Magnetic coupling between rare earth moments in some antiferromagnetic Gd compounds

ELSEVIER

Journal of Magnetism and Magnetic Materials 154 (1996) 96-100

~H ~H ~H

Journalof magnetism and magnetic materials

Magnetic coupling between rare earth moments in some antiferromagnetic Gd compounds L.D. Tung

a.b, K.H.J.

Buschow

a,

J.J.M. Franse

a, *,

N.P. Thuy b

a Van der Waals-Zeeman Institute, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands b Cryogenic Laboratory, University o f Hanoi, l-lanoi, Viet Nam

Received 17 July 1995

Abstract The rare earth intersublattice exchange coupling has been studied for several Gd-based antiferromagnetic compounds: GdSi, GdGe, GdSil.67, GdGeL67, GdAg 2 and GdAu 2 by means of the HFFP (high-field free powder) method. The values of the intersublattice coupling constants obtained by this method were compared with values derived from a mean field analysis of experimental values of the NEel temperature, T~, and paramagnetic Curie temperature, ~gp. For several of the compounds investigated a complete moment reversal from the antiparallel to the parallel configuration could be reached in the high-field regime. The reduced saturation moment of the Gd atoms in the parallel configuration is discussed in terms of a reduced moment contribution of the valence electrons.

1. Introduction In the past few years, measurements on free powder samples in high magnetic fields have become a useful tool for studying the intersublattice coupling constant, to z , in many binary and ternary compounds formed from 3d transition elements (T) and rare earth elements (R) [1,2]. This so-called high-field free powder (HFFP) method has tumed out to be useful, in particular when applied to compounds of the heavy rare earth elements in which the rare earth moments, M R, are coupled antiparallel to the 3d moments, M T. The method is based on the assumption that the powder particles are sufficiently small that they can be regarded as a collection o f single crystals that are able to rotate in the sample holder and adopt their equilibrium positions in the field applied. • Corresponding author. Fax: + 31-20-525-5788.

The magnetisation process can then be described as follows: the R and T moments, M R and M r , respectively, remain antiparallel in fields below the critical value, BCR,I = t o 2 J M R - - M T ] , where to 2 is the intersublattice coupling constant. In higher fields the two sublattices start to bend towards each other. The field dependence of the total magnetic moment, M, remains linear during the entire bending process. In fact, it is the slope of this linear part of the magnetic isotherm that offers the possibility to determine the intersublattice coupling constant via the relation M = B / t o 2. Eventually, beyond a second critical field, BCR.2 = 0921M R + M T[, both sublattice moments are parallel and the isotherm adopts a field-independent behaviour. The two sublattice moments show a large size difference in many of the R - T compounds, to the extent that the lower critical field, BCR,I = t o 2 [ M R -M-r I, falls outside or at the periphery of the field range available. This makes it impossible to apply

0304-8853/96/SI5.00 © 1996 El~vier Science B.V. All rights re~rved SSDI 0304-8853(95)00575-7

97

L.D. Tung et al. / Journal of Magnetism and Magnetic Materials 154 (1996) 96-100

the H F F P method without magnetic dilution o f one of the two sublattices. By contrast, a particularly advantageous situation is reached in cases where the two sublattice moments are equal and the linear field dependence c o m m e n c e s already at the origin of the isotherm. The latter situation is actually reached in antiferromagnetic materials in which two R sublattice moments, or two 3d sublattice moments, are coupled antiparallel. This offers the possibility to apply the H F F P method also to antiferromagnets. However, a prerequisite o f the applicability of the H F F P method as described above is that the magnetic anisotropy in one o f the two magnetic sublattices should be negligibly small. In that case the magnetic m o m e n t o f the anisotropic sublattice remains fixed along its easy direction during the entire bending process, and no anisotropy terms occur in the free energy expression. This means that magnetic anisotropy has to be absent altogether, when applying the H F F P method to antiferromagnets with its two identical sublattices. The situation o f negligibly small magnetic anisotropy is most likely met in compounds o f Gd, because o f the pure spin character of the G d m o ments. The present investigation has therefore been restricted to several antiferromagnetic Gd compounds. F o r these compounds, the values o f the intersublattice coupling parameter derived b y means o f the H F F P method will be compared with values obtained from a mean field analysis of the values o f the N r e l temperature, T N, and the asymptotic Curie temperature, ~gp. The latter values are derived from measurements o f the temperature dependence of the susceptibility.

2. Experimental Samples o f the compounds o f GdSi, GdGe, GdSi1.67, GdGel.67, G d A g 2 and G d A u 2 were prepared by arc melting from starting material of at least 99.9% purity. The alloy buttons were wrapped into Ta foil and annealed in evacuated quartz tubes for several weeks at temperatures between 800°C and 900°C. The annealed samples were investigated b y X-ray diffraction and found to be nearly single phase, except for G d G e where non-negligible amounts of an unidentified impurity phase were observed. Structural details of the c o m p o u n d s GdSi, G d G e , G d A g 2 and G d A u 2 can be found in Ref. [3]. The compounds GdSil.67 and G d G e 1.67 have a defect structure o f the A1B 2 type described in Ref. [4]. The temperature dependence of the magnetisation o f the samples was studied in a S Q U I D magnetometer in the temperature range 4 - 3 0 0 K. The field-dependence of the magnetisation at 4.2 K of all compounds was measured at the High-field Installation at the University o f Amsterdam [5]. For these measurements we used samples consisting of fine powder particles that were able to rotate freely in the sample holder into their equilibrium directions.

3. Results and discussion The temperature dependence o f the magnetisation is shown in Fig. 1. All compounds, except GdGe, show behaviour characteristic of antiferromagnets. The corresponding values of the N r e l temperatures are listed in Table 1. For temperatures sufficiently above the N r e l temperature all compounds, except

Table 1 Magnetic properties of several antiferromagnetic Gd compounds derived from SQUID measurements and by means of the HFFP method Compounds SQUID measurements HFFP method

GdSi GdGe [6] GdSi 1.67 GdGe i.67 GdAg2 GdAu2

Tr~ (K)

Op (K)

0"1 (Tkg/Am2)

0"2 (Tkg/Area)

t~eff (/~B)

0'2 (Tkg/Am2)

t~c~ (~B)

Bg~ (T)

56.2 62.0 40.0 15.7 25.0 50.0

-

0.09 0.13 - 0.10 - 0.03 - 0.11 0.29

-0.13 -0.21 - 0.30 - 0.14 -- 0.36 -- 0.37

8.63 8.21 8.10 8.08 7.72 8.18

-0.12 -0.21 - 0.31 - 0.17 - 0.34 -- 0.34

6.81 6.96 7.00

21.2 22.9 24.9

10.5 13.0 80.0 25.7 47.0 - 5.7

L.D. Tung et al. /Journal of Magnetism and Magnetic Materials 154 (1996) 96-100

98

2.0

GdGe, show Curie-Weiss behaviour. The temperature of the reciprocal susceptibility is shown in Fig. 2. The values of the Curie-Weiss intercept, Op, and effective moments, /zeff, derived from these plots are listed in Table 1. For GdGe, due to the contamination by the foreign phase(s), the values of TN and Op listed in Table 1 were taken from Ref. [6]. From the listed values of TN and Op, we have calculated the intrasublattice exchange coupling constant, 0)1, and intersublattice exchange coupling constant, 0)2, using the molecular field expressions oo, =

+

o9 2 = ( 3 k B / N t z 2 f f ) ( O p

-

T N

I

'

25

o [3

20

[3 [3 [3 D o £3 D [3

15

'

r

r

I

50

100

GdGe

O

GdSi

O

GdSi1.67

A

GdGe1.67

V

GdAg2

+

GdAu 2

200

'

I

'

I

'

++ - ++ ++ ++ +++

-

j Z5

2/ /oooooOO°°°°° "

+ vv

an @o~

0.4

0.2

,

'

I 50

,

I 100

,

I

~

I

150 208 Temperature (K)

,

I 258

I 300

Fig. 2. Temperature dependence of the reciprocal susceptibility of GdSi, GdSiL67, GdGel.67, GdAg z and GdAu 2 measured in a field o f l T.

[]

150

I

**

contributions of impurity phases. From the corresponding deviations we have estimated the approximate amounts of ferromagnetic impurity phases present to be about 25% for GdGe and about 5% for GdAg 2 . Obviously, for GdSil.67, GdGel.67, GdAu 2 and GdAg z there is no contribution of the anisotropy of the Gd sublattices to the magnetisation curves because the magnetisation increases linearly with increasing applied field. Therefore, the intersublattice exchange coupling constant, 0)2, can be obtained directly from the linear part of the isotherm representative of the bending process. The corresponding values, obtained by means of the expression 0) 2 =

8

GdSi1.67 GdGe1.67 GdAg 2 GdAu 2

~o

I

30

GdSi

O

08

),

'

O

A ~7 +

1.6

0 '

I

++_

1.8

o.ol I

'

+

where N is the number of atoms per volume unit, and k B is the Boltzmann constant. Fig. 3 shows the field dependence of the magnetisation of the various compounds. For two of the compounds investigated, the magnetisation curves do not start from the origin. This fact is attributed to the 35

1

_

250

380

Temperature (K)

Fig. I. Temperature dependence of the magnetisation of GdSi, GdGe, GdSiL67, GdGeL6 7, GdAg 2 and GdAu 2 measured in a field of 1 T.

B/M,

are given in Table 1. It may be seen from the results in Fig. 3 that the bending process reached Completion for the compounds GdSi, GdGeL6 7 and GdAu 2. The corresponding values of the saturation moments, listed as /ZOO in the table, are slightly lower than the

L.D. Tung et al. /Journal of Magnetism and Magnetic Materials 154 (1996) 96-100

free-ion value gJl~ B = 7/~ B. Estimates of values of the critical field, Bc~r x, at which the bending process is completed, are also listed in Table 1. The isotherm of the compound GdSi is special in that there is a jump-like phase transition at 17.3 T. Such spin-flop transitions usually occur in antiferromagnetic materials in which the magnetocrystalline anisotropy is no longer negligible. In order to deal with this problem we have included an anisotropy term in the free energy expression in the form of a first-order anisotropy constant KI: F = K 1 sin201 + K l sin202 + (-o2 M ? , 2 COS a - - r o B ,

250

~

where 01 and 0 2 a r e the angles between the easy axis direction and the directions of the sublattice moments M 1 and M 2, and a is the angle between the two sublattice moments. The absolute value of the net moment m equals MLz(2 + 2cos a)l/2. Following a procedure described in more detail in Ref. [7], this free energy expression was minimised with respect to a for each applied field strength B. Plots of m versus B were subsequently obtained, keeping K 1 and w 2 as adjustable parameters. The best fit with the experimental isotherm is included in Fig. 3. The corresponding value of K 1 is equal to 6.02 × 10 -23 J/f.u., and the corresponding value of a~2 is included in Table 1. 2oo

I

[ --

GdGe

2o0

150

J

150

8 ~ loo

i

o o

I

i

2O

Magnetic field (T) 150

o 40

o

200

I

C-'~Si 1 . 6 7

e,i

~ loo 8

g

99

//" GdGe1.67

15o

50 5o

r

20

0

40

'

I

I

2O

0

Magnetic field (T) 15o

40

I

:~ 100 ~

2o Magnetic field (T)

40

Magnetic field CO lOO

F

G6~t 2

I

C--~u 2

lOO

8

J

50

i

0

._~ 50

i

i

2O

Magnetic field (T)

40

0. 0

20

Magnetic field (T)

40

Fig. 3. Field d e p e n d e n c e o f the m a g n e t i s a t i o n at 4.2 K o f free p o w d e r s o f G d S i , G d G e , GdSi 1.67, GdGe~.r7, G d A g 2 and G d A u 2.

100

L.D. Tung et aL / Journal of Magnetism and Magnetic Materials 154 (1996) 96-100

Finally, we discuss the results obtained for GdGe. Indications for the presence of a ferromagnetic impurity phase obtained from the magnetic isotherm shown in Fig. 3 are confirmed by the SQUID measurements. The latter shows that the foreign phase is ferromagnetic with a value for the Curie temperature of about 170 K. A small anomaly occurs near 62 K in the temperature dependence of the magnetisation. This value corresponds to the value of the N~el temperature, T N, of GdGe reported previously in [6]. In view of the fact that the antiferromagnetic properties are completely obscured by the ferromagnetic impurity phase in the present temperature dependence of the magnetisation we present in Table 1 the values obtained for T N and ~gp in Ref. [6]. We believe that the high-field data shown in Fig. 3 are still sufficiently reliable to derive a value for the intersublattice exchange coupling constant, w 2, by subtracting the contribution of the ferromagnetic impurity phase for which the magnetisation can be regarded as field independent. The value obtained in this way for co2 is included in Table 1.

ration are generally smaller than the theoretical value gJl~ B = 7.00/x B. This can be taken as an indication that the valence electron spin density has been reduced or even has changed its sign when the Gd moments are forced into a direction that is opposite to that of the local exchange fields. These results are reminiscent of those obtained in ferrimagnetic G d - F e and G d - C o compounds for which band structure calculations [2] have revealed a strong reduction of the on-site valence electron spin density of the Gd atoms when the Gd moments are forced into a direction antiparaUel with the local exchange field, i.e. parallel with the 3d moments. The results obtained in the course of the present investigation have made it clear that a systematic investigation of anfiferromagnetic Gd compounds by means of the HFFP method offers the possibility to give experimental information of the relative importance of the Gd valence electron polarisation in mediating the exchange coupling between the localised 4f moments. Such a systematic study is currently being undertaken.

4. Conclusions

Acknowledgements

Inspection of the two sets of values of the intersublattice coupling constants, w 2, listed in Table 1 shows that these are in satisfactory agreement with each other. This means that the mean field approach leads to a consistent description when applied to the temperature dependence of the magnetisation and the field dependence of the magnetisation in these antiferromagnetic materials. A most interesting phenomenon is revealed when comparing the moment values of the Gd atoms in the antiparallel configuration with those in the parallel configuration. The former are listed in Table 1 in the form of effective moments ].Lef t . For S = 7 / 2 and L = 0 these values should be equal to g [ J ( J + 1)]l/2/xB = 7.94/z B. The experimental data are seen to be generally somewhat in excess of this value, indicating a valence electron contribution (mainly from the on-site 5d electrons) parallel to the 4f contribution. By contrast, the experimental values pertaining to the Gd moments in the parallel configu-

We would like to express our thanks to Drs F.E. Kayzel for his help during the SQUID measurements.

References [1] R. Verhoef, P.H. Quang, J.J.M. Franse and R.J. Radwanski, J. Magn. Magn. Mater. 74 (1988) 43. [2] J.P. Liu, F.R. de Boer, P.F. de Ch~tel, R. Coehoom and K.HJ. Buschow, J. Magn. Magn. Mater. 132 (1994) 159. [3] K.H.J. Buschow, Rep. Prog. Phys. 42 (1979) 1373. [4] P. Schobinger-Papamantellos, D.B. de Mooij and K.H.J. Buschow, J. Magn. Magn. Mater. 79 (1989) 231. [5] R. Gersdorf, F.R. de Boer, J. Wolfrat, F.A. Muller and L.W. Roeland, in: High-field Magnetism, ed. M. Date (North-Holland, Amsterdam, 1983) p. 277. [6] K.H.J. Buschow, P. Schobinger-Papamantellosand P. Fischer, J. Less-Common Metals 139 (1988) 221. [7] Z.G. Zhao, X.Y. Li, J.H.V.J. Brabers, P.F. de Ch~tel, F.R. de Boer and K.H.J. Buschow, J. Magn. Magn. Mater. 133 (1993) 74.