Mössbauer detection of magnetic clusters in disordered magnetic materials

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Mössbauer detection of magnetic clusters in disordered magnetic materials

F. Hartmann-Boutron, A. Aït-Bahammou, C. Meyer

To cite this version:

F. Hartmann-Boutron, A. Aït-Bahammou, C. Meyer. Mössbauer detection of magnetic clus- ters in disordered magnetic materials. Journal de Physique, 1987, 48 (3), pp.435-444.

�10.1051/jphys:01987004803043500�. �jpa-00210459�

435

Mössbauer detection of magnetic ^{clusters in} disordered magnetic

materials

F. Hartmann-Boutron, A. Aït-Bahammou and C. Meyer

Laboratoire de Spectrométrie Physique (*), Université Grenoble I, ^BP 87, 38402 Saint Martin d’Hères Cedex, France

(Reçu le 19 août 1986, révisé le 30 octobre, accepte le 3 novembre 1986)

Résumé.

En partant des théories développées par Mørup ^{et ses} collaborateurs pour interpréter ^les propriétés ^de particules superparamagnétiques indépendantes ^{ou en} interaction, ^nous montrons comment ces théories peuvent ^être adaptées à la détection et à l’étude des amas magnétiques (s’il ^en existe) dans les milieux magnétiques désordonnés tels que les ferromagnétiques réentrants, ^{les verres de} spins, ^les spinelles, ^{les matériaux} amorphes, ^{etc. Nous}

décrivons des expériences ^Mössbauer préliminaires qui suggèrent fortement que des ^amas ferromagnétiques ^sont présents ^{dans le} ferromagnétique ^réentrant Au1 - xFex (x > ¹⁵ %) au-dessus de la température de transition

magnétique ^en champ nul, Tp. ^{Nous montrons aussi que} Tp caractérise la mise en ordre des moments magnétiques géants (faiblement couplés) ^{des amas et non la mise en ordre des moments} atomiques individuels. Nous suggérons

que les anomalies observées au-dessous de Tf ~ ^{50 K} pourraient être associées à une transition de Gabay-Toulouse

pour les ^moments géants.

Abstract.

Starting from the theories developed by Mørup and coworkers for interpreting ^the properties ^of independent ^or interacting superparamagnetic particles, ^we show how these theories can be adapted ^to the detection and study ^of magnetic ^clusters (if they exist) in disordered magnetic materials such as reentrant ferromagnets, spin glasses, spinels, amorphous materials, ^{etc. We} report preliminary ^Mössbauer experiments ^which strongly suggest ^that ferromagnetic ^{clusters are} present ^{in the reentrant} ferromagnet Au1- xFex (x > ¹⁵ %) ^{above the} magnetic ^transition temperature Tp ^{in zero field. We} also show that Tp characterizes the ordering ^{of the} (weakly coupled) giant magnetic

moments of the clusters and not the ordering of the individual atomic moments. We speculate that the anomalies observed below Tf ~ ^{50 K} might be associated with a Gabay-Toulouse transition for the giant ^{moments of the}

clusters.

J. Physique ⁴⁸ (1987) ^{435-444 MARS} 1987,

Classification

Physics ^Abstracts

76.80

1. Introduction.

During ^{the recent} years, there has been a lot of interest in the alloys AU1-xFex with 0.15 x : 0.20. These

alloys ^are considered as reentrant ferromagnets [1-2]

which become ferromagnetic ^{below a} temperature

TP ^{and exhibit a canting} transition below a temperature Tf [3-10]. ^However the situation is far from clear:

- The samples ^are strongly ^affected by ^thermal

treatments [11] which may result in either clustering

effects or anticlustering ^effects [12]. ^Some people ^have

invoked the presence of iron platelets [13]..Other people ^{conclude to} the existence of iron rich zones and iron depleted ^zones [14].

(*) ^{Associe au C.N.R.S.}

- The existence of a ferromagnetic transition is not admitted by all authors. Beck [15-19] ^has interpreted

his magnetization measurements by invoking coupled superparamagnetic ^{clusters, but with} temperature ^de- pendent ^{size and} exchange coupling, and his model does not lead to a true ordering transition. Beck thinks his clusters might be related to platelets.

- The canting transition has been studied using 57 Fe Mossbauer effect. However the anomalous thermal variation of the hyperfine ^field is obtained from experi-

ments in zero field, ^{while the} canting angle ^{is deduced}

from experiments ^{in an} applied ^field Ho parallel ^{to the}

y ray (incomplete extinction of the intermediate M6ss- bauer lines). ^In [7], Ho = 6 ^{kOe, in} [3-4] Ho

^{20 kOe.}

However in this last case the thermal variation of the

hyperfine ^{field is} completely ^altered by ^the applied ^field

and this is not explained yet (see ^however [19]).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004803043500

-

In zero field and below Tf, the Mossbauer spec- trum seems to consist of two different subspectra ^with

different hyperfine fields and different quadrupole

parameters ^When

x > 15 %, ^{Fe atoms} may have ^a variety ^of surroundings

with n

0, 1, 2, 3, 4... ^{Fe nearest} neighbours ^{and if the} hyperfine ^{field has an} arbitrary ^{direction with} respect ^to these surroundings, for each value of n :0 ^{0 one} _gets

several values of E [20]. ^For yielding ^a single ^{value of E}

and at the same time being ferromagnetic, ^{a zone of the} sample should be such that all the iron atoms have the

same environment referred to the crystalline ^{axes and}

the magnetization ^{should have a} definite orientation with respect ^{to this common} environment. Such condi- tions could be satisfied with platelets ^{if the} magnetiza-

tion direction of each platelet is linked to this _very

platelet (for example by anisotropy effects). ^But then,

unless all platelets ^are parallel ^{in a} given ^{zone, the total} magnetization ^{of this zone,} M, ^{will be zero. On the} other hand when temperature increases, anisotropy

effects decrease [18] ^{and above a certain} temperature, the magnetizations ^{of the} platelets ^{or clusters} (if any)

should become parallel ^{to a common} arbitrary ^axis, M, will be non zero and e will vanish as observed in [5].

- Recently ^Mossbauer experiments ^{have been} per- formed on the matrix atoms 197Au in Au 16.8 % Fe [6]

and by ^{us on} substitutional 119Sn impurity ^{in a} sample A!!o.79Feo.19Sno.02 prepared by ^{I. A.} Campbell (to ^be published separately [30]). They yield ^a hyperfine ^field

at Au or Sn which is proportional ^{to the iron} hyperfine

field. This is in favour of a homogeneous magnetic

behaviour of the sample (and ^{of a} homogeneous canting ^below Tf [6]). On the other hand preliminary

Mossbauer experiments ^{on our} sample ^{in a} magnetic

field above the « magnetic transition temperature »

Tp - 122 ^K (see below) ^are strongly suggestive ^{6f the}

presence ^of magnetic clusters, ^{which seems to exclude a} homogeneous behaviour, unless the clusters fill up the whole sample (the ^{Sn atoms} might be inside Fe

platelets but the 79 % Au atoms of the matrix certainly cannot !).

The aim of the present paper ^{is not to} explain ^{all the}

above mentioned anomalies. It is simply ^{to show how,} by adapting ^{to AuFe} the models developed by Morup

et al. for superparamagnetic particles [21-27], ^{the M6ss-}

bauer effect might ^{be used to} investigate the existence and behaviour of magnetic ^{clusters in AuFe :}

-

if these clusters correspond ^{to chemical clusters,}

their size should be fixed as well as their exchange

interaction coupling constants ;

-

on the contrary ^{if these clusters are of} purely magnetic origin, ^{their size} might increase with decreas-

ing temperature ^{and their} coupling ^constant might vary

(as ^assumed by ^Beck [15-19]).

In what follows we will try and establish that:

-

ferromagnetic fluctuating clusters of size N - 170 atoms do exist in our Au 19 % Fe 2 % Sn sample ^at

T = 143 K, ^i.e. just ^{above the} ordering temperature

7p - ^{122 K detected by} the Mossbauer effect ;

-

the dramatic change ^of the observed hyperfine

field under application ^{of a} rather moderate external field 7/o 2013 ^{20 kOe can be} understood if Tp ^is interpreted

as the ordering temperature ^{of the} giant ^{moments of a}

system ^of weakly interacting superparamagnetic ^clusters (assumed ^{to have a fixed} size) ^{and not as the} ordering

temperature ^of individual moments (whose cooperative ordering inside each cluster takes place ^{at a much} higher temperature T, > Tp).

2. Adaptation ^of Mjirup’s theory. ^{Case of non interact-} ing particles.

Let us assume that we have a small particle ^of ferromagnetic ^material whose bulk Curie temperature is T,.

In the bulk we have average magnetic ^moments J1s(T)= 9 9B (S) T whose thermal variation is a func- tion of the reduced temperature r/Tc:

where f(T ITc) describes the evolution of the reduced spontaneous magnetization ^{of a} ferromagnet ^with spin

S and is tabulated for example by Darby [28].

Let us assume now that we have a small particle ^of

the same material with N atoms. Since the individual moments are rigidly coupled, its instantaneous moment

m, (T) ^{will have a} modulus jms(r)j I

N tL, (T), ^but,

due to thermal activation, ms(T) ^{will fluctuate between}

the different easy ^axes of the particle and the average

magnetic ^{moment of the} particle (ms(T)) ^{will be zero,}

unless the measurement time is smaller than the jump frequency ^{of the moment} (superparamagnetism).

If we apply ^{an external} magnetic ^field Ho, ^{it will} couple ^to the total moment m,,,(T) ^{and induce a}

moment on the particle (1) :

in which L (x ) ^{is the} Langevin ^function

and ms (T ) (or JLs(T)) ^{are assumed to be unaltered by}

the field because tk r , (T) Ho kB Tc (i.e. Ho ^{is much}

For simplicity anisotropy effects will be neglected ⁱⁿ

what follows ; this may ^not be quite correct at low temperat-

ures and/or low fields. However here we are mainly ^interested

in high temperatures (T::. 100 K ) ^and high ^fields

(Ho > 20 k0e ). Demagnetizing field effects are also neglected

(4 ^{7TM s 5} kOe in Au 19 % Fe).

437

smaller than the intracluster exchange field). ^{Then on}

each atom there will appear ^an average individual

moment:

By ^{contrast for an} individual paramagnetic spin ^we

would have

In which %, is the Brillouin function. We see that, in addition to the replacement ^{of L} by $s, ^{the two}

formulas differ by the presence of the reduction factor

f(T ITc) (1 > /(r/rj> 0) ^and by ^the large ^{size factor}

N (for example ^N = 150) ^{in the} argument ^{of the}

Langevin ^{function. Because of N, a} rather small

applied ^field (for example Ho

²⁰ kOe) ^{can induce a} large ^{moment on the} particle ^{even at elevated} tempera-

ture (for example ^{T- 125} K).

A conventional 57 Fe Mossbauer experiment yields ^a hyperfine ^field Hn(T) ^{which is} proportional ^{to the}

average individual moment FL (T) :

with A = 145 kOe/t’B [29] ^{and this} gives ^{us access to}

JL (T). ^In the presence of ^an applied ^field Hj, things ^are

a little more complicated, ^as the nucleus is submitted to the vectorial sum Hobs

Hn ⁺ Ho ^{in which} H. ^is antipa-

rallel to Ho.

In this case :

Experimentally ^we only ^know Hobs and Ho. Therefore :

-

if Hobs > Ho ^{we have} only ^{one solution}

-

while if Hobs Ho ^{we have two solutions}

When there is a distribution P (Hn ) ^of Hn, things ^are

even worse as the distribution P’ (Hobs) of Hobs ^for o - Hobs - Ho corresponds ^{to the} superposition ^of P(Ho-Hn) ^for 0 -- H. -- Ho ^and P(Hn-Ho) ^for HO-Hn-2HO’

In practice, ^{in the numerical} examples ^{we have been} considering (S = 1, g

2, ^N = 150, T,

²⁵⁰ K,

T = 137.5 K and 225 K, Ho varying from 10 kOe to

80 k0e), ^it appears that ^{we are} always ^{in the second}

case Hn:> Ho, ^whence H.

Ho ⁺ HObs’ ^{However, be-}

cause Hn ^{is a} function of Ho, ^{the variation of the} experimentally accessible quantity Hobs ^with Ho ^{is not}

monotonous. In addition, ^{at 225} K, H .bs -5 Ho, ^an ambiguous situation from an experimental point ^of

view. For this reason a complete study ^{of the thermal}

variation of Hobs ^{for each} Ho (which ^will yield ⁱⁿ particular ^the temperature ^{at which} Hobs

^{0 i.e.}

H.

Ho) may prove necessary in the future.

Let us now assume that Hn (T, Ho ) ^{is known. Accord-} ing ^to equation (4) ^{we have that:}

in which H, (T) is the bulk hyperfine ^field (H, (T)

=

AJLs(T». ^{When x ==} ms(T) HolkB T -> 1 (in practice x :> 2) :

whence:

Therefore, ^{as noticed} by MOrup [21], by plotting H.(T, Ho ) ^versus 11Ho ^{one should} get ^a straight ^line

which intersects the vertical axis at H,(T) -whence tk, (T) - ^{and the} horizontal axis at 1 IHO ms(T)/kB ^{T - whence} ms(T):ae NJLs(T), ^{from which,} knowing JLs(T), ^{we can deduce} the number N of

magnetic ^{atoms in the cluster. In the cases studied} by MØrup (Fe304, Fe203... ) the bulk does exist and

HS (T ) ^{is known} independently. ^{In AuFe there is no}

bulk available, only clusters of unknown nature, ^and both HS (T ) ^and ms (T ) ^{must be extracted from the} plot.

Knowing the thermal variation of HS(T) ^{one can} get the Curie temperature Tc which characterizes the

magnetic ordering ^{inside a} superparamagnetic ^cluster.

Note that Morup’s method could also be applied ^to

reduced magnetization measurements. Since :

a plot ^{of the reduced} sample magnetization M(T, Ho)/M(T, ^{Ho , oo ) versus 11Ho should yield} ms (T ) the average magnetic ^{moment of a cluster} (from

the intersection with the horizontal axis), ^{whence N} by

combining with Mossbauer data.

On the other hand, ⁱⁿ the small field limit, ^x 1,

L (x) = xl3. ^{Then :}

whence a susceptibility per ^atom:

which is strongly ^enhanced (« superparamagnetism »)

with respect ^{to the} susceptibility ^{of an isolated} spin :

JLs(T) being known from the Mossbauer experiment,

measurement of Xat (T ) (Eq. (18)) might provide

another determination of N. However, Xat (T ) being

very large, its determination requires ^{some caution}

because of demagnetizing ^{effects, see} [17], [2].

3. Adaptation ^of Morup’s theory. ^{Case of} interacting particles ^{or clusters.}

Let us assume that there exists an exchange coupling

between particles ^{or clusters}

giving ^{rise to a molecular field on one} particle ^{or cluster}

In what follows we will assume that, ^{if we are} dealing

with clusters, these clusters have a unique temperature independent ^size N, ^{and that} Kex ^{is also} temperature independent (i. e. the clusters behave like an assembly

of small particles). Then the average magnetization m(T, Ho ) ^{of a cluster} is the solution of the implicit equation already ^derived by M¢rup ^{in the case} Ho = 0 ([22] Eqs. (51), (52), [23] Eq. (11)) ;

’

3.1 MAGNETIC BEHAVIOUR IN ZERO FIELD [22- 24].

^When Ho

^{0 there is an} ordering temperature

Tp for the clusters which is the solution of the equation

obtained by expanding ^the Langevin function for small values of its argument :

whence:

which is an implicit equation ^for Tp ^{first derived by}

Morup ([22], Eq. (54)).

Let us assume for example ^{that S} = 1, g

2,

N = 150, Tc

^{250 K,} Tpl Tc ^{= 1/2, whence} f(Tp/Tc)

^{0.93657, ms(O)}

^{300 AB,} ms(Tp) = f (Tpl Tc) ^ms(O)

^{281 JLB. Then the} molecular field at 0 K is :

The reduced magnetizations m, (T)lm, (0) ^{of the}

bulk (if ^it exists), ^and m (T)lm, (0) ^{of the} coupled particles ^or clusters deduced from equation (22) ^with

S = 1, Tp/Tc = 1/2 and Ho

0, ^are represented ⁱⁿ figure ^{1 as functions of T. In AuFe,} where there is no

bulk, only ^{the second curve can be observed} (via ^the hyperfine ^field H.(T)). Note that the curve

m (T)/m., (0) =- H. (T)IH. (0) ^{does not exhibit} any break in slope ^{at low} temperature, contrary ^{to what is} observed in AuFe for the hyperfine ^{field of 57Fe below} Tf.

Fig. 1.

(Theoretical results for S = 1) ; ^curve (b) : ^reduced

thermal variation of the magnetization m,(T)lm,(O) = f(T /Tc) ^{of the bulk,} if it exists. Otherwise the curve

corresponds ^to the modulus of the fluctuating ^{moment of an}

isolated superparamagnetic cluster ; ^curve (a) : reduced ther- mal variation of the observable magnetization m (T)lm, (0)

or hyperfine ^field Hn(T)/Hn(O), ^{in zero external field, for a}

system ^of coupled clusters with Tp

^Tc/2.

Corresponding ^numerical values for m (T)/ms (0) ^are given ^{in table I.} They ^can be obtained by solving ^the

two parametric equations deduced from equation (22)

(0uoo ):

439

Table I.

Values of the reduced cluster magnetization m(T)lms(O) for coupled ^{clusters in zero} field (Eqs. (26), (27), (28)) ^{as a} function of TITP, ^{upon assuming that}

whence:

Note that in his calculations MØrup ^is only interested in the magnetization ^{referred to the bulk} ([23] Eq. (10)

and Fig. 8) :

while here, because the bulk is not available, ^{we have}

to consider tk (T)Iu r, (0 ).

A few remarks should be made:

- This system ^of weakly coupled clusters with giant

moments constitutes what Morup ^{et al.} [23] ^{call a}

« superferromagnet ^».

- Since with the numerical values considered above, ^the intercluster exchange ^field Hex (0 K) =

21 kOe, ^{it is} expected ^{that an} applied external field

Ho

²¹ kOe should be sufficient to strongly perturb

the system ^i.e. m(T) ^and H.(T) (see below).

- Because the implicit equation ^for m (T ) ^{involves a} Langevin function instead of a Brillouin function, ^the variation of m (T ) ^{and hence of} H. (T) ^{near T}

^{0 is}

anomalous. Instead of exhibiting ^a horizontal tangent,

it decreases linearly according ^to

or equivalently ([22] Eq. (60)) :

This linear decrease has apparently ^{been observed in}

some experiments.

- Since the superparamagnetic ^{clusters order, slow}

relaxation phenomena ^{will never} be observed in M6ss- bauer spectra.

3.2 COUPLED CLUSTERS IN THE PRESENCE OF AN APPLIED FIELD Ho.

^{Here we have to solve the two} parametric equations derived from equation (22) :

whence:

in which JLs(T) ^and m,(T) ^{are assumed to be unaltered} by ^{the field} except perhaps very ^near T,, ^because Ho is much smaller than the intracluster exchange ^field.

A way ^to solve the above system ^{is to choose}

T ITc (whence T/Tp) ⁱⁿ the first equation ^{and to}

determine u by successive approximations.

Table II. - Values of the reduced cluster magnetiza-

tion m(T, Ho)/ms(O) for coupled ^{clusters in a} field Ho

Kex ms(O) (Eqs. (32)-(34)) ^{as a} function of TIT,

upon assuming ^{that S}

1, Tp/Tc

^{1 /2.}

The numerical computation (Table II) ^was performed

for S =1, 3g = 2, Tp/Tc

^{1/2 and Ho .= Kex ms(0)}

(exchange field between clusters at 0 K). ^As previously, practical ^values corresponding ^{to this} situation could be : Tc

²⁵⁰ K, Tp

^{125 K, Ho}

^{21.06 kOe.}

In figure 2, ^curve a) corresponds to tL (T)l A, (0) H. (T)IH. (0) ^{in zero} field, ^curve b) ^to A (T, Ho)/JLs(O)ae ^Hn(T, Ho)/Hn(O) ^{in a field Ho}

Kex mr, (0), ^{and curve} c) ^{to the} observable hyperfine

field

Fig. ^2.

(Theoretical results for S = 1) ; ^curve 0 : ^reduced

thermal variation of the magnetization m (T)lm, (0) ^or hyper-

fine field Hn(T)/Hn(O) ^{for a system of} coupled clusters with

Tp

y2 ^{in zero field (same as curve oa in Fig. 1) ;}

curve b : ^{same reduced} quantities ^{as for curve} oa ^{but in}

the presence of ^an applied ^field Ho equal ^to the intercluster

exchange ^{field at 0 K :} Ho

Kex ms (0) ; ^curve (c) : ^variation

of Hobs (T, Ho)/Hn(O) ⁼ (Hn (T, Ho ) - Ho)/Hn(O) in the pre-

sence of the applied field ; ^curves oa ^and (c) ^{can also be}

considered as representing the observable hyperfine ^{fields :} Hn (T ) ^{in zero field and} Hobs (T, Ho ) in the presence of ^a field.

upon assuming ^that Hn (0 )

^{290 kOe} (S ^{= 1,} tL s (0)

2 JLB) ^and Ho

^{21.06 kOe}

^0.0726 Hn (0 ).

It can be seen in the figure ^{that the} applied ^{field has a} huge ^{effect on} the atomic magnetic ^{moment : indeed at}

T

Tp ^{where I-L} (F)

^{0 when} Ho

^{0, the field induces}

a moment i.L (T, HO) = ^0.772 iLs(O). ^{This is also re-}

flected in the variation of the observable hyperfine

fields : curve a) ^is proportional ^to Hobs(T)= Hn(T) ⁱⁿ

zero applied field and curve c) ^to Hobs ( T, Ho ) ⁼ Hn(T, Ho) - Ho in the presence of the field. Note that

curves a) ^and c) ^{do cross and that} Hobs(T, Ho ) ^remains

non zero at temperatures ^much higher ^than Tp : ^these

results are in qualitative agreement ^{with the} experi-

ments performed by ^{Brand et al. on Au 16.8 % Fe} [4]

and by ^{our own} group ^on Au 19 % Fe 2 % Sn in

Ho

^{20 kOe} [30].

We see that experiments ^{in an} applied field above

Tp ^{are a crucial test} for the existence of clusters :

-

in the absence of clusters :

-

in the presence of clusters :

and even a moderate field Ho ^is sufficient to induce a

large hyperfine splitting ^with Hn(T, HO) -> Ho.

Note that above Tp, ^{one can get a} reasonable order of magnitude ^{estimate of the moment of one cluster}

without taking ^account of the weak intercluster ex-

change. ^{Indeed at T}

Tp

^{Tc/2 in Ho}

^{Kex ms(O)}

(here ²¹ kOe), equation (2) ^{for the case without} exchange ^leads to JLind(Tp, Ho)/ P-s(O) = 0.647 while the equations (22) ^or (23), (24) ^with exchange ^{lead to}

JLex(Tp, Ho)/ P-s(O)

^{0.772 (see Table II).} This remark may be useful when ^a detailed study ^{of the} system ^has

not yet ^been performed ^and Tc ^{is not} precisely ^known.

Note also that in a small applied ^field (ms(T) Ho kB 7), ^{the induced moment above} Tp ^{is given by :}

whence a susceptibility per magnetic ^atom:

which is a generalization ^of equation (18) ^{in the}

presence of intercluster exchange. ^This susceptibility diverges ^at TP ^{as expected, but above} Tp ^{it does not}

obey ^{a standard} Curie-Weiss law: yc-’(T) Const/ ( T - Tp).

4. Preliminary ^Mossbauer experiments ^{on Au 19 °lo Fe}

2 % Sn.

A sample ^of A!!0.79 57Feo.l9ll9Sno.02 ^was prepared by ^I.

A. Campbell. ^The experimental study ^{of this} sample ^is

not yet completed and will be published ^elsewhere [30].

Let us just ^{mention that the} proportionality ^{of the} hyperfine ^{fields obtained} by ^Mossbauer spectroscopy

on 57 Fe and 119Sn leads to conclusions identical to those derived in reference [6] ^{with the} help ^of 197Au M6ss- bauer effect, i.e. that the canting ^{which occurs below} Tf ^is locally homogeneous : ^the transverse components of the magnetic ^moments which appear below Tf ^{on the}

Fe atoms are locally parallel ^{instead of} exhibiting ^{a 2D} spin glass-like ^{structure as} predicted by ^the theory [31].

On the other hand the hyperfine ^{field at} the iron is

strongly ^altered by ^the application ^{of a 20} kOe external field, ^as already ^{observed in reference} [4].

Here we will only present ^{a few} 57Fe Mossbauer spectra ^{obtained at 143} K, ^{i.e. above the} ordering temperature Tp ^{== 122 K of our sample, in the presence}

of an increasing applied external field : Ho

^{20, 50,}

80 k0e (these experiments ^were performed ^at C.E.N.G., Grenoble ^{Nuclear Center).}

According ^to figure ’3a, spectra ^{in zero field at room} temperature ^{and at 130 K are} essentially ^{the same and} correspond ^to pure quadrupole ^{doublets. On the con-}

trary, ^{as seen in} figure 3b, ^{at 143 K} application ^{of a}

field Ho

^{20 kOe} already ^{induces an} appreciable hyperfine ^structure «HObs(T, Ho) ^{= 123 koe ) which}

proves the existence of magnetic clusters ; ^{in addition}

the vanishing ^of the intermediate Mossbauer lines indicates that these clusters are ferromagnetic. ^When

the field increases _up to 80 kOe the splitting ^{does not}

441

Fig. ^3. (a) ^{57 Fe Mossbauer} spectra ^of Au ^{19 % Fe 2 % Sn at}

room temperature ^{and at 130 K in zero} applied fields ; (b) 57 Fe M6ssbauer spectra ^{of the same} sample ^{at 143 K in} applied ^fields Ho

20, 50, ^{80 kOe.}

vary very much : indeed the observed (average) hyper-

fine field is Hobs(T, Ho)

Hn(T, Ho) - Ho ^{in which}

both Hn (T, Ho ) ^and Ho ^{increase with} Ho : apparently ^at

143 K both variations approximately compensate. ^At this preliminary stage ^{of the} study, ^{it is} simpler ^to neglect ^the interactions between clusters ; ^then (see Eq. (15)), by plotting Hn(T, Ho)

Hobs(T, Ho) ⁺ Ho ^{as a} function of 1/Ho (Fig. 4), ^{we find that the} magnetic ^{moment of a cluster is :}

and that the saturation hyperfine field is :

Fig. 4. - Plot of (Hn(T, Ho) ^versus l/Ho (Eq. (15)) ^for Au ^{19 % Fe 2 % Sn at} 143 K. Intersection of the straight ^line

with horizontal axis yields m,(T) and with vertical axis yields H, (T) . (Hn(T, Ho) = 143:t 6; 187±9; 213:t 8 kOe for

Ho

20, 50, ^{80 k0e} respectively.

whence (using 145 kOel JLB) ^{an atomic} magnetic

moment:

and a cluster size :

These numbers should clearly be considered only ^as

orders of magnitude. ^In particular, by neglecting ^the

intercluster coupling ^we overestimate the cluster size

(see preceding chapter).

Other experiments ^were performed ^{at 220 K.} They suggest that the saturation hyperfine ^field H. (220 K) ^is

around 100-120 kOe, ^{i. e. we are still} slightly ^below Tc, ^{but their} precision ^{is too bad for} yielding ^reliable

estimates for the cluster moment and size. Note that the variation of H.(T, Ho ) ^{versus T for fixed} Ho ^also provides ^a determination of Tc (see ^{curve b of} Fig. 2).

Our experiments ^{in 20 kOe lead to} Tc - ^{250 K} [30].

5. Discussion.

The large difference between the hyperfine ^{fields in the}

presence ^or the absence of an applied ^{field of}

20 kOe, ^{as well as the} important hyperfine structure induced by ^{a beld at} temperatures ^above Tp ^{= 122 K,} strongly suggest ^that ferromagnetic ^{clusters do exist in}

Au 19 % Fe 2 % Sn and that Tp ^{is the ordering}

temperature ^of these clusters i.e. AuFe 19 % Sn 2 % is

a « superferromagnet ^{». It remains to} perform system-

atic experiments ^{in order to determine the} (average)

Curie temperature ^{of the} clusters, Tc, ^{and to} investigate

whether the (average) ^{size N of the clusters} depends ^on temperature.

It also remains to reconcile the existence of clusters with the rather homogeneous magnetic ^{behaviour of}

the AuFe samples ^as evidenced in particular by

’97Au [6] ^{and 119Sn} [30] Mossbauer data. A possibility

could be that at all temperatures the clusters occupy the whole volume of the sample ; this could occur if they correspond ^to adjacent ^{zones of the} sample separated by (fixed) boundaries along ^{which the} ferromagnetic exchange coupling happens ^{to be much smaller than in}

the remaining parts ^{of the} sample (boundaries ^which

are perhaps ^{of this} type have been found in 2D numerical simulations on Ising spin glasses [32]).

One should also explain ^{what occurs below} Tf. ^In

connection with this, ^{it is} interesting ^{to note that}

anomalous thermal variations of the hyperfine ^field

have also been observed in disordered spinels (in ^which canting ^is present ^{at low} temperatures) ^{and even in}

ordered insulating crystals.

Let us for example consider the crystal Fe2F5 (H20 )2 (inverse weberite) ^studied by Laligant ^{et al.} [33], ^which

exhibits magnetic frustration. In this crystal the thermal variation of the hyperfine ^{field at the Fe 3, ions} ([33]

Fig. 5b) looks like two successive magnetization ^cur-

ves : the first one (T > ²⁶ K) extrapolating ^to Hn -

300 kOe and the second _one, ( T ²⁶ K ), ^on top ^{of the} first _one, extrapolating ^to H. - ^{530 kOe. As one is} dealing ^{with Fe3 + ions one} knows that the saturation

hyperfine field of these ions at 0 K must be around 500 kOe. Then the ^« good » hyperfine ^{field value for} Fe3 + ions in inverse weberite is 530 kOe. Now in this

compound ^the origin ^{of the} anomalous variation of the

hyperfine field is identified : it is due to a change ^{of the} magnetic structure at 26 K accompanied by ^a change ^of

the thermal variations of the molecular fields. Similar

phenomena ^{are also} expected ^{to occur in} spinels ⁱⁿ

connection with canting ^effects.

It could be speculated ^{that the} phenomena ^observed

in AuFe below Tf might be associated with the existence of two types of intercluster couplings :

-

the ferromagnetic intercluster coupling ^{which is} responsible ^for the cluster ordering ^at Tp, ^and

-

a weaker antiferromagnetic intercluster coupling (associated ^with long range ^RKKY interactions ?)

which could come into play ^below Tf and would lead to

canting ^{of the cluster moments} (and ^not of the individu- al moments) ⁱⁿ agreement ^{with the} homogeneous

character of the canting ^as detected in 197Au [6] ^and 119Sn [30] ^Mossbauer experiments. This would corre-

spond ^{to a} Gabay-Toulouse [31] transition for the clusters. One should not forget, however, that mag-

netocrystalline anisotropy could also play a ^{role at low} temperatures. ^{As a matter of} fact, definite conclusions would require ^{a more} precise knowledge ^{of the micros-} copic ^structure.

6. Generalization to other cases.

Let us now abandon the specific ^{case of AuFe and turn}

to more general considerations.

First it should be recalled that, ^as pointed ^out by MOrup ^{et al.} [23], ferromagnetic clusters may give rise,

not only ^{to «} superferromagnets ^{», but also to «} supers-

pinglasses ^».

Second, ^there might ^also exist other types ^{of clusters :}

antiferromagnetic ^or speromagnetic ^{ones. A case of}

interest studied by M$rup ^{et al.} is that of speromagnetic particles ^of ferrihydrite [25]. ^{Here the} magnetic ^h.f.s.

of 57 Fe Mossbauer spectra disappears ^{above 80 K}

where the spectra ^{reduce to a} quadrupole ^doublet (Ref.

[25] ^{does not} specify ^{whether the} magnetic h.f.s. below 80 K is due to slowing ^{down of} superparamagnetic

relaxation or to cluster ordering). ^{At 80 K,} however, application ^{of a field} Ho

⁴⁰ kOe is sufficient ^to restitute a well developed magnetic h.f.s. This is

interpreted by assuming ^{that a} ferrihydrite particle ^{of N} magnetic ^{moments with} individual moduli JLs(T) ^{has an} uncompensated ^{moment of} length IN JLs(T) ^{to which}

the speromagnetic ^{moments are} rigidly linked. Above 80 K, ^{in zero field the} magnetic system fluctuates as a

whole, ^{but in a field} Ho, ^the uncompensated ^moment

tends to align along Ho, ^{i.e. the} angular fluctuations of each moment are reduced and become anisotropic.

Therefore there appears ^on each atom a non zero

average staggered ^moment with modulus

whence a hyperfine field whose dependence ^on Ho gives ^{access to} BIN-. ^{Note that if the} particles ^were antiferromagnetic ^{and not} speromagnetic, ^{one would}

expect ^an extinction of the intermediate lines in the presence of ^a field (staggered ^moments being parallel

or antiparallel ^{to the} aligned uncompensated one) ; ⁱⁿ

addition H obs (T, Ho ) ^{would take two values:}

Hn(T, Ho ) ± Ho. ^{This is not observed in} ferrihydrite ⁱⁿ

which there is no extinction; ^then H .bs(T, HO) H.(T, Ho ) ^and Ho merely ^{induces a line} broadening.

Note that observation of such effects requires ^an appreciable uncompensated ^moment IN JLs(T), ^{i.e. N}

has to be fairly large (N - ^{1 500 in the} ferrihydrite particles, ^{instead of N -} 170, ^{in AuFe} ferromagnetic clusters). ^In addition, ^{in the case of} antiferromagnetic

or speromagnetic ^clusters, rigid ^{behaviour of} the cluster

can be achieved only ^{if the} (intracluster) exchange coupling energy of ^the IN uncompensated ^moments

with their neighbours ^is large compared ^{to the total} anisotropy energy of the N ^{moments of} the cluster

(-,INHe"x" > NHA, ^{in which} HA ^{is the} anisotropy field).

The type ^of experiments ^and analysis ^{which we have}

described in this paper could clearly ^{be used to} investigate ^{the existence of} ferro and (not ^too small)

spero - ^or antiferro - magnetic ^{clusters in conven-}

tional spin glasses, amorphous materials, spinels ^etc.

[34-37]. The trick consists in applying ^{a moderate} magnetic ^field just ^{above the} temperature Tp ^{at which}

the magnetic hyperfine ^structure disappears ^{in the}

443

Mossbauer spectra, ^or alternately ^{to look at the effect}

of a moderate external magnetic ^{field on} the thermal variation of the observed hyperfine field both below and above Tp.

7. Summary.

Starting from the models developed by MOrup et ^{al. for} studying independent ^or coupled superparamagnetic particles, ^{we tried to} adapt ^{them to the Mossbauer}

detection of magnetic clusters in disordered magnetic

materials.

With AU1-xFex (x:> ¹⁵ % ) ⁱⁿ mind, ^we performed

some numerical calculations for the theoretical case of identical ferromagnetic clusters with a fixed size of N = 150 atoms having S ^{= 1} and g (0 K)

² tLB,

coupled ^{in such a} way that Tp

Tc/2, ^{in which} Tp ^{is the ordering} temperature ^{of the} giant ^{moments of}

the clusters and Tc ^the ordering temperature ^{of the} individual moments inside a cluster. Calculations were

performed ^{both for zero} applied magnetic field and for

an applied ^field equal ^{to the} intercluster exchange ^field

at 0 K.

The results of these calculations are in qualitative agreement ^{with the anomalous variation of the} Fe hyperfine ^{field in Au 16.8 % Fe and Au 19 % Fe 2 % Sn}

under application ^{of a 20 kOe} field, ^as observed in references [4] ^and [30].

We also present ^{a few} preliminary spectra ^obtained in Au 19 % Fe 2 % Sn at 143 K, i.e. above the zero field

magnetic ordering temperature Tp ^{= 122 K, in the}

presence of applied ^fields Ho

20, 50, 80 kOe. The

analysis ^{of these} spectra strongly suggests the existence of ferromagnetic ^{clusters of about 150-170 atoms in the} sample ^{at this} temperature. ^{It follows that} TP

122 K should be considered as the ordering temperature of the giant ^{moments of the clusters, while the} ordering

temperature Tc ^of the individual moments inside a

cluster is probably slightly ^{above 220 K.} According ^to

these results AU1-xFex (x ::. 15 9’o’) ^is probably ^a

« superferromagnet » ^{in the} MOrup’s sense, while the low temperature transition at Tf - ^{50 K} might perhaps

be a Gabay-Toulouse transition for the giant ^moments.

A more detailed study ^is currently underway.

Acknowledgments.

It is a pleasure ^{to thank S.} M¢rup (Lyngby) ^for communicating ^his unpublished ^{thesis, P. Bussi6re} (IRC, Lyon) ^{for the} long ^{duration loan of a tin source,}

I. A. Campbell (Physique ^{des Solides,} Orsay) ^who prepared ^the sample ^{on which the} preliminary spectra

were obtained, and the Mossbauer group ^at CENG - M. Bogd, ^C. Jeandey, J. L. Oddou et al.

where the in-field Mossbauer experiments ^were performed.

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