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Ferromagnetic behavior of the Kondo lattice compound Np2PtGa3

V. H. Tran,1 J. -C. Griveau,2 R. Eloirdi,2 and E. Colineau2

1Institute of Low Temperature and Structure Research,Polish Academy of Sciences,

P. O. Box 1410, 50-950 Wroc law, Poland2 European Commission, Joint Research Centre,

Institute for Transuranium Elements,Postfach 2340, D-76125 Karlsruhe, Germany

In this study we report the results of study of novel ternary Np2PtGa3 compound. The x-ray-powder diffraction analysis reveals that the compound crystallizes in the orthorhombic CeCu2-typecrystal structure (space group Imma) with lattice parameters a = 0.4409(2) nm, b = 0.7077(3) nmand c = 0.7683(3) nm at room temperature. The measurements of dc magnetization, specific heatand electron transport properties in the temperature range 1.7 - 300 K and in magnetic fields upto 9 T imply that this intermetallic compound belongs to a class of ferromagnetic Kondo systems.The Curie temperature of TC ∼ 26 K is determined from the magnetization and specific heat data.An enhanced coefficient of the electronic specific heat of γ = 180 mJ/(mol at. Np K2) and -lnTdependence of the electrical resistivity indicate the presence of Kondo effect, which can be describedin terms of the S = 1 underscreened Kondo-lattice model. The estimated Kondo temperature TK ∼

24 K, Hall mobility of ∼ 16.8 cm2/Vs and effective mass of ∼ 83 me are consistent with assumptionthat the heavy-fermion state develops in Np2PtGa3 at low temperatures. We compare the observedproperties of Np2PtGa3 to that found in Np2PdGa3 and discuss their difference in regard to changein the exchange interaction between the conduction and localized 5f electrons. We have used theFermi wave vector kF to evaluate the Rudermann-Kittel-Kasuya-Yosida (RKKY) exchange. Basedon experimental data of the (U, Np)2(Pd, Pt)Ga3 compounds we suggest that the evolution of themagnetic ground states in these actinide compounds can be explained within the RKKY formalism.

PACS number(s): 71.27.+a, 75.20.Hr, 75.30.-m

I. INTRODUCTION

f-electron intermetallics exhibit a variety of exoticphenomena including non-Fermi liquid behavior, heavy-fermion, unconventional superconductivity, etc.. Never-theless, their magnetic nature remains still unresolvedissue due to the complexity of different interactions andthe interplay with Kondo effect. In order to charac-terize complex phenomena, in parallel with theoreticalresearch, experimentally comparative study of physicalproperties of the intermetallics can often be undertaken.Exemplary investigations are just these on various seriesof 5f-electron intermetallics (see [1]). One of the mostimportant conclusions is that 5f-ligand hybridization isthe principal mechanism determining the magnetic order,and it causes the compounds with light actinides (U, Np)to have a narrow 5f band at the Fermi level. Furthermore,the 5f electrons in Np-based compounds have usually lessitinerant character than those in the corresponding Uones. Results of our systematic studies on 213-type sto-ichiometric compounds U2TGa3 (T = d-electron tran-sition metals),[2] U2(Pd, Pt)Ga3,[3] and Np2PdGa3,[4]have indicated that the degree of the 5f localization fol-lows the general trend in actinide intermetallics men-tioned above. In the recent work [4] we have discov-ered that Np2PdGa3 is a ferromagnetic Kondo lattice(FKL). The occurrence of a ferromagnetic ground statein this compound was explained with help of an oscil-lating character of the Rudermann-Kittel-Kasuya-Yosida

(RKKY) interaction. What more renders Np2PdGa3 aninteresting intermetallic compound is i) a competition of,at least, three different types of interactions - Kondo ef-fect, RKKY and crystal electric field (CEF), representedby an energy relationship TK < TRKKY ∼ ∆CEF , ii) fer-romagnetic Kondo lattice with considerably enhanced ef-fective mass of the charge carriers and iii) atomic disorderenabling to form random magnetic interactions. In viewof the difference in the d-electron numbers and covalentradii between Pd and Pt atoms involved in compounds,it is of interest to study a compound Np2PtGa3, aim-ing to make a comparative investigation of the magneticand electronic properties of these Np-based 213-type in-termetallics. It was the original purpose of this paperto report the synthesis and crystallographic characteri-zation, as well as to present the results of magnetic, spe-cific heat and electron transport measurements of a novelNp2PtGa3 compound.

Our measurements of bulk properties (see below) showthat Np2PtGa3 orders ferromagnetically at 26 K. Addi-tionally, the coefficient of the electronic specific heat ofγ = 180 mJ/(mol at.Np K2) is sizeably enhanced, to-gether with -lnT dependence of the electrical resistivity,classifying Np2PtGa3 to belong to relatively rare fam-ily of ferromagnetic Kondo lattices. It is worthwhile tomention that the coexistence of ferromagnetic order andKondo effect is most frequently found in Ce-based, [5-11] or U-based systems, [12-16] but much rarer in Np-compounds, since only two compounds NpNiSi2,[17] and

2

Np2PdGa3,[4] were reported so far. Moreover, it seemsthat there should be different approaches to ferromag-netic Kondo problems as regards to particular values ofspin angular momentum S of systems. For S = 1/2 sys-tems of the Ce-based compounds, both ferromagnetic or-der and Kondo effect are governed by the s - f exchangeinteraction between the localized S = 1/2 spins and theconduction electrons. Due to the competition of mag-netism and Kondo effect, the magnetic ordering of theS = 1/2 systems appears at relatively low temperatures(less than 10 K), and the systems can be nonmagneticif the localized moments are completely screened by theconduction electrons.[18] Otherwise, in the U- and Np-based compounds with 5fn, n = 2 or 3 electrons, theselarger spins (S ≥ 1) are partially screened by the con-duction electrons only. Appropriately, it is intuitivelyexpected that the coexistence of the Kondo effect andferromagnetic order may yield a high Curie tempera-ture. In fact, hitherto TC in the ferromagnetic U andNp-based Kondo lattices was reported to attain valuesbetween 50 and 100 K, i.e., of one order of magnitudelarger than those in the Ce-based compounds. In or-der to interpret the Kondo effect in the actinide ferro-magnets, Coqblin and coworkers. developed so-calledunderscreened Kondo lattice (UKL) model.[19, 20] Re-cently, the authors have obtained results for the case,where the Kondo temperature is smaller than the Curietemperature, and have compared to several bulk proper-ties of NpNiSi2, like magnetization, electrical resistivityand specific heat.[21] Therefore, it is very encouraging tostudy Np2PtGa3, not only as the physical properties canbe systematically investigated in the isostructural 213-type stoichiometric group, but also Np2PtGa3 as a newmember of FKL and it serves to test theoretical models.

II. SAMPLE PREPARATION ANDCHARACTERIZATION

A polycrystalline sample of Np2PtGa3 (0.5 g) was syn-thesized from high-purity elements Np 3N, Pt 4N, andGa 6N by arc-melting under Ti-gettered argon purifiedatmosphere. To improve homogeneity, the sample wasturned over and remelted several times. The ingot waswrapped in Ta foil and was annealed at 800 C for 14days in evacuated quartz tube. The weight loss dur-ing the preparation was less than 0.5 %. The quality ofthe sample was characterized by standard x-ray powderdiffraction. The analysis of the x-ray diffraction patternrevealed that the majority phase (> 95 mass. %) has theorthorhombic CeCu2-type structure, isostructural withU2(Pd,Pt)Ga3,[3] and Np2PdGa3.[4] Refinement of crys-tal structure of Np2PtGa3 based on 63 observed Braggreflections was done with the Rietveld method usingFullprof programm.[22] The Bragg reflections were fittedwith Pseudo-Voigt function profile and the final refine-ments converged at R-factor = 1.016 and RF-factor =0.6762. We obtained lattice parameters a = 0.4409(2)

nm, b = 0.7077(2) nm and c = 0.7683(3) nm. A compar-ison to the lattice parameters of Np2PdGa3 (a = 0.4445,b = 0.7089 and c = 0.7691 nm,[4]) discloses that the unitcell volume of the studied compound shrinks by 1 % rela-tive to that of Np2PdGa3. Impurity phases present in oursample were identified to be NpO2 (a = 0.5433 nm, cubicstructure with Fm-3m space group) and NpPtGa (a = b= 0.6733, c = 0.3837 nm, hexagonal ZrNiAl-type struc-ture with space group P6-2m). In the literature, NpO2

was reported to undergo into an electric quadrupole statebelow T0 =25 K,[23] whereas no information about themagnetic ground state of NpPtGa is available.

III. PHYSICAL PROPERTIES

A. Magnetic susceptibility and magnetization

Dc magnetization (M ) measurements were carried outin the temperature range 1.72 - 300 K and in magneticfields up to µ0H = 7 T, using a commercial QuantumDesign SQUID magnetometer. The Np2PtGa3 samplewas encapsulated in a specially designed sample holder.The response of the holder for magnetization was mea-sured separately before inserting the sample and thensubtracted from measured raw data. It turned out thatthe magnetic susceptibility, defined as χ = M/H , ofNp2PtGa3 above 80 K is independent of applied mag-netic fields and has a value of 3.26 × 10−3 emu/(molat. Np) at room temperature. Fig. 1 shows the temper-ature dependence of the inverse magnetic susceptibilityobtained in a field of 7 T. The high-temperature datawere fitted with the modified Curie-Weiss law χ(T ) =χ0 + NAµ

2eff/[3kB(T − θp)], where NA is the Avogadro

number and kB is the Boltzmann constant. The fityields the temperature independent susceptibility χ0 =1.04(0.05)×10−3 emu/(mol at. Np), effective momentµeff = 2.28 ± 0.1 µB/Np and paramagnetic Curie tem-perature θp = 33 ± 1 K. The temperature indepen-dent term χ0 usually accounts for the Pauli-type andVan Vleck paramagnetic susceptibilities. In the case ofNp2PtGa3, a large value of χ0 points to significant con-tribution of the conduction electrons to the density ofstates. After subtraction of χ0, the susceptibility dataof Np2PtGa3 (triangle symbols in Fig. 1) exhibit theCurie-Weiss behavior, indicative of the localized char-acter of the 5f electrons. However, in comparison withthe theoretical value of 2.68 µB/ Np for the electronicconfiguration 5f4 in the Russell-Saunders coupling, theobserved µeff value is noticeably reduced. This meansthat the 5f electrons are partly delocalized, presumablydue to a strongly electron correlation effect, such asthe hybridization of the 5f- with the conduction elec-trons and/or Kondo screening by the conduction elec-trons. The observed large and positive paramagneticCurie temperature indicates a dominant ferromagneticexchange interaction between the magnetic Np momentsin Np2PtGa3. This interaction becomes stronger with

3

decreasing temperature and finally causes an anomaly atlow temperatures. As shown in the inset of Fig. 1, mag-netization measurements at µ0H = 0.02 T under bothzero-field-cooled (ZFC) and field-cooled (FC) conditionsyield a broad maximum at Tmax = 24 K. Above Tmax themagnetization curves have the same temperature depen-dencies, but below this temperature the curves separatefrom each other leading to the occurrence of irreversiblemagnetization.

To gain an information about the magnetic groundstate, measurements of iso-field magnetization for se-lected fields in the temperature range 1.72 - 60 K as wellas isothermal magnetization for several temperatures infields up to 7 T were carried out. The left panel ofFig. 2 shows the experimental iso-field data. It is ob-served that the maximum of M(T) broadens upon ap-plication of higher field strengths and its precise posi-tion becomes hardly determined for fields larger than 5T. In such large magnetic fields no more maximum oc-curs in the MFC(T )-curves. Instead, a plateau formsin the low temperature range. It is worthwhile to dis-tinguish two characteristic temperatures Tir and Tinf ,which are obviously dependent on the applied fields. Tir

symbolizes the temperature where the irreversibility ofmagnetization sets in, whereas Tinf is defined as theminimum of the temperature derivative of the magne-tization. As shown in the right panel of Fig. 2, Tir

shifts down to lower temperatures, while Tinf moves up-ward to higher temperatures. These features resemblethe behavior of spin glasses,[24,25] ferromagnets with alarge magnetocrystalline anisotropy,[26] or with a ran-dom magnetic anisotropy, canted ferromagnets or anti-ferromagnets with competing antiferromagnetic and fer-romagnetic interactions.[27,28]

Figure 3 shows isothermal magnetization data at sev-eral temperatures up to 50 K. Concerning the 2 K-data,there is no saturation even in a high magnetic field of7 T. The tendency towards saturation of the magnetiza-tion suggests to invoke the local and magnetocrystallineanisotropy in the estimation of the saturated momentMs. From fitting of the 2 K-magnetization data to theformula: [29]

M(H) = Ms + a/H + b/H2, (1)

where the terms a/H and b/H2 correspond to the localand magnetocrystalline anisotropy, respectively, we ob-tain Ms = 0.9 µB/Np. This value is considerably reducedif compared to the theoretical value 2.4 µB for Np3+. Thefinding may imply an influence of the Kondo-type screen-ing of the conduction electrons on the localized magneticNp moments.

The magnetization data obtained below 10 K presentedin Fig. 3 a remark a sharp kink at a critical field Hcr,resembling the behavior of the metamagnetic transition.The simplest assumption to reconcile this metamagnetic-like transition is the spin flip transition in an antifer-romagnetic structure formed by magnetic Np moments.The other way to understand the magnetization behavior

is to assume the effect of magnetocrystalline anisotropy.Indeed, we determined values of Hcr as the peak of thefield derivative of the magnetization (see bottom panelof Fig. 3), which do not depend regularly of the ap-plied magnetic fields. In fact, Hcr attains its maximumvalue at T = 5 K, pointing rather to domain-wall motionand different types of magnetic anisotropy, than due toa change in the spin configuration affected by magneticfields. Moreover, the metamagnetic-like transition is ob-served only for increasing applied fields. During decreas-ing fields, there appears considerable hysteresis and re-manent magnetization. This behavior is consistent withthe irreversibility of magnetization observed below Tir

giving support for magnetocrystalline effect present inferromagnets.

The magnetization measurement at 25 K (see dM/dHin Fig. 3 b) indicates that the magnetic moment of Np3+

does not vanish yet. Above this temperature, e.g., at50 K the M(T) curve shows neither metamagnetic-liketransition, hysteresis nor remanence, that is typical forthe paramagnetic state.

In Fig. 4, we plot M2 as a function of H/M , so-calledArrott plot, for selected data obtained during decreas-ing applied magnetic fields. It is observed that the slopeof the M2(H/M) -curves is positive and the extrapola-tion of the 25 K-data yields the intercept close to zeroµB. These features serve as a convincing evidence for aferromagnetic order in Np2PtGa3 with the Curie temper-ature of approximately TC ∼ 25 K. The plot gives a lowremanent magnetization at 2 K ( ∼ 0.37 µB/Np ), whichwould suggest a small value of the ordered moment.

It is worthwhile to recall that the magnetic behav-ior of NpO2, which was identified as an impurity in thestudied sample, is unable to account for the magneticanomalies observed here. Since, NpO2 exhibits multi-polar order at 25 K, with a very small induced dipolarmagnetic moment and antiferromagnetic-like signaturesin bulk properties.[30-32]

B. Specific heat

Specific heat measurements were performed using the2-τ thermal relaxation method. The experiments wereconducted in the temperature range 1.8 - 300 K and inmagnetic fields up to 9 T, utilizing a commercial Quan-tum Design PPMS platform. The experimental data at0 T after correction for the addenda and sample holderare presented in Fig. 5. We have analyzed the high-temperature specific heat data, assuming the presence oftwo contributions: electronic and phononic. These con-tributions are described by the γHT coefficient and thehigh-temperature Debye temperature ΘHT

D , respectively.The lattice specific heat is expected to follow the Debyefunction:

Cph(T ) = 9Rn(T/ΘHTD )3

∫ ΘHT

D/T

0

x4exp(x)

[exp(x) − 1]2dx, (2)

4

where R is the gas constant and n is the number of atomsper formula unit. A fitting the specific heat data to thesum of Cph(T ) and γHTT yields ΘHT

D = 230 ±1 K andγHT = 5 ±0.5 mJ/(mol at.Np K2). The dashed lineshown in Fig. 5 is the result of the fit.

The temperature dependence of Cp(T ) in a low-enoughtemperature regime is usually expected to satisfy thestandard relation Cp(T ) = γT + βT 3 for metals, wherethe first term is the contribution of the conduction elec-trons and the latter is from the phonons. However, theCp/T data of Np2PtGa3 exhibit an upturn with decreas-ing temperature. It is seen also that the upward curva-ture of Cp/T shifts to higher temperature when a mag-netic field of 9 T is applied (see inset). Because the 237Npisotope with the nuclear moment µI =3.14 µN , may havesix nuclear energy levels ranging from I = -5/2 to 5/2,one can invoke the splitting of the nuclear ground-statelevel of the 237Np nuclei to explain the low-temperaturespecific heat of Np2PtGa3. Usually, the nuclear specificheat CN (T ) can be modeled with the Schottky specificheat CSch(T ). In a simple two-level system, CSch is givenby

CSch(T ) = R(ε

kBT)2(

g0g1

)exp( ε

kBT )

1 + g0g1

exp( εkBT )

, (3)

where g0 and g1 are the degeneracies of lower and upperlevels and ε/kB is an energy separation between theselevels. Taking into account the electronic, phononic andnuclear contributions, the low-temperature specific heatcan be written under the form:

Cp(T )/T = γ + βT 2 + CN/T. (4)

We fitted the specific heat data in the temperaturerange 1.8 - 5 K to Eq. [4] (see the inset of Fig. 5).As a result of the fitting we get ε/kB = 0.37 K in 0 Tand ε/kB = 0.40 K in 9 T. The splitting energy is asso-ciated with the hyperfine field Bhf via the relation:[33]

ε = R3kB

( I+1I )(gNµIµNBhf )2, where gN = 0.793 is the

gyromagnetic factor of 237Np. From the experimental εvalues we inferred the effective magnetic field Bhf = 214in zero applied field and 223 T in an applied field of 9T, corresponding to an ordered magnetic moment of ∼1 µB, if one assumes 1 µB = 215 T. As expected, thecoefficient β = 0.57 mJ/(mol at.Np K4) is independentof the applied magnetic field. From the β value and us-ing the formula: ΘD = [n12π4 R

5β ]1/3, we calculated the

low-temperature Debye temperature ΘD = 217 K, whichis in good agreement with that deduced from the high-temperature data. A remarkable result of our experimentis that the Sommerfeld coefficient γ = 180 mJ/mol.NpK2 is obtained from the fitting of the data in zero field,whereas γ = 186 mJ/(mol at. Np K2) from the data in 9T. The sizeably enhanced Sommerfeld coefficient mani-fests a strong correlation of the Np - 5f electrons and thisimplies that Np2PtGa3 can be classified to the class of theNp-based heavy-fermion compounds, like e.g., NpPd5Al2with γ = 190 - 200 mJ/(mol K2).[34]

A careful inspection of the experimental data shown inFig. 6 reveals an anomalous behavior of Np2PtGa3 asso-ciated with magnetic orders. We recognize two specificheat anomalies, at 26 K and 30 K, respectively. Fromthe temperature derivative of the ratio Cp(T )/T (see in-set of the figure), we suspect that the first transition isof the second-order while the latter is of the first-order.Based on the magnetic data and analysis of the specificheat data (see below) we suggest that the anomaly at26 K may be ascribed to a ferromagnetic order of the Npmoments. The broadened and smearing transition is pre-sumably due to disorder effects on magnetic interactions.Unfortunately, we have no explanation on the origin ofthe anomaly at 30 K, denoted as Ti. A comparison ofthe 0 T and 9 T data concludes that the application ofa magnetic field of 9 T has no influence on the positionof these anomalies. This fact could exclude spin-glasstype as an origin of the anomaly at 26 K. Concerning thefield dependencies of Tir and Tinf of the M(T) curves,two comments can be made. We cannot ascribe neitherTir(H) nor Tinf (H) to field dependencies of the mag-netic phase transition temperature TC . In our opinion,the reasons of the irreversibility Tir may be magnetocrys-talline anisotropy as we discussed earlier. On account ofTinf (H), we suspect it is due to the field-induced ferro-magnetic short-range correlations.

In Fig. 7 we show the temperature dependence of the5f-electron specific heat, which is obtained by the sub-traction of the nuclear, phononic and high-temperatureelectronic contributions from the total specific heat.Clearly, the specific heat jump in the C5f (T )/T at 30K is negligible and one reasonably ascribes to the con-tribution of an impurity. It appears that the C5f (T )/Texhibits a small jump at TC = 26 K, which may sup-port a long-range magnetic order in the studied com-pound. However, bearing in mind eventual contributionof impurity NpO2 phase possessing similar value of phasetransition temperature, we should take the data with cau-tion. When comparing the experimental data with thatreported for NpO2,[36,37] we see that for Np2PtGa3, thetransition at TC is rather broad, in contrast to very sharpin NpO2. Nonetheless, if NpO2 contributes to the mea-sured specific heat, then its content is of the order of 1 %of the investigated sample, since the specific jump at 26K in our sample is ∆Cmag/T = 0.88×10−2 J/(mol K2),compared to 0.86 J/(mol K2) found for NpO2 at 25.5 K.

We now consider the implications of the C5f (T )/Tdata, which exhibit a broad hump at about Tmax = 30K just above TC and a long tail above at higher tem-peratures. At first sight, it is likely that crystal elec-tric field splitting and/or short-range magnetic interac-tions contribute to the specific heat. If we assumed adoublet-doublet as possible CEF scheme and taking theposition of Tmax, we would expect a CEF splitting en-ergy ∆CEF /kB = 82 K. The CEF specific heat with such∆CEF /kB is illustrated as dotted line in Fig. 7. However,as can be seen, the contribution of such a CEF splitting ishard to reproduce fully the specific heat tail. Therefore,

5

it is possible that the 30 K - hump and heat capacity tailin Np2PtGa3 are due to the short-range magnetic correla-tions. The specific heat enhancement due to short-rangemagnetic correlations was studied theoretically, amongother researches, by Bonner and Fisher.[38]

Below TC , the 5f-electron specific heat consists, atleast, of two components Cmag and CK . The first is dueto the magnon excitations, being insignificant at temper-atures far below TC . Conversely, the second componentis supposing Kondo effect, which confers the large valueof the Sommerfeld ratio. This contribution is dominatingat low temperatures but decreases with increasing tem-perature. Within in the Coqblin-Schrieffer model, theKondo impurity problem has been numerically calculatedfor several angular momenta J by Rajan.[39] If we takethe Kondo temperature TK = 24 K and ground state J= 1/2 we may approximate the Sommerfeld ratio at lowtemperature, and then the Kondo specific heat CK(T )in Np2PtGa3, represented in Fig. 7 by the dashed line.Assuming that C5f (T ) = CK(T ) + Cmag(T ) we have ex-tracted the magnetic specific heat Cmag(T ) depicted inFig. 7 as closed circles. For data far below TC , we havefitted the Cmag(T ) data using the standard formula forthe magnon specific heat with an anisotropy energy gap∆ in magnon spectrum :

Cmag(T ) = αT 3/2exp(−∆/kBT ), (5)

where α is a constant. Fitting the experimental magneticspecific heat C5f (T ) with Eq. [5] gives α = 0.03 ± 0.006

J/(mol at. Np K5/2) and ∆/kB = 4.9± 0.2 K.The 5f-electron, magnetic and Kondo entropies are

calculated by integrating C5f (T )/T , Cmag(T )/T andCK(T )/T with respect to temperature and are plottedin the inset of Fig. 7 as solid, dotted and dashed lines,respectively. At TC , Smag(T ) reaches 4 J/(mol K), i.e.about 70 % of Rln2 - the expected value of the entropygain from a doublet ground state. The reduced magneticentropy can be attributed to the influence of the Kondoeffect.

C. Electron transport properties

Measurements of electron transport properties werecarried out by means of the standard ac four-probe tech-nique using a Quantum Design PPMS platform. Themeasurements were performed from 1.8 K to 300 K andin magnetic fields from -9 T to 9 T, with an excitationcurrent of j = 0.5 mA applied perpendicularly to the di-rection of magnetic fields. The temperature dependenceof the electrical resistivity of Np2PtGa3 is shown in Fig.8. The resistivity at room temperature amounts to 264µΩ cm. It increases logarithmically with decreasing tem-perature, in agreement with the single-site scattering ofthe Kondo effect. After showing a maximum at 14 K andminimum at 7 K, the resistivity increases logarithmicallyagain with further decreasing temperature. Such behav-ior of the resistivity can be attributed to the Kondo-

lattice formation and a competing influence of the Kondoand CEF effects. According to the theory developed byCornut and Coqblin,[40] the scattering of the conductionelectrons in the presence of well separated crystal-fieldlevels, would affect the C lnT dependence of the resistiv-ity in two temperature regions, where the coefficient C isgiven by

C ∝ J3cf

λ2i − 1

2J + 1. (6)

Jcf is the exchange interaction between the conductionand localized 5f electrons, λi are the effective degenera-cies of the crystal field 5f levels and J is the total angularmomentum of the Np3+ ions. We calculated the ratio ofslopes of the lnT -dependencies at low temperature andat high temperature regions ν = (λ2

l − 1)/(λ2h − 1) =

0.075, being close to that of a scheme where the 5f levelsplits in the doublet and the sextet states.

We wish to point out that the Curie temperature TC isdifficult to determine from the electrical resistivity data.This does not rule out the possibility of magnetic phasetransition at TC ∼ 26 K. The two following factors canaffect the lack of anomaly at TC . The random distribu-tion of Pt and Ga atoms and a tremendous contributionof the Kondo effect. As we will show below, the Kondoenergy scale in this compound is comparable to the mag-netic interaction strength. The inset of Fig. 8 comparesthe low-temperature resistivity of Np2PtGa3 at 0 and 9T. We observe that the applied magnetic field reducesthe resistivity. The behavior is consistent with the ferro-magnetic and Kondo properties of the compound.

Fig. 9 shows the magnetoresistance (MR), which is

defined as MR = ρ(T,H)−ρ(T,0)ρ(T,0) . As can be seen, MR is

negative in the range of fields 0 - 9 T. Below TC , MRreaches as large as - 3.6 % at 9 T. It is noted that theshape of the field dependence of the MR suggests theelectron scattering at the ferromagnetically coupled Npmoments under fields. In the range of magnetic fields-9 - 0 T, the MR data exhibit an irreversibility effect.Especially, the data obtained at 2.5 K display a posi-tive maximum at -3.5 T. The position of this maximummoves to 0 T as temperature increases. The MR behav-ior may be correlated with the magnetization reversal inthe ”metastable” ferromagnetic state, accompanied bythe magnetization hysteresis. The MR data at 50 K, i.e.above TC are due to short-range ferromagnetic correla-tions.

The Hall voltage VH(H) was measured between thetransverse contacts in magnetic fields up to 9 T, appliedperpendicularly to the sample surface and flow of the ap-plied current density j = 0.5 mA. VH(H) was calculatedaccording to:

VH(H) =1

2[V (H) − V (−H)], (7)

and the Hall resistivity was calculated from

ρH(H,T ) =VH(H,T )t

j, (8)

6

where t = 115 µm is the thickness of the sample. Theobtained isothermal Hall resistivity ρH of Np2PtGa3 atselected temperatures as a function of magnetic field ispresented in Fig. 10 a and b. We observe that in themagnetic field range up to 4 T, ρH exhibits a strong fielddependence on cooling through the magnetic phase tran-sition. Apparently, below TC (Fig. 10 a) there appearsa S-shaped ρH , thus a pronounced maximum is observedin the Hall coefficient, RH(H) = ρ(H)/µ0H (Fig. 10c). The RH maximum shifts down to lower tempera-tures with decreasing temperature. In the paramagneticstate, the Hall resistivity (Fig. 10 b) shows non-linearfield dependence, and steady increases with decreasingtemperature.

From the isothermal Hall data we have inferred theHall coefficient in fields of 2 and 9 T as solid symbolsin Fig. 11. The data in a field of 9 T agrees well withthe 9T-isofield data. A comparison of the 2T- Hall re-sistivity to the isothermal magnetization data (see Fig.2 -left panel) suggests that RH(T ) qualitatively behaveslike M(H). This behavior is consistent with the view thatspin-orbit coupling occurs during resonant scattering atthe sites of the Np ions. Phenomenologically, the Hall co-efficient is given by RH(H,T ) = R0 + RsM/µ0H , whereR0 is the ordinary Hall coefficient, which is mainly associ-ated with the Lorentz force on conduction electrons andRs is the anomalous Hall coefficient, which arises fromthe side-jump and/or skew scattering.[41,42] Taking intoaccount the Hall data and the isothermal magnetizationwe obtained values of R0 = -1.98×10−9 m3/C and Rs

= 10.33 ×10−7 m3/C. The fitted parameters reproducevery well the Hall coefficient in the paramagnetic region.Assuming only one type of carriers, R0 = 1/|ne|, theeffective carrier density n = 3.15×1027 m−3 can be esti-mated.

In the ferromagnetic range, the Hall coefficients R0

and Rs are temperature dependent. Therefore, in orderto separate R0 and Rs from the total RH we combinedisothermal M and RH data (Figs. 3 and 10). We applieda linear regression of the data ρH(H) vs. M(H), shownin Fig. 12 a. The resulting R0 and Rs values are plot-ted as a function of temperature in Fig. 12 b. Typicallyin f-electron materials the anomalous Hall coefficient ismuch larger than the ordinary one.[43-45] In the caseof Np2PtGa3, Rs/ R0 reaches a value of ∼ 500. It isnoticed that both R0 and Rs may have a rapid changebelow 5 K. At 1.8 K R0 amounts to 7.69 × 10−9 m3/C,corresponding to one-band carrier concentration of 8.12× 1026/m−3 (or 0.05 carrier/f.u). The small n value in-dicates that Np2PtGa3 is a low-carrier system. From thecarrier concentration at 1.8 K and the Sommerfeld co-efficient of 180 mJ/(mol at. Np K2) we evaluated theeffective mass m∗ = 83 m0 of the charge carries. Wealso calculated the Hall mobility µH = R0/ρ, which ap-pears to vary dramatically with change of temperature.µH falls down by almost two times from 28.3 cm2/Vs at50 K to 16.8 cm2/Vs at 1.8 K. Since µH ∝ τ/m∗, thescattering time τ of quasi-particles is expected to reduce

with lowering temperature.

IV. DISCUSSION

The measured physical properties show that the newintermetallic Np2PtGa3 exhibits interesting propertiessuch as the Kondo effect coexisting with ferromagneticorder. First, we discuss the origin of the ferromag-netic interactions in Np2PtGa3 in relation to other (U,Np)2TGa3 compounds. We mention that our previ-ous studies have revealed the antiferromagnetic order-ing in U2PdGa3 but ferromagnetic one in Np2PdGa3.[4]The evolution of the magnetic ground state in thisfamily of compounds has been interpreted based onan indirect RKKY exchange mediated via the conduc-tion electrons. Following the RKKY exchange Hamil-tonian Hex ∝ −J2

ex

∑i,j F (Ri,j)SiSj for the oscilla-

tory interactions between local spin Si and Sj sepa-rated with the interionic distance Rij , where F (Ri,j) =[2kFRi,jcos(2kFRi,j) − sin(2kFRi,j)]/R

4ij , we have gen-

erated the RKKY exchange in U2PdGa3 and Np2PdGa3(dashed lines) in Fig. 13. We used the Fermi wave vectorkF values inferred from the Hall effect data (kF = 0.93A−1 for U2PdGa3 and 0.44 A−1 for Np2PdGa3) and as-suming Jex ∝ Mord (Mord = 0.4 µB/U in U2PdGa3 and0.8 µB/Np in Np2PdGa3 from the magnetization data).In the same manner, we may plot the RKKY exchangeenergy (solid line in Fig. 13) for Np2PtGa3 adopting kF= 0.29 A−1 and Mord ∼ 0.37µB/Np. Considering therange of the interionic distance Rij , where two most im-portant distances between magnetic ions in the 213-typecompounds, i.e. the nearest neighbor d1 and next-nearestdistance d2 take place, we see that the RKKY exchangeenergy is positive for the Np-based compounds, whereasnegative for the uranium one. Thus, the long-range ferro-magnetic ordering observed in the Np2TGa3 compoundsaccords with positive values of Hex and this observationsuggests an intimate relationship between the magneticphase transition temperatures TC and amplitude of Hex

in actinide ferromagnetic Kondo lattices. Nonetheless,as considered in the INTRODUCTION, these materialshave commonly shown high Curie temperatures, in therange 50 - 100 K. Surprisingly, TC of Np2PtGa3 is foundto amount to 26 K only, thus TC value is decidedly dimin-ished. Therefore, it appears that high Curie temperaturemay be not general rule for the Kondo actinide ferromag-nets. In addition to the reason of partially screening ofthe S = 1 spins, an aspect on the relative strengths offerromagnetic interaction and Kondo effect is worthwhileto consider. The view of Np2PtGa3 is that TK is compa-rable to TC , and on contrary to Np2PtGa3, where TC =63 K is sizeably greater than TK = 35 K.

We wish to emphasize that the study of specific heat,electrical resistivity and Hall effect of Np2PtGa3 in thiswork and of Np2PdGa3 in ref. [4] give evidence that bothNp2PdGa3 and Np2PtGa3 belong to the same family ofcompounds where the Kondo effect and a ferromagnetism

7

coexist. A large effective mass of charge carriers with lowcarrier concentration found in these ferromagnetic Kondolattices can be understood in terms of the underscreenedKondo-lattice model, developed by Coqblin and cowork-ers.[19,20] for S = 1 interacting with a spin density of con-duction electrons via an on-site antiferromagnetic Kondocoupling. A characteristic parameter for a given Kondosystem is its Kondo temperature TK . We estimated theKondo temperature TK = 35 K for Np2PdGa3 and 24 Kfor Np2PtGa3. This result is different from what couldbe expected from the ”chemical pressure” effect alone,since the unit cell volume of Np2PdGa3 is larger thanthat of Np2PtGa3. In a Kondo lattice model, the Kondotemperature is given by:[46]

TK ∝ exp[−1/|JcfN(EF )|], (9)

where N(EF ) is the density of states at the Fermi levelEF and the exchange integral Jcf is obtained from theSchrieffer-Wolff transformation of the Anderson modelas:[47]

Jcf ∝< V 2

cf > U

εf(εf + U), (10)

where < Vcf > is the matrix element characterizing thehybridization between conduction and f electrons at EF ,U is the Coulomb integral and εf is the position of thef level relative to the Fermi level. The lowering TK inNp2PtGa3 compared to Np2PdGa3 would be due a de-creasing Jcf , which relates with an abating f-ligand hy-bridization or raising the distance between f and EF lev-els. The reduction of Jcf is articulated when assumingthat TC ∝ J2

cf , expected for RKKY interactions.

V. CONCLUSIONS

We have synthesized a novel intermetallic Np2PtGa3,which adopts the orthorhombic CeCu2-type crystal struc-ture. The magnetization, electron transport and specificheat data establish that the compound is a ferromag-netic Kondo system with the Curie temperature TC ∼26 K and the Kondo temperature TK ∼ 24 K. Thus,Np2PtGa3 becomes a new member of a relatively rarefamily of compounds where the Kondo effect and a fer-romagnetism coexist. For Np2PtGa3 and other actinide-based 213-type compounds, the magnetic ground statewould be interpreted qualitatively with the help of theRKKY exchange energy, which de facto is more sensitiveto change of kF . It may be remarked that Np2PdGa3 andNp2PtGa3 both exhibit a large effective mass of thecharge carriers and low carrier concentration, and bothmight be classified to the same family of the ferromag-netic Kondo lattices. However, the decrease of TK inNp2PtGa3 compared to that in Np2PdGa3 would not beinterpreted by ”chemical pressure” effect. The reason ofthis is presumably due to a decrease in the exchange be-tween the localized 5f and conduction electrons in thestudied compound.

VI. ACKNOWLEDGMENTS

We acknowledge the access to the infrastructure andfinancial support provided by the European Commissionin the frame of the Actinide User Laboratory programat JRC-ITU.

VII. REFERENCES

[1] V. Sechovsky and L. Havela, Handbook of Mag-netic Materials, volume 11, , Ed. K. H. J. Buschow,(North-Holland, Amsterdam, 1998), p. 1.[2] V. H. Tran, J. Phys.: Condens. Matter 8, 6267(1996).[3] V. H. Tran, F. Steglich, G. Andre, Phys. Rev. B 65,134401 (2002).[4] V. H. Tran, J.-C. Griveau, R. Eloirdi, W. Miiller,and E. Colineau, Phys. Rev. B 82, 094407 (2010).[5] S. K. Malik and D. T. Adroja, Phys. Rev. B 43,6295 (1991).[6] L. Menon and S. K. Malik, Phys. Rev. B 52, 35(1995).[7] E. Bauer, R. Hauser, E. Gratz, G. Schaudy, M.Rotter, A. Lindbaum, D. Gignoux and D. Schmitt, Z.Phys. B 92, 411 (1993).[8] J. Larrea J., M. B. Fontes, A. D. Alvarenga, E. M.Baggio-Saitovitch, T. Burghardt, A. Eichler and M. A.Continentino, Phys. Rev B 72, 035129 (2005).[9] T. Takeuchi, A. Thamizhavel, T. Okubo, M. Yamada,N. Nakamura, T. Yamamoto, Y. Inada, K. Sugiyama, AGalatanu, E. Yamamoto, K. Kindo, T. Ebihara, and Y.Onuki, Phys. Rev. B 67, 064403 (2003).[10] M. B. Fontes, S. L. Bud′ko, M. A. Continentino, E.M. Baggio-Saitovitch, Physica B 270, 255 (1999).[11] C. Krellner, N. S. Kini, E. M. Bruning, K. Koch, H.Rosner, M. Nicklas, M. Baenitz, and C. Geibel, Phys.Rev B 76, 104418 (2007).[12] J. Schoenes, B. Frick and O. Vogt, Phys. Rev. B30, 6578 (1984).[13] Z. Bukowski, R. Troc, J. Stepien-Damm, C.Su lkowski and V.H. Tran, J. Alloys Compd., 403, 65(2005).[14] V. H. Tran, R. Troc, Z. Bukowski, D. Badurski andC. Su lkowski, Phys. Rev. B 71, 094428 (2005).[15] D. Kaczorowski, Solid State Commun. 99, 949(1998).[16] J. Schoenes, R. L. Withers and F. Hulliger, J. Magn.Magn. Mater., 310, 1778 (2007).[17] E. Colineau, F. Wastin, J. P. Sanchez, and J.Rebizant, J. Phys.: Condens. Matter 20, 075207 (2008).[18] Doniach S. Doniach, Physica B - C 91, 231 (1977).[19] N. B. Perkins, M. D. Nunez-Regueiro, B. Coqblin,and J. R. Iglesias, Phys. Rev. B 76, 125101 (2007).[20] C. Thomas, A. S. R. Simoes, J. P. Iglesias, C.Lacroix, N. B. Perkins and B. Coqblin, Phys. Rev. B83, 014415 (2011).

8

[21] C. Thomas, A. S. R. Simoes, J. P. Iglesias, C.Lacroix and B. Coqblin, J. of Physics: Conf. Ser. 391,012174 (2012).[22] T. Roisnel and J. Rodriguez-Carvjal, in: Materi-als Science Forum, Proc. Seventh European PowderDiffraction Conference (EPDIC 7), Ed. R. Delhez andE.J. Mittenmeijer, (Barcelona, 2000), p. 118.[23] R. Caciuffo, J. A. Paixao, C. Detlefs, M. J. Long-field, P. Santini, N. Bernhoeft, J. Rebizant, and G. H.Lander, J. Phys.: Condens. Matter 15, S2287 (2003).[24] K. Binder, A. P. Young, Rev. Mod. Phys., 58, 801(1986).[25] J. A. Mydosh, Spin Glasses: An experimentalIntroduction (Taylor & Francis, London, 1993).[26] V. H. Tran, R. Troc, P. de V. du Plessis, G. Andreand F. Bouree, Phys. Rev. B 56, 11065 (1997).[27] J. B. Goodenough, R. I. Dass, J. Zhou, Solid StateSci. 4, 297 (2007).[28] G. Liang, F. Yen, S. Keith and M. Croft, J. Magn.Magn. Mater. 314, 52 (2007).[29] S. Chikazumi, Physics of Ferromagnetism (OxfordUniversity Press, New York, 1964), p. 274.[30] J. W. Ross and D. J. Lam, J. Appl. Phys. 38, 1451(1967).

[31] P. Erdos, G. Solt, Z. Zo lnierek, A. Blaise and J. M.Fournier, Physica B+C 102, 164 (1980).[32] P. Santini, S. Carretta, N. Magnani, G. Amoretti,and R. Caciuffo, Phys. Rev. Lett. 97, 207203 (2006).[33] A. Freeman and R. E. Watson, Magnetism Vol.IIa, ed. G. T. Rado and H. Suhl (New York Academic,1965), p. 168.[34] D. Aoki, Y. Haga, T. D. Matsuda, N. Tateiwa, S.Ikeda, Y. Homma, H. Sakai, Y. Shiokawa, E. Yamamoto,A. Nakamura, R. Settai, and Y. Onuki, J. Phys. Soc.Jpn, 76, 063701 (2007).[35] J.-C. Griveau, K. Gofryk, and J. Rebizant, Phys.Rev. B 77, 212502 (2008).[36] D. W. Osborne and E. F. Westrum, J. Chem. Phys.21, 1884 (1953).[37] N. Magnani, P. Santini, G. Amoretti, R. Caciuffo,, P. Javorsky, F. Wastin, J. Rebizant, G.H. Lander,Physica B 359 - 361, 1087 (2005).[38] J. C. Bonner and M. E. Fisher, Phys. Rev. 135,A640 (1964).

[39] V. T. Rajan, Phys. Rev. Lett. 51, 308 (1983).[40] B. Cornut and B. Coqblin, Phys. Rev. B 5, 4541(1972).[41] J. Smit, Physica (Amsterdam) 24, 39 (1958).[42] L. Berger, Phys. Rev. B 2, 4559 (1970).[43] J. Schoenes and J. J. M. Franse, Phys. Rev. B 33,5138 (1986).[44] D. Kaczorowski and J. Schoenes, Solid State Com-mun. 74, 143 (1990).[45] V. H. Tran, S. Paschen, R. Troc, M. Baenitz, and F.Steglich, Phys. Rev. B 69, 195314 (2004).[46] M. Lavagna, C. Lacroix and M. Cyrot, J. Appl.Phys. 53, 2055 (1982).[47] J. P. Schrieffer and P. A. Wolff, Phys. Rev. 149,491 (1966).

0 50 100 150 200 250 3000

100

200

300

400

0 10 20 30 40

0

10

20

30

-1(T) (

mol

.Np/

emu)

T (K)

Np2PtGa3

0H = 7 T

M (1

0-3

B/a

t. N

p)

T (K)

0H = 0.02 T

ZFC

FC

FIG. 1. (color online) Temperature dependence of the inversemagnetic susceptibility of Np2PtGa3 measured in a field of 7T. The solid line is a fit to the modified Curie-Weiss law. Thetriangle symbols are the data after subtraction of the tem-perature independent susceptibility χ0. The inset shows thetemperature dependence of the low-temperature magnetiza-tion M(T ) at 0.02 T, measured in ZFC and FC modes.

9

0 20 40 600.0

0.1

0.2

0.3

0.4

0.5

0.02 T 0.2 T 0.5 T 1.5 T 2.0 T

M

(B/a

t. N

p)

T (K)

Np2PtGa3Tinf

Tir

Tmax

0 20 40 60

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

dM(T)/d

T (a

rb. u

nits

)T (K)

Np2PtGa3

2 T

0.2 T

0.02 T

FIG. 2. (color online) Left panel: Temperature dependenceof the iso-field magnetization measured in selective fields upto 2 T. The dashed and dotted arrows indicate the data ob-tained in ZFC and FC modes, respectively. The solid arrowsdenote the positions of characteristic temperatures Tir, Tmax

and Tinf . Right panel: The temperature derivative of themagnetization dM(T)/dT vs temperature. For clarity of thefigure, the data at 0.02 and 2 T are shifted vertically by -0.02 and 0.02 µB/(at. Np K), respectively. The dotted anddashed lines, as guide to the eye, show the field dependenceof Tir and Tinf , respectively.

10

0 1 2 3 4 5 6 70.0

0.3

0.6

0.9

1.2

1.5

1.8

50 K

5 K

25 K

10 K

M (

B/N

p)

0H (T)

Np2PtGa32 K

a

0.04 0.1 1 70.0

0.3

0.6

0.9

50 K

25 K

10 K5 K

dM(H

)/dH

(B/T

)

0H (T)

2 Kb

FIG. 3. (color online) a) Isothermal magnetization at varioustemperatures as a function of applied magnetic fields. For thesake of clarity, the data at 2, 5 and 10 K are shifted upwardsby 1.8, 1.2 and 0.6 µB , respectively. The dotted line denotesa linear field dependence of the initial magnetization at 2 K.b) Field derivative of M(H) vs applied magnetic fields.

0 4 8 12 160.0

0.1

0.2

0.3

0.4

0.5

M2 (

B2 )

0H/M (T/ B)

Np2PtGa3

2 K

12.5 K

25 K

50 K

FIG. 4. (color online) Arrott plot for selected magnetizationdata obtained during decreasing applied magnetic fields. Thedotted and dashed lines are a guide for eyes.

11

1.5 10 100 3003000.0

0.2

0.4

0.6

0.8

1.5 2 3 4 5 6 70.18

0.21

0.24

Np2PtGa3

0 T HT + Cph(T)/T

C

p/T (J

/mol

Np

K2 )

T (K)

0 T 9 T

Cp/T

(J/m

olN

p K

2 )

T (K)

FIG. 5. (color online) Temperature dependence of the specificheat divided by temperature of Np2PtGa3 at µ0H = 0 T.The dashed line represents the sum of the phononic and high-temperature electronic contributions. The inset shows thelow-temperature data obtained in 0 and 9 T with the results offitting of the nuclear, phononic and electronic contributions.

10 15 20 25 30 35 400.2

0.4

0.6

0.8Np2PtGa3

0 T 9 T

Cp/T

(J/m

olN

p K2 )

T (K)

TC Ti

24 26 28 30 32

0.00

0.02

0.04

d[C

p(T)

/T]/d

T (J

/mol

.Np

K3 )

T (K)

0 T 9 T

FIG. 6. (color online) Temperature dependence of the specificheat divided by temperature of Np2PtGa3 in µ0H = 0 and 9T. The inset shows the temperature derivative of Cp/T in 0and 9 T.

12

1.5 10 1000.0

0.1

0.2

0.3

0.4

0 20 40 600.0

0.5

1.0

1.5

Cmag(T) fit

C5f/T CCEF/T CK/T

C

5f/T

(J/m

ol.N

p K2 )

T (K)

TC

Np2PtGa3ln4

S/R

T (K)

ln2

FIG. 7. (color online) Temperature dependence of the 5f-electron ( open symbols) and magnetic ( closed symbols) spe-cific heats divided by temperature of Np2PtGa3. The dashedline is the Kondo specific heat with the Kondo temperatureTK = 24 K. The dotted line is the specific heat due crystalelectric field splitting with an energy ∆CEF /kB = 82 K. Theinset shows the 5f-electron (solid line), magnetic (dotted line)and Kondo (dashed line) entropies as a function of tempera-ture.

1.5 10 100 300

1.00

1.02

1.04

1.06

1.08

1.10

0 10 20 30 40 501.00

1.01

1.02

1.03

(T)/

(300

K)

T (K)

Tmin

(T)/

(50

K)

T (K)

0 T

9T

Tmax

Np2PtGa3

FIG. 8. (color online) Temperature dependence of the nor-malized electrical resistivity ρ(T )/ρ(300K) of Np2PtGa3 inzero field. The solid lines are fits with -lnT dependencies.The inset shows field dependencies of the normalized electri-cal resistivity ρ(T )/ρ(50K).

13

-10 -8 -6 -4 -2 0 2 4 6 8 10-4-3-2-10123

-10 -8 -6 -4 -2 0 2 4 6 8 10-4-3-2-101234

1.8 K 2.5 K 5 K (+1 %) 15 K (+2 %)

(T,H

)/(T

,0) (

%)

0H (T)

a

20 K 25 K 30 K (+1 %) 40 K (+2 %) 50 K (+3 %)

(T,H

)/(T

,0) (

%)

0H (T)

b

FIG. 9. (color online) Magnetoresistance as a function of themagnetic field at different temperatures. The data at 5 and15 K are shifted vertically by 1 and 2 %, and data at 30, 40and 50 K by 1, 2 and 3 %, respectively.

0 2 4 6 8 10048121620

0 2 4 6 8 100

4

8

12

0 2 4 6 8 10020406080

1.8 K 3 K 5 K 10 K

H(H) (

cm

)

0H (T)

a

25 K 30 K 40 K 50 K

H(H) (

cm

)

0H (T)

b

1.8 K 4 K 5 K 7.5 K 10 K 12.5 K

RH (1

0-9 m

3 /C)

0H (T)

Np2PtGa3

c

FIG. 10. (color online) a and b) Hall resistivity ofNp2PtGa3 as a function of the magnetic field at differenttemperatures. The data at 3, 5 and and 10 K are shiftedvertically by 2, 4 and 6 µΩ cm, respectively. c) The field de-pendence of the Hall coefficient of Np2PtGa3 in the orderedstate.

14

0 10 20 30 40 500

10

20

30

40

50 2 T 9 T 9 T - isofield

RH (1

0-9 m

3 /C)

T (K)

FIG. 11. (color online) Temperature dependence of theisothermal (closed symbols) in fields of 2 and 9 T, and 9T-isofield (open circles) Hall coefficients. The dashed line is afit to the isothermal 2T data.

0 10 20 30 40 50-5

0

5

10

15

0 1 2 3 40

5

10

15

20

25

30

R0

RH (1

0-9 m

3 /C)

T (K)

10-2xRs

b

1.8 K 5 K 25 K

RH (1

0-9m

3 /C)

M/0H (102)

Np2PtGa3

a

FIG. 12. (color online) a) The Hall coefficient as a functionof M/µ0H . The dashed lines are linear fits to 1.8 K and 50K data. b) The temperature dependencies of the ordinaryR0, anomalous Rs and experimental RH (solid squares) Hallcoefficients of Np2PtGa3. The dashed line is the theoreticalline, simulated from the experimental M/µ0H and fitted R0,Rs values.

15

0.30 0.35 0.40-0.5

0.0

0.5

1.0

1.5

Np2PtGa3

Hex

(arb

. uni

ts)

R (nm)

Np2PdGa3

U2PdGa3

FIG. 13. (color online) The RKKY exchange energy Hex

as a function of distance Ri,j in U2PdGa3, Np2PdGa3 andNp2PtGa3. The exchange between nearest, next-nearest mag-netic ions are indicated by closed circles and squares, respec-tively.