Magnetic properties and giant moment clusters in Be2Mn 1-xFex compounds

HAL Id: jpa-00208881

https://hal.archives-ouvertes.fr/jpa-00208881

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Magnetic properties and giant moment clusters in Be2Mn 1-xFex compounds

R. Jesser

To cite this version:

R. Jesser. Magnetic properties and giant moment clusters in Be2Mn 1-xFex compounds. Journal de

Physique, 1979, 40 (1), pp.23-38. �10.1051/jphys:0197900400102300�. �jpa-00208881�

Magnetic properties ^and giant ^moment clusters in

Be2Mn1-xFex compounds

R. Jesser

Laboratoire Pierre Weiss, E.R.A. n° 464 au C.N.R.S., Institut de Physique,

67084 Strasbourg, ^France

(Reçu ^{le 19} juin 1978, accepté ^{le 9 octobre} 1978)

Resume.

Les propriétés magnétiques ^des composés Be2Mn, _xFex ^ont été etudiees sur toute l’étendue de concentration 0 x ~ 1 ^et de champ 0 ~ H ~ 150 kOe à basse temperature (T ~ ¹⁰⁰ K). ^Une representation

des données d’aimantations en 03C32

f(H/03C3) jusqu’a ¹⁵⁰ kOe, ^a confirmé la nature inhomogène de la transition

magnétique observée antérieurement dans ce systeme. ^{Mais les mesures} d’aimantations à bas champ (0 ~ ^{H 1} kOe) ^{ont montré} que ^cette transition était graduelle : ^évolution graduelle ^du paramagnétisme (x ~ 0,06) ^au mictomagnétisme (0,11 ~ x ~ 0,30) jusqu’au ferromagnétisme (0,30 ~ ^{x ~} 1,00). ^{Le moment}

moyen 03BC des berylliures ferromagnétiques (0,30 ~ ^{x ~} 1,00) ^décroît rapidement ^et de manière non linéaire

quand ^on augmente ^{la teneur en} Mn. Mais les valeurs supérieures ^{à l’unité que l’on a} trouvées pour le ^moment normalise du fer (rapport 03BC/x03BC0) indiquent que deux types ^d’atomes (le ^{Fe et le} Mn) peuvent porter ^{un moment} dans ces bérylliures. ^Les données d’aimantations des composés Be2Mn1 _xFex ^{à x allant de} 0,06 ^à 0,25, ^{ont été} analysées ^{en termes d’amas} magnétiques ^à moments et concentrations dépendant ^{de la} temperature. ^{Nous avons}

discuté les résultats insolites de cette analyse ^{et nous avons} tenté de les interpréter ^en invoquant ^les concepts (i)

d’amas à moments géants ayant leur propre point ^{de Curie} 03B8c, augmentant ^avec la taille des _amas, (ii) d’impuretés

presque magnétiques ^devenant magnétiques ^en abaissant la température, ^{vu les} champs ^élevés utilisés ici

(H ~ ⁸⁰ kOe), ^et (iii) d’interactions antiferromagnétiques ^{à courte} portée, ^{reliées au} comportement mictomagné- tique ^{de ces} composés. ^Tout l’ensemble des résultats obtenus dans ce travail, peut être décrit en termes de magné-

tisme d’environnement local, mais seulement dans un modèle adéquat, ^tenant compte ^{de 2} types d’atomes por- teurs de moments (Fe ^et Mn). ^{Il reste à élaborer un} tel modèle au moyen d’autres techniques ^{que les mesures}

d’aimantations (spectroscopie Mössbauer, diffraction de neutrons, etc.).

Abstract.

The magnetic properties of Be2Mn1 _xFex compounds ^{have been} investigated ^{over the whole concen-}

tration (0 ^{x ~} 1) ^{and field} (0 ~ H ~ 150 kOe) ranges ^at low temperatures (T ~ ¹⁰⁰ K). ^The inhomogeneous

nature of the magnetic transition previously observed in this system, has been confirmed by ^{means of 03C32 versus} H/03C3 plots up ^to 150 kOe. But low field (0 ~ ^{H 1} kOe) magnetization measurements showed that this transition is gradual : gradual evolution from paramagnetism (x ~ 0.06) ^to mictomagnetism (0.11 ~ ^{x ~} 0.30) ^{then to} ferromagnetism (0.30 ~ ^{x ~} 1.00). ^{The mean} magnetic moment 03BC ^of ferromagnetic beryllides (0.30 ~ x ~ 1.00)

shows a rapid ^non linear decrease with increasing ^{Mn content but the} corresponding normalized Fe moment

(03BC/x03BC0 ratio) ^{was found} higher ^than unity, indicating ^{that two kinds of atoms} (Fe ^and Mn) ^{are able to} carry ^a

magnetic ^{moment in these} beryllides. ^The magnetization ^{data on} Be2Mn1-xFex compounds ^{with x} ranging ^from

0.06 to 0.25, ^{have been} analysed ^{in terms of} magnetic clusters with temperature dependent ^{moments and concen-}

trations. The unusual results of this analysis have been discussed and tentatively interpreted by invoking ^the concepts of (i) giant ^moment clusters with their own Curie temperatures 0, increasing with the cluster size, (ii) nearly magnetic impurities which become magnetic by lowering ^the temperature, ^{in the} high fields considered here

(H ~ ⁸⁰ kOe), ^and (iii) antiferromagnetic short range interactions related ^to the mictomagnetic ^{behaviour of}

these compounds. ^All of the results obtained in this work may be described in ^terms of local environment magne- tism, ^but only ^{with an} appropriate model which takes into account two types ^of magnetic ^atoms (Fe ^and Mn).

Development ^{of such a} model would be aided by ^{the use of} techniques other than magnetization measurements

(Mössbauer spectroscopy, ^neutron diffraction studies, ^{and so} on...).

Classification

Physics ^Abstracts

75 . 30C

1. Introduction.

There are several alloy ^or compound systems ^{in which} magnetic properties ^are presently understood in terms of magnetic polarization

clouds (magnetic clusters) :

-

the inhomogeneous ^nature of the transition from

paramagnetism ^to ferromagnetism ^{observed in such}

systems, has been related to the existence of magnetic clusters ;

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197900400102300

-

giant ^{moment clusters} persist as superparama-

gnetic ^{entities well into the} paramagnetic composition

range, ^even in perfectly random solid solutions ;

-

the cluster concentration and magnitude ^increase

when the magnetic carrier concentration is increased up ^to the critical composition ;

-

the onset of ferromagnetism ^can be considered as

resulting ^{from the} ferromagnetic coupling ^of giant

moment clusters -;

-

these giant ^{moment clusters have to be related to}

local environment effects [ 1 ], [2].

Let us mention as a justification of the above

propositions, ^some typical investigations ^{on such} alloys ^or compounds ^{in the} papers referred to below.

In all these papers, the magnetization ^{data on the} investigated alloys ^or compounds, ^were analysed

with the concept ^of magnetic clusters and the results obtained were described or discussed using ^various

local environment models of magnetism.

The most extensively ^studied system is that of Ni

binary alloys, especially ^Ni-Cu [3] ; ^Ni-Rh [4] ; Ni-Cu, Ni-V and Ni-Mo [5] ; ^Ni-Pd [6]. ^{Giant moment clusters}

are shown to exist in other binary alloys, ^{such as}

Fe-V [7] ^{or Cu-Mn} [8].

It appears in several studies on MCX ^interme-

tallic compounds (with ^{c ~ 1, M}

^{Fe, Co or Ni}

and X being ^{a non} magnetic element) ^that giant

moment clusters can arise from excess M atoms

occupying ^{X sites. A detailed} study ^on Co,Ga ^com- pounds [9] shows the existence of non magnetic, nearly magnetic ^and magnetic impurities (Co ^atoms occupying ^Ga sites). ^The superparamagnetism

observed in Fe,Al, CoAl ^and Nival compounds ^was

also attributed to Fe, ^{Co or Ni atoms} occupying ^Al

sites [10].

The magnetism ^{of other} binary ^or ternary alloy

systems, ^which present ^a transition concentration _z from paramagnetism ^to ferromagnetism, ^{can be}

characterized in terms of magnetic ^{clusters. This is}

the case of the Be2Mn1 _xFex pseudo-binary ^system.

We summarize briefly ^some aspects ^of previous investigations ^{on these} compounds. ^{The ferroma-} gnetic compound Be2Fe ^{and the} paramagnetic ^com- pound Be2Mn ^{form an} uninterrupted series of hexa-

gonal C14 solid solutions Be2Mn1 _xFex ^{(0 x 1)} ferromagnetic for x > ^0.30 [11]. ^{The critical} compo- sition for ferromagnetism ^{in this system has been}

located at xc, ~- 0.18 by ^{means of} specific ^heat [12]

and magnetization [ 13] measurements. The properties

of Be2Mn1 _xFex compounds ^near the critical xCr

composition (0.06 x 0.25) have been attributed to magnetic ^{clusters :}

-

an essentially temperature independent compo- nent has been found in the specific heat ;

-

the large deviations from linearity observed for

some magnetization ^{62 =} f(Hla) isotherms showed that the ferromagnetism ^{occurs in an} inhomogeneous

way;

-

samples ^{in the} paramagnetic region (x ^{= 0.11}

to 0.175) ^{seem to} obey ^a simple model of cluster

superparamagnetism [14].

A more recent work [ 15] reports specific ^{heat measu-}

rements on Be2Mno.865Feo.135 ^{at low} temperatures (0.1 ^{K to 23} K). ^The temperature dependence ^{of the}

excess heat capacity (anomalous term), ^somewhat

like a Schottky function, ^{could be} reasonably ^inter- preted ^{in a} magnetic cluster model.

The present ^{work was} undertaken in order to obtain

more information on the magnetic behaviour of

Be2Mn1 _xFex compounds ^over the whole concen-

tration _range 0 x 1, ^with special regards ^{to the} compounds ⁱⁿ the critical composition range for ferro-

magnetism (0.06 x 0.25). Therefore, ^{we have}

carried out a systematic magnetization study ^{on these} beryllides ^over the whole field _range 0.00 ^to 150 kOe at low temperatures (T ¹⁰⁰ K). ^{After a brief des-} cription ^{of the} experimental procedures (section 2),

we report in section 3 the new series of magnetization

measurements on our Be2Mn1 _xFex samples (0.06 ^x 1.00) in fields _up to 150 kOe at low temperatures (T ¹⁰⁰ K). ^The high ^field magneti-

zation measurements offer a more accurate deter- mination of the saturation magnetization by allowing

a true evaluation of the superposed paramagnetic xH(T ) susceptibility. As will be seen in section 3,

we simplify ^our Q(H, T) ^data analysis by attributing

the main part y(H, T ) ^{of the} magnetization ^{to clusters}

assumed to exist in all the investigated beryllides (0.042 x 1.00) in different magnetic states (super- paramagnetic, -mictomagnetic ^or ferromagnetic, depending ^{on T and} x). ^{The new} measurements in low fields (0 ^{H 1} kOe) ^{enabled us to observe micto-} magnetic ^{behaviour on} Be2Mn1 _xFex samples ^with

0.11 x ^{0.30 at low} temperatures (section 4). ^The

occurrence of mictomagnetism ^was ignored ^{in our}

earlier investigations [13] ^{on these} compounds.

Section 5 deals with the magnetization ^data analysis

on Fe rich beryllides (0.30 x 1.00). ^{A detailed} analysis of the cluster superparamagnetism ⁱⁿ beryl-

lides with x around xCr (0.06 x 0.25) ^is presented

in section 6. The unusual results of this analysis (clusters ^with average ^moments and concentrations

depending ^{on T) are} discussed and tentatively ^inter- preted in section 7. Finally, ^a summary and a conclu- sion are given in section 8.

2. Expérimental procedures.

^The Be2Mn1 _xFex samples ^were prepared by melting together ^appro- priate ^{amounts of the} pure constituents [11]. ^{All the} beryllides ^{have the} expected hexagonal ^{C14 structure}

without _any parasitic phase, ^{as shown} by X rays

analysis ^{and Curie} temperature measurements. All

samples ^were slowly ^cooled (with ^{a rate of about}

150 °C . h -1) ^after annealing ^{in an} argon atmosphere

at 1 100°C for 48 h. Such a heat treatment cannot exclude _any partial ordering ^{in our} samples, ^{so we}

have to expect ^some deviation from complete ^random

solid solutions. But this heat treatment ensures very

homogeneous samples.

Magnetization measurements were carried out on

ellipsoidal samples ^{at different} temperatures ^between 1.7 K and 100 K in the field _range 0.00 to 150 kOe.

Two types ^of apparatus ^were necessary ^{to cover such}

a range of fields and temperatures. ^The measurements in low and moderate fields (0 H ²⁰ kOe) ^between

1.7 K and 120 K were performed ^{with a} temperature controlled Foner type vibrating sample magnetometer developed ^{in our} laboratory [16], [17] ^{and the measu-}

rements in high ^fields (H ¹⁵⁰ k0e) ^at temperatures between 4.2 K and 44 K (or ^{100 K for three} samples)

were performed ^{with the} experimental ^set up ^at the S.N.C.I. (Grenoble, France) described elsewhere [18].

The two sets of apparatus ^were calibrated against Gd2o3 [19] ^{and Ni} [20] standards. The relative uncer-

tainty ^{of our} magnetization a(H, T) ^versus tempe-

rature and field measurements is estimated to be less than 2 %.

3. Général features of the magnetization.

First,

we summarize briefly ^{some results on dilute} Be2Mn1 _xFex compounds (x 0.042) ^{in order to}

obtain the concentration where giant ^{moment clusters}

appear. Paramagnetic ^{behaviour was observed over the}

entire temperature range 4.2 K ^to 1 100 K on the

Be2Mn ^and Be2Mno.988Feo.012 compounds. ^{At 4.2 K}

these compounds ^{have a} magnetization linear with field from 0 to 20 kOe, ^with respective susceptibilities ^of

12 ^x 10- 6 and 15 ^x 10- 6 emu . g-1. Oe-1. The magne- tization versus H isotherm of Be2Mno.978Feo.022

at 4.2 K shows a part linear with field from 0 to 20 kOe, with a susceptibility ^{of 21 x 10-6} emu. g-1. Oe-1,

while the slight ^{curvature observed on} this isotherm for higher ^fields (30 kOe H ¹⁵⁰ kOe) may be attributed to the magnetism of isolated impurities. ^The

stronger ^{curvature observed on the} magnetization ^Q

versus H isotherm ofBe2Mno.958Feo.042’ ^{and its} higher

itiitial susceptibility (x = ^{55 x} 10 - 6 emu. g - 1 . Oe - ¹

between 0 and 2 kOe) ^{allow us to} locate the _appearance of giant ^moment clusters in the Be2Mn 1 _ xFex ^com- pounds ^{at a} concentration x between 0.03 and 0.04.

Therefore the interesting concentration _range for

investigations ^{on cluster} superparamagnetism ^lies

between ^x

0.04 and 0.25, but the available measu- rements we have, ^concern only ^the samples ^{in the.}

concentration _range 0.06 to 0.25.

Then, ^we report ^the magnetization, (in emu . g -’ )

of each Be2Mn1 _xFex sample in the critical concentra- tion _range 0.06 x 0.25, ^{at different} temperatures between 4.2 K and 44 K (or ^{more for three} samples) ^as

a function of field H (corrected ^for demagnetization)

from 1 kOe to 150 kOe. A a2 versus Hlu representation

of the data _up to 150 kOe confirms the inhomogeneous

nature of the magnetic transition previously ^observed [13] ^{in the} Be2Mn1-xFex system. ^{All Q versus H} isotherms show continuous curvatures over the whole

Fig. ^1.

Magnetization ^{isotherms a} (emu. g- 1) ^{versus H} (kOe) of some Be2Mn1-xFex compounds ^{at 4.2 K : + v} = 0.19 ;

OX = 0.175; x x = 0.16 ;>x = 0.135; A x = 0.11; 6x = 0.082;

y --, 0. 06.

field _range. Figure ¹ displays such isotherms at 4.2 K as examples.

Our new magnetization measurements on Fe rich

Be2Mn1 _xFex compounds (0.30 x 1.00) ^at

4.2 K, ^{in fields} ranging ^{from 4 kOe to 150} kOe, ^are presented ^{as a} (emu. g-1) ^{versus H isotherms} (Fig. 2),

the field H being corrected for demagnetization.

These compounds ^show ferromagnetic saturation in moderate and high fields, ⁱⁿ agreement ^{with our} earlier investigations [13]. ^{But the} higher fields avai- lable here enable us to determine the superposed paramagnetic susceptibility XH and the saturation

magnetization as ^{with a} higher accuracy (section 5).

Fig. ^2.

Magnetization ^{isotherms 6} (emu. g-1) ^{versus H} (kOe) of Fe rich Be2Mn1 _xFex compounds ^{at 4.2 K : + x} = 0.88 ; Ox=0.76;x x = 0.62; 0 x = 0.50; Yx=0.40; V x = 0.30.

We have now to choose a suitable model for ana-

lysing ^the a(H, T) ^{data on all the} investigated beryl-

lides (0.06 x 1.00). ^{The most} general view point

consists in attributing ^{the main} part ^{of the} magneti-

zation to the non localized and localized 3d states

(Fe ^and Mn) responsible ^{for the} magnetism ^{in these}

beryllides. ^{Such a} _procedure ^was successfully applied

by ^{Acker and} Huguenin [21] ] ^{to their} magnetization

data analysis ^on weakly magnetic ^Ni-V alloys. ^But

the analysis ^{of our} 6(H, T ) ^data using ^this procedure appeared ^rather complicated and needed some simpli-

fication. We attribute the main part y(H, T) ^{of the} magnetization z(7/, T ) ^to magnetic polarization ^clouds (clusters) ^{assumed to exist in all the} beryllides ^with 0.042 x 1.00. As will be shown in section 4, these clusters are mictomagnetic ^or superparamagnetic (depending ^on T ) ⁱⁿ beryllides ^{with 0.042 x} 0.25, and ferromagnetically coupled, forming ferromagnetic

domains in the Fe rich beryllides (0.30 x 1.00)

at sufficiently ^low temperatures. Therefore, ^we analyse

the Q(H, T ) ^{data on all} investigated beryllides (0.06 ^x 1.00) by ^{means of the} simplified expres- sion (1) : a(H, T) = y(H, T) ⁺ HxH(T).

The y(H, T) magnetization, considered as arising

from giant ^moment clusters in different magnetic

states (superparamagnetic, mictomagnetic ^{or ferroma-} gnetic, depending ^{on T and} x), may thus be described in a local environment model of magnetism. ^{All other} magnetic contributions (nearly magnetic ^{and non} magnetic impurities, magnetism ^{of the non localized}

3d states, host magnetism) ^are gathered ^{in the} unique magnetization ^term HXH(T) assumed linear with field up ^to 150 kOe and representing ^the superposed paramagnetism ^{of the} beryllides. ^The analysis ^{of our} experimental ^data by ^{means of the} simplified expres- sion (1) implies ^{the non evident} assumption ^{of a non}

localized 3d state magnetism linear with field _up to 150 kOe. Therefore, ^{it is} necessary ^to discuss the

validity ^{of our} 6(H, T) representation by expression (1)

over the whole investigated temperature ^{T and} composition x ranges ; this will be done essentially

in section 7. A brief comment will be useful here : for us an impurity ^is nearly magnetic ^{if it has a local} magnetic moment, but its magnetization component remains linear with field _up to 150 kOe.

Expression ^{(1) offers the} advantage ^of simplifying

our Q(H, T) ^data analysis by assuming ^an 1 IH ^or 1/H2 behaviour for the y(H, T) = a(H, T) - HxH(T) magnetization ^at sufficiently high fields. With this

assumption, expression (1) allows the best evaluation of the xH(T) susceptibility through ^the high ^field slope du(H, T )/dH ^and yields ^a good ^{fit with the} experimen-

tal data. The main results on the xH(T) susceptibility

are summarized in sections 5 (Fig. 8) ^{and 6} (Table II).

We treat the cluster magnetism ^{of all} investigated beryllides ^{in the} following ^classical way : ^we take the cluster, superparamagnetism ^{as ruled} by Langevin

functions (sections ^{3 and} 6) ^{and the} ferromagnetism

as ruled by classical saturation laws (section 5). Thus,

the asymptotical form of the cluster magnetization y(H, T) ⁱⁿ high fields, ^is given by the assumed 1 /H

or 1 /H 2 ^behaviour.

In a first step ^{of our cluster} superparamagnetism analysis ^on Be2Mnl _xFex samples ^with

we have verified that the simplified ^form (2) ^of expres-

sion ( 1 )

represents fairly ^{well the} magnetization ^{of these} beryllides ^{in the} high field limit Ha 60 kOe at all

investigated températures, the relative deviations did not exceed 1 %. ^{With the} assumption ^{of a cluster} superparamagnetism ^ruled by Langevin functions,

the as(T) ^and A(T) parameters ⁱⁿ (2) yield ^the average cluster moment M and concentration N independent

of the cluster size distribution. The quantities ^{M and N}

are found to be temperature dependent, their values

are not shown here ; ^we _report in section 6 an improved analysis ^{of the} magnetization ^data by taking ^into

account a small interaction between clusters, ^which

was neglected ⁱⁿ (2).

We also report in this section our initial _{Xi suscep-}

tibility ^{data on all} Be2Mn1 _xFex samples ^with

0.06 x 0.25, ^as (Xi - xH)-1 ^versus T plots (Fig. 3).

Fig. ^3.

Inverse cluster susceptibility (x 1-xH) -1 ⁱⁿ emu -1. g . Oe

versus T(K) ^{for some} Be2Mn1 _xFex compounds : Y ^x

^{0.06 ;} Ô x = 0.082 ; + x = 0. 1 1 ; o x = 0. 1 35 ; x x = 0. 1 6 ; A x = 0. 1 75 ; Aj-=0.19;Vjc=0.2î.

The initial susceptibility xi of each beryllide ^{is defined}

as the slope a / H of reversible magnetization ^{6 versus H}

isotherms in low fields (0 ^{H 1} kOe). ^A x; ¹

versus T representation of the data showed that no

classical Curie Weiss behaviour could be found on

any beryllide ^{in the} temperature range 4.2 K ^to 100 K : the inverse cluster susceptibility (x; - xH) -1 ^{1 shows}

continuous curvatures in its (x; - xH) -1 ^{1 versus T}

graphs. This fact too, supports ^the concept of super-

paramagnetic clusters with temperature dependent

moments in these beryllides.

4. Magnetic behaviour in low fields : mictomagnetism

and ferromagnetism.

^{Low field} magnetization

measurements performed ^on Be2Mn1 _xFex ^com- pounds ^{with 0.11 x 0.25 at} temperatures ranging

from 1.7 K to 20 K or more, indicate mictomagnetic

behaviour in the following way. Two series of measu- rements were done on each sample. ^{First, we measured}

the magnetic reversible susceptibility ^after cooling

the sample ^{in zero} field : this procedure ^{ensured us a} magnetization. proportional ^{to H at} sufficiently ^low

fields (0 ^{H 0.3} kOe) and defined the initial

susceptibility xi given in section 3. Then, ^{we deter-} mined the temperature T. of the reversible susceptibi- lity ^{maximum ;} measurements done on

Be2Mno.94Feo.o6 ^and Be2Mno.918Feo.082

indicated that the characteristic T. ^and Tf tempera-

tures of these samples (if they exist) lie below 1.7 K.

The second series of measurements were done by cooling ^each sample ^{in a} given ^field (H ^{= 0.1 to}

0.3 kOe, depending ^{on the} samples) and showed an

irreversible magnetization ^at temperatures ^{below the} characteristic Tf temperature higher ^than Tm. ^The

cases of Be2Mno.865Feo.135 ^and Be2Mno.81 Feo.19 ^are given ^as examples ⁱⁿ figure ^4. The values of the cha- racteristic temperatures Tf ^and T. ^are reported ^on

table I. Such behaviour is characteristic for spin glass

or mictomagnetic alloys [8, 22] ^with spin freezing temperature Tf where irreversible magnetization ^sets

in. No scaling ^law [23] ^is applicable here, allowing

us to consider these beryllides ^as mictomagnets.

However, the difference between Tf ^and T. ^seems

somewhat too high ^{and we have no} explanation ^for

this fact. The reversible magnetization ^{showed a time} dependence ^at temperatures ^below T., which is also

typical ^for mictomagnetic alloys [24, 25]. ^{In order to}

obtain more informations on the mictomagnetic

behaviour of these Be2Mn1-xFex compounds, ^we performed isothermal magnetization measurements at 4.2 K on some samples (x

^{0.16 to} 0.25) ^{in both}

states obtained after zero field cooling ^and after field

cooling (H ^{= 3 or 5} kOe). Figure ⁵ represents ^the

case ofBe2Mno.81 FeO.19 ^{as an} example. ^The hysteresis loop ^{of each} sample ^{at 4.2 K} (taken after field

cooling) ^is symmetrical, the coercive fields are low

Fig. ^4.

Mictomagnetic behaviour of Be2Mno.S65Feo.135 (a) and Be2Mno.,,Fe..,, (b); a (emu . g-1) ^versus T (K) ^isotherms

+ after zero field cooling and 0 after cooling in a field H= 0.3 kOe (a)

or H = 0.2 kOe (b).

(HC~ ^0.1 kOe), ^{but the reverse} sections of the loop

are time dependent ^{and the} magnetization ^curve starting ^{from the zero field} cooling ^{state lies} nearly

outside of the hysteresis loop. ^Such magnetization

isotherms were reported ^for Au4Mn compounds ^and

were attributed to mictomagnetism [26]. ^{From all}

the above mentioned properties, ^{we can} deduce that the Be2Mn1 _xFex compounds ^{with 0.11 x 0.25}

behave as mictomagnets ^{at low} temperatures ^{and are} superparamagnetic ^at temperatures above their spin freezing temperature Tf.

In order to examine the evolution of the magnetism through ^the Be2Mn, -xfex system, ^we have extended

our low field investigations ^{to more Fe rich} beryllides (0.30 x 1.00). ^{It is not} yet clear whether these

beryllides ^can be described as ferromagnets ^{or micto-}

magnets ^with high T. ^and Tf temperatures. ^These

samples clearly ^show ferromagnetic saturation in

Table I.

Characteristic Tm ^and Tf temperatures of Be2Mn1_xFex samples ^{in the} mictomagnetic ^{state :} Tm

temperature of maximal reversible susceptibility Tf spin freezing temperature.

Fig. ^5.

Magnetization ^isotherms of Be2Mno.8,Feo.19 ^{at 4.2 K :}

a (emu . g-1) ^versus H(kOe), corrected for demagnetization,

0 hysteresis loop ^after cooling ^the sample ^{in the + 2.85 k0e} field, ^{the dashed} portions ^{of the} loop ^{are found to be time} dependent ;

+ magnetization ^{curve after zero field} cooling.

moderate and high ^fields (Fig. 2), ^{but their} magnetic

behaviour in low fields resemble rather that of micto- magnets ^with high T. ^and Tf temperatures. ^The

Be2 Mno .7 oFeo.30 sample shows all characteristic _pro-

perties ^{of a} mictomagnet ^{at low} temperatures : ^the variation of its reversible magnetization (after ^zero

field cooling) ^with temperature, goes from a broad maximum at H ~ 0.1 kOe to a cusp ^at H ~ 0.013 kOe, time dependence of the reversible magnetization ^and

irreversible magnetization after field cooling ^{were also}

observed below the characteristic temperatures T. - ^{32 K and} Tf - ^{60 K. In} view of their magnetic

behaviour in low fields, Be2Mno.60Feo.40 ^and Be2Mno,soFeo.so ^may be considered rather as micto- magnets ^than ferromagnets ^{at low} temperatures : the broad maxima observed ^on their reversible _magne- tization (in ^{fields H N 25} Oe) ^versus T graphs, provided only ^an estimation to be made for the characteristic

T. (or Tc ?) temperature, but irreversible magneti-

zation was observed on each sample, after field cooling

below a Tf temperature higher ^than T. (Table I).

The reversible magnetization ^{of the Fe rich} beryllides (0.62 x 1.00) ^was only obtained after cooling

each sample ^{in a zero} field from 800 K (or more) ^to

300 K, ^{then to} 4.2 K. As will be seen below, ^the question whether these beryllides ^can be considered as

ferromagnets ^or mictomagnets ^with high Tm ^and Tf temperatures, ^remains open. The reversible _magne- tization of each beryllide (x

^{0.62 to} 1.00), ^{taken in a}

field H ~ 80 Oe, ^{was found to be} nearly ^{constant or to}

slightly increase with T over a wide _range of tempe-

rature (4.2 ^{K to more than 300} K), ^then rapidly

decrease on raising ^the temperature. ^The temperature T, corresponding ^{to the} rapid ^{decrease of this} magne- tization was identified in our earlier work [13] ^{as the} ferromagnetic ^Curie point ^{of each} beryllide. ^The magnetization irreversibility resulting from the field

cooling ^{of each Fe rich} beryllide ^{below its} Tf (Tf ~ Tc)

temperature, may be attributed to thermal effects

occurring for annealed ferromagnets ^{or to} high tempe-

rature mictomagnetism. However, isothermal _magne- tization measurements at 300 K showed _{very narrow,} but symmetrical hysteresis loops (Fig. 6) ^after cycling

each Fe rich beryllide (x ^{= 0.62 to} 1.00) ^{in a 16 kOe or}

18 kOe field (remanent magnetization a r ~ 0.2 emu. g -1,

Fig. ^6.

Hysteresis loop ^of Be2Fe ^{at 300 K :} magnetization

6 (emu . g-1) ^{versus H} (kOe), corrected for demagnetization 0

by decreasing H from + 14.7 kOe to - 14.7 kOe and + by increasing

H from - 14.7 kOe to + 14.7 kOe.

coercive fields HC ~ ^{5 Oe, while the} magnetization ^at

16 kOe _ranges from 74.7 emu. g-1 for x = 0.62 to

136.4 emu . g -1 ^{for x =} 1.00).

If, ^we interpret all the above mentioned _pro-

perties ^{on the Fe rich} Be2Mn1 _xFex compounds (0.30 ^x 1.00) by ^{the onset of} ferromagnetism,

this implies something unusual about this ferroma-

gnetic order : existence of a network of small domains, high anisotropy effects, ..., points which remain to be cleared _up by ^further investigations.

In an attempt ^to clarify ^the exact nature of the

magnetism ^{in our Fe rich} beryllides (0.3 x 1.00)

we used Môssbauer spectroscopy (14.4 ^{keV resonance}

of 57Fe). Preliminary ^Môssbauer experiments ^were performed ^{at 4.2 K on} Be2Mn1 _xFex compounds

with x ranging ^{from 0.175 to 0.40} [27]. ^{These com-} pounds ^were chosen, ^because they ^{cover the concen-}

tration _range where ferromagnetism ^is thought ^to

set in. An examination of the spectra (not ^shown here)

confirms the appearance of magnetic ordering ^{in the} Be2 Mn 1 _ xFex system ^{at a} concentration _XCr between 0.25 and 0.30. In the meantime, ^we simply interpret

this magnetic ordering ^as ferromagnetism resulting

from the formation of small domains by ^{the ferro-} magnetic coupling ^of giant ^moment clusters. This

interpretation ^{has to be} justified by ^{further investi-} gations.

We tentatively ^assume here that the magnetic

transition in the Be2Mn1 _xFex system ^occurs gra-

dually ^from paramagnetism (x 0.06) ^{to mictoma-} gnetism (0.11 x 0.30) ^{then to} ferromagnetism (0.30 ^x 1.00). ^This assumption may be reaso-

nable, according ^{to a} study ^{on Ni-Cu} alloys ^{of Ododo}

and Coles (1977), ^where it ^is predicted ^{that in} general

the onset of ferromagnetism ⁱⁿ giant ^moment alloys,

is necessarily preceeded by ^a mictomagnetic region.

5. Ferromagnetism ^{in the} Be2Mn1-xFex system.

This section deals with the ferromagnetic properties

of the Fe rich beryllides (0.30 ^x 1.00) ^{at 4.2 K}

in moderate and high fields (10 k0e ^H 150 k0e).

We analyse ^the magnetization ^{data on these} beryllides

at 4.2 K by ^{means of the} simplified expression (1)

mentioned in section 3 :

a(H, ^4.2 K) ⁼ y(H, ^4.2 K) ⁺ HXH (4.2 K) .

The high ^field slope ^{of a versus H isotherms} (Fig. 2) yields ^the XH (4.2 K) susceptibility. ^{As shown} by (Q - XH H) ^{versus H - 1 or H - 2} graphs (Fig. 7), ^the y(H) magnetization ^{of all Fe rich} beryllides ^{at 4.2 K}

could be represented by the classical expression y(H) ⁼ Qs - Am ^{H -M with an} accuracy better than 0.2 % ^{over a wide} range of moderate and high ^fields (H > ^{20 k0e to} H >, 60 k0e, depending ^{on the} samples). ^The integer m has the value + 1 for x ^0.50 and + 2 for 0.62 x ^1.00. This classical _expres- sion represents the rotation of the magnetization ^and yields ^the saturation magnetization ^{u. at 4.2 K} by

linear extrapolation ^to infinite fields of (a - XH H)

versus 1 /H ^or 1 /H 2. Moreover, the saturation _magne- tization _u. could be obtained directly ^for sufficiently

Fe rich beryllides (0.62 ^x 1.00) by full ^saturation

of their magnetization ^{in the} high ^fields available here

(H > ^{120 kOe to} H >, 70 k0e, depending ^{on the} samples). ^The relative difference between the two types of ₆₅ (4.2 K) values observed on all these samples, ^is

less than 0.1 % : ^the Be2Mno,12Feo.ss sample ^{has a} as(4.2K) value of 135.61 ± 0.01 emu . g -1 ^obtained

by full saturation of its magnetization ^{in fields}

H > 70 k0e, while the extrapolation ^to 1 /H 2 ^{= 0 of}

its (a - XH H) ^versus I/H2 graph, yields

as (4.2 ^{K) =} 135.70 ± 0.05 emu . g-1.

Fig. ^7.

Behaviour of Fe rich beryllides ⁱⁿ high ^{fields :} (a) ^linear part ^{of the} a-m H(emu.g-1) ^{versus H-2} (in Moe-2) ^isotherm

of ]Be2Mno.38Feo.62 ^at 4.2 K, corresponding ^to fields between 151.04 k0e and 24.65 k0e ; (b) ^linear part ^{of the} Q-xH H (emu . g-1)

versus H-1 (in MOe-1) isotherm of Be2Mno.6oFeo.4o ^{at 4.2 K,} corresponding ^to fields between 151.36 kOe and 49.58 kOe.

The _as (4.2 K) ^values agree qualitatively ^{for all Fe}

rich beryllides (0.30 x 1.00) ^{with that} reported

in our earlier work [13], ^{but no linear} relationship

could be found between _us (4.2 K) ^{and x for} high ^Fe

contents (0.76 ^x 1.00). ^The XH (4.2 K) suscep-

tibility is weak for beryllides ^with high ^{Fe content} (10’XH-5 ^{to 2} emu . g-1 ^{for x = 0.76 to} 1.00);

its order of magnitude is consistent with classical band polarization susceptibilities of transition metals.

The variations of as (4.2 K) and xH (4.2 K) ^{with x over}

the whole composition range 0.06 x 1.00, ^are illustrated by figure ^{8. The} as (4.2 K) ^and xH (4.2 K)

values for beryllides ^{with x} between 0.06 and 0.25, arise from our cluster superparamagnetism analysis (section 6). By raising ^{the Mn} content, ^{one observes a}

sharp ^non linear decrease of _as (4.2 K) ^{and correla-} tively ^a large increase of the _XH (4.2 K) susceptibility.

The maximum in the _XH (4.2 K) ^{versus x} graph, occuring ^{at the} concentration range 0.175 to 0.25, close to the concentration where ferromagnetism ^sets in, may be ascribed to exchange enhancements of the band polarization susceptibility, according ^{to Muell-}

ner and Kouvel [4]. ^{We have} performed magnetization

measurements over the field _{range 3} kOe to 150 kOe

Fig. ^8.

Results of the high ^field magnetization ^{data ;} analysis

on Be2Mn1-xFex compounds ^{at 4.2 K :}

-

left scale 106XH (emu. g-1. Oe-1) ^{versus Fe content x}

-

right ^scales

(a) ⁰ saturation magnetization 6S (emu . g-1) ^{versus x ;} (b) ^A normalized Fe moment (ulXuo ratio) ^{versus x.}

on the Be2Mno. 70Feo.30 ^and Be2Mno.6oFeo.4o samples

at 1.5 K in order to verify ^{that the} as (4.2 K) ^saturation magnetization represents ^the absolute as (0.0 K)

saturation magnetization ^{for all Fe rich} beryllides (0.30 x 1.00), within the experimental ^error.

The saturation magnetization as (1.5 K) ^of thèse samples ^{at 1.5 K was} determined by extrapolation ^of corresponding (a - ln H ) ^versus 1 /H plots. ^{It can}

be noted that (1s (1.5 K) ^{= 37.19} emu . g-1 against

as (4.2 K) ^{= 37.18} emu. g-1 ^for Be2Mno.70Feo.30,

while _QS (1.5 K)

^57.62 emu . g-1 against

for Be2Mno.6oFeo.40- ^We think that our saturation

magnetization 6S(t) ^{values are} given ^{with a relative} uncertainty ^{of 0.1} % ^{to 0.5} % (depending ^{on the} samples) ; ^the assumption 6S (4.2 K)

as

(0.0 K)

for all Fe rich beryllides (0.30 ^x 1.00) ^{is thus} justified. The QS (0.0 K) ^values yield the absolute

mean moment y ^{of each} beryllide (in y. per ^mean atomgram of transition metal) ^{and the} corresponding

Fe moment JlFe ⁼ MIX (in YB per Fe atomgram).

We call _po the Fe moment in the _pure Be2Fe ^com- pound ; ^{we found} po ⁼ 1.842 uB/Fe, ^{a value smaller}

than that of 1.87 uB/Fe extrapolated from u, (0.0 K)

data on BexFe1-x compounds ^near Be2Fe [28].

The observed difference in the _po value can be

explained by ^{small shifts} in the Be composition occuring ^{in the} preparation ^{of our} Be2 Mn 1 _ xFex samples.

We interpret ^{the obtained results on the Fe rich} beryllides ^{in a} local model of magnetism ^{and we} justify ^this interpretation ^{as follows. In our earlier}

work [13] ^we calculated a qC,qS, ^{ratio of} magnetic

carrier numbers _per mean atom of transition metal

(qC ^was deduced from paramagnetic ^{Curie constant}

measurements and qs from saturation magnetization values). This ratio was found to increase from 1.25 to 2.00 by decreasing x ^{from 1.00 to 0.40} and this led us to

interpret ^the magnetism ^{of these} beryllides ^as being

rather collective than localized. But Môssbauer _expe- riments performed ^{on the same} samples [29], [30]

showed that Mn and Fe do ^not form a common band in our beryllides, ^{but are} well localized : the isomer shift of 57Fe was found to be independent ^{of the Mn}

content over the whole investigated concentration range 0.06 x 1.00, ^{within the} experimental ^error.

If Fe is the sole transition element able to carry

a magnetic ^{moment in our} Be2Mn1 _xFex samples, ^the

ratio ,u/xuo called normalized Fe moment should remain less than unity ^{over the whole} composition

range 0 x 1. Figure 8 shows this ratio plotted against x ^{for 0.30 x 1.00. As can be seen on this} figure, ^the Jl/Xuo ratio becomes higher ^{than 1 for}

0.40 x 1, indicating that another element, ⁱⁿ

addition to Fe, ^{is able to} carry ^a magnetic ^moment

in these beryllides; ^{we assume} that it is Mn. This

explains why ^{an Fe atom with full Mn nearest} neigh-

bourhood (4 ^{Mn nearest} neighbours ^{in the} hexagonal

C14 structure) should still _carry a moment of 1 _uB,

according ^{to the Môssbauer} experiments ^{of Vincze}

et al. ( 1974).

The simple local environment model of magnetism

described by Jaccarino and Walker [1] ^and by ^Perrier

et al. [2] ^{or that} improved by Pataud et al. [7] ^{are not} applicable ^{in the} present ^{case. It} appears necessary ^to clear _up the role played by ^{the Mn atoms, in order to}

elaborate a local environment model of magnetism.

6. Analysis ^of the cluster superparamagnetism.

In this section, ^we _present ^{a detailed} analysis ^{of the}

cluster superparamagnetism ^{in the} Be2Mn1-xFex compounds around the critical composition range for

ferromagnetism (0.06 ^x 0.25). ^{It was not} pos- sible to use a simple model of local environment

magnetism, ^so allowing ^{us to} identify ^{the various}

cluster contributions to the magnetization by ^the

concentration dependence (simple ^cluster expansion

of the magnetization ⁱⁿ successive _powers of x) ^as

was done for Cu-Fe alloys [31] ^and Co,Ga compounds [9].

These beryllides ^are only superparamagnetic ^at sufficiently high temperatures (T > Tf, ^section 4).

Nevertheless, ^{we have} analysed ^the magnetization

data u(H, T ) ^{over the whole} investigated temperature and field _ranges with the general expression (3)

Although ^this analysis yields only qualitative ^features

of the cluster configuration ^for T T f (mictomagnetic state), ^this analysis ^{is worth} performing ^{over the}

whole investigated temperature and field _ranges

(sections ^{6 and} 7). ^In expression (3), ^L represents the Langevin ^{function, while} Mi and N; ^{are the indi-}

vidual cluster moments and concentrations. The values of xH(T) ^are given ^{in table II} (order ^of magni-

tude _{XH 1’-1} 25 ^x 10- 6 emu.g-1.0e-1 ^{and an} impor-

tant increase of _xH with T). ^No assumption ^{is made} concerning ^the parameters ⁱⁿ expression (3), except for the interaction field h between clusters, ^{taken as}

a molecular field h ⁼ W(a - XH H). ^{In low} fields, the magnetization ^is given by

with C(T) = E(i) ^N; pf/3 ^{k and} O(T) ⁼ W(T) C(T).

In the high ^field limit, ^the magnetization ^{reduces to}

From these two expansions ^{of the} magnetization,

we deduce, ^without any assumption ^on the cluster size distribution, ^{the three} quantities rx(T) = Ei N; ui2 ; us(T) = Xi Ni Mi ^and N(T) = Xi N;, ^which yield ^the

average cluster moment M(T) ^and total cluster concentration N(T).

The values of the W parameters ^{were estimated} from the T dependence of the inverse cluster _suscep-

tibility (Fig. 3) ^{written as}

A quantitative determination of W was not possible,

since the exact form of C(T) ^{is not} known ; ^we

simply ^assumed temperature independence ^{for the}

W parameters. ^We think that the interaction fields h between clusters are well represented by ^W para- meters of the order of + 1 kOe. g. emu -1 (Table II).

The determination of a(T) ⁼ Ei N; ,Mi2 ^{is achieved} by C(T) ⁼ T[W ⁺ (x; - XH)-1]-1. ^{For each} beryllide,

we have observed a maximum CM ⁱⁿ the variation of C(T ) ^{with T at a} temperature T1 higher ^{than the} spin freezing temperature Tf. The values of CM ^and Tl ^are listed in table II.

We have verified by ^means of a - XH H ^versus (H ⁺ h)-1 isotherms, ^{that the} magnetization ^{of the} beryllides ^{with 0.06 x} 0.25, ^at all the investi-

gated temperatures, follows the expression (4)

with an accuracy better than 1 % ^{in fields} H > 60 kOe.

Some (a - XH H) ^versus (H ⁺ h)-’ ^{isotherms are} displayed ^on figure ^{9 as} typical examples. ^The average cluster concentration N(T) ^{and moment} M(T) ^were

calculated by taking

and

in expression (4). The variations of M and N with temperature ^{T and} composition ^{x are shown on} figures 10a and b respectively. ^{The non-smooth}

variation of M(T, x) ^and N(T, x) ^{with x} may be

explained by ^{the onset of} partial ordering ^{in some}

of our samples (due ^{to the heat treatment} undergone by ^the samples, ^as mentioned in section 2). ^The

small values (M N ⁴ JJB) ^{of M} (4.2 K) correspond

rather to the paramagnetic ^{Fe moment} 1ÀF,, - 3.5 _YB

[ 11 ] ^{than to the} expected giant ^moment clusters. But

one notes an important increase of M(T) ^with T (M ~ ³⁰ UB ^or 40 _YB at 44 K) ^{and a} steady ^decrease

of N(T). ^{In order to} situate the magnitude ^of N(T),

we mention that the value N= 6.9 x 1019 cl . g-1 ^cal-

culated by Flotow et al. [ 15] ^from specific ^{heat data}

on Be2Mno.865Feo.135 corresponds ^{to its} N(15 K).

Table II.

Main results of the cluster magnetization ^data analysis ⁱⁿ high ^{and low} fields ^on Be2Mn1-xFex samples ^{with x around} XCr (0.06 x 0.25) ; susceptibilities xH ^{in emu.} g-1. Oe -1, interaction parameters ^W in k0e . g . emu-1, maximal Curie constants CM ⁱⁿ emu . K . g-1; saturation magnetization ^{at 15 K} (in emu . g-1) corresponding ^cluster concentration N (15 K) ^{in 1021 cl .} g-1.

LE JOURNAL DE PHYSIQUE.

T. 40, NO 1, JANVIER 1979

Fig. 9. - Cluster magnetization (1-XH H (emu.g-1) ^versus 1 OOO(H + h)-1 (in kOe-’) isotherms for Be2Mno.94Feo.o6 at

+ 4.2 K ; 0 8.0 K , ^x 15.0 K; O ^{22.0 K;} Y ^30.5 K; ^{V 41.3 K.}

Fig. ^10.

(a) Average ^{cluster moment M} (in IlB per cluster-gram)

and (b) total concentration N in Be2Mnl-xFex compounds ^with 0.06x0.25,atQ8.OK; x 15.0 K ; 0 33 K ; + 44 K.

The saturation magnetization 6S(T ) ⁼ N(T ) M(T)

of each beryllide decreases with T in spite ^{of the} increasing M(T) ; ^the as (15.0 K) ^{values are} reported

in table II. The ratio U = u2 >. u > - 2 gives ^an

indication of the cluster size distribution in our

Be2 Mn 1 _ xFe x compounds. This ratio was found to be temperature dependent ^{with a maximum} um ^{at a}

temperature ^{close to} Ti . The variation of _um with x

(Table II) is consistent with the concept ^{of a maximum}

giant ^moment increasing ^{with Fe content x. All these}

results concern only ^{the two} limiting parts ^{of the} magnetization ^{data on the} beryllides ^with 0.06 x 0.25 : low fields with _Mi H « kT and

high ^fields with Mi H » ^{kT. We have now to consider}

the whole set of data, ^{i.e. the field} dependence ^of

the magnetization a(H, T).

We separate the cluster magnetization u(H, T)- HxH(T) ^into its various components, according ^to expression (3) ^and using ^the quantities a(T), as(T)

and M(T). ^An attempt ^to fit the data with discrete bimodal distributions of moments M, ^and M2, ^was

unsuccessful. But all (6 - XH H ) ^versus (H ⁺ h). ^{T -1}

isotherms could be represented ^over the whole field range 1 kOe H 150 kOe with an accuracy better than 5 % by discrete distributions with three types of temperature dependent ^{moments :}

-

very high ^moments M3(T), ranging from 100 YB to 2 000 _y. or more, characterize large ^clusters

saturated in low fields (H - ^{2 to 3} kOe) ;

-

high ^moments M2(T), ranging ^from 15 uB ^to

500 _PB or more, characterize clusters of moderate

size, saturated in moderate fields (H - ^{30 to 70} kOe) ;

-

small moments M1(T), ranging ^{from 2} PB ^to 60 _IÀBI characterize small clusters saturated in high

fields (H > ⁹⁰ kOe).

Each isotherm was analysed ^{in the} following way.

The large ^{cluster moment} M3(T) and concentration

N3(T) ^were estimated from the low field (H ² kOe) dependence of the cluster magnetization (a - XH H ).

The cluster moments M2(T) ^and M1(T) ^{and their}

concentrations N2(T) ^and NI (T) ^were determined by

iteration on M2, according ^to the three quantities a(T), as(T) ^and N(T), until the best fit with the isotherm was reached over the whole field _{range 1} kOe to 150 k0e. The degree of fit varies with the field for each analysed ^{isotherm. At} high ^fields (H > ⁶⁰ kOe), the fit is excellent with all isothermal data (relative deviations less than 2 %). ^The poorest

degrees ^{of fit} (relative deviations - 5 % ^or more)

were found on isotherms corresponding ^{to small}

cluster magnetizations (Q - XH H HXH), ^{as on}

low field (H - ^{1 to 5} kOe) ^isotherm portions ^of samples ^{in the} mictomagnetic ^{state. An} example ^of

fit is given by figure 11 : the isotherms of

Be2Mn,.,4.Feo.16 ^are plotted ^as (a - XH H) ^versus (H ⁺ h) . T -1 and the solid curves represent ^{the cal-} culated values.

We summarize briefly the main results of our

three moment analysis. ^The very large ^clusters pro- vide a weak contribution to the magnetization ^and

a relatively important contribution to the Curie constant (N3 M3 ~ ^{0.001 to 0.3} emu . g- l, ^while N3 M 23 ~ ^{0.1 a to 0.4 a,} depending ^{on the} samples).

We have reported ⁱⁿ figure ¹² the variations with T of M(T), M,(T), M2(T) ^and M3(T) ^{for the} Be2Mno.86.5Feo.135 sample. M(T) ^and M1(T) ^were

found to steadily increase with T. But each large