ELSEVIER Journal of Magnetism and Magnetic Materials 152 (1996) 219-225

J H Journal of magnetism

~ H and magnetic

~ H materials

Magnetic and electrical properties of the R(Co, Si)2 compounds (R -- Gd, Tb, Dy) with invariable crystal unit cell parameters

Nguyen Huu Duc 1

Cryogenic Laboratory, Physics Department, University of Hanoi, 90-Nguyen Trai, Dongda, Hanoi, Viet Nam

Received 6 February 1995; revised 23 May 1995

Abstract The invariable crystal unit cell parameter compounds R(Co, Si) 2 (R = Gd, Tb and Dy) have been studied by mean of the

magnetization, ac susceptibility and resistivity measurements. By partial substitution Co by Si, the ordering temperature is almost constant for all of the considered compounds, whereas the reduction of the 3d magnetic moment is observed. In the condition of fixed volume, these findings suggest the important effects of the hybridization between the 3d states of Co and the p states of Si. The anomalies of magnetization, susceptibility, resistivity and the character of the magnetic phase transition at T c are also discussed for the compounds with Dy.

1. Introduct ion

The appearance of the weak itinerant ferromag- netism in the Laves phase compounds RCo 2 (R = Y, Lu, Sc) as AI is substituted for Co has generated a lot of interest in the last decade [1,2]. The role of the A1 atom is to change the density of the states at the Fermi level. However, there is still confusion as to whether it is due to the decrease of the 3d-electron concentration or the lattice expansion. There have been many works dedicated to isolating these two contributions. In a study of the invariable crystal unit cell parameter compounds (Y1- tLu /XC°l -xAlx)2 , Dubenko et al. [3] have shown that the magnetic behaviours obtained for this system can be compared well with those observed for the Lu(COl_xAlx) 2 system. By neglecting the difference between the 4d(Y)-3d and 5d(Lu)-3d hybridizations, the impor-

t Research address: Laboratoire de Magnetisme Louis Nrel, CNRS, BP 166, 38042 Grenoble Cedex 9, France.

tance of the concentration of the 3d electrons has been stressed. The analysis of the ordering tempera- tures in the R(Col_xAlx) 2 compounds (with R = magnetic rare earths), however, suggested strongly that the volume has a major influence [2]. The role of the volume effect can be isolated by high-pressure experiments [4,5]. It indicates, fortunately, that for the Y(COt_xAlx) 2 compounds the change in the chemical pressure between two concentrations of x = 0.145 and x = 0.16 is roughly equal to the change in the critical pressure required to destroy the mag- netic ordering in these compounds. In addition, the studies of the itinerant electron metamagnetism in the invariable 3d-elect ron concentra t ion Y(C°xAlyCUz)2 compounds [6] highlight the impor- tance of the magneto-elastic coupling to this picture. Furthermore, the band-structure calculation [7] has shown that the width of the 3d band is certainly narrowed by the lattice expansion, however, it is not this effect but the effect of the strong hybridization between the 3d states of Co and the 3p states of A! that plays an essential role to the onset of the mag-

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220 N.H. Duc / Journal of Magnetism and Magnetic Materials 152 (1996) 219-225

netic order in Y(Co, AI) 2. In order to obtain more information concerning the role of the substitution atoms at the Co sites, the R(Co, Si) 2 compounds would also be of special interest. In the periodic table, Si is directly to the right of A1; it adds one more conduction electron per substituted atom, whereas the lattice expansion is negligible for the investigated compounds [8]. Magnetic investigations, however, show that the substitution of Si for Co in the Y(Lu)(Co, Si) 2 compounds can only lead to susceptibility enhancement and to a reduction of the critical field for the metamagnetic transitions, but can not trigger the itinerant ferromagnetic state [8,9].

In this paper, we study the magnetization, ac susceptibility and resistivity of the R(Co]_xAI~) 2 compounds with magnetic rare earths R = Gd, Tb and Dy. Emphasis is put on the role of the p(Si)- d(Co) hybridization on the 3d magnetism and on the type of the magnetic phase transitions.

2. E x p e r i m e n t a l

Polycrystalline samples of the R(Co, Si) 2 (R = Gd, Tb and Dy) compounds were prepared by arc-melt- ing stoichiometric mixtures of R(4N), Co and AI(5N) under argon atmosphere. The melted buttons were wrapped in Ta foil and sealed under argon in silica tubes and annealed at 950°C for 60 h. The X-ray analysis shows that the samples are single phase with the C15 crystal structure. The magnetization was measured using the induction method in magnetic fields up to 14 T. Ac susceptibility measurements was performed by using a phase-sensitive detector. The electrical-resistivity data were obtained by means of a four-terminal measuring technique on bar-shaped samples (size about 1 × 1 × 7 mm3).

3. E x p e r i m e n t a l r e s u l t s a n d a n a l y s i s

Since the atomic radius of Si atoms is smaller than that of Co atoms, the lattice constant of R(Co n _ xSix)2 compounds is expected to be reduced. However, in the present investigation, within the experimental errors, we cannot detect the change in the lattice parameter with the Si substitution in the compounds with R = Gd, Tb and Dy. These result

7 0 i i ~ I

Gd(COl_xSix) z 60 H=0.16 T

~ so N

~ 4o

b 30

20

lo

0 i i i 100 200 300 4-00

T (Z)

Fig. 1. Temperature dependence of the magnetization for the Gd(Co I _ ~Si,) 2 compounds.

are consistent with those previously reported for Y(COl_xSi~) 2 and Sc(COl_xSix) 2 compounds [8]. In the recent work of Murata et al. [9], a linear decrease of lattice constant with a rate of d a / d x =

- 0 . 4 ,~ /% at was shown for the Lu(Cot_xSix) 2 coml~ounds. This is negligible compared to that of 5.5 A / % at in the Y(COl_~Alx) 2 compounds [10], and we can consider these series of compounds as an invariable crystal unit cell system.

6 0

5 0

tm

"~ 4 0

3 0 b

2 0

10

I I

Tb(COl_xSix) ~ H=0.16 T

0 I I I

50 150 200 250 300 T (K)

o x = 0 . 0 5

• 0 , 1

v 0 . 1 5

• 0 , 2

I

I 0 0

Fig. 2. Temperature dependence of the magnetization for the Tb(Col _ xSix) 2 compounds.

N.H. Duc / Journal of Magnetism and Magnetic Materials 152 (1996)219-225 221

0.2 - - ~ H=0.I0 T 1

-

r "1 I I I 80 1 0 0 1 2 0 1 4 0 1 6 0 100

T (K)

Fig. 3. Temperature dependence of the magnetization for the Dy(Col_ xSi ~) 2 compounds.

The temperature dependence of the magnetization in applied magnetic field of 0.16 T is presented in Figs. 1-3 for Gd(Co, Si) 2, Tb(Co, Si) 2 and Dy(Co, Si) 2 compounds, respectively. The Curie temperature (T c) was determined by ac susceptibility measure- ments (see below). The results are listed in Table 1. It is clearly seen that for all the systems T c is not very sensitive to the Si substitution. In Gd(COl_xSix) 2, T c slightly decreases from 395 K (for x = 0) to 385 K (for x = 0.1), further increase of Si concentration makes no effect on T c. The later behaviour is observed for whole range Si content in T b ( C O l _ x S i x ) 2 , whereas in Dy(Co~_xSix)2 a slight enhancement of T c (about 5 K) is found around x = 0.05. For DyCo 2, the first-order transition is characterized by a sharp change of magnetization at the transition temperature. Upon substitution Of Co by Si this sharp transition disappears at x = 0.05. For the remaining samples a gradual change of the magnetization is observed around T c. This difference in behaviour is ascribed to the change-over from a first-order transition to a second-order one.

Fig. 4 presents the magnetization curves measured at 4.2 K for Dy(Co, Si) 2 compounds. For all the

Table 1 The values of T o spontaneous magnetization (M~) and 3d-mag- netic moment (M3d) in the R(Co I _ ,S i , ) 2 compounds

R = G d R = Tb R = Dy

T c r c T c M~ M3d (K) (K) (K) (/,L 8 / f .u . ) ( P'B/at)

0.0 395 227 142 7.0 ~ 1.0 0.025 - - 142 6.75 1.15 0.05 390 230 148 6.7 1.20 0.075 - - 146 6.8 1.18 0.10 385 230 146 7.05 1.08 0.15 385 230 143 7.4 0.94 0.20 385 230 143 7.75 0.78

a Data taken from Ref. [12].

investigated Dy(Co, Si) 2 compounds, the magnetiza- tion is almost saturated in the applied magnetic field of 14 T. The saturation magnetization (M s) is listed in Table 1. We note that M s starts to decrease with increasing Si concentration and then strongly in- creases. Taking the value of 9.0 /~s /a t as reported for Dy magnetic moments in DyCo 2 [12] and assum- ing that this value is independent with Si substitu- tion, we then obtain the value of the magnetic mo- ment of the 3d sublattice as listed in Table 1. For comparison, we present in Fig. 5 the 3d-magnetic moment for R(Co, Si) 2 (R = Dy and Lu [9]) and Ho(Co, A1) 2 [11]. It is seen that the 3d-magnetic moment in Dy(Co, Si) 2 is slightly higher than that in

A--- ~ ~nnlhul m l / I m m m nm m m m m un n m m m

niece-S . 6 i |

ee

4 D y ( C ° l . x S i x ) 2

• x = 0.025 o 0.05

2 "A • 0.10 • [] 0.15

• 0.20

0 5 1 0 1 5 B ( T )

Fig. 4. Magnetization curves for the Dy(Co i - xSi ~)2 compounds at 4.2 K.

222 N.H. Duc / Journal of Magnetism and Magnetic Materials 152 (1996) 219-225

~ 1.4

= 1.2 :::k

,~ 1.0

0.8

0.6

," 0.4

E 0.2 |

0 0

' ' ' ' 1 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' '

I I , , I i i i t I i i i i I , , i i [ t i i

0.05 0.1 0.15 0.2 0.25 X

Fig. 5.3d-magnetic moment in the for R(Co, Si)2, Lu(Co I _ ,Si, )2 [9] and Ho(Co, AI) 2 [11].

Ho(Co, A1) 2, but their variation is rather similar: initially the 3d magnetic moment increases, reaches a small maximum at x = 0.05 and finally decreases with increasing Si(A1) concentration. The decrease of the 3d magnetic moment is also observed for the Lu(COl_xSix) 2 compounds. For the R(Co, Si) 2 sys- tem, the 3d moment is induced by both of the internal and external fields over the series. The Lu(Co, Si) 2 compounds are paramagnets at zero field. For these compounds, the plotted value of the 3d magnetic moment is that just after the metamag- netic transition. The larger 3d-magnetic moment ob- served in R(Co, Si) 2 than that in Lu(Co, Si) 2, in one hand, can be account for the influence of the R - C o exchange field. On the other hand, it can be com- bined with the different effects of the external and internal (molecular) magnetic fields on the degree of the 3d-5d hybridization in the Lu- and R-com- pounds, respectively [13].

In Fig. 6, ac susceptibility data of the Dy(Co, Si) 2 compounds are presented as a plot of the reduced X a e / / X m a x against T, where Xm,x is the highest maxi- mum value of X~- For the samples with x = 0.0 and 0.025, for which compounds the para-ferromagnetic transition is of first order, x ~ ( T ) curves are charac- terized by a double peak Xk (at low temperature side) and Xm (at high temperature side) in the vicin- ity of the transition. We note that Xm appears at the temperature at which the discontinuity in magnetiza- tion occurs. In Table 1, this temperature is given as

T c. With increasing Si concentration the low-temper- ature peak (i.e. Xk) becomes weaker and broader, and finally it is absent at the second transition of x = 0.05 compounds. Similar behaviour was ob- served for the (Er, Y)Co 2 and (Dy, Y)Co 2 com- pounds [14,15]. In dc magnetic field, this peak is depressed, becomes broader and shifts to a lower temperature. It originates from the details of the magnetization process (see e.g. Ref. [15]).

The temperature dependence of the electrical re- sistivity of the Dy(Co, Si) 2 is shown in Fig. 7. For all samples, the resistivity tends to saturate above T c. In the compounds with x < 0.05, the first-order tran- sition shows an almost discontinuous change in the resistivity at T c. For the samples with x > 0.075 the resistivity appears to increase with decreasing tem- perature in the ordered magnetic phase. Around Tc, in the RCo 2 compounds, the resistivity is governed by spin-disorder scattering on the (fluctuating) rare- earth and cobalt magnetic moments [14,16]. In these compounds, the drop of resistivity just below T c is thought to be related to the decrease of the spin disorder and the suppression of spin fluctuations in

i J i I i

Dy(C°I-xsi~Tc

~ 0 . 0 2 5

I I I I I

80 100 120 140 160 180

T (K)

Fig. 6. Ac susceptibility of the Dy(Col- ~ Six)2 compounds.

N.H. Due/Journal of Magnetism and Magnetic Materials 152 (1996) 219-225 223

. , . . . . - . . . . . -o:.d

0.075

| ' ' I I

50 100 150 200 250 300 T (K)

Fig. 7. The temperature dependence of the resistivity of the Dy(C01_ xSix) 2 compounds.

the magnetic phase. We see now that by replacing some Co by Si, this picture is no longer valid in the compounds with x > 0.075. A similar result was reported for the R(Co, A1) 2 compounds [16,17]. In Ref. [17], another mechanism was found for the resistivity enhancement, and was related to the for- mation of the (intrinsic) magnetic moment in the 3d sublattice and as expected for a pure volume effect it forms a quadratic relation between the resistivity and spontaneous magnetization. In addition, the contribu- tion due to the peculiarities in the band structure would be taken into account. Obviously, these con- tributions to the resistivity enhancement are much larger than the decrease expected on the basis of the usual spin-disorder scattering mentioned above.

4. Discussion

The analysis of the Curie temperature [2] has suggested a major contribution of volume effects on the 3d magnetism in the R(Co l_xAlx)2 compounds: the volume expansion enhances the magnetic charac- ter of the 3d subsystem and the ordering temperature. The invariable Curie temperature observed in the

R(Co, Si) 2 system with invariable lattice parameters seems to be consistent with this suggestion of the volume effect. In addition, by partial substitution Co by A1, the Y(CoI_~Alx) 2 becomes weak ferromag- nets in the concentration range 0.12 < x < 0.2 [1], whereas the formation of ferromagnetism does not take place in the Y(Co, Si) 2 compounds. However, in this condition of fixed volume, the observed varia- tion of the 3d magnetic moment is still rather similar with that in the R(Co, A1) 2 compounds. In a more detailed analysis, these findings may relate to the d - p hybridization, which shows various effects on the magnetic behaviour [8,9] and on the 4f -3d ex- change interaction [18]. Band calculations performed for Y(Co, A1) 2 and Y(Co, Si) 2 [7] have show that the density of states for Y C o 2 is characterized by the double-sharp peaks near the Fermi level (EF). By partially substituting A1 for Co, the sharp peak at higher energy is reduced. However when E F shifts towards lower energy and goes across this peak the density of states is relatively high and the ferromag- netic state is formed in the Y(Co, A1) 2 compounds. In the case of Si substitution, the peak of d(Co) density of states at higher energy has already de- stroyed at x = 0.25, whereas a broad peak at E F is established in the local S i p density of states. Addi- tionally, it was found that the height of the p(Si) density of states is larger than the p(A1) ones and most of the occupied p(Si) states appear in the lower energy region. This difference in the degree of the p - d hybridization is due to Si atom having an 3p electron compared to A1 and is the reason for the differences in the magnetic ordering phenomena ob- served in these two systems.

The magnetic phase transition in RCo 2 has been well explained well in terms of the Inoue-Shimizu model ([19]; see also Ref. [20]), considering the combination of both effects of the 3d-itinerant elec- trons and localized spins. In this model, the type of the phase transition is determined by the sign of the coefficient c 3 ( T c ) / / 4 of the M 4 term in the expan- sion of the free energy as a function of the total magnetization M = M R +Mco. The value of c 3 at T c is given by

c 3 = {a 3 + b 3 ( n R c o / b , ) 4 } / ( l + n R c o / b l ) . (1)

In this expression, b 1 and b 3 are the coefficients of

224 N.H. Duc / Journal of Magnetism and Magnetic Materials 152 (1996) 219-225

the MR 2 and M 4 terms, respectively, in the expan- sion of the free energy of the R-sublattice magnetiza- tion [24]. The coefficient b I can be written as b I = b ° -nRR, where b ° equals T/c R. a 3 is the corre- sponding coefficient in the expansion of the free energy of Co 3d-subsystem.

Following Bloch et al. [21], the approximation of temperature dependence of a 3 is given as

a3(T ) -- a3(0){1 - (T/T3)2}. (2)

Here, a3(0) is negative; T 3 is a characteristic temper- ature depending on the detailed band structure, but it is more suitable to regard T 3 as the temperature at which a3(T) change sign. In recent theoretical work of Yamada [22], it was confirmed that T 3 is close to the temperature Tin, at which the 3d susceptibility reaches a maximum. Moreover, a generalized condi- tion for the metamagnetic transition is given as

3 /16 < a = alas/a ~ < 9 /20 (3)

where a~, a 5 > 0 and a 3 < 0. The sign of c3(T c) is practically governed by that

of a3(Tc). Thus, the possibility of the appearance of a first order transition in RCo 2 is, first of all, deter- mined by the metamagnetic behaviour of the 3d subsystem. For the compounds under investigation, this can be understood by considering the magnetic behaviour of the Lu(Co, Si) 2. In the work of Murata et al. [9], the metamagnetic transition was observed for the Lu(COl_xSix) 2 with x < 0.09. This indicates that, at low temperatures, not only a 3 is negative but the generalized condition (3) for the metamagnetic transition is satisfied for x < 0.09. However, as men- tioned above, the first-order transition at T c is only observed for the Dy(COl_xSix) 2 with x_< 0.025. A similar phenomena was found for R(Co, A1) 2 sys- tem. Experimentally, guided by the linear relation- ship between the critical field of the metamagnetic transition b c and the temperature T m [1], a scaling between T m and T 3 has been made for the R(Co, AI) 2 compounds [11]. It gives an explanation that the cross-over of the decreased T3(x) and increased Tc(x) agrees with the observed change of the type of the phase transition in the R(Co, A1) 2 compounds. However, this assumption gives rise to a rather large difference between the T 3 and T m. Following Ya- mada's theory [22], instead of the condition of a 3 < 0,

the condition (3) is more general for the considera- tions of the first-order transition. At present, we can qualitatively discuss this problem as follows.

As can be seen from Eq. (2), a3(T) changes its sign from negative to positive at T 3 ( = Tm). This mean that a3(T) becomes zero at T m. On the other hand, aj(T) ( = Xco(T) -1) does not change sign at any temperature. Therefore, a ( T ) increases with increasing temperature at T < T~ and diverges at T m. If a ( T c) > 9 / 2 0 is satisfied, the transition becomes second order even with al, a 5 > 0 and a 3 < 0. This usually occurs just below T m. The fact that T m decreases by replacing Co by Si means that the validity of the condition (3) for the first order transi- tion will shift to lower temperatures. For the investi- gated Dy(Co~_~Si~) 2, the cross-over of the de- creased Tin(x) and the invariable Tc(x) occurs at x = 0.04, and, experimentally, the change from a first-order to a second transition is observed at x = 0.05 (see Figs. 3, 6 and 7). In a combined system of itinerant electrons and localized spins, the effect of exchange interaction from rare-earth moments must be taken into account. In this case, not only the relation between the a~, a 3, a 5 coefficients, but the relation between the c z, c 3, c 5 coefficients (e.g. Eq. (1)). However, such a approximation is not devel- oped yet.

5. Concluding remarks

In the invariable crystal unit cell parameter R(Co, Si) 2 compounds, the electronic properties (in particu- lar 3d magnetic moment and resistivity) strongly change when Co is replaced by Si. In the condition of the fixed volume, the hybridization between the Co d states and S i p states shows an important role on the 3d magnetism. The magnetic phase transition in these compounds is of special interested because of the enhancement of 3d susceptibility and the reduction of the critical field for the metamagnetic transition. At low temperatures, the induced charac- ter of 3d-magnetic moment is observed and the internal (molecular) field acting on the 3d-subsystem is larger than the field required for the metamagnetic transition. However, the decrease of T 3 (i.e. T,,) shifts the border between the first-order and second- order transitions to lower temperatures and then the

N.H. Duc / Journal of Magnetism and Magnetic Materials 152 (1996) 219-225 225

character o f the first order transition is no longer

exist.

Acknowledgements

Exper iments in the temperature range of l iquid

n i t rogen were pe r fo rmed by N g u y e n Song Binh. The

author is indebted to Prof. H. Yamada for valuable

discussions. A stay of N.H.D. at Louis NEel Labora-

tory, C N R S (Grenoble , France) has been very useful

for the comple t ion o f this work.

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