Short Notes K29

phys. stat. sol. (b) 176, K29 (1993)

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

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

4f-3d Coupling in the Dy,(Ni, -xCo,)l, Compounds

BY NGUYEN Huu Duc

Introduction In the rare earth-transition metal intermetallics, it is generally accepted that there are three types of interactions, namely, the R-R interactions between the magnetic moments within the R-sublattice, the T-T interactions between the magnetic moments of the T-sublattice, and the R-T intersublattice interactions. The T-T interactions are direct exchange interactions between the 3d spins, whereas the R-R interactions are indirect, presumably proceeding via the 4f-Sd-Sd-4f mechanism. The R-T interactions are also indirect, being a combination of the intraatomic 4f-5d and interatomic 5d-3d exchange interactions [l]. As a general rule, the latter interactions are found to be antiferromagnetic for electrons residing in a less than half-filled d band (the 5d band) interacting with electrons in a more than half-filled d band (the 3d band). By means of this scheme, it can be understood that the magnetic ordering in the R-T intermetalliccompounds is either of the ferromagnetic type, if R is a light rare earth element, or of the ferrimagnetic type, if R is a heavy rare earth. This was first suggested, on the basis of experiment, by Campbell [l]. Recently, Brooks et al. 121 were able to add to this picture the importance of the 3d-5d hybridization. Following this model, when a moment develope at the T-sites, the energy of spin-up 3d states is lowered, reducing the 3d-5d hybridization for the spin-up states. This lowers the occupation of the 5d spin-up states. The opposite effect occurs for the spin-down states and the 5d moment which is related to the 5d occupation is induced. The 4f-5d and thus the 4f-3d interactions are created. In the R-T compounds having a large magnetic moment of the T-sublattice, i.e. possessing a large 3d band splitting, the hybrized states will have more spin-down character. This leads to an increase of the 4f-3d interactions with increasing T magnetic moment. Experimentally, a decrease of the 4f-3d exchange interactions, i.e. a decrease of the 3d-5d hybridization, with increasing magnetic moment of the T-sublattice (M.l.), has been found for almost all of the R-Fe and R-Co compounds [3 to 61. However, it was shown in [7] that in the compounds, where the 3d magnetism is well established, the variation of M , does not depend strongly on the 3d band splitting, but is mainly governed by the decrease of the 5d magnetic moment. The Brooks model, thus, may directly be examined on a few series of compounds such as R2Nil,, RCo,,Be, RCo,, and RCo,B [7]. In these compounds, the small value of MT is related to a weak 3d band splitting, and any increase in M , is thought to result from the increase of the 3d band splitting. As regards the value of M,, the studies on the nickel-rich R-(Ni, Co) or R-(Ni, Fe) systems can extend the latter group of compounds. The aim of the present note is to evaluate the 4f-3d coupling parameter in the DY,(Nil -xCox)17 compounds by analysing the Curie temperature and the compensation points. The results are discussed on the basis of the Brooks model. -~

') 90 Nguyen Trai Str., Dongda, Hanoi, Vietnam.

21'

K30 physica status solidi (b) 176

Experimental results and analysis Polycrystalline samples of the Dy,(Ni, -xCo,)17 compounds (x = 0, 0.1,0.2, and 0.4) were prepared by arc-melting under argon atmosphere. Magnetisation measurements were performed by an induction method, whereas a phase sensitive detector method was used to measure the ac susceptibility. The temperature dependence of the magnetisation of the investigated compounds in an applied field of 0.2 T is presented in Fig. 1. All compounds are ferrimagnetic as follows from the observed compensation points at a temperature denoted by Tk. Values of T, and Tk are collected in Tables 1 and 2, respectively. These results were confirmed by ac susceptibility measurements.

Usually, the simplest .approximation to the interactions which couple the directions of 4f and 3d spins can be expressed as an effective exchange of the Heisenberg type,

30

20

I so 5 7 00 200 300

b

20

10

0 200 400 600 T(K1-

Fig. 1. Magnetisation as a function of temperature for the Dy,(Ni, -xCox)l, compounds

Short Notes K3 1

where S , and S , are the spins at the R- and T-sites, respectively. A,, is the exchange coupling between the neighbouring R- and T-spins.

In a two-sublattice model, the molecular field approximation leads to an expression for the exchange energy

E,, = -n,,M,M, . (2)

I f only nearest neighbours are considered and assuming that the R-T exchange coupling is spatially isotropic and distance independent, the molecular field coefficient nRT is related to A , , through

(3)

where Z,, is the number of the nearest T-neighbours of a given R-atom, N , the number of the T-atoms per mole, and other terms have their usual meaning. Analogously, one can define a molecular coefficient nTR, proportional to A,,( = ART) and the number of nearest R-neighbours of a T-atom Z,,, as

(4)

An indirect method used to evaluate the value fo A,, is to compare the magnetic ordering temperature of isostructural compounds with magnetic and non-magnetic R-elements according to the mean-field expression [3]

lZRT = 'RTART(g - ')/gpgNT 3

nTR = 'TRARTk - l)/gpiNR.

= 914T,(Tc ~ TT)/~ZRTZTRGRGT, ( 5 )

where T , is the Curie temperature, T, represents the contribution to T, due to T-T interactions. G, is the de Gennes factor (8, - 1)' J ( J + 1) for rare earth atoms; G,, the corresponding factor for the transition metal, is inserted to obtain a symmetric expression. Assuming that the orbital moment of a T-atom is quenched leads to g, = 2 and

At present, the T , values were obtained from the ordering temperature of the Y, (Nil -xCo,)l compounds [8]. In the high temperature approximation of the mean-field model, the effective spin value S , can be determined from the data of the 3d effective paramagnetic moment, peff. In R,Nil,, pefr = 1.51pB/at [8], whereas the magnetic moment in the ordering state Md(0) equals 0.33pB/at. It turns out that the ratio of pCf,/Md(O) = 4.6. This ratio is larger than that (about 2) reported for almost all of the R-Co and R-Fe intermetallics [8]. It reflects the itinerant character of the 3d electrons in these compounds. For other investigated compounds, only Md(0) is reported (see Table l), the Pctf value is

G , = ST(S., + 1).

T a b l e I The experimental T, and deduced exchange coupling parameter A,, for the Dy,(Ni, -xCo,), , compounds. The values of TT, Md(0), and perf (see text) are also listed

0.0 162 141 0.33 1.50 0.63 0.1 300 268 0.47 2.17 0.79 0.2 390 353 0.58 2.67 0.88 0.4 660 583 0.85 3.92 1.36

K32 physica status solidi (b) 176

Table 2 The experimental Tk and deduced intersublattice molecular field coefficient nRT and exchange coupling parameter A,, for the Dy,(Ni, -xCox)17 compounds

0.0 100 1.99 0.66 0.1 120 2.31 0.77 0.2 140 2.69 0.89 0.4 208 4.19 1.39

thus derived by keeping the same ratio of peff/Md(0). Finally, the crystal structure of the R,Ni,, compounds involves average numbers of ZRT = 19 and Z,, = 2.5. The corre- sponding value for ART estimated from ( 5 ) after substituting these parameters is listed in Table 1. We noted that the result obtained by this way for Dy,Ni,, is in good agreement with that deduced from the high field magnetisation measurements [9].

The exchange interaction parameter can also be evaluated from the temperature of the compensation point. In this case, we approximate the temperature dependence of the rare earth moment by a Brillouin function,

The value for M , is determined from experiments. Assuming that the 3d magnetic moment is less temperature dependent in the temperature range which is much lower than T,, here we can employ the results obtained at 4.2 K. The resulting values for nRT (and A,,) are collected in Table2. This value is in satisfying agreement with that deduced from the expression for T,.

Discussions It follows from the values listed in Tables 1 and 2 that there is a fairly strong increase of the intersublattice coupling strengths when increasing the Co content. In order to understand the present result, we relate ART with the magnetic moment of the T-sublattice as plotted in Fig. 2. For comparison, data reported for GdCo,,B,, GdCo,B, and GdCo, compounds [4,5] are also plotted in the same figure. We note that A,, increases almost linearly with increasing M , and shows a tendency to vanish at M , = 0. The interactions between 4f and 3d spins are mediated entirely by 5d spins induced by the hybridization with the 3d bands [2]. Within the concept of the 3d-5d hybridization this feature can be understood as follows.

Before hybridization between the two sets of d bands, the pure 3d bands are almost filled and the pure 5d bands are almost empty. The pure 3d and 5d bands hybridize to form a hybridized region at the top of the 3d bands and at the bottom of the 5d bands. However, when the 3d band is not split, i.e. no magnetic moment develops at the T-sites, the occupation of the 5d spin-up and spin-down states is the same and the 5d magnetic moment at R-sites equals zero. In this case, 4f-3d interactions do not exist. When a moment develope at the T-sites, the energy of spin-up 3d states is lowered, reducing the 3d-5d hybridization for the spin-up states. This lowers the occupation of the 5d spin-up states. The opposite effect occurs for the spin-down states and the 5d moment which is related to the 5d occupation

Short Notes K33

.--. -3

Y N

4 - 1.0 2

0.5

0

Fig. 2. Variation of A,, as a function of magnetic moment of the T-sublattice in the Dy,(Ni, -xCox)17 compounds. Data are included for GdCo,,B,, GdCn,B, and GdCo, [5]

is induced. The 4f-5d and thus the 4f-3d interactions are created. The induced 5d magnetic moment would, therefore, strengthen with increasing 3d band splitting and the observed increase of A,, with M , is understandable.

Acknowledgement Part of experimental works in this note has been performed by Do Dieu Huong.

References

[I] I . A. CAMPBELL, J. Phys. F 2, L478 (1991). [2] M. S. S. BROOKS, L. NORDSTROM, and B. JOHANSSON, Physica 172B, 95 (1991). [3] N . H. Duc, phys. stat. sol. (b) 164, 545 (1991). [4] N . H. Duc, T. D. HIEN, and D. GIVORD, J. Magnetism magnetic Mater. 104-107, 1344 (1992). [5] N . H. Duc, T. D. HIEN, D. GIVORD, J. J. M. FRANSE, and F. R. DE BOER, J. Magnetism magnetic

[6] F. R. DE BOER and K. H. J. BUSCHOW, Proc. Conf. on RHMF, Amsterdam 1991; published in

[7] N. H. Duc, phys. stat. sol. (b) 175, K63 (1993). [8] H. R. KIRCHMAYR and C. A. PODY, J. Magnetism magnetic Mater. 8, 1 (1978). [9] X. P. ZHONG, F. R. DE BOER, T. H. JACOBS, and K. H. J. BUSCHOW, J. Magnetism magnetic Mater.

Mater. (1992), in the press.

Physica B (1991).

92, 46 (1990).

(Received October 16, 1992)