Eur. Phys. J. B 80, 65–71 (2011) DOI: 10.1140/epjb/e2011-10726-9 THE EUROPEAN PHYSICAL JOURNAL B Regular Article Inhomogenous magnetic ground state in CeAgGa J. Gorausa , A. Ślebarski, M. Fijalkowski, and L  . Hawelek Institute of Physics, University of Silesia, 40-007 Katowice, Poland Received 21 September 2010 / Received in final form 9 February 2011 c EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2011 Published online 9 March 2011 –  Abstract. CeAgGa crystallizes in CeCu2 Imma structure with Ag and Ga atoms randomly distributed at 8h sites. The magnetic and transport properties of the orthorhombic CeAgGa compound have been obtained from the analysis of ac magnetic susceptibility χac , magnetization M vs. magnetic field, specific heat C and electrical resistivity ρ. The results provide evidence for the formation of a spin-glass state with a freezing temperature Tf = 5.1 K. The randomness in the Ce-Ce magnetic exchange interactions seem to arise from a statistical distribution of Ag and Ga atoms on a crystallographic site of the CeAgGa crystal lattice. The results provide also evidence for the formation of ferromagnetic-like order at the temperature TC ≈ 3.6 K. Band structure calculations for a disordered system give magnetic moment similar to saturation moment obtained from magnetization measurements, however, its calculated value is insensitive on Ga/Ag off-stoichiometry in the 8h position. Complex behavior of CeAgGa Kondo-lattice compound is discussed in terms of interplaying Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, Kondo effect and structural disorder. 1 Introduction Cerium-based Kondo- (Anderson-) lattice systems exhibit various ground states which sensitively depend on the balance between the on-site Kondo and the intersite Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interactions. Generally, the coupling constant Jf s , between the localized 4f spins and the conduction electron spins as well as the hybridization energy between the 4f and the conduction electron states Vf s , determine their ground state properties. The first qualitative picture of both heavy-Fermi (HF) and magnetically ordered metals was based on the idea that the ground state results from a competitive character of the Kondo and RKKY interaction [1]. While the RKKY interaction temperature TRKKY ∝ Jf2s N (EF ), where N (EF ) is the density of states (DOS) at the Fermi level EF , the Kondo temperature is given by TK ∝ exp(−1/|Jf s N (EF )|). Since in general Vf s and hence the Kondo coupling decreases with increasing volume of the unit cell, the RKKY interaction dominates over the Kondo effect and the magnetic ordering can occur as in the case of CeAgSn [2]. On increasing Jf s , the system shows a HF or valence fluctuating regime, as has been observed, e.g., in CeNiSn [3]. Studies of the ternary CeTX system, where T is a transition metal and X = Sb, Sn, Ga, or Al provide an opportunity to investigate the effect of variation of Jf s by varying T or X element on the magnetic/nonmagnetic properties of the ground state. For the series of elements: Sb, Sn, Ga, and a e-mail: jerzy.goraus@us.edu.pl Al an atomic radius systematically increases, therefore the CeTAl or CeTGa compounds are expected to be magnetic, which indeed has been reported [4]. Galium rich Ce-Ag-Ga systems have been recently characterized in reference [5]; the equiatomic CeAgGa system which crystallizes in CeCu2 type structure was investigated too [6–8]. CeAgGa is known to be ferromagnetically (FM) ordered below TC ∼ 5.5 K, with the saturation moment µsat ∼ 1.12 µB /f.u. [6] which is strongly reduced in comparison to a value expected for free Ce3+ ion (2.14 µB ). The similar lowering of µsat was also reported for isostructural CeAgAl system [9], where the value of µsat ∼ 0.94 µB /f.u. was explained by the strong Kondo screening effect. Here, we present the magnetic ac and dc susceptibility, specific heat and electrical resistivity data which show more complex magnetic structure of CeAgGa than that, reported previously in reference [6]. 2 Experimental and calculation details Polycrystalline CeAgGa sample have been prepared by arc melting the constituent elements on a water cooled copper hearth in a high-purity argon atmosphere with an Al getter. The sample was remelted several times to promote homogeneity and annealed at 800 ◦ C for 2 weeks. The powder diffraction pattern was measured on RigakuDenki D/MAX RAPID II-R diffractometer (Rigaku corporation, Tokyo, Japan) with a rotating anode AgKα tube (λ = 0.5608 Å), an incident beam (002) graphite 66 The European Physical Journal B Fig. 1. (Color online) Observed, calculated and difference X-ray diffraction pattern of CeAgGa. Table 1. Rietveld refinement results for CeAgGa (space group Imma); lattice parameters: a = 4.6766(9) Å, b = 7.4136(13) Å, c = 7.9436(15) Å, Bragg factor RB ∼ 2.9%, the atomic positions are listed in the table. Atom Ce Ag/Ga x 0 0 y 0.25 0.9521(2) z 0.5335(3) 0.8348(4) Biso (Å2 ) 0.65(4) 1.06(5) Table 2. Nearest neighbour distances. Atom 1 Ce Ce Ag/Ga Atom 2 Ce Ag/Ga Ag/Ga (Å) 3.745 3.194 2.698 monochromator and an image plate in the Debye-Scherrer geometry. XRD data were refined using FULLPROF program [10] with pseudo-Voigt line shape, the refined atomic positions and lattice parameters are given in Table 1. These parameters were also used in our band structure calculations. Rietveld plot is presented in Figure 1 (we do not show hkl indexes because they are very densely situated and would make the figure unreadable, however, all lines were succesfully indexed within Imma space group and no extra lines were observed). The nearest neighbour distances are given in Table 2. Thermodynamic properties were measured with quantum design physical properties measurement system (QD PPMS): resistivity with ACT, susceptibility with ACMS, and magnetization with VSM option. Resistivity and specific heat were measured down to 0.4 K with He3 option, ac magnetic susceptibility was carried out down to 1.9 K for frequency (0 ≤ ν ≤ 9000 Hz) and for the amplitude of the driving field B = 1 G and 12 G. Magnetization M , dc susceptibility, and magnetic relaxation on CeAgGa were also performed on a MPMS Quantum Design SQUID magnetometer. Band structure calculations were carried out using FPLO 5.00–20 computer code [11–15]1 with PerdewWang exchange-correlation potential [16,17]. We used 171 k-points in the irreducible Brilloiun Zone. We chose as the valence states: 4f , 6s, and 5d for Ce, 5s and 5p for Ag, and 4s, 4p, and 3d for Ga, respectively. The following states were chosen as the semicore states: (5s5p) and 6p for Ce, (4s4p) and 4d for Ag, and (3s3p) for Ga, parenthesis denote grouping (the same compression factor) in that notation. An atomic disorder at the 8h position has been taken into account within coherent potential approximation (CPA) approach. 3 Results and analysis 3.1 Magnetic susceptibility and magnetization results In Figure 2, the real part of the ac susceptibility χac at frequency ν = 10 kHz is presented as a function of temperature. The maximum at TM = 5.1 K corresponds to the temperature of the magnetic phase transition. Also is shown the static magnetic susceptibility χdc (thick solid line), which has not a maximum at TM , but it exhibits a saturated curve below this temperature, that signals the ferromagnetic ordering. The inset 1 www.fplo.de J. Goraus et al.: Inhomogenous magnetic ground state in CeAgGa 67 ′ Fig. 2. The real part of ac magnetic susceptibility χac measured in the field B = 12 G at frequency 10 kHz (circles) and dc susceptibility χdc in the field B = 20 G (continuous thick ′ line). The inset displays a Curie-Weiss fit to the χac data in the temperature region T > 100 K. From the measured bulk properties of CeAgGa results that TM ≡ Tf . ′ to the figure displays 1/χac between 1.8 K and 300 K µ2 and a Curie-Weiss (CW) fit of the form χ(T ) = 81 T −θeffCW to the inverse susceptibility. This fit yields effective moment value µeff ∼ 2.5 µB /at.Ce which is within experimental error very close to the free Ce3+ ion value (2.54 µB ) and the negative CW paramagnetic temperature ΘCW ∼ −43 K. The negative value of ΘCW in the possible ferromagnetic Kondo lattice suggests the Kondo temperature TK = |θCW |/4 ≈ 11 K [18]. ′ ′′ The real (χ ) and imaginary (χ ) part of the magnetic ′ susceptibility are depicted in Figures 3a and 3b. Both (χ ) ′′ and (χ ) components exhibit a quite marked maxima at ∼5 K with amplitudes and positions depending on the ′ frequency of the applied magnetic field, while χ has a ′′ shoulder at about 3.6 K, that is not observed in the χ (T ). This behaviour signals second magnetic phase transition at ∼3.6 K. The heat capacity measurements also confirm the more complex magnetic properties of CeAgGa. Specific heat C divided by temperature, C/T , shows the maximum at T = 3.8 K with a strong field dependence, and a distinct shoulder at ∼4.9 K, the data are discussed below. ′ ′′ The temperature of the maximum of χ and χ at 5 K could be attributed to a spin glass transition at Tf . The frequency (ν(Tf )) dependence follows the Vogel-Fulcher law (see inset of Fig. 3b) characteristic of a spin-glass behaviour [19], ν = ν0 exp[−Ea /kB (Tf − T0 )], where ν0 , T0 , and E0 are the fitting parameters. The inset to Figure 3b displays the linear behaviour in Tf vs. 1/ln(ν0 /ν). Considering a typical constant value of ν0 = 1013 Hz [20] we obtained Ea = 14.6 K and T0 = 4.4 K. T0 has not yet precise physical meaning, some attempts have been made to relate it to the interaction strengths between the clusters in a spin glass, or T0 might be related to the true critical temperature when Tf > T0 is only a dynamic manifestation of the phase transition (for detailes see [19]). The fre′ quency shifts of the maxima in the χ susceptibility yield Fig. 3. (a) The real and imaginary component of the ac mag′ ′′ netic susceptibility, χac and χac , as a function of temperature measured at different frequencies for CeAgGa, the amplitude of the magnetic field was 1 G. Inset shows the field-cooled and zero-field-cooled magnetization M devided by the applied magnetic field (B = 100 G), χdc ≡ M/B, vs. temperature. (b) The real and imaginary component of the ac magnetic sus′ ′′ ceptibility, χac and χac , as a function of temperature measured at different frequencies for CeAgGa, the amplitude of ′ the magnetic field was 12 G (the value of the maximum of χ decreases in comparison to Fig. 3a). Inset shows the frequency dependence of the temperature maximum Tf , the line fits the Voguel-Fulcher law. ratio δTf = ∆Tf /Tf ∆ log10 ν ≈ 0.012 which is typical for metallic spin glasses [19]. Figure 3a (inset) compares the temperature variation of the dc susceptibility χ ≡ M/H measured in the field cooling (FC) mode and in the zero-field cooling (ZFC) mode for magnetic field 100 G. The inset shows a difference between FC and ZFC branches below characteristic temperature Tir , which again signals the spin-glass-like behaviour in CeAgGa. In order to get a deeper understanding of the nature ′ of the 5 K maximum of χ we present the isothermal remanent magnetization MIRM as a function of time t (cf. Fig. 4). The sample was first zero-field cooled from T ≫ Tir to 3.5 K, then a magnetic field of 0.5 T was applied for 5 min and switched off (t = 0). The observed time dependence of MIRM at 3.5 K is characteristic of the canonical spin glasses and can be fitted by The European Physical Journal B µ 68 Fig. 4. Time dependence of the isothermal remanent magnetization MIRM of CeAgGa measured at T = 3.5 K, i.e., below Tf . The solid line represents least-squares fit using the expression MIRM (t) = M0 + αlnt + β exp[−t/τ ]. µ Fig. 6. Arrot plots: M 2 = f (B/M ) at different temperatures near Tf . Fig. 5. (Color online) Magnetization M vs. field measured at different temperatures. The inset exhibits M in the low fields (|B| < 50 mT) and at T = 2 K. The width of the hysteresis loop is 23 mT. expression MIRM (t) = M0 + α ln t + β exp[−t/τ ] with M0 = 0.444 emu/g, α = −0.005 emu g−1 s−1 , β = −0.014 emu g−1 , and τ = 4.95 × 103 s. The magnetization M (B) of CeAgGa, shown in Figure 5, does not saturate up to 7 T. An extrapolation from the linear field dependence of M (1/B) at T = 2 K yields a value of 1.2 µB /Ce, when 1/B → 0 in the B-range 9 > B > 3.3 T. The estimated saturated value of M (µsat ) is in good agreement with the value previously reported in reference [6]. The inset displays a low field M (B) dependence in order to make visible a small hysteresis loop of ∼23 mT width at T = 2 K. A very small, but significant hysteresis loop was also detected for CeAgGa at T = 4 K, while any hysteresis loop was not observed at higher temperatures (i.e., at T > 4 K). The experimental remanence effect and magnetic relaxation on a macroscopic time scale obtained for CeAgGa resemble the properties of archetypal spin glasses below the spin freezing temperature Tf . Figure 6 displays Arrot plots of M 2 as a function of B/M . The M 2 (B/M ) curves near an ordering temperature are not typical for ferromagnetic materials and also suggest inhomogeneous magnetic phase below ∼5 K. Now, we discuss the reason for the magnetic inhomogeneity observed in CeAgGa. CeAgGa crystallizes in a disordered derivative of the orthorhombic CeCu2 -type structure with Ag and Ga atoms distributed randomly at the 8h position. As the Ce-Ce exchange interactions depend on the random occupation of the 8h sites, a spin glasslike state would be introduced the randomly frustrated Ce-Ce exchange interactions. We know several examples of such nonmagnetic atom disordered spin glasses; e.g., CeAgAl [21], URh2 Ge2 [22] or U2 PdSi3 [23]. The second reason for the inhomogeneous magnetic state would be a distance between the magnetic ions in the unit cell. In reference [24] 80 binary Ce compounds have been compared to find the relation between the distance dCe−Ce of the nearest Ce atoms and the magnetic ground state properties of these compunds. General tendency has been observed, that compounds with dCe−Ce < 3.7 Å order antiferromagnetically (AFM), whereas these with 3.7 Å < dCe−Ce < 4.1 Å are ferromagnetically (FM) ordered. Considering the distance dCe−Ce as a condition of the magnetic ground state properties of the system, CeAgGa with dCe−Ce = 3.745 Å lies on the border between AFM and FM ordering. In that way one can expect the highly unstable magnetic ground state for this compound. 3.1.1 Magnetic ground state obtained from DFT calculations From FPLO-CPA band structure calculations we obtained magnetic ground state of CeAgGa with 1.41 µB /f.u., which is very close to the experimental µsat ∼ 1.2 µB /f.u. Magnetic moments located on Ce atoms are ∼0.72 µB , J. Goraus et al.: Inhomogenous magnetic ground state in CeAgGa 69 while the moments located on Ag and Ga atoms are very small of ∼0.01 µB and with magnetization opposite to Ce atoms. We also carried out the calculations for the off-stoichiometry CeAg0.4 Ga0.6 , CeAg0.45 Ga0.55 , CeAg0.55 Ga0.45 , CeAg0.6 Ga0.4 compounds where the Ag/Ga ratio at the 8h site was changed. From our calculations results, that with increasing of Ag concentration, the magnetic moment per formula unit only slightly increases from the value of 1.395 µB /f.u. up to 1.415 µB /f.u. The small off-stoichiometry doesn’t change the magnetic properties significantly, we conclude therefore that the complicated magnetic structure observed experimentally probably results from the dCe−Ce distance between Ce atoms, which is tuned by the Ag/Ga occupation of the 8h position and is on average ∼3.74 Å for CeAgGa. For comparison, dCe−Ce ∼ 3.24 Å for isostructural CeAg2 with well defined AFM ground state [25]. 3.2 Specific heat Figure 7 displays the low-temperature specific heat C of CeAgGa measured in several magnetic fields up to 2 T. In the figure we also present the C/T data at various magnetic fields. It can be seen that the zero-field heat capacity C(T ) has not λ-shaped anomaly, the C(T )/T measured at H = 0 has a maximum at 3.95 K and the shoulder at ∼5 K. With rising magnetic field, both C(T ) and C(T )/T display only one maximum, which shifts to higher temperatures, which characterizes the ferromagnetic or spinglass behavior. If TC = 3.95 K, than above TC the contributions to the magnetic specific heat may arise from short-range-order correlations and/or from both Kondo resonance and crystal-field effects. In the low-symmetry structure of CeAgGa the J = 5/2 multiplet splits into three doublets. A typical energy scale for a crystal-field splitting is of about 102 K, therefore a Schottky-type contribution to the specific heat of CeAgGa is expected at temperatures above TC . The electronic coefficient of the specific heat γ = C(T )/T could give valuable information about the Kondo interaction. For T < 3.9 K, C(T ) can be well described by the expression for a strongly anisotropic magnetic system with a gap δ in the magnon dispersion: C(T ) = γT + BT n exp(−δ/T ), where the fitting parameters are: γ ∼ 0.146 J/(mol K2 ), B ∼ 0.97 J/mol Kn , n = 1.78. The best fit gives exponent n ≈ 1.8 near to n = 3/2 value typical for the ferromagnetic or spin-glass system. We note, however, that in the narrow T -region two effects due to magnetic ordering at ∼3.9 K and ∼5 K contribute to C(T ) data, what strongly complicates the analysis of the data. As we mentioned above, the Kondo temperature TK obtained from the CW behaviour is ∼11 K. A comparable values of TK can also be estimated from the specific heat data. Firstly, we consider the reduction of the magnetic entropy at TC from the value of R ln 2 expected for a doublet ground state. Figure 7b shows T ) C/T as well as entropy, S(T ) = 0 C(T T dT , from the both quantities there was subtracted the phonon contribution (obtained from the best fit of Debye function Fig. 7. (Color online) Low temperature specific heat C (in panel a) and the specific heat divided by temperature, C/T , (in panel b) measured at various magnetic fields. The low-T specific-heat data for T < TC are well approximated by equation C = γT + BT n exp(−δ/T ) for an anisotropic ferromagnetic system. The low temperature entropy subtracted by the phonon contribution to the specific heat is presented in panel b. A strong reduction of entropy in relation to the expected R ln 2 values suggests the Kondo-type interaction. to the C(T )-data above T = 20 K, it is discussed in the section below). At the temperature TC = 3.9 K the value of S ∼ 3.3 J/(mol K) is 0.57R ln 2. Within a simple two level model and energy splitting of kB TK the magnetic entropy of a magnetic Kondo system is related to the ratio  [26],  TK /TN in the following manner −TK /TN e S(TK /TN ) = R ln(1 + e−TK /TN ) + TTK −TK /TN . The N 1+e Kondo temperature estimated from this relation is ∼10 K; this value is nearly the same as that derived from the magnetic susceptibility data. Figure 8 displays specific heat in zero magnetic field versus temperature in wide T -range. It seems for us surprising that C(T ) can be well fitted by full Debye expression:  ΘD /T x4 ex 3 Cp = 9RnD (T /ΘD ) dx (ex − 1)2 0 in the wide T -range, when the crystal-field contribution is neglected. The least-squares fit of this expression to the 70 The European Physical Journal B where: ρph T 4 = 4RT ( ) ΘD  0 ΘD T x5 dx , (ex − 1)(1 − e−x ) ρM = −KT 3 , Fig. 8. Specific heat for CeAgGa measured in the wide temperature range and a fit of the Debye function to the experimental data. ρ0 is the residual resistivity, ΘD stands for the Debye temperature and R is a constant, whereas the cubic term KT 3 describes interband scattering processes [27]. At the temperature range T > 8 K the fit gives ρ0 ≈ 214.48 µΩ cm, ΘD ≈ 102.99 K, R ≈ 2.03 µΩ cm K−1 , and K = 5.58 × 10−7 µΩ cm K−3 . The small value of the ratio ρ300 K /ρ2 K ∼ 1.16 indicates structural disorder in CeAgGa, that can be responsible for the inhomogeneous magnetic ordering in CeAgGa. The inset to Figure 9 clearly shows the magnetic phase transition at ∼5 K in the resistivity data. 3.4 Conclusions Fig. 9. Electrical resistivity ρ and a fit of the Bloch-GrüneisenMott (BGM) function to experimental data. The inset shows a hump at ∼4.7 K due to the magnetic transition. experimental data yield a reasonable value of Debye temperature θD ≈ 197 K and a number of atoms in formula unit nD ≈ 3.07. A very good quality of the fit, as well as the fact that nD is essentially equal to assumed composition lead us to conclusion that the contribution to specific heat resulting from crystal field effect is in CeAgGa relatively small. Adroja et al. reported [6] that the inelastic neutron scattering measurements show two very broad crystal field transitions. This broadening was discussed as an effect of the crystallographic disorder between the Ag and Ga atoms. 3.3 Resistivity As seen in Figure 9, in the paramagnetic region the electrical resistivity ρ(T ) exhibits metallic conductivity, well approximated by the Bloch-Grüneisen-Mott formula ρ(T ) = ρ0 + ρph + ρM The low-temperature magnetic properties of CeAgGa provide evidences of Kondo-lattice character with an abnormal magnetic behavior. The evidences indicating Kondolattice effect are: (i) the reduction of the Ce3+ magnetic moment, (ii) the negative value of the paramagnetic Curie temperature θCW , (iii) the analysis of the magnetic entropy which is in ∼50% reduced at TC and (iv) the relatively high value of the Sommerfeld coefficient γ. Structural disorder at 8h position leads to distribution of Ce-Ce distances dCe−Ce , and in consequence to distribution of the exchange integrals between the neighbouring Ce atoms which carry magnetic moment in CeAgGa. For CeAgGa the distance dCe−Ce is exactly on the empirical border between ferromagnetic and antiferromagnetic ordering, when one considers the magnetic ground state properties of the series of the binary Ce-compounds [24] with respect to the value of dCe−Ce . CeAgGa compound can be viewed as the binary Ce compound with an effective Ag/Ga atom at 8h position. In an average geometry picture we have calculated that small off-stoichiometry at the 8h position doesn’t significantly change the magnetic moment of Ce. We conclude therefore that the distance between Ce atoms (which is smaller when Ag atom occupy the 8h position, compare it to dCe−Ce ∼ 3.2 Å in CeAg2 [25]) is the reason that causes the inhomogenous magnetic ground state. There are known examples of Ce-based Kondo lattices with nonmagnetic transition elements, which (if they are disordered in the crystal) introduce a varying electronic environment around the Ce ions occupying a periodic lattice [28]. As the Ce-Ce exchange interactions depend on the random occupation in the vicinity of the Ce ions, a spin-glass-like ordering is possible (the effect is known as nonmagnetic atomic disorder (NMAD) spin glasses). The strong disorder in CeAgGa, we believe, is a reason of possible short-range ordering above TC with a freezing temperature of ∼5 K. There are known some examples of similar behaviors [29], e.g., in CeNi1−x Cux , where disorder leads to existence of a spin-glass-like state above the J. Goraus et al.: Inhomogenous magnetic ground state in CeAgGa Curie temperature TC in the strongly correlated electron system. From theoretical point of view, model of these underscreened Kondo lattices with the interplay between the Kondo effect, the spin glass and the magnetic order (antiferromagnetic or ferromagnetic) was proposed by Coqblin et al. [30,31]. CeAgGa seems to be such a system classified to the group of Ce-compounds with complex of magnetic interactions, Kondo effect and strong atomic disorder. The authors thank the Polish Ministry of Science and Education for support from Project No. N N202 032137. References 1. S. Doniach, Valence Instabilities and Related Narrow Band Phenomena, edited by R.D. Parks (Plenum, New York, 1977), p. 169 2. J. Sakurai, S. Nakatani, A. Adam, H. Fujiwara, J. Magn. Magn. Mater. 108, 143 (1992) 3. T. Takabatake, F. Teshima, H. Fujii, S. Nishigori, T. Suzuki, T. Fujita, Y. Yamaguchi, J. Sakurai, D. Jaccard, Phys. Rev. B 41, 9607 (1990) 4. A. Szytula, Crystal structures and magnetic properties of RTX rare earth intermetallics, edited by J. Hrycyk (Jagiellonian University Press, Kraków, 1998) 5. R.V. Gumeniuk, L.G. Akselrud, B.M. Stelmakhovych, Yu.B. Kuzma, J. Alloys Compd. 389, 127 (2005) 6. D.T. Adroja, B.D. Rainford, S.K. Malik, Physica B 186-188, 566 (1993) 7. S.K. Malik, B.D. Dunlop, A.E. Dwight, J. Less- Common Met. 127, 261 (1987) 8. D. Rossi, R. Ferro, J. Alloys Compd. 317-318, 521 (2001) 9. A. Ślebarski, D. Kaczorowski, W. Glogowski, J. Goraus, J. Phys.: Condens. Matter 20, 315208 (2008) 10. J. Rodriguez-Carvajal, Physica B 192, 55 (1993) 11. K. Koepernik, H. Eschrig, Phys. Rev. B 59, 1743 (1999) 12. I. Opahle, K. Koepernik, H. Eschrig, Phys. Rev. B 60, 14035 (1999) 71 13. K. Koepernik, B. Velicky, R. Hayn, H. Eschrig, Phys. Rev. B 55, 5717 (1997) 14. H. Eschrig, M. Richter, I. Opahle, Relativistic Solid State Calculations, in Relativistic Electronic Structure Theory, Theoretical and Computational Chemistry Part 2. Applications, edited by P. Schwerdtfeger, (Elsevier, 2004), Vol. 13, pp. 723–776 15. H. Eschrig, K. Koepernik, I. Chaplygin, J. Solid State Chem. 176, 482 (2003) 16. J.P. Perdew, Y. Wang, Phys. Rev. B 45, 13244 (1992) 17. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45, 566 (1980) 18. A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993) 19. J.A. Mydosh, Spin Glasses: An Experimental Introduction (Taylor and Francis, London, 1993) 20. J.L. Tholence, Solid State Commun. 35, 113 (1980) 21. K.G. Suresh, S.K. Dhar, A.K. Nigam, J. Magn. Magn. Mater. 288, 452 (2005) 22. S. Süllow, G.J. Nieuwenhuys, A.A. Menovsky, J.A. Mydosh, S.A.M. Mentink, T.E. Mason, W.J.L. Buyers, Phys. Rev. Lett. 78, 354 (1997) 23. D.X. Li, Y. Shiokawa, Y. Homma, A. Uesawa, A. Dönni, T. Suzuki, Y. Haga, E. Yamamoto, T. Honma, Y. Onuki, Phys. Rev. B 57, 7434 (1998) 24. J.G. Sereni, Rev. Bras. Fis. 21, 280 (1991) 25. A. Landelli, A.P. Palenzona, J. Less-Common Met. 15, 272 (1968) 26. H. Yashima, H. Mori, N. Sato, T. Satoh, J. Magn. Magn. Mater. 31-34, 411 (1983) 27. N.F. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, 1958), p. 240 28. A. Ślebarski, J. Alloys Compd. 480, 9 (2009) 29. J.G. Soldevilla, J.C.G. Sal, J.A. Blanco, J.I. Espreso, J. Rodriguez Fernandez, Phys. Rev. B 61, 6821 (2000) 30. B. Coqblin, J.R. Iglesias, S.G. Magalhaes, N.B. Perkins, F.M. Zimmer, J. Optoelectronics Adv. Mater. 10, 1583 (2008) 31. B. Coqblin, Acta Physica Polonica A 115, 13 (2009)