Curie-Weiss law, we obtain ef-fective magnetic moments of 2.5(1) µ B , 2.7(1) µ B , 3.2(1) µ B , and 3.7(1) µ B for x Nd = 0 . , . , . , .
9, respec-tively. These calculated values are in good agreementwith the theoretical values of 2.59 µ B , 2.69 µ B , 3.05 µ B ,and 3.52 µ B , respectively. We also obtain the paramag-netic Curie-Weiss temperature, θ poly , which averages outcrystal electrical field (CEF) effects. The inset of Fig. 2b
01 0 02 0 03 0 04 0 0 b )
H = 1 k O e c (10-2 emu/mol) x N d = 0 . 0 5 x
N d = 0 . 1 4 x
N d = 0 . 4 7 x
N d = 0 . 9
H | | c - a x i sH = 1 k O eH | | a b - p l a n e a )
T ( K ) c p (mol/emu) q (K) x N d q c q a b q p o l y FIG. 2. a) Temperature dependence of the magnetic suscepti-bility, χ c ( T ), of representative samples in the Ce − x Nd x RhIn series in a field of 1 kOe applied along the c -axis. Insetshows the inverse susceptibility of the polycrystalline aver-age vs temperature. Solid lines are linear fits to the data.b) Temperature dependence of the magnetic susceptibility, χ ab ( T ), for the same samples in a field of 1 kOe applied alongthe ab -plane. Inset shows the Curie-Weiss temperature, θ , forall compositions of Ce − x Nd x RhIn . shows θ poly as well as θ c and θ ab . In a molecular fieldapproximation, θ poly is proportional to the effective ex-change interaction, J , between rare-earth ions. The factthat θ poly is negative is in agreement with the AFM cor-relations found in the series. A reduction of θ poly is ob-served going from CeRhIn ( θ poly = −
31 K) to NdRhIn ( θ poly = −
17 K), which suggests within a molecular fieldmodel that J also decreases along the series. As a con-sequence, this reduction in J would be expected to de-crease the AFM ordering temperature. The experimen-tal data, however, shows the opposite behavior: T N inNdRhIn ( T Nd N = 11 K) is almost three times larger thanin CeRhIn ( T Ce N = 3 . , θ poly also includes the AFM Kondo ex-change that tends to reduce T N relative to that expectedsolely from the indirect Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction [12]. Because there is no Kondo ef-fect in NdRhIn , the variation in θ poly with x Nd impliesa suppression of the Kondo contribution and increaseddominance of the RKKY interaction. This is reflected in the ratio T N /θ poly , which is 0 .
12 in CeRhIn and 0 . . As illustrated in the inset of Fig. 2b, θ poly reaches a plateau between x Nd = 0 .
23 and 0 .
47, sug-gesting that Kondo interactions are essentially quenchedbefore x Nd = 0 .
47. Consequently, one might expect T N to increase initially as Nd replaces Ce and then to re-main approximately constant for x Nd > .
47. As we willcome to, this is not the case and T N is a non-monotonicfunction of Nd content. The above discussion indicatesthat there is another relevant mechanism determining themagnetic ordering in the series Ce − x Nd x RhIn . Fromthe nearly constant values of θ c and pronounced changeof θ ab , which anisotropy is a consequence of CEF effects,it is reasonable to expect that CEF effects play an impor-tant role. In fact, from the high-temperature expansionof χ ( T ) we can readily observe that the main tetragonalCEF parameter, B ∝ ( θ ab − θ c ), systematically decreaseswith Nd concentration. b )a ) H | | a b - p l a n e T = 1 . 8 K
M ( m B) x N d = 0 . 0 0 . 0 5 0 . 1 4 0 . 4 7 0 . 9
H | | c - a x i sT = 1 . 8 K
M ( m B) H ( k O e )
FIG. 3. a) Field dependence of the magnetization at 1 . c -axis. Data for x Nd = 0 coincide withthat for x Nd = 0 . H ≤
50 kOe. b) Field dependence ofthe magnetization at 1 . ab -plane. Figures 3a and b show the H -dependence of the mag-netization, M ( H ), at 1.8 K for fields applied along the c -axis and ab -plane, respectively. Although M c ( H ) forCeRhIn displays a linear response with field, at low Ndconcentrations ( x Nd = 0 . , .
14) there is a non-linearbehavior that resembles a Brillouin function. This sup-ports our interpretation of the origin of the low- T Curietail in χ c for low Nd content, namely that Nd ions at lowconcentrations act as free paramagnetic entities. Becausethe Brillouin-like contribution to M c ( H ) is substantiallylarger than expected from just a simple free Nd moment,this behavior implies that Nd moments also are locallyinducing free-moment like character on neighboring Ceatoms. This is most pronounced for H || c due to themuch higher susceptibility of Nd moments along this di-rection. At light Nd doping, then, Nd acts as a ratherdifferent type of “Kondo hole” compared to that inducedby non-magnetic La substitution for Ce. The Nd ionscarry a net magnetic moment that is not quenched bythe Kondo-impurity effect. At high x Nd , M c ( H ) displaysa field-induced transition to a spin-polarized state, as ob-served in NdRhIn . When the field is along the ab-plane,pure CeRhIn also displays a weak field-induced anomalyin M ab ( H ) ( H c ∼
22 kOe), which signals a change in or-dering wavevector [13] and is suppressed with x Nd . b )a ) C/T (J/mol.K2)
L a R h I n C e R h I n x N d = 0 . 0 5 x
N d = 0 . 1 4 x
N d = 0 . 4 7 x
N d = 0 . 9
H = 0 k O e
Cmag/T (J/mol.K2)
T ( K )
Snorm/Ce
R l n 2
FIG. 4. a) Temperature dependence of the specific heat,
C/T ,of LaRhIn , CeRhIn and representative samples of the seriesCe − x Nd x RhIn . b) Magnetic contribution to the specificheat, C mag /T , as a function of temperature. Inset shows theentropy per Ce normalized by R ln2. Figure 4a shows the temperature dependence of theheat capacity over temperature,
C/T , for four represen-tative Nd concentrations. LaRhIn , the non-magneticmember, and pure CeRhIn also are included. The sharppeak at T N = 3 . first decreaseslinearly with Nd concentrations up to x Nd = 0 .
14. At x Nd = 0 .
14, the transition at T N starts to broaden andfurther increase in x Nd reveals an enhancement of T N , inagreement with χ ( T ) data.Figure 4b shows the magnetic contribution to the heatcapacity, C mag /T , after subtracting LaRhIn from thedata. The transition temperature at which C mag /T peaks is marked by the arrows. As the temperature islowered further, an upturn is observed for all crystalswith finite x Nd , including NdRhIn , suggesting that theNd ions are responsible for it. Reasonably, the upturnmay be associated with the nuclear moment of Nd ions,and it can be fit well by a sum of both electronic ( ∝ γ )and nuclear ( ∝ T − ) terms [14], consistent with the pres-ence of a nuclear Schottky contribution.The magnetic entropy as a function of temperature isobtained by integrating C mag /T over T . The inset ofFigure 3b shows the T - dependence of the magnetic en-tropy recovered per Ce ion. The entropy is normalized by R ln2, which is the entropy of the ground state doublet.In pure CeRhIn (black bottom curve), the magnetic en-tropy increases with T followed by a kink at T N . Weobserve an increase in the recovered entropy below T N even when a very small amount of Nd is introduced (e.g., x Nd = 0 . x Nd = 0 . r ( mW .cm) T ( K ) x N d = 0 . 0 5 x
N d = 0 . 1 4 x
N d = 0 . 4 7
T ( K ) x N d = 0 . 0 5 x
N d = 0 . 1 4 x
N d = 0 . 4 7 x
N d = 0 . 9 0
FIG. 5. a) In-plane electrical resistivity, ρ ab ( T ), ofCe − x Nd x RhIn as a function of temperature. b) Low tem-perature ρ ab ( T ) data. Arrows mark T N . Finally, we discuss the temperature dependence of thein-plane electrical resistivity, ρ ab ( T ), of Ce − x Nd x RhIn .Figure 5a shows ρ ab ( T ) for samples with x Nd < .
5. At x Nd = 0 . ρ ab ( T ) is very similar in magnitude and T -dependence to that of pure CeRhIn . In particular, thebroad peak at ∼
40 K indicates the crossover from in-coherent Kondo scattering at high temperatures to theheavy-electron state at low temperatures. As x Nd is in-creased, ρ ab ( T ) decreases monotonically with temper-ature and the initial peak turns into a broad featurearound 70 K when x Nd = 0 .
47. We note that the sec-ond CEF excited state of NdRhIn is near 68 K, suggest-ing that the broad feature in ρ ab ( T ) is likely associatedwith CEF depopulation [15]. This evolution is consis-tent with an increase in the local character of the 4 f sys-tem. Further, the low-temperature data shown in Fig. 5bdisplay an increase in ρ . Typically disorder scatteringwould be expected to be a maximum near x = 0 .
5, butthis is not the case. As shown in Ref. [15], the resid-ual resistivity of pure NdRhIn is much lower than thatof our Ce . Nd . RhIn crystal. This difference impliesthat spin-disorder scattering plays a significant role indetermining ρ in this series. IV. DISCUSSION
In Figure 6 we summarize our results in a T − x phasediagram, in which two distinct regimes become clear.The first one, at low Nd concentrations, presents a lineardecrease of T N with x Nd . Interestingly, a linear depen-dence of T N also has been observed in Ce − x La x RhIn ,where La creates a “Kondo hole” in the system via dilu-tion. In the La-doping case, however, T N extrapolates to T = 0 at a critical concentration of x c ∼ D lattice. Here, Nd-dopedCeRhIn displays a smaller x c of ∼ L o c a l M o m e n t A F M
TN (K) x E D S
C e
N d x R h I n K o n d o A F M
FIG. 6. T − x phase diagram of the series Ce − x Nd x RhIn . It has been shown − both theoretically and experi-mentally − that T N in tetragonal structures is enhancedwith respect to their cubic R In ( R = rare-earth ions)counterparts whenever R has an Ising magnetic struc-ture, i.e., spins polarized along the c -axis [16, 17]. Thisis due to the fact that the tetragonal CEF parameters inthese structures favor a groundstate with Ising symme-try, as supported by the fact that the c -axis susceptibil-ity is larger than the ab -plane susceptibitility in memberswhose R element has finite orbital momentum. BecauseNdRhIn displays commensurate Ising-like order below T N = 11 K, it is reasonable to assume that Nd ionswill retain their Ising-like character when doped into theCe sites [18]. CeRhIn , however, has an incommensu-rate magnetic structure with spins perpendicular to the c -axis [19]. Hence, a crystal-field frustration of the in-plane order in CeRhIn is induced by Nd Ising spins.As a consequence, T Ce N of the Ce sublattice extrapolatesto zero before the percolation limit and T Nd N of the Ndsublattice is stabilized. V. CONCLUSIONS
In summary, we synthesize single crystals ofCe − x Nd x RhIn using the In-flux technique. X-raydiffraction and microprobe measurements show a smoothevolution of lattice parameters and Nd concentration,respectively. Across the doping series, there is a com-plex interplay among Kondo-like impurity physics, mag-netic exchange and crystal-field effects as the Nd contentchanges. At low x Nd , there is an unusual type of magnetic“Kondo hole” and T Ce N decreases linearly with x Nd . Theextrapolation of T Ce N to zero temperature occurs belowthe 2D percolation limit due to crystal-field frustrationeffects. Around x Nd ∼ .
2, the Ising AFM order from Ndions is stabilized and T Nd N increases up to 11 K in pureNdRhIn . Further investigation of the Ce − x Nd x RhIn series under pressure will be valuable to understand thisinterplay in the superconducting state. ACKNOWLEDGMENTS
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