Magnetic Properties and Giant Moment Clusters in Be2mn 1-Xfex Compounds R

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

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Classification Physics Abstracts 75 . 30C

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. 2014 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. 2014 The magnetic properties of Be2Mn1 _xFex compounds have been investigated over the whole concentration (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 concentrations. 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 magnetism, 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...).

1. Introduction. - There are several alloy or - the inhomogeneous nature of the transition from compound systems in which magnetic properties are paramagnetism to ferromagnetism observed in such presently understood in terms of magnetic polarization systems, has been related to the existence of magnetic clouds (magnetic clusters) : clusters ;

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197900400102300 24

- giant moment clusters persist as superparama- - samples in the paramagnetic region (x = 0.11 gnetic entities well into the paramagnetic composition to 0.175) seem to obey a simple model of cluster range, even in perfectly random solid solutions ; superparamagnetism [14]. - the cluster concentration and magnitude increase A more recent work [ 15] reports specific heat measu- when the magnetic carrier concentration is increased rements on Be2Mno.865Feo.135 at low temperatures up to the critical composition ; (0.1 K to 23 K). The temperature dependence of the - the onset of ferromagnetism can be considered as excess heat capacity (anomalous term), somewhat resulting from the ferromagnetic coupling of giant like a Schottky function, could be reasonably inter- moment clusters -; preted in a magnetic cluster model. - these giant moment clusters have to be related to The present work was undertaken in order to obtain local environment effects [ 1 ], [2]. more information on the magnetic behaviour of over the whole concen- Let us mention as a justification of the above Be2Mn1 _xFex compounds tration 0 x 1, with to the propositions, some typical investigations on such range special regards in the critical for ferro- alloys or compounds in the papers referred to below. compounds composition range we have In all these papers, the magnetization data on the magnetism (0.06 x 0.25). Therefore, carried out a on these investigated alloys or compounds, were analysed systematic magnetization study over the whole field 0.00 to 150 kOe with the concept of magnetic clusters and the results beryllides range at low 100 After a brief des- obtained were described or discussed using various temperatures (T K). local environment models of magnetism. cription of the experimental procedures (section 2), we report in section 3 the new series of magnetization The most extensively studied system is that of Ni measurements on our Be2Mn1 _xFex samples binary alloys, especially Ni-Cu [3] ; Ni-Rh [4] ; Ni-Cu, (0.06 x 1.00) in fields up to 150 kOe at low Ni-V and Ni-Mo [5] ; Ni-Pd [6]. Giant moment clusters temperatures (T 100 K). The high field magneti- are shown to exist in other such as binary alloys, zation measurements offer a more accurate deter- Fe-V [7] or Cu-Mn [8]. mination of the saturation magnetization by allowing It in several studies on interme- appears MCX a true evaluation of the superposed paramagnetic tallic c ~ 1, M = Fe, Co or Ni compounds (with xH(T ) susceptibility. As will be seen in section 3, and X a non that being magnetic element) giant we simplify our Q(H, T) data analysis by attributing moment clusters can arise from excess M atoms the main part y(H, T ) of the magnetization to clusters X sites. A detailed on com- occupying study Co,Ga assumed to exist in all the investigated beryllides pounds [9] shows the existence of non magnetic, (0.042 x 1.00) in different magnetic states (super- and atoms nearly magnetic magnetic impurities (Co paramagnetic, -mictomagnetic or ferromagnetic, Ga The occupying sites). superparamagnetism depending on T and x). The new measurements in low observed in and was Fe,Al, CoAl Nival compounds fields (0 H 1 kOe) enabled us to observe micto- also attributed to Fe, Co or Ni atoms Al occupying magnetic behaviour on Be2Mn1 _xFex samples with sites [10]. 0.11 x 0.30 at low temperatures (section 4). The The magnetism of other binary or ternary alloy occurrence of mictomagnetism was ignored in our systems, which present a transition concentration z earlier investigations [13] on these compounds. from paramagnetism to ferromagnetism, can be Section 5 deals with the magnetization data analysis characterized in terms of magnetic clusters. This is on Fe rich beryllides (0.30 x 1.00). A detailed the case of the Be2Mn1 _xFex pseudo-binary system. analysis of the cluster superparamagnetism in beryl- We summarize briefly some aspects of previous lides with x around xCr (0.06 x 0.25) is presented investigations on these compounds. The ferroma- in section 6. The unusual results of this analysis gnetic compound Be2Fe and the paramagnetic com- (clusters with average moments and concentrations pound Be2Mn form an uninterrupted series of hexa- depending on T) are discussed and tentatively inter- gonal C14 solid solutions Be2Mn1 _xFex (0 x 1) preted in section 7. Finally, a summary and a conclu- ferromagnetic for x > 0.30 [11]. The critical compo- sion are given in section 8. sition for ferromagnetism in this system has been located at 0.18 by means of heat xc, ~- specific [12] 2. Expérimental procedures. - The Be2Mn1 _xFex and magnetization [ 13] measurements. The properties samples were prepared by melting together appro- of Be2Mn1 _xFex compounds near the critical xCr priate amounts of the pure constituents [11]. All the (0.06 x have been attributed composition 0.25) beryllides have the expected hexagonal C14 structure to magnetic clusters : without any parasitic phase, as shown by X rays - an essentially temperature independent compo- analysis and Curie temperature measurements. All nent has been found in the specific heat ; . samples were slowly cooled (with a rate of about - the large deviations from linearity observed for 150 °C . h -1) after annealing in an argon atmosphere some magnetization 62 = f(Hla) isotherms showed at 1 100°C for 48 h. Such a heat treatment cannot that the ferromagnetism occurs in an inhomogeneous exclude any partial ordering in our samples, so we way; have to expect some deviation from complete random 25 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 measurements 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]. Fig. 1. - Magnetization isotherms a (emu. g- 1) versus H (kOe) of some at 4.2 K : v The two sets of apparatus were calibrated against Be2Mn1-xFex compounds + = 0.19 ; OX = 0.175; x x = 0.16 ;>x = 0.135; A x = 0.11; 6x = 0.082; and Ni standards. The relative uncer- Gd2o3 [19] [20] y --, 0. 06. tainty of our magnetization a(H, T) versus temperature and field measurements is estimated to be less than 2 %. field range. Figure 1 displays such isotherms at 4.2 K as examples. Our new magnetization measurements on Fe rich

3. Général features of the magnetization. - First, Be2Mn1 _xFex compounds (0.30 x 1.00) at 4.2 in fields from 4 kOe to 150 are we summarize briefly some results on dilute K, ranging kOe, Be2Mn1 _xFex compounds (x 0.042) in order to presented as a (emu. g-1) versus H isotherms (Fig. 2), the field H obtain the concentration where giant moment clusters being corrected for demagnetization. These show saturation in appear. Paramagnetic behaviour was observed over the compounds ferromagnetic moderate and in with our entire temperature range 4.2 K to 1 100 K on the high fields, agreement Be2Mn and Be2Mno.988Feo.012 compounds. At 4.2 K earlier investigations [13]. But the higher fields available here enable us to determine the these compounds have a magnetization linear with field superposed from 0 to 20 kOe, with respective susceptibilities of paramagnetic susceptibility XH and the saturation with a 12 x 10- 6 and 15 x 10- 6 emu . g-1. Oe-1. The magne- magnetization as higher accuracy (section 5). 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 1 itiitial susceptibility (x = 55 x 10 - 6 emu. g - 1 . Oe - between 0 and 2 kOe) allow us to locate the appearance of giant moment clusters in the Be2Mn 1 _ xFex compounds 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 measurements we concern the in the. have, only samples - 2. isotherms 6 versus ’ Fig. Magnetization (emu. g-1) H (kOe) concentration range 0.06 to 0.25. of Fe rich Be2Mn1 _xFex compounds at 4.2 K : + x = 0.88 ; we the Then, report magnetization, (in emu . g -’ ) Ox=0.76;x x = 0.62; 0 x = 0.50; Yx=0.40; V x = 0.30. of each Be2Mn1 _xFex sample in the critical concentration range 0.06 x 0.25, at different temperatures between 4.2 K and 44 K (or more for three samples) as We have now to choose a suitable model for ana- a function of field H (corrected for demagnetization) lysing the a(H, T) data on all the investigated beryl- from 1 kOe to 150 kOe. A a2 versus Hlu representation lides (0.06 x 1.00). The most general view point of the data up to 150 kOe confirms the inhomogeneous consists in attributing the main part of the magneti- nature of the magnetic transition previously observed zation to the non localized and localized 3d states [13] in the Be2Mn1-xFex system. All Q versus H (Fe and Mn) responsible for the magnetism in these isotherms show continuous curvatures over the whole beryllides. Such a procedure was successfully applied 26

by Acker and Huguenin [21]] to their magnetization we have verified that the simplified form (2) of expres- data analysis on weakly magnetic Ni-V alloys. But sion ( 1 ) 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 represents fairly well the magnetization of these (clusters) assumed to exist in all the beryllides with beryllides in the high field limit Ha 60 kOe at all 0.042 x 1.00. As will be shown in section 4, investigated températures, the relative deviations did these clusters are mictomagnetic or superparamagnetic not exceed 1 %. With the assumption of a cluster on T ) in with 0.042 x 0.25, (depending beryllides superparamagnetism ruled and ferromagnetically coupled, forming ferromagnetic by Langevin functions, the as(T) and A(T) parameters in (2) yield the average domains in the Fe rich beryllides (0.30 x 1.00) cluster moment M and concentration N independent at sufficiently low temperatures. Therefore, we analyse of the cluster size distribution. The quantities M and N the Q(H, T ) data on all investigated beryllides are found to be temperature dependent, their values (0.06 x 1.00) by means of the simplified expres- are not shown here ; we report in section 6 an sion + improved (1) : a(H, T) = y(H, T) HxH(T). analysis of the magnetization data by taking into The considered as y(H, T) magnetization, arising account a small interaction between clusters, which from moment clusters in different giant magnetic was neglected in (2). states (superparamagnetic, mictomagnetic or ferroma- We also report in this section our initial Xi suscep- gnetic, depending on T and x), may thus be described tibility data on all Be2Mn1 _xFex samples with in a local environment model of magnetism. All other 0.06 x 0.25, as (Xi - xH)-1 versus T plots (Fig. 3). 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 expression (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 experimental data. The main results on the xH(T) susceptibility are summarized in sections 5 (Fig. 8) and 6 (Table II). Fig. 3. - Inverse cluster susceptibility (x 1-xH) -1 in emu -1. g . Oe We treat the cluster magnetism of all investigated 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 ; in the classical we take beryllides following way : Aj-=0.19;Vjc=0.2î. 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 initial susceptibility xi of each beryllide is defined the asymptotical form of the cluster magnetization as the slope a / H of reversible magnetization 6 versus H 1 y(H, T) in high fields, is given by the assumed 1 /H isotherms in low fields (0 H 1 kOe). A x; or 1 /H 2 behaviour. versus T representation of the data showed that no In a first step of our cluster superparamagnetism classical Curie Weiss behaviour could be found on analysis on Be2Mnl _xFex samples with any beryllide in the temperature range 4.2 K to 100 K : the inverse cluster susceptibility (x; - xH) -11 shows 1 continuous curvatures in its (x; - xH) -1 versus T 27 graphs. This fact too, supports the concept of superparamagnetic 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 compounds 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 measurements 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 determined the temperature T. of the reversible susceptibility maximum ; measurements done on Be2Mno.94Feo.o6 and Be2Mno.918Feo.082 indicated that the characteristic T. and Tf temperatures 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 at temperatures below the magnetization - 4. behaviour of (a) characteristic than The Fig. Mictomagnetic Be2Mno.S65Feo.135 Tf temperature higher Tm. and Be2Mno.,,Fe..,, (b); a (emu . g-1) versus T (K) isotherms cases of Be2Mno.865Feo.135 and Be2Mno.81 Feo.19 are + after zero field cooling and 0 after cooling in a field H= 0.3 kOe (a) given as examples in figure 4. The values of the cha- or H = 0.2 kOe (b). 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 (HC~ 0.1 kOe), but the reverse sections of the loop temperature Tf where irreversible magnetization sets are time dependent and the magnetization curve in. No scaling law [23] is applicable here, allowing starting from the zero field cooling state lies nearly us to consider these beryllides as mictomagnets. outside of the hysteresis loop. Such magnetization However, the difference between Tf and T. seems isotherms were reported for Au4Mn compounds and somewhat too high and we have no explanation for were attributed to mictomagnetism [26]. From all this fact. The reversible magnetization showed a time the above mentioned properties, we can deduce that dependence at temperatures below T., which is also the Be2Mn1 _xFex compounds with 0.11 x 0.25 typical for mictomagnetic alloys [24, 25]. In order to behave as mictomagnets at low temperatures and are obtain more informations on the mictomagnetic superparamagnetic at temperatures above their spin behaviour of these Be2Mn1-xFex compounds, we freezing temperature Tf. performed isothermal magnetization measurements at In order to examine the evolution of the magnetism 4.2 K on some samples (x = 0.16 to 0.25) in both through the Be2Mn, -xfex system, we have extended states obtained after zero field cooling and after field our low field investigations to more Fe rich beryllides cooling (H = 3 or 5 kOe). Figure 5 represents the (0.30 x 1.00). It is not yet clear whether these case ofBe2Mno.81 FeO.19 as an example. The hysteresis beryllides can be described as ferromagnets or micto- loop of each sample at 4.2 K (taken after field magnets with high T. and Tf temperatures. These cooling) is symmetrical, the coercive fields are low 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. 28

slightly increase with T over a wide range of temperature (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 magnetization 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 temperature mictomagnetism. However, isothermal magnetization 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. 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 mictomagnets with high T. and Tf temperatures. The Be2 Mno .7 oFeo.30 sample shows all characteristic properties 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 In 32 K and 60 K. view of their - T. - Tf - magnetic Fig. 6. Hysteresis loop of Be2Fe at 300 K : magnetization behaviour in low fields, Be2Mno.60Feo.40 and 6 (emu . g-1) versus H (kOe), corrected for demagnetization 0 Be2Mno,soFeo.so may be considered rather as micto- by decreasing H from + 14.7 kOe to - 14.7 kOe and + by increasing magnets than ferromagnets at low temperatures : H from - 14.7 kOe to + 14.7 kOe. the broad maxima observed on their reversible magnetization (in fields H N 25 Oe) versus T graphs, provided only an estimation to be made for the characteristic coercive fields HC ~ 5 Oe, while the magnetization at T. (or Tc ?) temperature, but irreversible magneti- 16 kOe ranges from 74.7 emu. g-1 for x = 0.62 to was on = zation observed each sample, after field cooling 136.4 emu . g -1 for x 1.00). , below a Tf temperature higher than T. (Table I). If, we interpret all the above mentioned pro- The reversible magnetization of the Fe rich beryllides perties on the Fe rich Be2Mn1 _xFex compounds (0.62 x 1.00) was only obtained after cooling (0.30 x 1.00) by the onset of ferromagnetism, each sample in a zero field from 800 K (or more) to this implies something unusual about this ferroma- 300 K, then to 4.2 K. As will be seen below, the gnetic order : existence of a network of small domains, question whether these beryllides can be considered as high anisotropy effects, ..., points which remain to be ferromagnets or mictomagnets with high Tm and Tf cleared up by further investigations. temperatures, remains open. The reversible magne- In an attempt to clarify the exact nature of the tization of each beryllide (x = 0.62 to 1.00), taken in a magnetism in our Fe rich beryllides (0.3 x 1.00) field H ~ 80 Oe, was found to be nearly constant or to we used Môssbauer spectroscopy (14.4 keV resonance 29 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 compounds were chosen, because they cover the concentration 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 ferromagnetic coupling of giant moment clusters. This interpretation has to be justified by further investigations. We tentatively assume here that the magnetic transition in the Be2Mn1 _xFex system occurs gradually from paramagnetism (x 0.06) to mictomagnetism (0.11 x 0.30) then to ferromagnetism (0.30 x 1.00). This assumption may be reasonable, 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). Fig. 7. - Behaviour of Fe rich beryllides in high fields : (a) linear We the data on these analyse magnetization beryllides part of the a-m H(emu.g-1) versus H-2 (in Moe-2) isotherm at 4.2 K by means of the simplified expression (1) of ]Be2Mno.38Feo.62 at 4.2 K, corresponding to fields between mentioned in section 3 : 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, 4.2 = 4.2 + a(H, K) y(H, K) HXH (4.2 K) . corresponding to fields between 151.36 kOe and 49.58 kOe. The high field slope of a versus H isotherms (Fig. 2) yields the XH (4.2 K) susceptibility. As shown by versus H - 1 or H - 2 7), the (Q - XH H) graphs (Fig. The as (4.2 K) values agree qualitatively for all Fe of all Fe rich at 4.2 K y(H) magnetization beryllides rich beryllides (0.30 x 1.00) with that reported could be the classical represented by expression in our earlier work [13], but no linear relationship = H -M with an accuracy better than y(H) Qs - Am could be found between us (4.2 K) and x for high Fe 0.2 over a wide range of moderate and fields % high contents (0.76 x 1.00). The XH (4.2 K) suscep- 20 k0e to H >, 60 on the (H > k0e, depending tibility is weak for beryllides with high Fe content The has the value + 1 for x 0.50 samples). integer m (10’XH-5 to 2 emu . g-1 for x = 0.76 to 1.00); and + 2 for 0.62 x 1.00. This classical expres- its order of magnitude is consistent with classical sion represents the rotation of the magnetization and band polarization susceptibilities of transition metals. the saturation magnetization u. at 4.2 K by yields The variations of as (4.2 K) and xH (4.2 K) with x over linear extrapolation to infinite fields of (a - XH H) the whole composition range 0.06 x 1.00, are versus 1 /H or 1 /H 2. Moreover, the saturation magne- illustrated by figure 8. The as (4.2 K) and xH (4.2 K) tization u. could be obtained directly for sufficiently values for beryllides with x between 0.06 and 0.25, Fe rich beryllides (0.62 x 1.00) by full saturation arise from our cluster superparamagnetism analysis of their magnetization in the high fields available here (section 6). By raising the Mn content, one observes a (H > 120 kOe to H >, 70 k0e, depending on the sharp non linear decrease of as (4.2 K) and correla- samples). The relative difference between the two types tively a large increase of the XH (4.2 K) susceptibility. of 65 (4.2 K) values observed on all these samples, is The maximum in the XH (4.2 K) versus x graph, less than 0.1 % : the sample has a Be2Mno,12Feo.ss occuring at the concentration range 0.175 to 0.25, value of 135.61 ± 0.01 obtained as(4.2K) emu . g -1 close to the concentration where ferromagnetism sets by full saturation of its magnetization in fields in, may be ascribed to exchange enhancements of the H > 70 k0e, while the to = 0 of extrapolation 1 /H 2 band polarization susceptibility, according to Muell- its (a - XH H) versus I/H2 graph, yields ner and Kouvel [4]. We have performed magnetization as (4.2 K) = 135.70 ± 0.05 emu . g-1. measurements over the field range 3 kOe to 150 kOe 30

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 experiments 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

Fig. 8. - Results of the high field magnetization data ; analysis remain less than unity over the whole composition on Be2Mn1-xFex compounds at 4.2 K : range 0 x 1. Figure 8 shows this ratio plotted - left scale 106XH (emu. g-1. Oe-1) versus Fe content x against x for 0.30 x 1.00. As can be seen on this - right scales figure, the Jl/Xuo ratio becomes higher than 1 for (a) 0 saturation magnetization 6S (emu . g-1) versus x ; 0.40 x that another in (b) A normalized Fe moment (ulXuo ratio) versus x. 1, indicating element, 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- on the Be2Mno. 70Feo.30 and Be2Mno.6oFeo.4o samples bourhood (4 Mn nearest neighbours in the hexagonal at 1.5 K in order to verify that the as (4.2 K) saturation C14 structure) should still carry a moment of 1 uB, magnetization represents the absolute as (0.0 K) according to the Môssbauer experiments of Vincze saturation magnetization for all Fe rich beryllides et al. ( 1974). (0.30 x 1.00), within the experimental error. The simple local environment model of magnetism The saturation magnetization as (1.5 K) of thèse described by Jaccarino and Walker [1] and by Perrier at 1.5 K was determined of samples by extrapolation et al. [2] or that improved by Pataud et al. [7] are not versus It can corresponding (a - ln H ) 1 /H plots. applicable in the present case. It appears necessary to be noted = 37.19 that (1s (1.5 K) emu . g-1 against clear up the role played by the Mn atoms, in order to = 37.18 for as (4.2 K) emu. g-1 Be2Mno.70Feo.30, elaborate a local environment model of magnetism. while QS (1.5 K) = 57.62 emu . g-1 against 6. Analysis of the cluster superparamagnetism. - In this section, we present a detailed analysis of the cluster superparamagnetism in the Be2Mn1-xFex for Be2Mno.6oFeo.40- We think that our saturation compounds around the critical composition range for magnetization 6S(t) values are given with a relative ferromagnetism (0.06 x 0.25). It was not pos- uncertainty of 0.1 % to 0.5 % (depending on the sible to use a model of local environment the = simple samples) ; assumption 6S (4.2 K) ass (0.0 K) so us to the various for all Fe rich beryllides (0.30 x 1.00) is thus magnetism, allowing identify contributions to the the justified. The QS (0.0 K) values yield the absolute cluster magnetization by concentration dependence (simple cluster expansion mean moment y of each beryllide (in y. per mean of the in successive of as atomgram of transition metal) and the corresponding magnetization powers x) was done for Cu-Fe and = alloys [31] Co,Ga compounds Fe moment JlFe MIX (in YB per Fe atomgram). [9]. We call po the Fe moment in the pure Be2Fe compound ; we found po = 1.842 uB/Fe, a value smaller These beryllides are only superparamagnetic at than that of 1.87 uB/Fe extrapolated from u, (0.0 K) sufficiently high temperatures (T > Tf, section 4). data on BexFe1-x compounds near Be2Fe [28]. Nevertheless, we have analysed the magnetization 31 data u(H, T ) over the whole investigated temperature simply assumed temperature independence for the and field ranges with the general expression (3) W parameters. We think that the interaction fields h between clusters are well represented by W parameters 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, this features Although analysis yields only qualitative we have observed a maximum CM in the variation cluster for of the configuration T T f (mictomagnetic of C(T ) with T at a temperature T1 higher than the state), this analysis is worth performing over the spin freezing temperature Tf. The values of CM and and field whole investigated temperature ranges Tl are listed in table II. (sections 6 and 7). In expression (3), L represents We have verified by means versus the function, while Mi are the indi- of a - XH H Langevin and N; that the of the vidual cluster moments and concentrations. The (H + h)-1 isotherms, magnetization with 0.06 x 0.25, at all the investi- values of xH(T) are given in table II (order of magni- beryllides gated temperatures, follows the expression (4) tude XH 1’-1 25 x 10- 6 emu.g-1.0e-1 and an important increase of xH with T). No assumption is made concerning the parameters in expression (3), except for the interaction field h between taken as clusters, with an accuracy better than 1 % in fields H > 60 kOe. a molecular field h = In low W(a - XH H). fields, Some (a - XH H) versus (H + h)-’ isotherms are the is magnetization given by displayed on figure 9 as typical examples. The average cluster concentration N(T) and moment M(T) were calculated by taking

k and = with C(T) = E(i) N; pf/3 O(T) W(T) C(T). and In the high field limit, the magnetization reduces to in expression (4). The variations of M and N with temperature T and composition x are shown on 10a and b The non-smooth From these two expansions of the magnetization, figures respectively. variation of M(T, x) and N(T, x) with x may be we deduce, without any assumption on the cluster the onset of in some size distribution, the three quantities rx(T) = Ei N; ui2 ; explained by partial ordering of our to the heat treatment us(T) = Xi Ni Mi and N(T) = Xi N;, which yield the samples (due undergone the as mentioned in section 2). The average cluster moment M(T) and total cluster by samples, concentration N(T). small values (M N 4 JJB) of M (4.2 K) correspond rather to the paramagnetic Fe moment 1ÀF,, - 3.5 YB The values of the W parameters were estimated than to the moment clusters. But from the T dependence of the inverse cluster suscep- [ 11 ] expected giant one notes an increase of M(T) with tibility (Fig. 3) written as important 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- A quantitative determination of W was not possible, culated by Flotow et al. [ 15] from specific heat data since the exact form of C(T) is not known ; we 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 32

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 Fig. 9. - Cluster magnetization (1-XH H (emu.g-1) versus fields (H > 90 kOe). 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. 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 11 : the isotherms of Fig. 10. - (a) Average cluster moment M (in IlB per cluster-gram) given by figure and (b) total concentration N in Be2Mnl-xFex compounds with Be2Mn,.,4.Feo.16 are plotted as (a - XH H) versus 0.06x0.25,atQ8.OK; x 15.0 K ; 0 33 K ; + 44 K. (H + h) . T -1 and the solid curves represent the calculated values. We summarize briefly the main results of our The saturation magnetization 6S(T ) = N(T ) M(T) three moment analysis. The very large clusters pro- of each beryllide decreases with T in spite of the vide a weak contribution to the magnetization and increasing M(T) ; the as (15.0 K) values are reported a relatively important contribution to the Curie in table II. The ratio U = u2 >. u > - 2 gives an constant (N3 M3 ~ 0.001 to 0.3 emu . g- l, while indication of the cluster size distribution in our N3 M 23 ~ 0.1 a to 0.4 a, depending on the samples). Be2 Mn 1 _ xFe x compounds. This ratio was found to We have reported in figure 12 the variations with T be temperature dependent with a maximum um at a of M(T), M,(T), M2(T) and M3(T) for the temperature close to Ti . The variation of um with x Be2Mno.86.5Feo.135 sample. M(T) and M1(T) were (Table II) is consistent with the concept of a maximum found to steadily increase with T. But each large 33

Fig. 11. - Cluster magnetization y = a-XH H (emu . g-1) of Be2Mno.84Feo.16 against x = (H + h).T-11 (in kOe.K-1) isotherms : experimental values at + 4.2 K ; 0 8.0 K ; x 15.0 K ; 0 33.2 K ; V 43.9 K and calculated values represented by the solid curves (-). cluster moment M2(T) and M3(T), presents a temperature range of irregular decrease, yielding nearly constant in these values M2 and M3 temperature Fig. 12. - Different cluster moments M, Ml, M2 and M3 (in J.lB ranges, close to T 1. For Ml ( T ), only a temperature per cluster-gram) for Be2 Mn 0. 8 6.5 Fe 0. 13 . at different temperatures : range of minimal increasing rate (inflection point in left scale 0 M and 0 M1; right scale + M2 and x M3/10. The values of the cluster moment Mare included for the versus T graph) could be defined, yielding a average comparison Ml with characteristic Mi value for this type of cluster moment. M1. We have verified that the cluster moments M(T), M1(T), M2(T) and M3(T) of the other beryllides ture is slightly higher than T1. All cluster concentra- showed approximatively the same properties and we tion and moment values listed in table IV are taken have listed in table III the characteristic Ml, M2 as values characterizing the cluster and M3 cluster moment values of all these beryllides, superparamagnetism in the beryllides with 0.06 x , 0.25, for a with the temperature ranges. The corresponding reason in section 7. cluster concentrations and found to given Nl, N2 N3 were We have also analysed the steadily decrease with T. In order to specify their XH(T) susceptibility through the small cluster concentration Nl. The magnitude, we have listed in table IV a whole set separation of into two components was of cluster moments and concentration values at a XH (T) possible only for the samples with characteristic temperature T* included in each tem- Be2Mn1 _xFex perature range given in table III. This T* tempera- 0.06x0.175,

Table III. - Three moment analysis of the cluster superparamagnetism in Be2Mn1 _xFex compounds around XCr : characteristic values of the Ml, M2 and M3 moments, the moment values (in JlB per cluster-gram) given in this table correspond respectively to the following temperature ranges : - minimal increasing rate of Ml with T - nearly constant M2 values - nearly constant M3 values. 34

Table IV. - Three moment analysis of the cluster superparamagnetism in Be2Mn1-xFex compounds with x around XCr : a complete set of cluster moment and concentration values at a characteristic temperature T* included 1iii each temperature range given in table III. The moments are expressed in JlB per cluster-gram and the concen- 1tration N* in 1021 ci. g-1. The relative concentration values provide a simple comparison of Nl, N2 and N3 with the total cluster concentration N*.

(*) We estimate T* N 57 K for the Be2Mno.84Feo.16 sample, in view of its Ml, M2 and M3 versus T graphs ; but we have no available high field magnetization data on this sample at T > 43.9 K.

owing to sufficiently weak contributions from the 17.8 x 10 - 6 emu . g -1. Oe -1 at 44 K for other moments. The separation procedure is illus- Be2Mno.82_5Feo.17_5) and the x’ susceptibility has an trated by figure 13 (XH versus n11 plots, with important value n, = Ni m/A, m = molar mass of each beryllide, A = Avogadro number). The component roughly proportional to N, is identified as the nearly magnetic in total disagreement with earlier paramagnetic sus- contribution x", according to Amamou et al. [5], while ceptibility measurements at high temperatures the extrapolated component x’, shown tempera- (T,> IOOK)yieldingX’-- 6x 10-’emu.g-’.Oe-’[11]. ture and composition independent, represents the We have no explanation for this discrepancy (if one non magnetic contribution (due to the non magnetic excludes a possible exchange enhancement effect), but the behaviour of the nearly magnetic contribution x" will be explained in section 7. The magnetization data analysis exposed in this section, has related the superparamagnetism in the Be2Mn1 _xFex compounds (0.06 x 0.25) to clusters with temperature dependent moments. All the obtained results, described in this section, appear to be unusual, according to the widespread view, that in superparamagnets, the cluster moments are essentially temperature independent. Therefore, our results call for an explanation, this point forms the subject of section 7.

7. Discussion and interprétation of the results on the cluster superparamagnetism. - The magnetization data analysis on the Be2Mn 1 _ xFex compounds Fig. 13. - Separation of xH into its two components x’ and x" : with x between 0.06 and 0.25, described in sections 3 106XH (emu.g-I.0e-1) versus 103 nI’ with n1= N1m/A where and 6, is based on the of our m is the molar mass of each beryllide and A the Avogadro number, essentially validity for all Be2Mn1 _xFex samples with 0.06 x 0.175 at + 4.2 K ; representation of the high field magnetization (expres- 08.OK; x 1 5.0 K ; O 33 K and V 44 K. sions (1), (3) and (4)). The main part y(H, T ) of the magnetization represents the cluster magnetism, while the superimposed HxH(T) term, assumed linear with impurities, to the non localized 3d states and field up to 150 k0e, includes all other magnetic to the host). The nearly magnetic suscepti- contributions (nearly magnetic and non magnetic bility x" increases strongly with temperature impurities, non localized 3d states, host magnetism). ( x" = 10.3 x 10-6 emu.9-l.Oe-1 at 4.2 K to This procedure was implicitly justified by the excel- 35 lent representation of the high field magnetization the validity of expressions (1), (3) and (4) for our data by (u - XH H) versus (H + h)-1 straight lines cluster magnetization data analysis (sections 3 and 6). (Fig. 9). But it is not evident that the non-localized (ii) The cluster magnetization 3d state magnetization remains linear with field up to 150 k0e, because these 3d states (Fe and Mn) can induce in these beryllides a paramagnetic suscepti- in the with 0.06 x 0.25 arises from a bility sufficiently enhanced to become field dependent beryllides continuous cluster distribution of individual mo- at low temperatures in the high fields considered ments ui, the average value of which is determined here (strong paramagnetism). This should imply an overestimation of the cluster magnetization in these by M(T) = Xi Ni Mi/Xi Ni us ,(T)IN(T), average cluster moment (sections 3 and 6). From this beryllides and an underestimation of the X. suscep- repre- tibility, which becomes field dependent. The impor- sentation of the cluster magnetization by a discrete trimodal cluster distribution of moments tance of such strong paramagnetism appears fairly Ml, M2 and these moments also as well in a recent study [6] on dilute PdNi alloys (Ni M3 (section 6), appear cluster moments of different sizes : content less than 2 at. %), where the author attributed average Mi, and which are the the main part of the high field magnetization to the M2 M3 respectively average moments of moderate and clusters in strong paramagnetism of the P_dNi matrix and he small, large the with 0.06 x 0.25. found only a small contribution of the clusters to beryllides the magnetization which saturated in low fields. The As mentioned at the beginning of section 6 and confirmed the existence of a maximal Curie cluster magnetization was shown to arise from a by constant at T = the of single type of magnetic impurity (groups of three CM Ti (Table II), analysis the cluster in our Ni atoms which polarize the host around them), superparamagnetism beryllides by while the high field variation of the magnetization, means of Langevin functions (expression (3)) is only valid in the limited T > the due to the strong paramagnetism of the PdNi matrix, temperature range T i : cluster moments M, and then was mainly related to non-localized 3d states (Pd average Ml, M2 M3 a true of the cluster in the and Ni atoms not involved in clusters). give picture configuration in this The fact On the other hand, we think that in the beryllides only temperature range. that and were found constant at Be2Mnl-xFex compounds there is a continuous M2 M3 nearly distribution in the cluster size, ranging from large temperatures T close to T * (Tables III and IV), sup- clusters saturated in low fields to small clusters ports the above proposition. Although the micto- state is attained at saturated in high fields. The large clusters are mainly magnetic only temperatures lower than we think that deviations from the contributing to the low field magnetization (initial Tf, susceptibility), while the small clusters contribute classical superparamagnetic behaviour of the clusters in the occur at T It is essentially to the high field variation of the magne- beryllides, already Tl. clear that the behaviour of the clusters tization. This point of view, which we intend to magnetic in the at T is to be diffe- justify by further investigations, enables us to draw beryllides Tl likely quite rent from the classical thermal which would the two following propositions. flipping lead to a cluster magnetization ruled by Langevin (i) By assuming that the high field variation of functions. Nevertheless, our analysis of the cluster the is due to small clusters, magnetization partly magnetism in terms of Langevin functions provides we reduce the importance of the role played by the a rough estimate of the effective cluster moments non-localized 3d states in the beryllides. This fact and concentrations for T Tl, from which two is by the rather small susceptibility increase supported interesting considerations can be drawn (considera- observed on dilute Be2Mn1 _xFex compounds, com- tions in steps (ii) and (iii) of our tentative interpreta- to that observed on dilute PdNi pared alloys, sug- tion reported below). the matrix much less easily gesting Be2Mnl-xFex Then, we try to interpret the results of section 6, the matrix. At 4.2 K and magnetized _PdNi Be2Mn especially the temperature dependence of the M, Ml, have susceptibilities of Be2Mno.988FeO.012 respective M2 and M3 the average cluster moments and N, Ni, N2 and N3 the corresponding concentrations. This will be done in three steps. and x = 15 x 10- 6 emu.g-1’Oe-’1 (section 3) (i) The temperature dependence of the different while at 1.4 K, according to Chouteau [6] cluster moments and concentrations for T > T*, x = 7 x 10- 6 emu. g-1. Oe-1 for pure Pd and can be interpreted by means of the following consi- x = 30 x 10-6 emu.g-1.0e-1 for PdO.987Nio.013 at deration. A giant moment cluster (p > 10 JlB) can 20 kOe. These arguments led us to think that results be considered as a magnetic entity with its own obtained in section 6 by choosing a non localized Curie temperature 0c, the larger the cluster the 3d state magnetization linear with field up to 150 k0e, higher its Oc. As a matter of fact, it has been formerly give a sufficiently true picture of the cluster magnetism shown [32] that small magnetic particles (Fe, Co in these beryllides. We justify in this tentative way or Ni based alloys) dissolved in non magnetic alloys 36 or amalgams, behave as superparamagnetic clusters a magnetic cluster. This suggests that in these beryl- with their own Curie temperatures 0,,, much lower lides more and more numerous nearly magnetic impu- than the ferromagnetic Curie point Tc, of the corres- rities become magnetic when the temperature is lower- ponding bulk alloy. The 0c of each particle was ed from the characteristic T* temperature to 4.2 K. The found to increase with its size (the diameter d for strong increase of the cluster concentration N and spherical particles). The 0c/Tc ratio, much less than 1 the corresponding decrease of the average cluster (Oc/Tc "-1 0.5 for d - 30 A), increases strongly with d moments M and Mi observed by decreasing T when d is less than 100 Â and approaches 1 for from T* to 4.2 K, result mainly from the count particles with diameter d of about 100 Â to 200 Â. of such impurities as magnetic clusters. For instance, One notes that an iron particle of diameter 20 Â has Be2Mno.86_5Feo., 3. shows a cluster concentration N a moment of about 800 PB. Following these results, increasing from 0.25 x 102° cl . g-l at 44 K (T*) to we consider the giant moment clusters (,u > 10 JlB) 1.97 x 102° cl. g-1 at 4.2 K and an average cluster in the beryllides with 0.06 x 0.25 as magnetic moment M decreasing from 25.4 PB at 44 K to 4.9 PB entities with their own Curie temperatures 0c increasing at 4.2 K. The non linear variation of the magnetiza- with the cluster size and ranging from T* to 100 K tion of dilute Be2Mn1 _xFex compounds (x 0.022, or more. Then, the observed increase in the average section 3) with fields higher than 30 kOe, may also cluster moments M, Ml, M2 and M3 with T increasing be ascribed to such impurities, if one excludes the above T* (Fig. 12), may be understood in the following possibility of strong paramagnetism (due to non way. When the temperature is raised above T*, the localized 3d states) non linear with field. The existence clusters disappear progressively, the relatively small of nearly magnetic impurities which become magnetic clusters (,u ~ 10 ,MB) are the first to disappear, while at lower temperatures, is reflected in the important the largest clusters (y > 1 000 JlB) disappear only at decrease of the nearly magnetic susceptibility x" higher temperatures (T > 100 K). Each cluster dis- (Fig. 13) when the temperature is lowered from 44 K appears by dissociating into smaller clusters and to 4.2 K. This explains the corresponding decrease individual paramagnetic moments, the latter contri- of the xH susceptibility observed (Table II). The bute to the XH susceptibility through the nearly important magnetic susceptibility magnetic contribution x". This enables us to explain the increase of the average cluster moments M, M, and observed on all when T increases M2 beryllides may be attributed to the host and to the non localized above T* (section 6) - the existence of relatively 3d states in the Be2Mn1-xFex compounds with small clusters at high temperatures (T - 100 K), 0.06 x 0.175, but the difference with the value to the values at corresponding M, (M1 ~ 25 MB x ’ = 6 x 10 - 6 emu . g -1. Oe -1 resulting from the 44 K to ~ 40 at 85 the decrease Ml1 JlB K) - steady paramagnetic behaviour at higher temperatures observed for the different cluster concentrations N, (T > 100 K), remains unexplained, if one excludes Nl, N2 and N3 for T > T* - the increase of the XH possible exchange enhancement effects. to 100 K of susceptibility up (increase XH effectively (iii) The decrease in the average moments M2 observed on the with x = 0.135 ; 0.19 and samples and M3 of moderate and large clusters and the cor- 0.25 up to 85 K or more) - according to its high responding increase of their concentrations N2 and N3, the cluster moment should remain values, large M3 seem to support the unusual view of moderate and nearly constant over a much larger temperature large clusters decoupling into smaller clusters by than that observed range experimentally (Table III), decreasing T from T * to 4.2 K. At first sight, this but this is not so if one considers the important, fact has no evident physical meaning and emphasizes used for the determination very qualitative procedure the inadequacy of our cluster magnetization ana- of this of cluster moment type (section 6). lysis for T T*. In fact, we think that all experimental (ii) The strong increase of the cluster concentra- results concerning the moderate and large clusters tion N and the corresponding decrease of the average for T T*, are related to mictomagnetism and moments M and Mi observed on all beryllides could be explained in a model which assumes that (0.06 x 0.25) by decreasing T from T * to 4.2 K short range antiferromagnetic interactions appear at (Figs. 10 and 12), may be related to impurities which temperatures below T*, in addition to the ferro- are nearly magnetic at moderate temperatures and magnetic interactions responsible for the cluster become magnetic at lower temperatures in the high formation. Several authors have invoked such anti- fields considered here (H > 80 kae). To specify this ferromagnetic interactions in order to interpret the idea, let us consider an impurity in the Be2Mn 1 -,,Fex magnetic properties of some Fe or Mn based alloys host, which has a moment of Y 1 PB and bears at low temperatures. The magnetic properties of only the interaction h = W(U - XH H ) defined in Fe-Al ordered and disordered alloys have been section 6 : for (H + h) ~ 160 kOe and T ~ 40 K, interpreted in a model which includes antiferro- p(H + h)IkT - 0.3, the impurity is nearly magnetic magnetic indirect Fe-Al-Fe interactions in addition at 40 K ; but for (H + h) - 160 k0e and T - 4 K, to direct Fe-Fe ferromagnetic interactions [33]. A p(H + h)/kT = 3, at 4.2 K the impurity behaves as detailed model has been proposed [34] which gives a 37 consistent interpretation of the low temperature establish the increase of the giant moments with Fe magnetic behaviour of mictomagnetic alloys, espe- content x (0.06 x 0.25), a fact which is consistent cially Cu-Mn and Ag-Mn alloys. According to this with a classical model of local environment magne- model, the magnetic unit of the alloy system is an tism, as described by Jaccarino and Walker [1]. ensemble of mutually interacting ferromagnetic and But, we have verified that the classical models of antiferromagnetic domains. These domains are local environment magnetism found in the literature assumed to result from short range forces, the net (the simple one proposed by Jaccarino and Walker [1], effect of which is to couple the nearest neighbour or the improved one proposed by Pataud et al. [7] Mn atoms antiferromagnetically and those of larger taking into account the first and the second coordi- separation ferromagnetically. This last assumption nation shells of the magnetic atoms) fail to satisfac- has been confirmed by neutron diffraction on Cu-Mn torily describe the characteristic cluster magnetiza- alloys [35]. The magnetic properties of Au4Mn tion af = N* M* (Table IV) of the Be2 Mn 1 _ xFex compounds [26] at low temperatures, especially the samples in the critical concentration range decrease of the average cluster moment and the 0.06 x 0.25. This fact emphasizes the existence increase of the cluster concentration by lowering of two types of magnetic moment carriers (Fe and Mn) the temperature, were also related to the increasing in the beryllides over the whole concentration range importance of antiferromagnetic interactions. The 0.06 x 1.00 and shows us (as already mentioned assumption of antiferromagnetic interactions in the in section 5) that a more elaborated model of local BeZMn 1 _ xFex compounds at low temperatures seems magnetism is needed for a concise interpretation of reasonable, because these beryllides are also Fe and the magnetic properties of the Be2Mn1 _xFex samples Mn compounds ; but the origin of antiferromagnetic over the whole concentration range 0 x 1. coupling is at present not clear, since we ignore the Moreover, the characteristic cluster moments M*, exact role played by the Mn atoms. According to M*, M2 , M3 and the corresponding concentrations the above mentioned arguments, we tentatively ascribe (Tables III and IV), obtained from averaged moments the mictomagnetism and the other related properties of differently sized clusters, have no evident physical (behaviour of C(T), u, average cluster moments M2 meaning and the exact role of the Mn atoms in the and M3, their concentrations N2 and N3 at T below T * ) magnetism of these beryllides, has yet to be deter- to the increasing importance of antiferromagnetic mined. interactions by lowering T from T* to 4.2 K. Thus, the observed decrease and and the increase of M2 M3 8. Summary and conclusion. - The main results of and appear as reflections of these antiferro- N2 N3 obtained in the present work on the magnetic pro- in this that it seems rea- magnetic interactions, way perties of the investigated Be2Mn1 _xFex compounds sonable to consider the effective moments and concen- (0.06 x 1), may be summarized as follows. trations of the moderate and large clusters in our A Q2 versus Hlu representation of the magnetization as being nearly temperature independent beryllides data up to 150 kOe, confirms the inhomogeneous in the T* to 4.2 K, with values range corresponding nature of the transition from paramagnetism to listed on tables III and IV. ferromagnetism in the Be2Mn1 _xFex system. Low We have made the temperature T* play an impor- field magnetization data show that this transition tant role in our tentative of the results interpretation may be considered as being gradual in this system. in section because T* lies in the reported 6, tempe- When the Fe content x is raised, the magnetic pro- rature range where the effects mentioned in steps (i), perties of the compounds evolve gradually from (ii) and (iii) are minimal (minimal increasing rate paramagnetism (x 0.06) to mictomagnetism of Mi with T, nearly constant M2 and M3 values, (0.11 x 0.30) and to ferromagnetism (x > 0.30). appearance of the antiferromagnetic interactions). But the unusual behaviour of the so called ferro- we take the values and Therefore, M*, M 1 *, M2 magnetic samples (weak remanence and very low of the cluster moments and N * of the M 3 * average coercive fields, shown on figure 6), has to be cleared cluster concentration in table as values given IV, up by further investigations. We have simplified our characterizing the giant moment clusters in our magnetization data analysis (section 3, expression (1)) beryllides. The M* values, ranging from 6 ,uB to by attributing the main part y(H, T) of the magne- more than 50 ,uB, seem to be a little high, if compared tization to giant moment clusters, existing in diffe- to giant moment values in other Fe based alloys, rent magnetic states (superparamagnetic, mictoma- especially Fe-V alloys with p - 10 YB to 30 PB [7]. gnetic or ferromagnetic, depending on T and x). The slight fluctuations observed in the variations A sharp non linear decrease of the mean moment of M*, M* and Mi with Fe content x, may be (section 5) was observed for the Fe rich beryllides attributed to some partial ordering in our samples ; (0.30 x 1.00) on increasing the Mn content, but but the more important fluctuations on the M* the corresponding normalized Fe moment (plxpo values result mainly from the qualitative estimate of ratio) was found to be higher than unity, indicating the large cluster moment M3. Nevertheless, these that two kinds of atoms (Fe and Mn) are able to results are sufficiently accurate to experimentally carry a magnetic moment in these beryllides. A 38

detailed analysis of the magnetization data on beryl- our work lies in the description of the magnetism of lides in the critical concentration range 0.06 x 0.25, our Be2Mnl _xFex samples (0 x 1) in the frame shows the existence of superparamagnetic clusters of local environment magnetism. This description with average moments and concentrations depending uses only the magnetization a(H, T) data and is on temperature (sections 3 and 6). A characteristic based on experimental observations (except the temperature range (Tl, T*) exists corresponding to assumption of a non localized 3d state paramagnetism characteristic values of the different cluster para- linear with field up to 150 kOe), but it leaves several meters (CM and um maxima of the Curie constant problems unsolved. The most important of these and cluster size distribution ratio, table II, average are : the exact role of the Mn atoms in our beryllides cluster moments M*, M 1*, Mi , M 3 * and corres- remains to be determined. The physical meaning of ponding concentrations listed in table IV). A tenta- the characteristic M*, M*1, Mi and Mj average tive interpretation of the results of section 6, is given cluster moments is not evident. It appears difficult in section 7 by invoking the concepts of (i) giant to elaborate a model of local environment magnetism, moment clusters with their Curie temperatures suitable for a concise interpretation of the magnetic increasing with the cluster size, (ii) nearly magnetic properties of the Be2Mn, -xfex compounds over the impurities which become magnetic at lower tempe- whole concentration range 0 x 1, without using ratures and (iii) antiferromagnetic interactions related other techniques (Môssbauer spectroscopy, neutron to the mictomagnetic behaviour of these samples. diffraction, and so on...) in addition to the magne- Finally, we have verified (sections 5 and 7) that the tization measurements. Therefore, further investiga- classical models of local environment magnetism tions on these Be2Mnl -xFe,, compounds are needed. failed to satisfactorily describe the results of our on magnetization data analysis all investigated beryl- Acknowledgments. - We wish to thank Professor lides (0.06 x 1.00), indicating that a more ela- R. Pauthenet and his fellow workers at the Service borated model of local magnetism is needed for a National des Champs Intenses (S.N.C.L), Grenoble, concise interpretation of the magnetic properties of France, for their hospitality and their help with the the Be2Mn1 _xFex compounds over the whole con- magnetization measurements. centration range 0 x 1. We are also grateful to Professor F. Gautier for As a conclusion, it can be said that the interest of his critical reading of the manuscript.

References

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