Random anisotropy effects on the phase transition of amorphous Dy xGd1-xNi

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Random anisotropy effects on the phase transition of amorphous Dy xGd1-xNi

B. Dieny, B. Barbara

To cite this version:

B. Dieny, B. Barbara. Random anisotropy effects on the phase transition of amorphous Dy xGd1-xNi.

Journal de Physique, 1985, 46 (2), pp.293-302. �10.1051/jphys:01985004602029300�. �jpa-00209968�

293

Random anisotropy ^{effects on the} phase ^transition

of amorphous DyxGd1-xNi

B. Dieny ^{and B. Barbara}

Laboratoire Louis Néel CNRS-USMG, 166X, 38042 Grenoble Cedex, ^France (Reçu ^{le 3 mai} 1984, révisé le 11 octobre, accepté ^{le 23 octobre} 1984)

Résumé. 2014 Nous avons étudié, par des ^mesures d’aimantation en champs faibles, le rôle d’une anisotropie ^aléatoire

sur les propriétés critiques ^des amorphes DyxGd1-xNi.

A l’équilibre, ^les exposants critiques ^sont donnés, discutés, ^et comparés ^{à ceux} précédemment obtenus pour d’autres systèmes.

Des effets hors d’équilibre ^ont été examinés et montrent l’existence de lignes d’irréversibilité dans les plans H-T, T-(D/J) ^et (D/J)-H.

Abstract. 2014 The influence of the magnitude ^{of a random} anisotropy ^{on the critical} properties ^of amorphous DyxGd1-xNi ^{has been studied} by ^{means of low field} magnetization experiments.

At equilibrium, ^critical exponents ^are given, discussed and compared ^{to those} previously ^{obtained on other} systems.

Non equilibrium ^{effects have been} investigated showing the existence of irreversibility lines in the planes H-T, T-(D/J) ^and (D/J)-H.

J. Physique ⁴⁶ (1985) 293-302 FÉVRIER 1985,

Classification

Physics ^Abstracts

75.SOK

1. Introduction.

Topological disorder in amorphous alloys ^{leads to}

distributions of random fields at the atomic scale.

Two extreme cases are usually considered :

-

« spin glasses ^» in which random fields result from a wide distribution of positive ^and negative exchange interactions with an average around _zero;

-

« amorphous magnets » ^with essentially posi-

tive exchange interactions at the atomic scale and a

distribution of local anisotropy directions.

This _paper deals with such « amorphous magnets » and particularly ^{with the nature of the} phase ^transition they undergo ^{at a} temperature Tf between the _parama-

gnetic and the low temperature phases. ^This study ^has

been stimulated by the theoretical work of Aharony

and Pytte ^who pointed ^out that random anisotropy systems should have qualitatively different characte- ristics from those of ferromagnets [1 ]. ^{Von Molnar}

et al. have shown [2] ^that amorphous GdAg (case ^{of a}

low anisotropy ^to exchange ^ratio D/J) presents ^an apparent divergence ^{of the} susceptibility ^at T f ^but only ^an extremely ^small spontaneous magnetization

below this temperature; ^{on the} opposite, amorphous DyCu (case ^{of a} large D/J ratio) ^{exhibits a} finite initial

susceptibility xo, at any temperature. ^Some comple-

mentary studies have been done by O’shea et al. [3].

More recently, it has been theoretically ^demons-

trated that _xo may ^not diverge ^if D/J ^{is not too} small;

in such a case xo - (J/D)4 in three dimensions [4, 5].

In order to study the influence of the anisotropy

to exchange ^ratio D/J ^{on the nature of the} phase

transition at Tf, ^{we have} prepared ^five amorphous samples ^of DYxGd1-xNi ^{for the} following ^nominal compositions ^x

0, 0.25, 0.5, 0.75, ^{1. In all these} samples, ^{Ni is not} magnetic. ^{When x} varies from 0 to

1, ^the anisotropy ^to exchange ratio increases by ^about

one or two orders of magnitude. ^{An accurate determi-}

nation of this ratio will be published ^later together

with a quantitative study of the evolution of the phase

transition of DYxGdl-xNi ^{as a} function of D/J. ^This

determination of D/J is carried out by fitting ^isother-

mal magnetization ^{curves in the} high ^field region

where the HPZ model [6] ^{is valid.}

In this _paper, we will give only ^a general qualitative

outline of our study. ^{In a first} part (section 3) ^{we refer to}

the properties ^at the thermal equilibrium. ^{The second} part (section 4) is devoted to the non equilibrium ^pro- perties in connection with the onset of irreversibility

in spin glasses.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004602029300

2. Experimental ^methods.

Our samples ^were prepared by sputtering ^from alloy targets ^onto liquid nitrogen ^{cooled Al} substrates.

The resulting ^film thickness, of the order of 20-50 _Jlm, allowed us to perform magnetic studies in absence of _any substrate.

The amorphous ^{character was checked} by X-ray scattering; ^{we find an} upper limit of microcrystal ^size of 15 Á.

The chemical composition ^{of our films was checked} by ^{an atomic} absorption method; ^these compositions

are the following : GdNi1.27’ Gdo.77Dyo.23Nil.19, Gdo.48DYo.52Nil.35’ Gdo.27DYo.73Nii.18, DyNil.32-

D.C. magnetization measurements have been _per- formed by ^{two methods : a} classical induction one for intermediate and high fields and a method based ^on

SQUID ^detection in low fields (SHE SQUID Magne- tometer). ^The magnetic ^{field was} always applied ^{in the} plane ^{of our films} leading ^to extremely ^low demagne- tizing ^effects.

3. Reversible magnetization measurements.

Except for GdNi which exhibits few irreversible

effects, magnetization measurements were performed

at constant field and by decreasing ^the temperature from T = 100 K down to 4.2 K. The Arrott plots ^for

three samples GdNi, ÐYo.5Gdo.5Ni ^and DyNi (nomi-

nal compositions) ^are given ^{in the} figure 1, ^{2 and 3.}

3.1 GdNi. CASE OF A LOW ANISOTROPY.

The

general features of our results for GdNi (Fig. 1) ^are

very similar to those predicted theoretically by Aharony ^and Pytte in their earlier article in which D J [1]. These authors _propose the following equation ^{of state in 3D :}

T f ^{is the} ordering temperature, ^{s = 4 - d where d} is the dimensionality ^{of the} system, ^and y

1, ^{if the} thermal fluctuations are not taken into account

The last term AM2(H/M)-e/2 ^{results from an} expansion ^{to the} leading ^{term in} DIJ : A - (D/J)2.

On the theoretical Arrott plot, ^{this term induces a} change ^of sign ^{of the} curvature at the temperature Tf

and leads to the absence of finite intercept ^{with the M2}

axis below Tf. On the other hand, ^a divergence ^{of the}

initial susceptibility is reminiscent from the non

random case.

On the Arrott plots ^of a-GdNi, ^{we observe similar} properties :

-

The change ^of sign ^{of the curvature} of the iso- thermal lines indicates that the phase transition ^tem- perature Tf is between 61.4 and 62.4 K.

-

The susceptibility ^{seems to} diverge ^{at this} temperature (see ^{also Ref.} [5]).

-

The important ^{curvature near the} origin ^without

any finite intercept (within ^{our error} bars) with the line of zero internal field traducts an absence of sponta-

neous magnetization ^at Tf ^{and until some} degrees

below Tf. However, ^{at lower} temperature, ^{a second}

regime appears characterized by ^{the arise of a} sponta-

neous magnetization. ^{This can be} clearily ^{seen on the} M(H) ^{curves where a linear} part (demagnetizing

field line) is observed at lower temperature (Fig. 4) ^and disappears ^{above ~ 55 K. This} spontaneous magneti-

zation (magnetization ^{in zero internal} field) grows up ^{to a} value of 25 % of the satured magnetization Msat ^{at 4.2 K.}

At low temperature, ^the spontaneous magnetiza-

tion is Ms - Msat ^{for a collinear} ferromagnet ^and Ms ~ ^0.5 Msat ^{for an} asperomagnet Thus, ^the long

range magnetic order of a-GdNi characterized by

the existence of a small spontaneous magnetization

at low temperature ^cannot simply be of collinear

ferromagnetic ^{or of} asperomagnetic type.

Fig. 1.

^{Arrott plots for amorphous GdNi. N is the} demagnetizing factor. M is given ⁱⁿ JIB/formula, ^{H in Oe.}

295

Fig. ^2.

^Arrott plots ^for amorphous DyNi.

From a practical point ^of view, the existence of a

spontaneous magnetization ^{at low} temperature ⁱⁿ GdNi allowed us to measure the demagnetizing ^field

factors of ^our in-plane field film : N

24.0 Oe. for-

mula/,uB (Fig. 4), this value is _very close to the one

estimated by assuming ^{that the} sample ^{is an oblate} ellipsoid. ^This demagnetizing field factor has been used in the determination of critical exponents ⁱⁿ GdNi.

Before studying the critical behaviour of this system, it is useful to stress possible origins for the observed small but finite spontaneous magnetization ^{at T} Tf.

Such an observation is in contradiction with the macro-

scopic isotropy ^{of ideal} amorphous alloys. ^The point

here is that our system ^{and more} generally any soft

amorphous system ^cannot be considered as ideally

disordered from the point of view of their magnetism.

Sample inhomogeneities ^{such as tensile or} compressive stresses, ^thermal strains, anisotropic microstructures...,

lead to non random anisotropy components. Aharony

and Pytte [1 ] pointed ^out that the effect of a non

random anisotropy, for instance a cubic anisotropy

term - Do(S: + S4y ^{+ S4z)} would be drastic even if

Do ^D. Chudnovsky and Serota [5] ^have recently

studied the effect of the superposition ^{of an uniaxial}

coherent anisotropy ^onto the local random aniso- tropy. ^This superposition gives ^{rise to a} divergency

of _xo and to a spontaneous magnetization given by :

Our preliminary study ^{of the} anisotropy ^of DyxGd1 -xNi alloys gives D/J ~ ^{10-2 for GdNi and}

therefore if Ms ~ ^0.25 Msat ^then D0 ~ ^{10-g D which}

is extremely ^small. Although ^{we have to be} very careful in using quantitatively theoretical expressions, ^this

result clearly indicates that even very small uniform

anisotropy components ^can explain ^the spontaneous

magnetization ^{observed in} a-GdNi. This result is also

Fig. ^3.

^Arrott plots ^for amorphous DYo.sGdo.sNi.

Fig. ^4.

^{Low field} magnetization ^curve of a-GdNi. The

departure ^{from the} straight ^{line occurs for M}

Mr ^and

H

NMS ^{where N is the} demagnetizing field factor.

valid for other Gd-based alloys ^{in which} D/J ^is always

of the order of 10- 2 and more generally ^{for soft} amorphous materials. Therefore the observation of a

divergence of the initial suscpptibility ^{in these mate-}

rials is also, ^{at least for a} part, ^{due to} sample ^inhomo-

geneities. ^{In these} circumstances, ^{it seems} presently hopeless ^{to find} any experimental proof ^{in favour or} against ^{an intrinsic} divergence ^{of the} susceptibility ⁱⁿ

these materials. In the opposite ^{limit of} large ^aniso- tropies, it is rather easy ^to show that the susceptibility

does not diverge [2]. Our results ^on DyNi ^and DYxGdl-xNi (see below) ^confirm strikingly ^this

observation. Therefore, ^{there must be a transition}

versus D/J ^{above which} Xo does not diverge ^{and below}

which it does diverge. ^From the theoretical point ^of

view of Aharony ^and Pytte [4], this transition takes

place ^{at D}

0. If this was really ^the case, it would be

extremely ^{difficult to show it} experimentally. ^The

best would be to increase progressively D/J ^{and to}

observe when the breakdown of the divergence ^of xo

occurs. The study ^{of some} alloys ^{with 0 x 0.25}

will be useful in order to get ^some insight ^{into the} understanding ^{of this} « ferromagnetic » ^{to «} spin glass » transition versus D/J.

Whatever the origin ^{of the} divergence [5] ] ^of Xo in a-GdNi, ^{it is} interesting ^to know the value of the critical exponent y. Assuming ^the usual x - (1 - T/Tf)-Y ^{form, we have} plotted X/(dX/d7) ^versus

T (see Fig. 5). ^{If the} susceptibility diverges ^at T f, ^one

must observe a linear dependence ⁱⁿ temperature ^for T > T f ^{with the} slope 1 / y. This is what we get ^{and the} value _y

1.40 ± 0.06 is close ^to what is generally

observed with ferromagnets ^or extremely ^{soft amor-} phous magnets [7, 8] y

1.33. The deviation from the linear dependence ^for T f ^{T 1.05} T f ^is probably

due to our measurement field, ^{still too} large (10 One).

However, ^a breakdown of the divergence ^of xo ^near

Tf ^{in a-GdNi cannot be} totally ^excluded.

The field exponents 6 ^and 62 ^defined by ^{M - Hl/ðl}

at T f ^{and M - H1/u2} below T f have also been extract- ed from our low field experiments simply by plotting log ^{M versus} log Hint ^{at different} temperatures (Hint

H - NM). ^This procedure ^{which does not take into}

account higher ^{order terms} in the field expansion ^is

rather tricky except ^at T f ^{and below} Tf. Around this temperature, Ms ^{M(H) even} for fields of the order of some tens of Oe.

Fig. ^5.

Determination of _y and Tf from x/(dx/dT) =

-1(T - Tf) in a-GdNi. The measurement field is equal ^to

y 10 Oe.

The result given ⁱⁿ figure ^{6 shows} that 61

^{2.25 ±}

0.10 and £52

^{6.0 + 0.1.} These values _may be _compar- ed to the predicted ^{mean field} exponents [1] : 61

7/3

and b2

^{5. The agreement is} amazingly good, espe-

cially ^{if we} consider the role of sample inhomogeneities

mentioned above. Furthermore, ^von Molnar et al. [2]

got nearly ^the same 61 exponent ⁱⁿ a-GdAg. Therefore,

it seems probable ^{that the} extremely ^weak sponta-

neous magnetization ^{observed at T} ~ Tf ^{does not}

affect seriously the value of the field exponent b1 ^at Tf.

In conclusion of this part, ^{our low field measure-}

ments in a-GdNi allow to check qualitatively ^{the two}

limits of the equation ^{of state of} Aharony ^and Pytte :

the limit T

T f ^{where M}

^H1/ð1 and the limit T _ y B’y

T > Tf f ^where X - x T Tf Tf y. . The measured _expo-

Tf ) p

nents 61 ^and b2 ^{are not very} different from those _pre- dicted within a mean field hypothesis : ð1

^2.25 compared ^to 7/3, b2

⁶ compared ^{to 5. The value}

y

1.4, compared ^{to the mean field one :} y

1, shows that critical fluctuations must be taken into account in a-GdNi.

Fig. ^6.

Thermal variation of 6 defined by H - ^M,3. Only the values 6 at T f, ^and 6, ^below Tf are significant.

a : GdNi ; ^{b :} DyNi.

297

It would be of interest to know the theoretical exponents 61 ^and 62 within the framework of the second scaling hypothesis ^of Aharony ^and Pytte [4]

in which _xo does not diverge.

Table I shows the critical exponents ^determined from low field experiments ^{on soft} amorphous alloys.

The values of 61 ^are definitely different from those

expected ^for ferromagnets. However this difference becomes smaller with YFeo3, ^{a weak} ferromagnet

The _very existence of 62 ^{shows a} qualitative ^diffe-

rence with ferromagnets for which this exponent has no meaning ^{due to finite} M..

These results contradict the conclusions drawn from large ^field experiments ^{such as} in a-GdAu [7]

or from low field experiments ⁱⁿ extremely ^{soft met-} glas [8] ^where D/J -> ⁰ (a hopeless ^case for determin-

ing intrinsic characteristic of disorder, although ^this

material constitutes one of the most important appli-

cations of amorphous alloys ⁱⁿ magnetism). ^{In both}

cases, too large applied ^fields and/or ^uniaxial parasitic anisotropy components ^break up the spherical sym- metry and therefore induce a spontaneous magnetiza-

tion.

Before ending ^{with soft} amorphous systems, ^{let us} mention a possibility ^{of crossover} between the random

anisotropy regime ^{and a} ferromagnetic ^like regime

induced by dipolar energy effects [9]. Following ^the simple argument ^of competition ^between exchange

and random field (Imry ^{and Ma} [10]), it is shown that

a random anisotropy system ^breaks up into domains of size lc/a ~ (J/D)1/(2-d/2) in which the spins ^are nearly aligned (M - MJ.

But the magnetization being ^non uniform from one

domain to another, it induces local dipolar effects. The

dipolar energy of order N(I/a)d Ms (N ^effective demagnetizing ^{factor of a} domain, a interatomic

distance) ^must compete ^{with the} anisotropy energy

D(I/a)d/2.

Two ^{cases can} be considered :

i) ^low dipolar ^{effects :}

The domain size is unchanged

ii) large dipolar ^effects

The domain size is modified /’

^J and is The domain size is modified l’c _a

- 1 _NM2 ^{and is}

independent ^{of the} dimensionality. Within this hypo-

thesis l’c ^{is always} smaller than Ic. ^{Such a} reduction of the domains size can be important ^{in soft} amorphous

materials and _may be understood in terms of a break-

ing up of Imry ^{and Ma} domains into Weiss domains.

In the case of a-GdNi, D/J ~ 10-2 , HA

D/Ms ~ 103 Oe and HD

NMS N ^{102 Oe. A} breaking up of

Imry ^{and Ma domains} implying HD/HA >> (D/J)3

for d

3 could occur in this system ^{at low} tempera-

ture. A crossover from Weiss-type ^{domains to} Imry

and Ma domains _may occur at To ^when M. ^decreases

i.e. when the temperature approaches Tf. ^{Such an}

intrinsic effect _may explain ^the rapid increase of the

Table I.

Critical exponents 6 determined on amorphous alloys from ^low field experiments (H/M

^Xo 1(D/J) ⁺

X 1 (DIJ) M" - 1).

measured spontaneous magnetization ^{for T $} To Tf.

3.2 DyNi. ^CASE OF A LARGE ANISOTROPY.

The

general ^features of the Arrott plot ^{for this} system

(Fig. 2) ^where D/J = ^{1 are} quite different from those of GdNi (low D/J case). On the other hand, ^these

features are similar to those obtained in spin glas-

ses [2, 12].

As in spin glasses ^and contrarily ^{to the low aniso-}

tropy ^case, it is difficult to see on these plots ^{at which}

temperature the transition occurs. However, ^{we know} from field measurements of M(T) ^{or of} XO(T) (Fig. 8. 2a) that, if there is a transition, ^{it should occur}

around 13-14 K. At this temperature Xo ’(7)

570 Oe/ JlB/form ^{is clearly far from the} demagnetizing

factor limit N ⁼ 6.5 Oe/,uB/form demonstrating ^that

there is no divergency ^{of the} susceptibility ⁱⁿ a-DyNi.

The field exponents of DyNi, 61 ^and 62 ^{are determin-}

ed using ^an Arrott-like plot :

in which the susceptibility is assumed finite : a(T) - 1/xo(T) ~ function of D/J. ^The exponent 6 is obtained from a log-log plot ^of 1/xo - H/M ^{vs. M. Such a} procedure ^{is not} necessary in a-GdNi and more

generally ^{in soft} systems ^where X0-1 ~ ^{0. As indicated}

before only ^the exponents ⁶

61 ^at T f ^{and 6 =} ð2

below T f ^are relevant. We got ðl

62

^{2.40 ± 0.05} (Fig. 6b). This result is in agreement with that obtained for DyCu [2] ^{and seems to indicate a} general ^behaviour

of amorphous magnets ^with large D/J. This result could also be valid for the low D/J ^case if the field exponent ^below Tf, 62 ^{was, to some extent,} changed by ^the parasitic ^uniform anisotropy components, ^a

plausible hypothesis.

3.3 Dyo.5Gdo.5Ni. INTERMEDIATE CASES.

In this system ^{with an} intermediate value of D/J, ^{the Arrott} plot (Fig. 3) ^{shows a behaviour} very similar to that

predicted by Aharony ^and Pytte [1]. However, ^the measuring ^{fields are too} large ^to provide good enough

information. As an example, ^{it is not} possible ^{to know}

with certainty ^whether xo diverges ^{or not from} figure ^{3. Low field} experiments ^{on this} system ^{and with} other compositions ^{are in} progress. We have already

measured the _xo in _very low fields. They ^are compared

to the demagnetizing ^field susceptibilities ⁱⁿ figure ^7.

It is clear that xo ^{does not} diverge whatever is the value of x i.e. of D/J, except perhaps ^{with GdNi}

which has been discussed above. In a coming paper, xo will be plotted ^vs. D/J, ^{in order to see whether}

the recent prediction, Xo - (D/J)4, ^is right ^{or not.}

4. Onset of irreversibility.

The onset of irreversibility in random anisotropy systems ^{has not been} really studied. We give ^{here a}

first approach ^{based on an} analogy ^with spin-glasses

Fig. ^7.

^Low field initial susceptibility ^{measured at} Tf ⁱⁿ DYxGd1-xNi. ^The demagnetizing field limit is given ⁱⁿ

dashed line. The ratio D/J ^varies by ^{at least one order of} magnitude ^{between x}

0.25 and x

1.

for which this problem has been crucial for _many years. It is now starting ^{to be} understood in terms of a crossover between weak and strong irreversibi-

lity [I I along ^{the line H2 ~} (Tf - T)cP where p ~ ³

is the usual crossover exponent [12] associated with the Edwards-Anderson order parameter [13]. ^However

this point is still controversial and one may also think that the exponent 2/3 ^{of H vs.} (Tf - ^T) characterizes

a true transition in the Heisenberg ^model [14] ^{or is}

related to a breaking ^{of the} replica symmetry ⁱⁿ Heisenberg [15] ^{or in} Ising [16] ^models.

The line above which irreversible effects vanish

can be obtained from the M(T) ^{curves measured} by increasing ^{and then} by decreasing ^the temperature, the sample having previously ^{been zero} field cooled.

Some of these curves are given ⁱⁿ figure ^{8a for mode-}

rate fields. The temperature above which M(T) ^is reversible, ^{for a} given field, gives ^a point of the irre-

versibility ^{line. In these} materials, ^this temperature ^is

slightly ^above M(T) peak. ^{Such a} line has been plotted figure ^{9 for} DYo.sGdo.sNi. ^{We have used 12 different}

fields between 13 and 2 000 Oe. The H(T) ^function

decreases and vanishes at Tf, ^{a result} normally expect- ed. More interesting is the linear plot obtained for

log H ^vs. log (Tf - ^T). Furthermore, ^the temperature exponent ^{is found} equal ^to 1.57 ± 0.02, ^{which is} very close to the one observed in Heisenberg spin glasses,

and the coefficient is equal ^{to 5.5} Oe/(K’-5’).

This result shows a striking analogy ^{between ran-}

dom anisotropy magnets ^and spin-glasses, ^{which is} already suggested by ^the general behaviour of the

magnetization ^curves (see Fig. 8a, b). ^{A detailed} study

of this question ^{will be} published ^{soon. Another} very

interesting point ^{to look at is the} possibility ^{of an}

extension of the study ^{of the onset of} irreversibility

on the (D/J)-T ^and (D/J)-H planes. ^In spin glasses,

it is extremely ^{difficult to} modify continuously ^the

frustration and therefore there are no studies of

irreversibility, except ^{on the H-T} plane.

As we have not yet determined accurately D/J ^{vs. x}

we will just give ^{here some results versus x.}

299

Fig. ^8.

(a) ^zero field cooled ( ) ^and field cooled (....) magnetization ^versus temperature ⁱⁿ a-Dy xGd1-xNi (b) Hysteresis loops ^{measured at 4.2 K in} a-Dy,,Gd, - _,Ni.

1) For 0 K x 0.5. 2) ^For 0.75 - x - ^1.

Fig. ^9.

Irreversibility line in the random anisotropy system a-DYo.sGdo.sNi.

Insert : Log-log plot ^of H(Oe) ^vs. T(K) giving ^H

^{5.5 x} (Tf - T)1.S7. ^f

Let us consider for example ^the (D/J)-T plane

for which H

0 or any parallel plane ^defined by

H

constant. Irreversibility lines for the limit T Tf, analagous ^{to the H2 ~} (T f - T)J> ^{line of the H-T} plane, ^{can be} deduced from the magnetization ^curves

measured in a constant field H; ^these irreversibility

lines will be given ^elsewhere.

For T T f, ^one expects ^another type ^{of crossover} between a non equilibrium ^{state dominated} by ^ther-

mal activation (kT D/J) ^{and a state at} equilibrium (kT » D/J ; D/J represents ^{here the} average height

of _energy barriers). ^{In this} case, the crossover line should be given by (D/J) - ^TI". Several criteria _may be used to determine such a line : we have chosen to

plot ^{the ratio} T;/T f ^{versus x where} Ti is ^the tempera-

ture of the inflexion point ^{of the zero} field cooled

M(T) ^curve. Figure ¹⁰ shows that this ratio decreases

abruptly ^{between x}

^{0.5 and x}

^{0.25. The same}

feature is also observed on the coercive field (Fig. 8b)

but some more experiments ^{are needed to show this}

301

Fig. ^10.

^Inflexion point ^{of the zero} field cooled M(T)

curve versus the content of dysprosium. ^{This curve can be}

considered as an irreversibility line in the (D/J)-T plane.

clearly. ^This abrupt decreasing ^{around x}

0.25 may be due to the functional dependence ^{of x vs.} D/J ; ^it

may also indicate a very rapid drop of irreversible effects near the weak anisotropy regimes.

Many interesting questions arise from this first

study ^{on the onset of} irreversibility in random aniso- tropy systems ^{which we will} try ^{to answer} in the future.

5. Conclusions.

This _paper summarizes some recent magnetization

measurements performed ^{at low and} moderate fields

on the model system a-DYxGdl-xNi where Ni is non

magnetic ^{and the} anisotropy ^to exchange ^ratio D/J changes continuously ^{with x.}

We have confirmed some previous equilibrium

results on a-GdAg ^and a-DyCu [2] ^{and we have shown}

that both low and large anisotropy systems obey ^a

field _power law M - H1/b at T f ^and just ^below Tf.

At Tf, 61 = ^2.3, whatever the value of D/J ^{is. Below} T f large anisotropy systems give b2

61 - ^{2.3 ± 0.1}

and for low anisotropy systems ð2 ~ 5-6. This last result _may simply ^not be relevant due to the effect of

sample inhomogeneities ^{in soft} amorphous ^materials.

In the low field limit, ^the alloys of formula

Dy,,Gd, -.,Ni (except ^x

0), ^{in which} D/J changes by

at least one order of magnitude, ^{do not show any} divergency ^of xo at Tf. ^The particular ^{behaviour of}

GdNi has been discussed in details :

Because of the weakness of the ratio D/J, ^coherent anisotropy components ^{due to internal stresses lead}

to an apparent divergency ^of xo ^at Tc; ^{but a} slight

increase of the random anisotropy suppresses this effect. Similarly, ^{one could} expect that chemical disorder can destroy ^the divergency of xo ^at Tc ⁱⁿ crystalline magnets.

Such a possibility ^{has been} proposed among others

by Mukamel and Grinstein [18].

Finally, ^we have studied the onset of irreversibility

in these amorphous alloys showing ^the existence of a

line _very similar to the so-called ^« de Almeida-Thouless line » [16] ^of spin glasses. Furthermore, ^{we have} given preliminary ^{results of a} study ^{of the} irreversibility

versus D/J.

The global behaviour of our model system

DyxGdl _xNi ^{shows an} evolution from a « spin-glass

like » to a « ferromagnetic like » behaviour which can

be interpreted roughly ^{in terms} of (D/J)

dependent

intrinsic domains introduced by Imry ^{and Ma} [10].

This point ^{as well as} others mentioned in this _paper will now be developed

Acknowledgments.

We gratefully acknowledge ^A. Lienard and G. Fillion for their help during ^the preparation ^of amorphous samples ^and SQUID measurements and S. von

Molnar, ^T. McGuire and D. Gambino for their association in the early stage of this work.

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