Correlation between charge density waves and antiferromagnetism in Nd 1−x Gd x NiC 2 solid solution
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Correlation between charge density waves and antiferromagnetismin Nd − x Gd x NiC solid solution Marta Roman, Tomasz Klimczuk, Kamil K. Kolincio
Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland
We report a study on the evolution of a charge density wave and antiferromagnetism in the seriesof the polycrystalline solid solution Nd − x Gd x NiC (0 ≤ x ≤
1) by means of magnetic and transportproperties measurements. The experimental results reveal the violation of the de Gennes law and astrong correlation between the Peierls, N´eel and Curie-Weiss temperatures, which strongly suggests acooperative interaction between the charge density wave state and antiferromagnetism due to Fermisurface nesting enhancement of the RKKY interaction. We also find that, the obtained results forthe Nd − x Gd x NiC (0 ≤ x ≤
1) series overlap with the T CDW trend line in the phase diagram forRNiC family. I. INTRODUCTION
Quasi low-dimensional systems offer a large variety ofunique physical properties such as charge density wave(CDW) or spin density wave (SDW) instabilities . Thelow dimensionality of the electronic structure is also seenas an important ingredient of high temperature super-conductivity (SC) and the charge density wave state hasbeen found to be universal feature in the phase diagramsof the cuprate superconductors family . For this rea-son, the interplay between various types of ordering suchas CDW, SC and magnetism is a central issue in solidstate physics . The rich phase diagram of the low-dimensional rare earth nickel dicarbides RNiC in whichvarious ground states such as ferromagnetic (FM), anti-ferromagnetic (AFM), superconducting and charge den-sity wave states have been reported so far, makes themembers of this family appropriate candidates for theinvestigation of the relations between numerous types ofordering. The ground state of the members of this fam-ily depends on the rare-earth metal component denotedby R. LaNiC is a noncentrosymmetric superconductorbelow T sc =2.7 K , SmNiC undergoes a ferromag-netic transition at T C =17.5 K and the rest of the com-pounds (apart from Pr where a weak magnetic anomaly isobserved ) order antiferromagnetically . In thissystem, the magnetic order originates entirely from the4 f electrons of the rare earth ions R acting as localmagnetic moments interacting through the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. The CDWstate has been found for most of the members of theRNiC family (R = Pr - Lu) with the temperature rang-ing from 89 K for PrNiC to 463 K for LuNiC . Re-markably the Peierls temperature T CDW and the lock-intransition temperature T have been found to scale lin-early with the unit-cell volume for R ranging from Smto Lu . This effect has been tentatively attributed tothe evolution of the Fermi surface (FS) topology result-ing in the modification of the nesting conditions. Inter-estingly, the Peierls temperature for Nd and Pr bearingcompounds deviates from the linear trend observed forthe rest of the family.The CDW in RNiC has been found to interact with the magnetic state. For SmNiC , the Peierls instability iscompletely suppressed below the Curie temperature ,in contrast with PrNiC , where the magnetic anomalyhas been found to have a constructive impact on thenesting properties . In the compounds showing an-tiferromagnetic ground state, a CDW partially survivesbelow the N´eel temperature . Recently Hanasakiet al. suggested that the AFM order originates fromthe cooperative effect involving a CDW and spin oscilla-tions. These reports inspired us to explore the evolutionof a CDW instability and magnetism on the path betweenNdNiC and GdNiC , both exhibiting an antiferromag-netic ground state and standing on opposite sides of thedeviation from the linearity on the RNiC phase diagram.In this paper we report a detailed investigation on thesolid solution Nd − x Gd x NiC (0 ≤ x ≤
1) by means ofpowder X-ray diffraction, AC and DC magnetic suscepti-bility and electrical resistivity. The results were discussedwith a particular emphasis on the interrelationship be-tween a CDW state and antiferromagnetic ordering.
II. EXPERIMENTAL
The series of the polycrystalline Nd − x Gd x NiC solidsolutions for Gd concentration 0 ≤ x ≤ ≈ ≈ o C for 12 days and cooled down to roomtemperature by quenching in cold water. Overall loss ofweight after the melting and annealing process was negli-gible ( ≤ c)b) a ( ¯ ) b ( ¯ ) c ( ¯ ) x nom. in Nd Gd x NiC
33 34 35 36 37 38 39 40 41 Nd Gd NiC NdNiC ( deg) GdNiC
20 30 40 50 60 70
NdNiC x=0.2 x=0.4 x=0.6 x=0.8 ( deg) N o r m a li z ed i n t en s i t y x=0.9 x=0.1 x=0.3 x=0.5 x=0.7 GdNiC a) Nd Gd x NiC FIG. 1. a) Powder X-ray diffraction (pXRD) patterns for the series Nd − x Gd x NiC (0 ≤ x ≤ − x Gd x NiC . Arrows indicate the peaks corresponding to residual carbon content. b) Expanded view ofthe main reflection line (111) showing a shift towards higher angles by substituting Gd for Nd. Open circles denote experimentalpoints, whereas calculated diffraction patterns are represented by the solid blue lines. Differences between experiment and amodel are shown by the red lines. c) Change of a , b and c lattice parameters for the series Nd − x Gd x NiC (0 ≤ x ≤ X’Pert PRO-MPD, PANalitycal diffractometer with CuK α radiation, in the 2 θ range from 20 o to 75 o . Thelattice parameters were determined from a LeBail pro-file refinement of X-ray diffraction patterns for the en-tire Nd − x Gd x NiC series executed using FULLPROFsoftware .The physical property measurements were performedin the temperature range of 1.9-300 K by using a commer-cial Physical Property Measurement System (QuantumDesign). Magnetization measurements were carried outusing the AC and the DC Susceptibility Option (ACMS).A standard four-probe contact configuration was used tomeasure the electrical resistivity and the platinum wires( φ = 37 µ m) were attached to the polished samples byspot welding. III. RESULTS AND DISCUSSION
The phase composition and crystallographic structureof the obtained samples were checked at room temper-ature by powder X-ray diffraction which revealed thatall observed reflections for the Nd − x Gd x NiC (0 ≤ x ≤
1) series are indexed in the orthorhombic CeNiC -typestructure with the space group Amm
2. The pXRD pat-terns for Nd − x Gd x NiC solid solutions are presented in Fig. 1 a). Only for the x=0.8 and x=1 samples, ad-ditional weak reflection lines (marked by arrows) corre-sponding to residual carbon content are observed. Thesubstitution of Nd with Gd does not change the crystalstructure symmetry. However, one can observe that theBragg reflection lines are shifted towards higher angleswith an increase in the Gd content (shown in Fig.1 b)).This behavior is consistent with Gd having a smallerionic radius than Nd and confirms successful chemicalalloying.The unit cell parameters determined from LeBail re-finement for the parent compounds NdNiC and GdNiC were found to be: a = 3.783(1) ˚A, b = 4.536(1) ˚A, c =6.129(1) ˚A and a = 3.647(1) ˚A, b = 4.514(1) ˚A, c =6.069(1) ˚A, respectively. These values are in good agree-ment with those reported in the literature . The refinedlattice parameters for the intermediate samples from theNd − x Gd x NiC series are shown in Fig.1 c). The a , b and c parameters decrease linearly with an increase inthe Gd concentration for the whole x range, and henceobey Vegard’s law. The a constant expands by almost4% wheras the changes of the b and c parameters are lesspronounced (below 1%). The smallest change is observedfor the b parameter, which could be associated with rigidthe C-C dimers along the b axis .The electrical resistivity for the Nd − x Gd x NiC (0 ≤
80 100 120 140 160 180 200 2200.40.50.60.70.80.91.0 x=0x=1 Nd Gd x NiC x=1 x=0.9 x=0.8 x=0.7 x=0.6 x=0.5 x=0.4 x=0.3 x=0.2 x=0.1 x=0 / K T (K) x=1 x=0.8 x=0.6 x=0.4 x=0.2 x=0 / K T (K)
FIG. 2. Temperature dependence of the normalized electricalresistivity ρ/ρ K (T) for Nd − x Gd x NiC (0 ≤ x ≤ x ≤
1) series was measured without an applied magneticfield in the temperature range 1.9 – 250 K and the results( ρ/ρ K vs. T) are shown in Fig. 2. The whole seriesexhibits typical metallic behavior at high temperaturesshowing a decrease of the electrical resistivity with de-creasing temperature. With further cooling, a minimumfollowed by a hump well known to be a characteristicfeature of a charge density wave transition, is observedfor the entire concentration of Gd in the Nd − x Gd x NiC series. The temperature of the CDW formation ( T CDW )was obtained from the temperature derivative of the re-sistivity ( dρ/dT ) and for the parent compounds NdNiC and GdNiC , T CDW is 130 K and 197 K, respectively.The inset of Fig. 2. shows the expanded view of the nor-malized electrical resistivity in the vicinity of the CDWtransition for selected Nd − x Gd x NiC samples. With theincrease in the Gd concentration, the temperature of theCDW transition ( T CDW ) for the Nd − x Gd x NiC seriesstarts to decrease from 130 K for x = 0 (purple spheres),reaching a minimum of 123 K for the Gd concentration x= 0.2 (blue spheres) and then increases more rapidly witha further increase of Gd up to 197 K for x = 1 (brownspheres). Upon further cooling, the electrical resistivityfor the whole series continues to decrease until the visibledrop in resistivity at low temperatures. For GdNiC andNdNiC this effect has been reported to be caused byan antiferromagnetic transition, and therefore it is rea-sonable to expect the same behavior for the intermediatecompounds.The temperature dependence of the magnetic suscep-tibility χ (T) for the Nd − x Gd x NiC (0 ≤ x ≤
1) seriesmeasured with a µ H = 1 T applied magnetic field isdepicted in Fig. 3 a) (shown only for selected samplesfor better clarity). At high temperatures the entire seriesshows paramagnetic behavior. Between 16 K and 22 K(depending on x ), χ ( T ) reveals a sharp maximum. The N´eel temperature ( T N ) was estimated as the maximumof the temperature derivative of the magnetic suscep-tibility multiplied by the temperature (d( χ T)/dT).The obtained T N values are in good agreement withthose determined from the resistivity measurement. Anadditional minimum followed by a further increase isobserved for most members from the Nd − x Gd x NiC series and can be attributed to a spin-flop transition asreported for the GdNiC compound . x=0 x=1 Nd Gd x NiC x=0 x=0.1 x=0.2 x=0.4 x=0.5 x=0.6 x=0.7 x=1 Curie-Weiss fit M ( e m u R - m o l - ) a)b) x=0 H=1 T ( M - ) - ( R - m o l e m u - ) T (K)x=1
FIG. 3. Temperature dependence of the molar magneticsusceptibility χ M (a) and of the reciprocal molar magneticsusceptibility ( χ M - χ ) − (b) for selected samples from theNd − x Gd x NiC (0 ≤ x ≤
1) series.
Above T N , the entire series obeys the Curie-Weisslaw. The χ (T) were fitted using the Curie-Weiss lawexpression: χ ( T ) = CT − θ CW + χ (1)where C is the Curie constant, θ CW is the Curie-Weisstemperature and χ is the temperature independentmagnetic susceptibility which is related both to thesample and the sample holder (a small diamagneticcontribution from sample straw). An exemplary fit tothe data is shown with a solid line in Fig. 3. The resultsof the magnetic susceptibility with a clear magneticanomaly at T N were also presented as a function ofthe reciprocal magnetic susceptibility with temperature( χ M - χ ) − vs. T in Fig. 3 b). Above the AFMtransition temperature, all ( χ M - χ ) − plots show anapproximate linear dependence.Having determined the value of the Curie constantC from the Curie-Weiss fit, the effective magneticmoment µ eff was calculated for each compound of theNd − x Gd x NiC series using the formula: µ eff = s Ck B µ B N A (2)where k B is the Boltzmann constant, N A is the Avogadronumber and µ B is the Bohr magneton.The Curie-Weiss temperature and the effective mag-netic moment versus Gd concentration ( θ CW ( x ) and µ eff ( x )) are presented in Fig. 4 a) and b), respectively.Estimated θ CW for GdNiC denotes -18.85 K and standsin good agreement with previously reported values .The θ CW = -22.93 K obtained for NdNiC is howevervisibly different from the value reported by us previously(-5.9 K) . The θ CW in this compound has been foundvery sensitive to the direction of magnetic field and varyfrom -17.8 K along b axis to 24.6 along a axis . The in-consistency with our last results can then be attributed toa difference in the samples microstructure. The negativesign of the Curie-Weiss temperature indicates antiferro-magnetic fluctuations. Upon the crossover from NdNiC to GdNiC , the θ CW initially shifts towards less negativevalues and reaches a maximum for the intermediate com-pound Nd . Gd . NiC ( θ CW = - 1.35 K). The proximityto zero suggests the weakness of the magnetic interactionsbetween magnetic ions. With a further increase of the Gdconcentration, θ CW becomes more negative again, whichis a signature of the enhancement of antiferromagneticinteractions. For x = 0.9, a deviation from the curve isobserved and the origin of this anomaly is unknown.In the RNiC family, nickel atoms do not contributeto the magnetic moment and the magnetic ordering orig-inates only from the 4 f electrons of rare earth ions R .The effective magnetic moments of the parent compoundsdetermined from the Curie-Weiss fit, ( µ eff = 4.11 µ B and 8.66 µ B for NdNiC and GdNiC , respectively) arelarger than the values expected for free R ions (3.62 µ B for Nd and 7.94 µ B for Gd ) but close to the val-ues reported previously . The change of the effectivemagnetic moment with increasing level of the Gd con-centration µ eff (x) could be considered as linear with asmall deviations for the parent compounds (NdNiC andGdNiC ). This result is consistent with what can beexpected from electron introduction when Gd (4 f ) re-places Nd (4 f ) and the deviation from linearity couldbe caused by a disorder effect introduced by doping. -25-20-15-10-50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0456789 Nd Gd X NiC C W ( K ) a) x nom. in Nd Gd x NiC b) e ff ( B R - m o l - ) FIG. 4. Change of the Curie-Weiss temperature θ CW (a) andeffective magnetic moment µ eff (b) for Nd − x Gd x NiC (0 ≤ x ≤ The de Gennes law describing the strength of theindirect exchange coupling between local moments pre-dicts that, for the systems in which the magnetic groundstate originates from the RKKY interaction, the N´eeltemperature is expected to be related to the bulk elec-tronic density of states at the Fermi level N ( ǫ F ) withrelationship: T N ∼ N ( ǫ F ) k B I dG (3)where k B is the Boltzmann constant and I is the ex-change integral. The de Gennes factor ( dG ) is given bythe formula: dG = ( g J − J ( J + 1) (4)where g J is the Land´e factor and J is the total an-gular momentum of the R ion following Hund’s rulein the ground state. The effective dG factor forthe Nd − x Gd x NiC solid solutions was calculated as aweighted average of the two elemental dG factors: dG eff = (1 − x ) dG Nd + ( x ) dG Gd (5) Nd Gd x NiC RNiC La/Lu DyHoErTm GdTbNdCe T N ( K ) dG FIG. 5. The N´eel temperature as a function of de Gennesfactor for RNiC family, including Nd − x Gd x NiC solid solu-tion. Fig. 5 depicts de Gennes scaling for the members of theRNiC family exhibiting an AFM transition, includingNd − x Gd x NiC studied in this paper. A clear deviationfrom the expected de Gennes trend indicates that thebulk RKKY interaction is not essential to describe themagnetic transition in Nd − x Gd x NiC and other factorshave to be considered. Previously, the breakdown of the dG scaling for TbNiC has been explained by the influ-ence of the crystalline electric field (CEF) . This sce-nario could be relevant in the case of Nd − x Gd x NiC ,since the deviation from the dG scaling is visibly en-hanced with an increase of the Nd content. This typeof crossover can be expected based on the behavior ofthe parent compounds: GdNiC shows negligible CEF ,while the crystalline field plays a more important role inNdNiC . One must however find, that the violationof the de Gennes law being observed for NdNiC is no-tably more pronounced than the deviations from the dG scaling seen for Er and Tm bearing compounds. This ob-servation stands in contrast with the comparison of thevalues of the CEF parameters A and A reported forthese three compounds, which for NdNiC are an orderof magnitude lower than for ErNiC and TmNiC .For that reason, the alternative mechanisms have to betaken into account to explain this unusual effect.According to equation 4, in the discussion of T N be-havior one must also consider the role of the density ofstates, which is expected to be modified upon undergoinga Peierls transition inducing the opening of the electronicgap at the Fermi level and condensation of the free elec-tronic carriers into the CDW state.In Fig. 6 we compare the CDW transition temperature T CDW (panel a) and the N´eel temperature T N (panel b)plotted against the values of the Gd concentration in theNd − x Gd x NiC (0 ≤ x ≤ Nd Gd x NiC T CD W ( K ) T N ( K ) x nom. in Nd Gd x NiC
105 104 103 102 101 100
V ( ¯ ) FIG. 6. Evolution of T CDW (a) and T N (b) as a function ofGd concentration x nom. in the Nd − x Gd x NiC (0 ≤ x ≤ acter of the evolution of these transition temperatures issimilar and reminiscent of the behavior of θ CW ( x ) - bothcurves reveal minimum with the composition correspond-ing to x = 0.3.The correlation between the T CDW and T N suggests astrong interrelationship between the charge density wavestate an antiferromagnetism. According to the de Gennestheory, one would expect a negative coupling, since theCDW transition decreases the N ( ǫ F ), thus, according toeq. 3, the CDW should have a negative impact on themagnetic interactions. The stronger effect is expectedto occur when the Peierls temperature is higher and theelectronic gap is increased. In the mean field approach ,these quantities are correlated by:2∆ = 3 . k B T CDW (6)Nevertheless, one should not underestimate the roleplayed by the Fermi surface nesting vectors. As estab-lished from both theoretical predictions and experi-mental results , in the case of a non-trivial topologyof the Fermi surface, the RKKY interaction becomes sen-sitive to the delicate character of the nesting conditions.The direct link with the FS curvature makes the RKKYinteraction strongly anisotropic and leads to the devia-tions from the simplistic isotropic approach expressed byequation 3. The common aspect of the FS nesting andmomentum dependent RKKY interaction lies in the factthat both phenomena are associated with the generalizedelectron (spin) susceptibility represented by the Lindhardfunction : χ ( q ) ∼ X k f k + q − f k ǫ k + q − ǫ k (7)where f k is the Fermi distribution function and ǫ k de-notes for the energy corresponding to the state withwavevector k . The course, or more strictly, the maxi-mum or a singularity of χ ( q ) leading to the nesting ofthe Fermi surface can significantly enhance the strengthof the indirect interaction between the magnetic mo-ments. Simultaneously the Fermi surface nesting is acommon feature associated with the formation of chargedensity waves . The same Lindhard function deter-mines the energy gain from the electronic part of theCDW. Thus, this function often plays a decisive role forthe preferred q vector of the CDW modulation , whichin most CDW systems is identical with the FS nestingvector. The anisotropic RKKY interaction is thereforesignificantly enhanced in the specific reciprocal space di-rections, when the magnetic propagation vector coincideswith the values of q corresponding to the maximum of χ ( q ), consistent with the CDW modulation. The ex-perimental evidence for such nesting enhanced behaviorhas been reported for Gd PdSi , Tb PdSi , GdSi ,Yttrium or Gd-Y alloys . The CDW modulation vec-tors for NdNiC and GdNiC defined from X-ray diffusescattering experiment, respectively q Nd = (0.5, 0.52, 0) and q Gd = (0.5, 0.5, 0) have also been theoreticallypredicted as genuine FS nesting vectors . These vec-tors stand in agreement with the wavevectors describingthe AFM order (0.5, 0.5, 0) observed for NdNiC and proposed for GdNiC . It is reasonable to assumethat this coincidence is relevant also for the solid solu-tions between NdNiC and GdNiC , giving rise to anenhancement of the AFM order due to a cooperative ef-fect with FS nesting accompanying the Peierls instability.The scenario of affirmative coupling between the CDWand magnetism in these systems is also supported by therecent work of Hanasaki et al. , who suggested that theorigin of the antiferromagnetic ground state in GdNiC lies in the spin density wave constructed upon the preex-isting CDW. In this model, the charge density modulatedas a result of the Peierls instability is composed of twodistinct spin-up and spin-down charge distributions andwhile the presence of strong magnetic moments producesa phase shift between them, the periodical spin densitymodulation is formed, giving rise to the enhancement ofantiferromagnetic coupling between local f moments.The values of T CDW and T N determined in this workhave been imposed on the phase diagram of the RNiC family, shown in Fig. 7 as a bright green region. It FIG. 7. Phase diagram of the RNiC family includingNd − x Gd x NiC (0 ≤ x ≤
1) solid solution. Upper panel (a)shows the variation of the Peierls ( T CDW ) and lock-in ( T )temperatures with the unit cell volume .Lower panel (b) depicts the magnetic groundstates with theircharacteristic temperatures: T N (N´eel), T C (Curie) and T M for the paramagnetic anomaly (PA) observed in PrNiC . T SC marks the onset of superconductivity for LaNiC . can-not escape from the viewer’s eye that, these resultsconverge with the trend line T CDW ( V ) and T N ( V ) forRNiC . It is visible that near the point correspondingto SmNiC , the charge density wave temperature scal-ing starts to deviate from linearity. Our results (see Fig.3) reveal the AFM ground state of all the studied com-pounds from the Nd − x Gd x NiC series, even those in aclose proximity to SmNiC , which is a ferromagnet. Toconfirm the genuine AFM character of the magnetic tran-sitions of the Nd − x Gd x NiC series , we have measuredthe M vs. H (not shown here) indicating that no fer-romagnetic ground state exists below T N . Additionally,in contrast to SmNiC which shows a rapid drop in re-sistivity below the magnetic transition temperature dueto complete destruction of CDW and release of the elec-tronic carriers , a less abrupt decrease of the ρ ( T )curve is seen for Nd − x Gd x NiC series. The behavior ofthe solid solutions is reminiscent of the features reportedfor parent Nd and Gd bearing compounds. In NdNiC and GdNiC , the CDW state partially survives the AFMtransition and the similarity between the parent com-pounds and their solid solution suggests the identity ofthe observed mechanisms. IV. CONCLUSIONS
In this article we have examined the transport andmagnetic properties of the Nd − x Gd x NiC (0 ≤ x ≤ towards GdNiC . The variation of the Peierlstemperature of Nd − x Gd x NiC as a function of the unitcell volume covers suitably the deviation from the lineartrend observed in the previous study. We also report the breakdown of the de Gennes scaling in the studied series.The results are discussed in terms of the electric crystalfield and indirect Ruderman-Kittel-Kasuya-Yosida inter-action between local magnetic moments. The correla-tion between the Peierls, N´eel and Curie-Weiss tempera-tures suggests a strong coupling between the Fermi sur-face nesting and the antiferromagnetic ground state, de-scribed by the compatible wavevectors. We also suggestthat this hypothesis can be confirmed by angle-resolvedphotoemission spectroscopy (ARPES) experiment per-formed on single crystals. ACKNOWLEDGMENTS
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