Physica B 319 (2002) 17–20 Intersublattice exchange coupling in rare earth–iron-based R-Fe–LT intermetallics (LT=light transition elements Ti, V) N.H Duca,*, N.D Tana, B.T Conga, D Givordb a Faculty of Physics, Vietnam National University, 334-Nguyen Trai Road, Thanh Xuan, Hanoi, Viet Nam b Laboratoire de Magnetisme Louis N!eel, CNRS, BP-166, 38042 Grenoble Cedex 9, France Received February 2002 Abstract The values of the d-sublattice magnetic moment (Md ) and the Gd–Fe exchange coupling parameter (AGdFe ) were derived for the R(Fe1ÀxTix)2, R(Fe1ÀxTix)3 and RFe12ÀxVx (R=Gd, Lu and Y) compounds As the Ti(V) concentration increases, a tendency of Md to decrease is found, whereas AGdFe is enhanced These behaviours are discussed in terms of the similar role of the 3d(Fe)–5d(R) and 3d(Fe)–3d(Ti,V) hybridizations on the negative polarization of both the 5d(R) and 3d(Ti,V) electrons The arguments are reinforced by the analysis of the magnetic valence and a linear relationship between AGdFe and Md is presented r 2002 Elsevier Science B.V All rights reserved Keywords: Rare earth–transition metal compounds; Exchange interactions; Hybridization effects The understanding of magnetism in rare earth (R)—heavy transition-metal (HT=Fe,Co) intermetallic compounds has considerably progressed in the last two decades [1–3] It has been realized that the specific magnetic behaviours observed result not only from the 3d and 4f electrons independently, but also from their association, especially from 4f–3d exchange interactions The values of the 3d-magnetic moments as well as the strengths of the 4f–3d interactions depend on the nature of both the transition metal and the rare earth element These physical parameters show systematic variations as a function of the rareearth concentration [1,4] These were discussed by Duc et al [5] on the basis of the model proposed by Campbell [6] and reinterpreted by Brooks et al [7] Accordingly, the T-magnetic moment de*Corresponding author Tel./fax: +84-4-8584438 E-mail address: duc@netnam.org.vn (N.H Duc) creases whereas the strength of the 4f–3d coupling increases as the degree of 3d–5d hybridization increases The role of the light 3d elements, LT=Ti, V,y, in establishing the magnetic properties is not understood quantitatively, however In the 1:12 system, beside the phase stablising role, the LT elements have a pronounced influence on the 4f–3d exchange interaction strength [8,9] In Ref [9], the enhancement of the 4f–3d exchange coupling associated with the introduction of LT elements in the compounds was ascribed to the fact that 5d(R)–3d(LT) hybridization must be weaker than 5d(R)–3d(Fe,Co) hybridization as shown by the non-existence of R–LT compounds As a consequence, in R–(Fe1ÀxLTx) compounds, the fraction of electrons which can participate in 3d(R)–3d(Fe) hybridization must increase with x: In this paper, we discuss systematically the influence of LT substitution on the d-sublattice magnetic moments and the 4f(R)–3d(Fe) exchange 0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V All rights reserved PII: S - ( ) 1 - 18 N.H Duc et al / Physica B 319 (2002) 17–20 interactions in R(Fe1ÀxTix)2 (0XxX0:065), R(Fe1ÀxTix)3 (0XxX0:10) and RFe12ÀxVx (0XxX4:0) compounds with R=Gd, Lu and Y The compounds were prepared by arc-melting Their magnetic properties were investigated by means of magnetization measurements in the temperature range from 4.2 to 800 K and in magnetic fields up to 10 T The d-sublattice magnetic moment (Md ) was deduced from the isotherm magnetization measured at 4.2 K The ordering temperature (TC ) was determined from the thermal variation of magnetization in an applied field of 0.1 T Md and TC in various compounds are collected in Table It is seen that in all three investigated systems, TC and Md decrease with increasing x: Similar result was reported earlier for R(Fe1ÀxVx)12 [8] In these three pseudo-binary compounds, the influence of the LT elements on the magnetic behaviours seems thus to be similar The value of the intersublattice exchange coupling parameter ART (in the Hamiltonian Hex ¼ ÀSART SR ST ) was derived in the same way as in our previous papers [4,5]: ðART =kB Þ2 ¼ 9ðTC À TR ÞðTC À TT Þ=4ZRT ZTR GR GT ; ð1Þ where TC is the Curie temperature, TR and TT represent the contribution to TC due to R–R and T–T interactions, respectively GR is the de Gennes factor gR 1ị2 JJ ỵ 1ị for rare-earth atoms GT ; the corresponding factor for the transition metal, GT ¼ p2eff =4: peff is the T-effective paramagnetic moment, obtained by assuming that the ratio between peff and the spontaneous moment (i.e Md ) equals about [4,5] For these three series of compounds, TR was determined from TC of the RNi2 compounds (TC GdNi2 ị ẳ 75 K) and TT was taken as the Curie temperatures of the corresponding Lu (or Y) compounds Finally, ZRT (respectively, ZTR ) is the number of TðRÞ neighbours of one R ðTÞ atom The value of ZRT and ZTR is given in Ref [4] On the basis of Eq (1), the Gd–Fe exchange-coupling parameter was evaluated for all investigated compounds The obtained results are listed in Table AGdFe strongly increases with increasing Ti(V) concentration Table The values of the d-sublattice magnetic moment Md (in mB/at), Curie temperature TC (in K), contribution of the 3d–3d interactions to ordering temperature TT (in K) and Gd–Fe exchange parameter AGdFe (in 10À23 J) for Gd(Fe1ÀxTix)2, Gd(Fe1ÀxTix)3 and GdFe12ÀxVx compounds TC TT AGdFe Compounds Md R(Fe1ÀxTix)2 x ¼ 0:0 0.015 0.030 0.045 0.050 0.065 1.5 1.4 1.35 1.32 1.30 1.26 780 775 768 760 755 750 495 490 485 480 475 470 16.2 17.6 17.2 18.3 18.6 19.3 R(Fe1ÀxTix)3 x ¼ 0:0 0.025 0.050 0.075 0.10 1.75 1.64 1.51 1.37 1.20 712 705 697 670 660 505 502 496 489 485 12.1 12.7 14.1 17.9 18.5 R(Fe12ÀxVx) x ¼ 0:0 1.0 2.0 2.5 3.0 3.5 4.0 2.07a 1.85 1.60 1.45 1.30 1.15 0.90 768a 682.5 597.5 555 512.5 476 427.5 670a 579 488 442.5 397 351 306 11.3 12.4 13.0 14.5 16.2 18.8 22.5 a Data extrapolated for the hypothetical compounds We suggest that the above behaviours can be understood in terms of hybridization between the various d-states in the compounds Let us discuss first the value of the 3d moment, Md ; in these systems on the basis of the magnetic valence model [10,11] In this approach, the magnetic moment of an alloy is not considered in terms of magnetic and non-magnetic atoms, but rather in terms of the magnetic moment averaged over all atoms present in the alloy The mean magnetic moment (M) is then expressed as m M ẳ Zm ỵ 2Nsp ; ð2Þ m where Zm is the magnetic valence, 2Nsp is the number of s, p electrons in the spin-up state band m The value of Nsp usually ranges from 0.3 to 0.45mB [10] At present, as mentioned below, we use m Nsp ¼0:45: N.H Duc et al / Physica B 319 (2002) 1720 Zm ẳ 2Ndm yị ZFe yị y0 ZR ỵ y00 ZLT Þ: ð3Þ The calculated (mean) magnetic moment is presented in Fig as a function of Zm for the compounds of R(Fe1ÀxTix)2, R(Fe1ÀxTix)3 and RFe12ÀxVx (R=Gd, Lu and Y) The continuous line in Fig was obtained with Nsp ¼ 0:45: Qualitative agreement is found between the experimental and calculated values Both the calculated and experimental mean magnetic-moment shows a similar reduction with increasing R and LT (Ti,V) concentration This finding stresses Magnetic moment (µB/at) 2.0 1.5 1.0 Gd(Fe,Ti) Y(Fe,Ti) Gd(Fe,Ti) 0.5 Y(Fe,Ti) Lu,Y(Fe,V)12 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Magnetic valence (Z m ) Fig Magnetic moment as a function of the magnetic valence in the pseudo-binary R(Fe1ÀxTix)2, Gd(Fe1ÀxTix)3 and R(Fe12ÀxVx) systems 25 Gd(Fe,Ti) 20 Gd(Fe,V)12 -23 J) Gd(Fe,Ti) AGdFe (10 In this model of the magnetic valence, the Gd– Fe–LT can be considered as alloys of the transition metals Fe with Gd and LT elements In this case, not only the transfer of the rare earth 5d,6s(Gd) electrons, but also the contribution of the 3d(LT) electrons to the 3d(Fe) band can reduce the average magnetic moment Redenoting the Gd–Fe–LT intermetallics as Gdy0 Fe1yLTy00 (y ẳ y0 ỵ y00 ), Zm is then determined by the chemical values ZFe ð¼ 8ị; ZGd ẳ 3ị; ZTi ẳ 4ị and ZV ẳ 5Þ [10,11] of the corresponding Fe, Gd, Ti and V elements, respectively, in the alloys and by the number of the d electrons in the spin-up state band (Ndm ), which is per atom for a strong ferromagnet 19 15 10 0.0 0.2 0.4 (R and LT) concentration Fig AGdFe as a function of the R- and (Ti,V) concentration in the binary Gd–Fe and pseudo-binary Gd(Fe1ÀxTix)2, Gd(Fe1ÀxTix)3 and Gd(Fe12ÀxVx) systems the related contributions of the 5d(R) and the 3d(LT) electrons on the magnetic properties of the Gd–Fe–LT alloys Both the 5d(R) and 3d(LT) electrons are found to be negatively polarized with respect to the 3d(Fe) ones This is in agreement with Campbell’s model [5] treating the rare earth in R–M (M=Fe, Co or Ni) compounds as light transition elements In a recent work, Chelkowska et al [12] have calculated the electronic structure for the Gd(Al1ÀxLTx)2 (LT=V,Ti) and found that a ferromagnetic coupling between 5d(R) and 3d(LT) moments is favoured 3d(Fe)–3d(LT) coupling must then be antiferromagnetic as observed here Whereas the variation of the magnetic moments in the compounds was discussed above in terms of a global model in which all electrons are included, the understanding of exchange interactions in these systems requires that the role of the various electrons is discussed separately The non-existence of compounds between the rare earth and LT elements, such as Ti and V, suggests that in R(Fe– LT) compounds, the 5d states hybridize more with the 3d-Fe states than with the 3d-LT states In a given series of R(Fe1ÀxLTx) compounds, as x increases, more electrons can participate in 5d–3d(Fe) hybridization, thus leading to the observed increase in R–Fe coupling [8,9] Actually, N.H Duc et al / Physica B 319 (2002) 17–20 the variation of AGdFe obtained for these three investigated Gd–Fe–Ti(V) systems follows a common law when described in the relation with R- and LT concentration, i.e in the relation with y ẳ y0 ỵ y00 ị (see Fig 2) The inuence of introducing LT elements in R–Fe compounds has two complementary effects On the one hand, 3d(LT) electrons hybridize with 3d(Fe) electrons, on the other hand, each LT atom introduced in the lattice replaces the Fe atom and thus 3d–5d hybridization per Fe atom is favoured A consequence of this hybridization is that more spin-down 3d(Ti,V)electrons appear in the lattice The present enhancement of the Gd–Fe exchange coupling may be related to the increased number of negatively polarized spins around the magnetic R atoms The variation of AGdFe as a function of Md is presented in Fig for the pseudo-binary Gd–Fe– LT compounds An almost linear decrease of AGdFe is observed with increasing Md : This behaviour is a result of the influence of the same hybridization effects on the d-sublattice magnetic moment and 4f–3d exchange [13] In concluding, we would like to point out that, the nature of LT elements plays an important role in establishing the magnetic properties of the pseudo-binary R–Fe–LT Unlike remarks in the literature ([7] and references therein) suggesting that 4f–5d exchange is important, the mechanism of R–Fe exchange interactions must be understood on the basis of the global spin polarization induced by hybridization between d Fe, LT and R states This work was partly supported by the State Programme of Fundamental Research of Vietnam, under project 420.301 References [1] J.J.M Franse, R.J Radvanski, in: K.H.J Buschow (Ed.), Handbook of Magnetic Materials, Vol 7, Elsevier Science, Amsterdam, 1993, p 307 25 20 AGdFe (10 -23 J) 20 15 Gd(Fe,Ti)2 10 Gd(Fe,Ti)3 Gd(Fe,V)12 0.5 1.0 1.5 2.0 M d (µ B/at) Fig Relationship between AGdFe and Md in in the pseudobinary R(Fe1ÀxTix)2, Gd(Fe1ÀxTix)3 and R(Fe12ÀxVx) systems [2] H.S Lee, J.M.D Coey, in: K.H.J Buschow (Ed.), Handbook of Magnetic Materials, Vol 6, Elsevier Science, Amsterdam, 1991, p [3] N.H Duc, P.E Brommer, in: K.H.J Buschow (Ed.), Handbook of Magnetic Materials, Vol 12, Elsevier Science, Amsterdam, 1999, p 259 [4] N.H Duc, in: K.A Gschneidner Jr., L Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol 24, Elsevier Science, Amsterdam, 1997, p 338 [5] N.H Duc, T.D Hien, D Givord, J.J.M Franse, F.R de Boer, J Magn Magn Mater 124 (1993) 305 [6] I.A Campbell, J Phys F (1972) L47 [7] M.S.S Brooks, B Johansson, in: K.H.J Buschow (Ed.), Handbook of Magnetic Materials, Vol 7, Elsevier Science, Amsterdam, 1993 [8] X.P Zhong, F.R de Boer, D.B de Mooij, K.H.J Buschow, J Less-Common Metals 163 (1990) 305 [9] N.H Duc, M.M Tan, N.D Tan, D Givord, J Teillet, J Magn Magn Mater 177–181 (1998) 1107 [10] A.R Williams, V.L Moruzzi, A.P Malozemoff, K Terakura, IEEE Trans Magn 19 (1983) 1983 [11] J.P Gavigan, D Givord, H.S Li, J Voiron, Physica B 149 (1988) 345; J.P Gavigan, D Givord, H.S Li, J Voiron, Physica B 158 (1996) 719 [12] G Chelkowska, H Ufer, G Borstel, M Neumann, J Magn Magn Mater 157–158 (1996) 719 [13] N.H Duc, Phys Stat Sol (b) 175 (1993) K63  ... increases with increasing Ti (V) concentration Table The values of the d-sublattice magnetic moment Md (in mB /at) , Curie temperature TC (in K), contribution of the 3d–3d interactions to ordering... treating the rare earth in R–M (M=Fe, Co or Ni) compounds as light transition elements In a recent work, Chelkowska et al [12] have calculated the electronic structure for the Gd(Al1ÀxLTx)2 (LT= V,Ti)... introduced in the lattice replaces the Fe atom and thus 3d–5d hybridization per Fe atom is favoured A consequence of this hybridization is that more spin-down 3d(Ti,V)electrons appear in the lattice