NCUYEN Huu Duc: R-T Spin Coupling Parameter in R-T Intermetallics 545

phys. stat. sol. (b) 164, 545 (1991)

Subject classification: 75.30; S1.2; S1.4

Cryogenic Laboratory, Department of Physics, University of Hanoi')

An Evaluation of the R-T Spin Coupling Parameter in the Rare Earth-Transition Metal Intermetallics

BY NGUYEN Huu Duc

For the purpose of the evaluation of the R-T spin coupling parameter, ART, an analysis of the Curie temperature is made for the rare earth-transition metal systems R,T, (R rare earth; T = Fe, Co; m/n = 1/2, 1/3, 6/23, and 2/17) and some systems of recent and growing interest, such as R,T,,B, RT,,Ti, RT,,V, and their ternaries R,(Co, Fe),. Besides the enhancement of A,, in the light rare earth compounds, the dependence of A,, on the magnetic moment of the 3d electrons is presented.

A J I X OLWHKH IIapaMeTpa CnHHOBOrO COeAHHeHHX A,, 6b1n CAeJIaH aHaJIH3 KWPH TeMIIepaTypbI B CHCTeMaX peAKO3eMeJIbHO-IIepeXOAHbIX MeTaJIJIOB R,T, (R peAKO3eMeJIhHble eneMeHTb1; T = Fe, CO; m/n = 1/2, 1/3, 6/23 II 2/17) HeKOTOPbIX CHCTeMaX, HMeKJWHX HOBhIe y PaCTyWHe HHTepeCbI KBK

PeAK03eMeJIhHbIX COeAHHeHHXX, 3aBHCHMOCTb A,, OT MarHHTHOrO MOMeHTa 3d 3JIeKTPHOB 6b1na R,T,,B, RT,,Ti, RT,,V, H HX s a ~ e l r ~ a e ~ b ~ x R,(Co, Fe),. KpoMe ysemremx ART B nerKnx

IIpeAcTaBneHa.

1. Introduction

Recently much effort has been paid to estimate the strength of the intersublattice interaction in the rare earth-transition metal (R-T) intermetallics. While calculating the molecular field assigned to the R site, Radwanski [I] assumed that the R-T spin coupling parameter (ART) in these compounds was insensitive to the kind of the R-atom as well as T composition. The calculated data of Belorizky et al. [2] showed that in the R,Fe, intermetallics the R-T interaction changes over a given series. According to a two-sublattice model, the spin coupling constants were also deduced by analysing the temperature dependence of the saturation magnetisation [3]. Their results demonstrated the complexity of the R-T interaction in the R,T, compounds. These authors claimed that it is due to the variety and complex structure of the investigated compounds. The Landau theory of phase transitions has been also found to be very useful in discussing magnetic materials of many different types. Following this way the magnetic properties of the heavy rare earth-Co, compounds, in particular the Curie temperature and type of magnetic phase transition, have already been discussed in terms of the s-d model by Bloch et al. [4], Inoue and Shimizu [5 ] . The Curie temperatures calculated by applying the formalism of this s-d model can also be extended to the R,Co, compounds by taking the change of the composition into account [63. Starting with the T, data for all R,T, and R,T,,B (T = Fe, Co) we have quite recently pointed out that the agreement with the observed T, shown graphically by Kirchmayr and Poldy [7] and tabulated by Buschow [8] can be obtained with ART values of about 1.00 x J and 0.80 x J for the rare earth compounds with T = Co and Fe, respectively [9].

I) Thuong Dinh Dong da, Hanoi, Vietnam.

35*

546 NGUYEN Huu Duc

In this paper, by considering the number of nearest neighbours for the exchange interaction, our analysis of the Curie temperature for the R,T, compounds, some systems of recent and growing interest, such as R,T,,B, RT,,Ti, RT,,V, and that of their ternary R,(Co, Fe), analogue shows that the R-T spin coupling parameter systematically changes with the variation of the magnetic moment of the 3d electrons.

2. The Expression of the Curie Temperature

The rare earth-transition metal intermetallics, for simplicity, are usually considered as a magnetic material with two sublattices of different nature. Neglecting the interaction between the rare earths themselves, the effective molecular fields can be written as

HR == Ho + nRTMT,

HT = Ho + ~TRMR + nTTMT >

(1)

(2)

where H , and H , are the fields acting in the R and T sublattices, respectively, H , is the external magnetic field, MR the magnetic moment per mole of the R sublattice, M , that of the T sublattice, nij are molecular field coefficients. Under the assumption that the interaction is isotropic and only between the nearest neighbour atoms, the molecular field coefficients, nRT and nTR, are related to A,, by

, (4) ZRTART(g - l)

~ R T = g p a ,

where Z,, is the number of T nearest neighbours of an R ion, Z,, the number of R nearest neighbours of a T ion, N, and NT are the number of R and T atoms per mole, respectively.

From (1) to (4) it is easy to find an expression for Tc as follows:

where G is the de Gennes factor, xT(TC) the susceptibility of the 3d electrons at T,, measured on the corresponding R,T, compounds with non-magnetic R elements (R = La, Lu, Y); for the ferromagnetic Lu,T, or Y,T, compounds

with peff and d d being the effective paramagnetic 3d moment and ordering temperature, respectively.

It is clearly seen that ( 5 ) for T, has the same form as those reported in [4 to 6, 91 taking the numbers of nearest neighbours into account.

3. The Evaluation of the R-T Spin Coupling Parameter

Based on (5 ) the value of the R-T spin coupling parameter, A,,, can be deduced from the experimental T, values and the paramagnetic susceptibility of the 3d electrons. The values

R-T Spin Coupling Parameter in the Rare Earth-Transition Metal Intermetallics 547

Table 1 The values of the effective moment (perf), the ordering temperature (6,) for the 3d electrons, and the number of nearest neighbours of R and T atoms (ZRT and ZTR) used for the evaluation of R-T spin coupling parameters in the rare earth intermetallics

RCo, RCo, RZCO,, R2C014B RCo ,Ti

RFe, RFe, R6Fe23

R2Fe17

R2Fe14B RFe, ,Ti RFe 1 OV2

12 18 19 18 17

12 18 18 19 18 17 17

6 4 2.5 2.5 2

6 4 3 2.5 2.5 2 2

- 2.8 3.3 3.3 3.0

3.4 3.5 3.7 4.0 4.0 3.7 3.7

- 335

1145 955 965

528 520 475 265 535 488 485

of the effective paramagnetic 3d moment, pefr, the contribution of the 3d electrons to the ordering temperature, O,, and the numbers of nearest neighbours, ZR, and ZTR, used in these calculations for the considered compounds are listed in Table 1. It can be seen from this table that the values of peff are mainly taken from literature [7, 103, the Od values which were rather close to the ordering temperatures of the corresponding R,T, compounds with non-magnetic R elements (R = La, Lu, Y) were chosen in order to obtain the best fit of the Curie temperature for each series of R,T, compounds [9].

For the RCo, compounds, the value of the R-T spin coupling constant, ARCo, has been deduced by taking the temperature dependence of the magnetic susceptibility measured in LuCo, [ll] for the enhanced susceptibility zT. The results are listed in Table 2. We note that for the heavy rare earth-Co, compounds the obtained A,, are almost constant

Table 2 Experimental Tc (K) and deduced spin coupling constant ART(lO-” J) for a number of rare earth-cobalt intermetallics

RE RCo2 RCo, R2Co17 R2Co14B RCo,,Ti

Tc ART Tc ART TC ART Tc ART TC ART

La Pr Nd Sm Gd Tb

Ho Er Tm Lu Y

DY

54 4.66 95 3.32

240 3.10 400 2.01 227 2.02 140 2.01 75 2.04 33 2.00 7 2.40

995 350 1.44 1160 2.44 994 4.00 395 1.90 1183 2.62 1006 3.00

615 1.73 1240 1.46 1050 1.40 506 1.49 1195 1.24 1030 1.50 450 1.46 1188 1.44 418 1.49 1183 1.70 400 1.70 1160 1.40 370 1.73 1180 301 1192 390 1167

1190 1.86 1030 2.15 1004 2.40

548 NGUYEN Huu Duc

(732 x lo-” J), the enhancement of A,, can only be observed in the light rare earth compounds. A small difference between the present result and that of Belorizky et al. [2] is due to the thermal variation of x,.

In the RFe, compounds, xT( T,) has been taken as the magnetic susceptibility described by the Curie-Weiss law (6) with the values of peff = 3.4pB/atom and 8, = 518 K [12]. The value of ARFe now is determined for RFe, from the experimental T, and the above-given zT. The results are shown in Table 3.

The R-T spin coupling constants A,, for the other R,T, (m/n = 1/3; 6/23; 2/17), R,T,,B, RT,,Ti, and RT,,V, are also estimated as performed for RFe, compounds. The results are listed in Tables 2 and 3a, b. From these tables one can see that the results quantitatively are in good consistence with those obtained by analysing the different experimental

Table 3 a Experimental Tc (K) and deduced spin coupling constant ART(lO-ZZ J) for a number of the rare earth-iron intermetallics

La Pr Nd Sm Gd Tb

Ho Er Tm Lu Y

DY

543 578 680 780 713 640 614 575 563 558 518

2.00 1.78 2.02 1.50 1.54 1.45 1.59 1.50 1.84

650 728 648 600 565 550 535

490

1.71 1.25 655 1.12 574 1.06 545 1 .oo 509 1.02 495 1.07 483

471 478

283 327 385

1.30 460 1.12 408 1 .oo 363 1 .oo 325 0.92 310 1.10 276

265 302

1.42 1.92 1.87 1.06 1.37 1.32 1.20 1.11

Table 3 b Experimental Tc (K) and deduced spin coupling constant ART(10-22 J) for a number of the rare earth-iron intermetallics

La Pr Nd Sm Gd Tb DY Ho Er Tm Lu Y

542 565 2.01 592 1.95 621 1.57 640 1.06 620 1.03 590 0.99 570 0.96 555 0.96 545 1.34 534 565

495

527 2.08 584 1.98 607 1.20 554 1.04 534 1.04 520 1.09 505 1.04 496 1.04 488

58

570 3.21 610 2.30 616 1.26 570 1.20 540 1.16 525 1.22 505 1.14 496 1.30 483 532

R-T Spin Coupling Parameter in the Rare Earth-Transition Metal Intermetallics 549

Table 4a The values of spin coupling constant AR,(10-22 J) deduced from the experimental Tc (K), the ordering temperature fld (K), the effective moment perf (pL,/atom), and magnetic moment M , (pB/atorn) of the T sublattice in the Er(Co, -*FeJ2 and Gd2(Coi -xFex)17 compounds (see text)

compound TC ed Perf MT ART

Er(Co, -,Fe& x = 0.0 33 1.00 2.01

0.2 395 285 2.90 1.36 1.65 0.3 496 450 3.30 1.55 1.29 0.4 575 525 3.40 1.60 1.40 0.6 640 610 3.65 1.71 1.06 0.8 628 600 3.75 1.70 1 .oo 0.9 613 580 3.50 1.64 1.14 1 .o 575 518 3.40 1.60 1.50

Gdz(Coi -xFex)i7 x = 0.0 1250 1145 3.3 1.50 1.46

0.2 1200 1125 3.5 1.80 1.21 0.4 1120 1085 4.0 2.10 1.12 0.6 1000 900 4.4 2.30 1.04 0.8 7 80 670 4.2 2.20 0.95 0.9 600. 500 4.1 2.15 1.05 1.0 500 265 4.0 2.10 1.06

Table 4 b The values of spin coupling constant ART(10-22 J) deduced from the experimental Tc (K), the ordering temperature Od (K), the effective moment perf (pB/atom), and magnetic moment M, (pB/atom) of the T sublattice in the Gd,(Co, -xFex)14B and Sm(Co, -xFex)l,Ti com- pounds (see text)

compound TC ed Perf MT ART

Gd2 (cOl -xFex)14B x = 0.00 1050

0.14 1015 0.29 928 0.43 873 0.7 1 783 1.0 640

Sm(Co, -*FeJl ,Ti x = 0.00 1004

0.36 1005 0.45 950 0.64 866 0.82 729 0.91 66 1 1 .oo 584

950 927 830 767 670 535

965 945 924 848 719 630 488

3.3 1.45 1.40 3.5 1.73 1.20 3.8 2.10 1.09 4.0 2.25 1.00 4.2 2.35 0.96 4.0 2.25 1.06

3.0 1.40 2.40 4.2 1.95 1.81 4.3 2.05 1.78 4.2 2.00 1.84 4.1 1.90 1.86 4.0 1.85 1.84 3.7 1.75 1.98

550 NCUYEN Huu Duc

Fig. 1. The deduced A,, as a function of the 3d magnetic moments for a number of Gd-T inter- metallics. The line is a guide for the eye.

techniques as high field measurements [ 11, compensation point [13], neutron scattering [ 141, Mossbauer spectroscopy [ 151, etc. The derived values indicate that for given R,T, series A,, is enhanced when going not only from heavy to light rare earths, but also from Fe to Co. For a given rare earth element when going from this series to other ART does not change very much but one can find that in each system with T = Co and Fe ART decreases with increasing T composition. In order to have a common picture for both the values of ARCo and ARFe we described the change of A,, with the variation of the magnetic moments of 3d electrons. The demonstration is shown in Fig. 1 for the compounds with R = Gd. We note that A,, is systematically decreased with increasing 3d magnetic moment. In connection with this remark, it is very interesting to look how the ART change in the ternary systems of R,(Co, Fe), compounds. We present here the evaluation of A,, for Er(Co,-,Fe,),, Gd,(Co, -,Fe,)17, Gd,(Co, -xFe,)14B, and Sm(Co, -xFex)liTi.

For the Er(Co, Fe), compounds A,, has been deduced according to our experimental T, and 3d magnetic moment M , values and those reported for Y(Co, Fe), (see [16] and references therein) with the note that peff(x) can be obtained from the MT(x) values by scaling peff(X)/MT(X) = peff(x = ~)/M,(x = 1) = 2.1. The results are listed in Table 4a.

For Gd,(Co, Fe),, compounds, the experimental data are taken from literature [17, 181. The data for Gd,(Co, Fe),,B are reported in [19]. In these two series, because T, of the compounds with Y is not sufficient for characterizing the contribution to the ordering temperature of the 3d electrons, the O,(x) are chosen by scaling T, (x) of Y,(Co, -,FeJ17 and Y,(Co,-,Fe,),,B with dd(x = 1) equal to 265 and 535 K and O,(X = 0) equal to 1145 and 990 K for RE,(Co, -,Fe,),, and RE,(Co, -xFe,)14B, respectively. The concentration dependence of peff(x) follows the M,(x) behaviour with the ratio of peff(X)/MT(X) equal to that determined for peff(x = l)/M,(x = 1). In order to have a good view, the data for all mentioned parameters together with the obtained A,, values are listed in Table 4a and b.

The Curie temperatures of Sm(Co, -,Fe,),,Ti reported by Cheng et al. [20] are analysed in the same way with the T, and M , values Y(Co,-,Fe,),,Ti [21]. We note that Tc of the latter compounds can be described by the expression T,(x) = 965 - 445x3. It is used to determine O,(x) for the whole range of Sm(Co, -,FeJl ,Ti intermetallics.

The concentration dependence of A,, in these four tenary systems has a common behaviour: with increasing Fe content, A,, decreases initially and then increases, thus A,,(x)

R-T Spin Coupling Parameter in the Rare Earth-Transition Metal Intermetallics 551

Fig.2. The deduced A , as a function of the 3d magnetic moments for a) Er(Co, -,FeJ2,

Sm(Co,-,Fex),,Ti. The lines are guides for the eye EdCo,, FeXb b) Gd2(Col-xFex)17, Gd2(Col-,Fex)14B, and i j z 0 E j D c

h 9

15 z.0 10

70

shows a minimum at the composition corresponding to the maximum in the MT(x) curves. In connection with this remark the plots of A,, as a function of the 3d moment are presented in Fig. 2a for Er(Co, Fe), and in Fig. 2b for Gd,(Co, Fe),,, Gd,(Co, Fe),,B, and Sm(Co, Fe), ,Ti compounds. It is clearly seen from these figures that ART gradually decreases with increasing 3d moments.

4. Conclusions

On the basic of isotropic exchange interaction between 3d and 4f spins and attributing the molecular field to nearest neighbours the analysis of the Curie temperature within a two-sublattice model has been made in order to estimate the R-T spin coupling parameter for the rare earth-transition intermetallics. The derived values indicate that (i) for a given R,T, system ART is enhanced when going from heavy to light rare earth elements, (ii) for a given rare earth element from one compound to another A,, does not change very much, but one can describe it in relation with the variation of the magnetic moment of the 3d electrons, i.e. with the electron configuration of the 3d layer.

In concluding, it is worthwile to mention here that the ART value in this approach has the meaning of an effective interaction parameter for both R-R and R-T interactions. However, the R-R contribution is quite different in the rare earth intermetallics (for example in 1/5 and 2/17 compounds the R-R contribution to Tc is less than 5%, but in 112 compounds it amounts to one fourth [l]). Thus to get the exact value of the parameter describing the R-T interaction needs a more detailed study, especially for the 112 systems. Anyway, comparing with the results from different experimental techniques one can say that the present values of A,, are good to estimate the effective magnetic field acting on the RE moments.

552 NGUYEN Huu Duc: R-T Spin Coupling Parameter in R-T Intermetallics

Acknowledgements

The author would like to thank Prof. J. J. M. Franse (University of Amsterdam) for his advice and encouragement. He is much indebted to Prof. T. D. Hien, Dr. N. P. Thuy, and Dr. N. H. Luong (of this laboratory) for useful discussions.

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