A spin-glass state in the itinerant magnet systems Y(Co1−xMnx)2 and Lu(Co1−xMnx)2

Journal of Magnetism and Magnetic Materials 119 (1993) 294-300 North-Holland

A spin-glass state in the itinerant magnet systems Y(COl_xMnx) 2 and Lu(Col_xMnx) 2 R. B a l l o u a B. B a r b a r a a n d A.S. M a r k o s y a n b

a,

Z.M. Gamishidze

b,

R. L e m a i r e c, R . Z . Levitin b

a Laboratoire L. N~el, CNRS, 166X, 38042 Grenoble cedex, France b Physics Department, M V. Lomonosov Moscow State University, Leninskie Gory, 119899 Moscow, Russian Federation c Universitg Evry Val d'Essonne, Boulevard des Coquibus, Evry, France Received 24 July 1992

Magnetic properties of the Y(COl_xMnx) 2 and L u ( C o l _ x M n x ) 2 Laves phase systems are studied. S p i n - s p i n correlations are found to increase as the M n concentration increases from x = 0, and to pass over a m a x i m u m for x = 0.35. A spin-glass state is established within limited ranges of the Mn concentration x, b o u n d e d to = 0.04 < x < 0.4 in the Y based c o m p o u n d s and to = 0.04_< x < 0.5 in the Lu based compounds. Emphasize is m a d e on the Stoner-character of the m a g n e t i s m of the compounds, which should lead to a spin-glass state distinguishing itself by frozen longitudinal spin fluctuations below the spin-glass freezing temperature Tsc.

I. I n t r o d u c t i o n

The cubic Laves phase YCo 2 and LuCo 2 are exchange enhanced itinerant paramagnets [1]. The criterion for the existence of ferromagnetism (Stoner criterion) IN(E e) > 1 (where I is the d - d exchange integral and N ( E f ) is the density of d-states at the Fermi level) is not fulfilled for these compounds though they are very close to be ferromagnetically ordered (IN(Ef)=0.9 [2,3]). Owing to this circumstance and the fact that the density of states near Ef depends strongly on energy, the magnetic properties of these compounds, as well as those of the isostructural intermetallics RCo 2 with magnetic Rare earths R, show a high sensitiveness to various substitutions in the d-subsystem which act on the position of the Fermi level and (or) on the shape of N(E) near Ef [4]. It was established that small substitutions of aluminium for cobalt intensify the spin-spin cotCorrespondence to: Dr. R. Ballou, Laboratoire L. N~el, CNRS, 166X, 38042 Grenoble cedex, France.

relations in the RCo 2 intermetallics. This leads to the onset of a ferromagnetic order in the R ( C o 1 - x A l x )2 compounds with nonmagnetic rare earths i.e. with Y and Lu [5-8] while the Curie temperature Tc of the RCo 2 compounds with magnetic rare earths increases rapidly at these substitutions [9,10]. Recent investigations of the R(Co~_xMnx) 2 compounds with magnetic rare earths show a similar increase of the spin-spin correlations in the itinerant d-subsystem at also small substitutions of manganese for cobalt [11]. Nevertheless, it is difficult to study the intrinsic magnetic properties of the d-subsystem in these R(COl_xMnx) 2 compounds because of the strong f - d exchange field acting on the d-subsystem modifying its magnetic behavior in an essential way. We found it therefore interesting to study the magnetic properties of the Y(COl_xMnx) 2 and Lu(Col_xMnx) 2 compounds. The experimental investigations already performed on the former appears at a first sight rather contradictory. It has thus been been reported that a ferromagnetic order is stabilized in Y(COl_xMnx) 2 for x >_ 0.1

0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

295

R. Ballou et al. / Spin-glass state in T(Co 1 _ xMnx)2 and Lu(Co s _ xMnx)2

[12]. On the other hand, electrical resistivity m e a s u r e m e n t s [13] and small angle neutron scattering [14] suggest that no long-range order is occurring at least up to x = 0.2. Analogous investigations for the Lu(COl_xMnx)2 compounds are still lacking. W e p e r f o r m e d a systematic study of the magnetic characteristics of the Y(COl_~Mn~) 2 and Lu(COl_xMnx) 2 compounds in wide ranges of the concentration x and of the temperature. A main purpose of these investigations was to elucidate the magnetic ground state of these systems and build their magnetic phase diagrams.

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

Polycrystalline samples of the Y(COl_xMnx) 2 and Lu(COl_xMn~) 2 compounds were p r e p a r e d from the starting elements, under an argon atmosphere, in an induction furnace with a watercooled copper crucible, providing a quasilevitation regime of the melting process. T h e obtained ingots were then wrapped in tantalum and annealed for 140 h at 720°C under vacuum in a quartz tube. After annealing, the samples were analyzed by the X-ray D e b y e - S c l r e r r e r method. A single C15 cubic Laves phase was found in the whole 0 < x < 1 concentration range for the Y(Col_xMnx)2 compounds (as opposed to the data of ref. [12]). On the other hand, for the Lu(COl_xMnx) 2 compounds a single C15 cubic Laves phase was found only within the 0 _
Different m e a s u r e m e n t s were performed on the p r e p a r e d samples in the 4-300 K temperature range i.e. magnetization in fields up to 70 kOe either by making use of a vibromagnetometer or by the axial extraction method, magnetic susceptibility under ac magnetic fields up to 3 Oe by the bridge method and thermal expansion by means of X-ray diffraction.

3. Results

Our m e a s u r e m e n t s showed that for some Y(COl_xMnx) 2 and Lu(COl_xMnx) 2 compounds, the initial magnetic susceptibility has a nonmonotonic thermal variation and exhibits a pronounced cusp (fig. 1). In effect, these cusps are observed within given ranges of the Mn concentration x, bounded to = 0.04 < x < 0.4 in the Y based compounds and to = 0.04 < x < 0.5 in the 1

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i

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X

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0.20

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]~k

i ....

i ....

i ....

Y(C°l.xMnx) 2 =

.~ o.o "~ 0.4 <

0.2 0

0

"~

10

20

30 40 50 60 Temperature (K)

Lu(C°l-xMnx)2 X

~

x.o,o

1/

,,o

.R

70

80

X 0.30 =

=0.10

0.6

"~. 0.4 m 0.2 < 0

. . . .

0

i

10

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i

20

. . . .

i

30

. . . .

i

40

. . . .

I

50

,

,

,

,

60

Temperature (K) Fig. 1. Thermal variation of the initial ac magnetic susceptibility of the Y(Co l_xMnx)2 and Lu(Co l_xMnx)2 compounds.

296

R. Ballou et aL / Spin-glass state in T(Co 1_ xMnx)2 and Lu(Co 1 _ xMnx)2

50

g

0.6

40

o

' /

0

° Lu(C°lxMnx)2

....

~.

. . . .

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. . . .

i

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i

. . . .

o.7

"~ m°'2

t

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0.3

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0.1

i

. . . .

i

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-

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. . . .

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i

10

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~

20

. . . .

i

30

. . . .

40

50

A p p l i e d field (kOe) Fig. 4. Magnetic isotherms M ( H ) of the Lu(Co0.7Mn0.3) 2 compound at different temperatures.

lar features with respect to the Mn concentration x, only the magnetic data of one of these two series of compounds will now be reported in this section. According to wether the compounds belong to the SG-region or not, the measured magnetic field dependence of the magnetization is very different. Within the SG-region the magnetic isotherms are nonlinear and show a tendency for a saturation in high magnetic field (fig. 3). On the other hand, at low temperature the magnetization process shows an irreversibility (see inset of fig. 3). At increasing the temperature the nonlinearity of the magnetic isotherms dwindles away 0.8

. . . .

. . . .

I

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~

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•

0.7

T-2K

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x = 0.25 x = 0.30

0.6

.o

x == 0 . 1

~e~ 0.2

. . . .

Lu(C " o o0. . 77Mno. o.:3) 2

0

0.4 -

I

I f

x=0.4

.~0.0,

0.3

=

o.1

N

"~

. . . .

~~ ' -

i

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t

. . . .

I

. . . .

I'

0.4 I

N

•-

• Y (2C O t ..x M n x ) . X

/

zl. 0.5 •.

i

Lu(Co I xMnx)2

~.... .'~

•~

~

0

Lu based compounds (cubic phase) and named hereafter as SG-regions. Out of these SG-regions, the initial magnetic susceptibility depends but slightly on the temperature• The cusp temperatures TsG of both the Y and Lu based compounds are shown in fig. 2 as a function of the Mn concentration x. The maximal values of TsG are reached in both the Y and Lu based compounds for the same Mn concentration x--0.35 which is close to the concentration (x = 0.25) at which the maximal values of the Curie temperature are observed in the R(COl_xMnx) 2 compounds with magnetic R species [11]. As the evolution of the magnetic properties of both the Y and Lu based compounds show simi-

~". . . . . . . .

0.4

0.5

Fig. 2. Variation of the ac susceptibility cusp temperature TSG with respect to the Mn concentration x for the Y(Co t _~Mn~) 2 and Lu(Col_xMnx) 2 compounds.

0 . 8

~

i

i .... i .... i .... ~. . . . . 0.1 0.2 0.3 0.4 Mn Concentration x

0

. . . .

o sl o

20

L) =

i

T=2K: ~ T = 3 0 K _

30

i

. . . .

i. Z

\

4 / ,d

o Lu(Col.xMnx)2 ,

"t',

H

= 30

kOe

0.3

~D

o I~' 0

I'

4 []

[]

0.2

o.

0.1

I'

i f

7,'/

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20

30

40

50

60

A p p l i e d field ( k O e ) Fig. 3. Magnetic isotherms M ( H ) of some Lu(Co]_xMnx) 2 compounds at 5 K. The inset shows an hysteresis loop for Lu(Co0.6Mn0.4) e at the same temperature.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mn Concentration x Fig. 5. Variation with respect to the Mn concentration x, of the magnetization measured at 30 kOe and at 2 K on the Y(Co I _xMnx)2 and Lu(Co I _xMnx)2 compounds.

R. Ballou et al. / Spin-glass state in T(Co 1 _ xMnx)2 and Lu(Co l _ xMnx)2

.-.

700

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.

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.

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r

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.

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.o..,......e- o- oo,,- Oo

Lu(C°o.4Mno.6)2

500

i

ab.~.4 -~¢

t~. °"

~ ..o .o. 4- -'o"'°"

.ffJff"

N 300

&

r/l

"N 200

/

, ~ , 100

Lu(C°o.6Mno.4)2

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i

50

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.

i

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100

i

150

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200

Temperature (K) Fig. 6. Thermal variation of the reciprocal susceptibility of the Lu(Coo.6Mno.4) 2 and Lu(Coo.4Mno.6) 2 compounds.

and disappears progressively above Tsc (fig. 4). Out of the SG-region the magnetization varies linearly with the applied field. It may be noticed that the magnitude of the magnetization under a given magnetic field is much higher within the SG-region than out of it. This is well illustrated in fig. 5 where the value of the magnetization measured under an applied field of 30 kOe is reported with respect to the Mn concentration x. In the paramagnetic phase the tiaermal behavior of the magnetic susceptibility depends also on whether the compound belongs to the SG-region or not. As to illustrate this we show in fig. 6 the thermal variations of the reciprocal susceptibility of the Lu(Co0.6Mn0.4) 2 and Lu(Co0.4Mn0.6) 2 compounds which are respectively inside and beyond the SG-region. While inside the SG-region a Curie-Weiss type behavior with an effective moment of about 3.6/.~B is observed, beyond the SG-region the susceptibility is rather characteristic of a spin-fluctuation system, with a spin fluctuation temperature which when estimated at the inflection point of the thermal variation reaches about 100 K.

4. Discussion Inside the SG-region the magnetic behaviors of the compounds differ basically from the exchange enhanced paramagnetism of the com-

297

pounds which do not belong to this SG-region. On various respects, the observed properties (e.g. the nonlinearities and hysteresis of the magnetization curves at low temperature) show up the onset of finite 3d moments within the limited range of the Mn concentration x that defines the SG-region. An explanation for this onset is that the spin-spin correlations are enhanced when Mn is substituted for Co. A similar enhancement is induced by AI substitution leading to a ferromagnetism in the Y(COl_xAlx) 2 and Lu(Col_xAlx) 2 compounds [5-8]. At large Mn concentration magnetic frustration come into play to inhibit the onset of the magnetic moment. A highly exchange enhanced spin fluctuation state then set up again. Such a frustration induced vanishing of moments is expected in systems close to a magnetic-nonmagnetic instability [16]. In the Y based compounds, a magnetic moment is restored when reaching the YMn z limit as the stability of Mn magnetism in this compound overcome frustration effects. It is clear that when the 3d moments are not to vanish they will interact with each other, with in particular positive Co-Co interactions and negative M n - M n interactions. Consequently, the chemical disorder inherent to the random substitution of Mn for Co should lead to a spin-glass state, in contradiction with earlier conclusions stating that the compounds in the SG-region should be ferromagnetically ordered [12] but in agreement with more recent studies [13,14] according to which no long-range magnetic order sets up in the Y(Cot_xMn~)2 compounds at least up to x = 0.2. An analysis of the magnetic isotherms in terms of Arrott-Belov plots (M 2 vs. H / M ) corroborate the assumption of a spin-glass state. Indeed, the magnetic equation of state of a ferromagnet near the Curie temperature writes H = A M + B M 3 where A < 0 in the ferromagnetic phase, A > 0 in the paramagnetic phase and A = 0 at the Curie point. Arrott-Belov plots of the Y (Co0.75Mn0.25) 2 and Lu(Co0.75Mn0.25) 2 compounds having strong spin-spin correlations are displayed in fig. 7, at different temperatures above and below TsG. As shown up in the figure, the coefficient A is always positive and does not

298

R. Ballou et al. / Spin-glass state in T(Co~ _ x M n x ) 2 a n d L u ( C o I _ x M n x ) 2

0.25

. . . .

,

. . . .

,

. . . .

,

. . . .

. _ _

,

. . . .

T= 36K

Y(Co0 . 7 5 Mn0 . 2 5 ) 2

0.2

T s G = 38 K 0.15

~,~ T =--38 K o ~

~"~

°°° ~.

c~.,~'~" ~ ~¢

¢;:9"

0. l 0.05

-

.~o,O OT-42K

T=48K

M = C,(H/T)

L ~ ° ' °G I

0 "0

5

10 15 20 H/M (kOe/g~)

25

30

0.3 [ . . . . ' . . . . ' . . . . ' . . . . T= 20'K ,." ' T - 3 b K t 0.25 f L u ( C o O 7sMno 2s)2 ~ P ~ T = 34 q [ T "- 3 6 K "#gl'd~"Al~T = 38 K 1 ~

01

o.15

freezing point i.e. TsG (whereas it has to diverge at the Curie point for a ferromagnet) and it is the third order susceptibility X3 which diverges at Ts~. In fact it may reveal more convenient to expand the magnetization M by including its temperature dependence i.e. to write:

T=10K

+ C3(H/T) 3 + ''',

where the C z are generalized Curie constants. C 1 remains constant for a spin-glass (whereas Xl shows a cusp at Tsc) and C 3 has to diverge (as does X3) when the temperature falls down to TsG. Experimentally, this is roughly what is obtained as shown in fig. 8, where the temperature dependences of C 1 and C 3 for the Y(Co0.75 Mn0.25) z and Lu(Co0.75Mn0.25) z compounds are reported. A rapid increase of C 3 is observed as the temperature falls down to Tso while C 1 changes regularly but does not show any tendency

0.1

0.05[ ~¢~tee-.at ~'~--T -- 54"7 K 0 . . . . . n~'Y~.,,~%.. ~ ' . . . . . . . . . . . . . . . . 0 10 20 -30 40 50 60 70 H/M (kOe/kta)

7O

t

/

~" 80

Fig. 7. Arrott-Belov plots of the Y(Coo.75Mno.25) z and Lu(Coo.75 Mno.25)2 compounds.

change its sign as the temperature falls down to Tsc and below it. It may then be concluded that no ferromagnetic ordering is occurring. In fact the Arrott-Belov plots in fig. 7 are very similar to those used to describe the properties of random anisotropy or spin glass systems (see e.g. refs. [17,18]), which enforces the reliability of the interpretation of all the phenomena observed in the SG-region of both the Y and Lu based compounds in terms of spin-glass ones. Going further in the spin-glass interpretation, the magnetization M of the compounds in the SG-region, at temperatures above Tsc, can be expanded in terms of the applied field H as

¢-

= X1H

+ X3 H3

+

• • • ,

where the Xz are the ith order susceptibility. According to refs. [19,20], Xl remains finite for spin-glasses as the temperature falls down to the

!.

I

8

5o

N

40

,~

30

~

20

~

10

t

~'~ '~

'~

~=

8

....

40

~ ....

i ....

6

i ....

i ....

i ....

i ....

i ....

L u ( C o 0.7S Mn °

'~

T

'~

(..)

~ . . . . ~ . ° 7 "~.: .. ~ , m . . _ . ,eSj _" " "/': 45 50 55 60 65 70 Temperature (K)

~,~,- C3.10_3 ~I

•, =

SG

~ ....

35

9

Y(COo.TsMno.25) 2 T =38K

°" "°" x~. ~" ~ 8 .r~.~ .o _....o _ . -

CI

....

30

10

3

~. ~ , C3.10-

0

~.

SG

=

36

2S)2

~

K

'.

2

r~

M

60

*,,p xo 0 ' " ~ . . . . ~. . . . ~ ' " ~ T : ' : : ~ ' - ' - ' ~ - ' - ~ ..... 30 35 40 45 50 55 60 65 70 Temperature (K)

Fig. 8. Thermal variation of the generalized Curie constants of the Y(Coo.75Mno.25) 2 and Lu(Co0.75Mn0.25) 2 compounds.

R. BaUou et al. / Spin-glass state in T(Cot_ xMnx) 2 and Lu(Col_ xMnx)2 Table 1 Spin-glass freezing temperatures TSG and critical parameters A' and a of the Lu(Cox_xMnx) 2 compounds x 0.10 0.15 0.25 0.40

~

A'

(~

~Oe/~n)

19 29 36 39

37 ± 2 22 ±1 8.5±1 75 ± 2

6 2.3±0.2 2.4±0.2 2.2±0.2 2.4±0.2

to diverge. A variation of C 1 implies in fact a nonsymmetric configurational exchange distribution. One might also believe that, beside a canonical spin-glass state, the compounds under interest have dominant ferromagnetic interactions (as actually suggested by the thermal variation of the first order generalized Curie constant C 1) and therefore behave like random magnets with weak anisotropy. One then gets a magnetic equation of state writing.:

H / M =A' + B'M a-l, where, according to ref. [21], 6 should be equal to 7/3 and the coefficient A' should remain positive at crossing TsG. We recall that ~ - - 3 and A ' = 0 at the Curie point of a ferromagnet. The values of 6 and A' of some Lu(Col_xMnx) 2 compounds, deduced from the Arrott-Belov plots at TsG, are listed in table 1. It is seen that the values of 6 are close to the theoretical value of 7/3 mentioned in ref. [21] and to the experimental one found in the random magnet with weak anisotropy GdNi [18]. The same results are obtained for the Y(COl_xMnx) 2 compounds. A basic difference must exist, which should be emphasized, between the spin-glass state in the Y(COl_xMnx) 2 and Lu(COl_~Mnx)2 compounds and that one in the compounds with ionic or atomic moments. In the later compounds, a spinglass state is formed as a result of a freezing, in a random spatial distribution, of the sole angular (transverse) components of the moments [22]. On the contrary, in the itinerant magnets like those studied here, amplitude (longitudinal) components of the moments must also be involved,

299

especially near the boundary (x = 0.35) where these moments are very close to cancel. In compounds close to a magnetic-nonmagnetic instability, longitudinal spin fluctuations are easily excited leading to large dynamical amplitude fluctuations of the moments. It is expected that magnetic frustration will enhance these fluctuations where at producing static spatial fluctuations of the amplitude of the moments: a strong frustration in an exchange loop may then lead to large variations of not only the angles between consecutive moments but also of the amplitudes [16]. As a result, a map of the spin density below TSG would represent a randomly frozen distribution of moments in directions and in moduli as well. In analogy with the concepts used in the local band model of itinerant magnetism [23] it would then be fair to admit the coexistence of a frozen local band structure together with a fluctuating one, to characterize the ground state of the Y ( C O l _ x M n x ) 2 and Lu(COl_xMnx) 2 compounds in the SG-region. A band spin-glass state can be characterized by an Edwards-Anderson order parameter for amplitude fluctuations (/~2), defined as the trace of the second-rank tensor order parameter q~a = ([/X"]a-[/X~]T)av where [ ]T means a statistical average and ( )av a configurational average and where ~'~ is the a component of the magnetic moment variable. A value of the magnetic autocorrelation function (/x2) in zero applied magnetic field can be estimated from thermal expansion data. A freezing of the amplitude fluctuations of the moments will indeed lead to a magnetovolume effect expressing in the usual form as AV/V= KC(I.L2>, where KC is the magnetovolume coupling coefficient, K being the compressibility. No experimental deviation from the Debye law of the temperature dependencies of the lattice parameter of the Y(COi_xMnx) 2 and Lu(C01_ xMnx) 2 compounds has been shown up below TsG. It results that A V / V is less than 10 -4 (the sensibility of the X-ray method used for the thermal expansion measurements). One then finds, for both the Y(~t.=_xMnx02 and Lu(Co m_xMnx)2 compounds, ~(/.~2) <0.31zB, taking the same

300

R. Ballou et al. / Spin-glass state

in T(Co 1 _

m a g n e t o v o l u m e c o u p l i n g coefficient x C as in the R C o 2 c o m p o u n d s (2 × 10-3p, B 2 [24]): a v a l u e essentially s m a l l e r t h a n the m a g n e t i z a t i o n of the d - s u b s y s t e m of the isostructural R C o 2 a n d R ( C O l _ x M n x ) 2 with m a g n e t i c R species, which exceeds 1/z B p e r 3d a t o m at the same M n conc e n t r a t i o n [11]. It w o u l d b e desirable to study the Y(Col_xMnx02 and Lu(Col_xMnx) 2 compounds by o t h e r e x p e r i m e n t a l m e a n s which could p r o b e the m a g n e t i c a u t o c o r r e l a t i o n f u n c t i o n (/.L2) in zero a p p l i e d m a g n e t i c field (as e.g. N M R w h e r e a d i s t r i b u t i o n of hyperfine fields should b e expected). It can b e c o n c l u d e d that we have established the existence of a spin-glass state in the i t i n e r a n t p a r a m a g n e t s Y C o 2 a n d L u C o 2 as resulting from partial s u b s t i t u t i o n of M n for Co. A basic distinguishing f e a t u r e of this spin-glass state is that the frozen m a g n e t i z a t i o n density m u s t fluctuate n o t only in angle b u t also in a m p l i t u d e . It defines a n e w class of m a t e r i a l s which are almost n o t studied b o t h theoretically a n d e x p e r i m e n t a l l y [25] a n d could b e n a m e d as " i t i n e r a n t spin-glass".

Acknowledgement W e t h a n k J. Souletie for helpful discussions.

References [1] H.R. Kirchmayer and C.A. Poidy, in: Handbook on the Physics and Chemistry of Rare Earths, eds. K.A. Gschneidner Jr. and R. Eyring (North-Holland, Amsterdam, 1978). [2] M. Cyrot and M. Lavagna, J. de Phys. 40 (1979) 763.

xMnx)2 and L u ( C o I _ xMnx)2

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