On the nickel magnetic behaviour in rare-earths compounds

The x-ray photoelectron spectroscopy (XPS) study, magnetic measurements and band structure calculations were performed on RNi2, RNi3, RNi5 and R2Ni17 compounds, where R is a rare-earth or yttrium. The presence of small nickel moments was shown in almost all compounds with magnetic rare-earths. The nickel moments are dependent on the site location, their local environment, respectively. The R5d bands are negatively polarized, their values M5d, being determined by additive contributions resulting from local 4f-5d and short-range 5d-3d interactions. The R5d band polarizations mediate the exchange interactions within the spatial extension of the unit cell. The Curie temperatures for a given series are linearly dependent on M5d values with the same rate for both heavy and light rare-earth compounds.


Introduction
The R-Ni phase diagrams, where R is a rare-earth or yttrium, in the composition range 66.7-88.5 at%, show the presence of RNi 2 , RNi 3 , R 2 Ni 7 , RNi 5 and R 2 Ni 17 series [1]. The RNi 2 compounds crystallize in a cubic-type structure, the RNi 5 in hexagonal CaCu 5 -type lattice, RNi 3 in a rhombohedral structure havingR 3m space group, R 2 Ni 17 in hexagonal P6 3 /mmc and R 2 Ni 7 series crystallize in both hexagonal (P6 3 /mmc) and rhombohedral ( ) R m 3 type structures. In cubic RNi 2 Laves phases, each R and Ni atoms are located on only one type of site, while in RNi 5 , the R atoms occupy 1a site and Ni the 2c and 3 g positions. The number of inequivalent R and Ni sites is higher in other R-Ni compounds, two R and three Ni in RNi 3 compounds and two R and four or five Ni sites in R 2 Ni 17 and R 2 Ni 7 series [1], respectively.
The R-Ni compounds have interesting physical properties as well as technical applications, as for example RNi 5 series, which are used for hydrogen storage [2]. The R-Ni compounds generally show collinear magnetic structures. Little canted magnetic structures were reported in RNi 3 (R=Tb, Dy) [3] and Tm 2 Ni 17 [4] compounds. The nickel, generally has been reported to be non-magnetic in RNi 2 [5], RNi 3 [3] and RNi 5 [6] compounds, or to have a small magnetic moment, of 0.2-0.3 μ B /Ni atom, in R 2 Ni 7 [7] and R 2 Ni 17 [4,8,9] series. When nickel has a magnetic moment, the compounds, with magnetic heavy rare-earths, are ferrimagnetically ordered, while those with light rare-earth, show parallel orientations of R and Ni moments. Later on, by means of magnetic circular dichroism study on GdNi 2 , has been evidenced that nickel has a magnetic moment of M Ni ≅0.2 μ B [10]. Information concerning the presence of nickel moment in Ni-based alloys has been obtained also by x-ray photoelectron spectroscopy (XPS) [11,12]. The presence of 6 eV satellites in XPS core level and valence band spectra were associated with the partially filled Ni3d band which allows the creation of two hole bond state on Ni atoms after photoionization event [13,14]. The intensities of the satellites can give information about the Ni3d hole density in nickel alloys [15,16] or rare-earth-nickel intermetallic compounds [17][18][19]. Small Ni moments were determined by means of band structure calculations of RNi 2 and RNi 5 series with magnetic rare-earths [20].
The Curie temperatures, T C , of the RNi 2 , RNi 3 , RNi 5 and R 2 Ni 17 series follow linear dependencies on the De Gennes factor, interactions at the level of the unit cell. The exchange interactions between rare-earths and nickel atoms are best described by the 4f-5d-3d model, being mediated by the R5d band polarizations, M 5d [20,21]. The M 5d values, as evidenced in R-Co compounds, mirror all the changes in their magnetic properties resulting from the substitutions at R and Co sites as well as those resulting from the pressure effects [22]. Starting from the band structure calculations and based on the 4f-5d-3d exchange interactions model, it is our aim to analyze: (1) the presence and the values of the nickel moments and R5d band polarizations in R-Ni series, as well as their site (local environment) dependencies, respectively; (2) the reason for different rates of T C versus G, for a given series in the light and heavy rare-earths nickel compounds. Thus, in addition to the previous data obtained from band structure calculations on RNi 2 , RNi 5 and R 2 Ni 17 heavy rare-earth compounds [20], the band structures of the corresponding compounds with light rare-earths as well as of RNi 3 series are now reported. The XPS study for some RNi 5 compounds as well as the results of the magnetic measurements, particularly the T C values, of some R-Ni compounds are also presented and correlated with those determined from the band structure calculations.
Starting from the computed magnetic properties as well as the experimental data, the presence of small nickel moments are evidenced in nearly all compounds with magnetic rare-earths. The R5d band polarizations mediate the exchange interactions within the spatial extension of the unit cell. Consequently, for a given series, linear dependence of T C versus M 5d is evidenced with the same rate for both heavy and light rare-earth-nickel compounds.

Experimental and computing methods
The x-ray photoelectron spectroscopy (XPS) measurements were performed using a PHI5600ci multitechnique system. The spectra were recorded using the monochromatized K α radiation of Al. The total energy resolution of the electron spectra, as determined at the Fermi level of gold foil, was 0.3-0.4 eV. Binding energies are given with reference to the Fermi level, E F . The spectra were recorded in vacuum below 5·10 −10 mbar. The fracturated samples contained only a tiny amount of oxygen and carbon.
The magnetic measurements have been performed for R 2 Ni 17 (R=Dy and Er) and SmNi 5 compounds for which the previously reported Curie temperatures and magnetizations covered a large range of values [1]. The present data were obtained by using a VSM equipment, in the temperature range 4.2-300 K and external fields up to 7 T.
The band structure calculations were performed in the framework of density functional theory (DFT) with two different schemes. The greatest part of data (RNi 3 , RNi 5 , R 2 Ni 17 , Y 2 Ni 7 ) were obtained assuming localized 4 f electrons, by using tight-binding linear muffin-tin orbital (TB-LMTO) formalism [23][24][25]. The exchange correlation energy was the free electron gas parameterization of Von Barth and Hedin [26]. Relativistic effects were included. Band structure calculations were also performed for RNi 2 , RNi 5 and some RNi 3 compounds, considering the 4f electrons in the valence band, within the LSDA+U approach, respectively [27]. An intraatomic Coulomb interaction parameter U f =9 eV and exchange interaction J f =0.9 eV were used for rareearths [27,28]. For nickel, the parameters U d =2 eV and J d =0.9 eV were considered [29]. The determined nickel moments, as well as the R5d band polarizations, obtained by the above approaches are rather close as evidenced in RNi 2 , RNi 5 and RNi 3 series [20]. Only the magnetic properties of Y 2 Ni 7 compound were investigated from R 2 Ni 7 series.

Results and discussions
The Ni2p 3/2 and Ni2p 1/2 core level lines of NdNi 5 compound are plotted in figure 1. The decomposed spectrum is also shown. As in case of metallic nickel, the Ni2p 3/2 and Ni2p 1/2 lines are located at ≅852.5 eV and 869.8 eV.
In the spectrum the presence of the 6 eV nickel satellite at higher binding energy is evidenced, suggesting that there are unoccupied Ni3d states. The intensities of the above satellites are smaller that those characteristic for pure nickel, evidencing a decrease of the number of unoccupied states, in Ni3d band.
The XPS valence bands, recorded on RNi 5 compounds, show that 4f orbitals keep their localized character and consequently the presence of multiplet structures-figure 2. The valence band spectra, in case of pure nickel show a main line at ≅0.6 eV binding energy. In case of RNi 5 compounds these lines are little shifted from the above value being now located at ≅0.7 eV. The 6 eV nickel satellite line in the valence band of RNi 5 compounds cannot be unambiguously observed due to superposition of R and Ni lines [19]. The, valence band spectra of RNi 5 compounds around E F are somewhat similar to that of pure nickel, but the density of states at Fermi level, are diminished due to R5d-Ni3d hybridization effects.
The partial densities of states of the constituent atoms in GdNi 3 and Gd 2 Ni 17 compounds, as determined by band structure calculations are given, for example, in figure 3. The nickel moments and R5d band polarizations, theoretically determined, show interesting behaviour. The computed nickel moments in RNi 2 , RNi 3 , RNi 5 and R 2 Ni 17 series follow linear dependences on De Gennes factor, with different rates for heavy (h) and light (l) rare-earth compounds-figures 4(a)-(d).
The ratio of the above rates, / a a @  1.6 0.1 l h seems to be not dependent on the nickel content in a given series. Consequently, for the same G value, the nickel moments are somewhat higher in compounds with light than in those with heavy rare-earths.
The M Ni values, for a given RNi n (3n8.5) series, are dependent on site location, their local environment, respectively. In RNi 5 compounds, the higher Ni moment is located at 3 g site, having R 4 Ni 8 environment, decreasing at 2c site, where in their first coordination shell, R 3 Ni 9 , are only three R atoms. In R 2 Ni 17 series, the Ni12k site having R 3 Ni 9 coordination has the greater moment, the smaller one being located at Ni4f site with only one R atom (R 1 Ni 13 ) in their nearest neighbour. These data evidence the part played by R atoms in inducing a magnetic moment on neighbour nickel atoms by 4f-5d-3d exchange path. More clear evidence on this effect can be seen in RNi 3 series. When R=Y which is non-magnetic, the M Ni (6c) having R 3 Ni 9 atomic environment is the highest one and the smaller at Ni(3b) with R 6 Ni 6 atoms situated in their first coordination shell. When R is a magnetic rare-earth, this sequence is reversed.
The rates of M Ni versus G dependences are also higher when the number of R atoms situated in the first coordination shell to a given Ni site is greater. Thus, in RNi 5 series, the are obtained, confirming the part played by the R atoms in inducing an additional Ni moment. As a general trend, for all Ni sites, the mean dN Ni /dG rates decrease as the nickel content, in a given series, is greater- figure 5.  The R5d bands are negatively polarized, their polarizations, M 5d , in absolute magnitude, increasing linearly with De Gennes factor, G, with different rates for light (l) and heavy (h) rare-earths compounds-figures 4(a), (c), (d). As already reported [17,20], the M 5d values are determined by additive contributions of polarization, M 5d (f), resulting from 4f-5d local exchange and of M 5d (d) due to R5d-Ni3d short range interactions, hybridization effects, respectively: The linear dependences of M 5d versus G are due to M 5d (f) term, having different rates for light (i=l) and heavy (i=h) rare earth compounds. 6±0.15) was shown, in the investigated RNi 2 , RNi 5 and R 2 Ni 17 , series. The above trend can be correlated with lanthanide contraction [30]. The radii of 4f shells r 4f , in light rareearths are in the range 1.11 Å (R=Pr) and 0.98 Å (R=Sm), while in heavy rare earths are significantly smaller, decreasing from 0.85 Å (R=Gd) to 0.80 Å (R=Dy) [31]. As a result, the exchange splitting of R5d band by 4f-5d local interaction, is significantly higher in nickel compounds with light rare-earths. Thus, for the same G value, a higher nickel moment is induced in compounds with light than in those with heavy rare-earths through R5d-Ni3d short range interactions. This mechanism explains also the different rates of the Curie temperatures for light and heavy rare-earth series, when plotting on De Gennes factor. The The M 5d (d) contributions to R5d band polarizations, have been analysed starting from the Hamiltonian describing the interactions of R atom with their z i Ni nearest neighbours. In the mean field model, M 5d (d) is proportional to the number z i of Ni atoms situated in the first coordination shell to a given R atom as well as their magnetic moments M Ni i [17,20]. ( ) The γ i values, for a given series, determined at unequivalent R sites are rather close, these decreasing when increasing the nickel content- figure 5 inset. The γ i ·n product is only little dependent on the investigated RNi n series compositions.
The computed magnetic moments per formula unit were compared with experimental values. In addition to previous data [1,3,9,17,32,33], magnetic measurements were also performed on SmNi 5 and R 2 Ni 17 (R=Dy and Er) compounds The saturation magnetizations, experimentally determined are rather close to the computed values, the mean differences being of the order of 5%.  / dM dG Ni rates in heavy rare-earths RNi n compounds with n=2, 3, 5 and 8.5. In inset are given the values as function of nickel content, n per one R atom. The corresponding value for Y 2 Ni 7 is also given. When there are unequivalent R and Ni sites, the mean / dM dG The M 5d values are influenced by substitutions both at R and Ni sites, respectively. When a rare-earth, R, is partially replaced by another one, R′, in ¢ -R R Ni 5 as for example in Gd x La 1-x Ni 5 series [33]. When Ni is replaced by another magnetic or non-magnetic element, the M 5d (d) values are changed, according to relation (4), as evidenced YNi 3-x Co x [34], NdNi 5-x Cu x [19] or DyNi 5-x Al x [17] pseudobinary compounds. The mean band polarizations 〈M 5d 〉 versus T c in pseudobinary compounds follow the same trend as in the corresponding binary series- figure 6. These data are further support on the part played by R5d band polarizations in describing the exchange interactions within the spatial extension of the unit cell.

Conclusions
The XPS studies on RNi 5 compounds suggest the presence of unoccupied Ni3d states. The densities of states at the Fermi level have mainly d character, being somewhat diminished as compared to that of Ni metal due to Ni3d-R5d hybridization. The band structure calculations show the presence of small nickel moments, for the RNi n (n=2, 3, 3.5, 5 and 8.5) series, when R is a magnetic rare-earths. The nickel moments are dependent on the site location, their local environment, respectively. The R5d band polarizations mirror all the changes in magnetic properties, resulting from substitutions both at R and Ni sites. Further evidence for the part played by the R5d band polarizations in mediating the exchange interactions in binary and pseudobinary compounds, is given by the linear dependences of the Curie temperatures on M 5d values, with the same rate for both heavy and light rare-earth compounds. The computed moments per formula unit agree rather well with those experimentally determined.