Fe interparticle interactions in Fe
xAg
100−xgranular alloys
„2⬍x⬍50…
J. M. Soares and F. L. A. Machado
Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil
J. H. de Araújo and F. A. O. Cabral
Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil
M. F. Ginani
Departamento de Química, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil
共Received 8 July 2005; revised manuscript received 23 August 2005; published 3 November 2005兲
Samples of FexAg100−x, with 2 %艋x艋50%, were produced using a new preparation route based on the ionic
coordination reaction technique. X-ray diffraction and transmission electronic microscopy showed that the samples are granular alloys and that they have a high degree of purity, good homogeneity, small variations in the Fe concentration, and the mean size of the grains was approximately 30 nm for any Fe composition. Magnetization measurements showed that the coercive field of the samples presented a fairly complex behav-ior. It was also observed, by means of time decay of the thermoremanent magnetization, three dynamical regimes. The existence of these regimes are in good agreement with what is expected from the analysis using the Henkel and␦M plots. In addition, it was observed an onset to a long range magnetic order共LRMO兲 in the
Fe30Ag70sample, culminating in a superferromagnetic order in Fe50Ag50.
DOI:10.1103/PhysRevB.72.184405 PACS number共s兲: 75.50.Bb, 75.50.Tt, 75.30.Et
I. INTRODUCTION
An important goal in material science is to develop new materials at the nanometric scale because their properties change dramatically with both the size and the local structure of the grains. This behavior has opened the possibility of applications of nanomaterials in different fields such as ca-talysis, magnetism, optoelectronics, and medicine.1–3
Granular magnetic materials composed of magnetic nano-particles embedded in a nonmagnetic matrix show magnetic properties that are strongly dependent on the interactions among the magnetic nanoparticles. The isolated noninteract-ing nanoparticles show themselves interestnoninteract-ing physical prop-erties, such as superparamagnetism共SPM兲, giant magnetore-sistance 共GMR兲 and giant magnetoimpedance.4–6 The development of new sample preparation techniques and an understanding of the interparticle interactions are quite im-portant nowadays from both scientific7–25and technological views.26–29 When the interparticle interactions become sig-nificant the system displays a rich variety of magnetic con-figurations resulting from competing magnetic interactions. Such materials have been produced as films by sputtering, as ribbons by melt spinning, and as powders by sol-gel methods,30,31and by mechanical alloying.32
One of the aims in preparing this kind of material is to obtain particles with uniform size and a well-defined surface. Recently, various ionic reactions based on synthesis methods were used to obtain nanoparticle materials.33 The ion-coordination reaction process using chitosan was used to ob-tain Mn-doped ZnS nanocrystallites, for instance.34
In this paper it is shown that the ionic coordination reac-tion 共ICR兲 technique can also be used to prepare granular magnetic materials with a high degree of purity and homogeneity. A series of FexAg100−x granular alloys with 2 %艋x艋50% were produced using this technique yielding
an Fe nanoparticle with an average size practically unaf-fected by Fe concentration in a so-wide range. The influence of the Fe concentration on the magnetic properties was in-vestigated by dc and time-dependent magnetization measure-ments. It was found that the interactions between Fe particles yield three distinct regimes. An onset to a long-range mag-netic order state 共LRMO兲, characterized by exchange inter-actions of Fe particles, was observed for samples with
x艌30%.
II. EXPERIMENTAL PROCEDURES
Samples of granular alloys of FexAg100−x, with x varying from 2% to 50%, were produced using an ICR technique. The start solution was prepared from an aqueous solution of Fe and Ag nitrates and a chitosan solution mixture. This mixture solution was burned at an ambient atmosphere for 4 h at a temperature of 300 °C, leading to a precursor powder. The powder was then reduced at a hydrogen atmosphere for 2 h at a temperature of 400 °C. The structural characteriza-tion was made by an x-ray diffraccharacteriza-tion共XRD兲 technique us-ing the Cu-K␣radiation. The samples were also analyzed by transmission electron microscopy共TEM兲. The structural and compositional analyses showed that the samples are made of iron particles embedded in a silver matrix. Therefore, the nominal composition x represents the atomic percentage of iron used to prepare the alloys. The magnetic properties of the samples were measured using a vibrant sample magneto-meter共VSM兲 and a mutual inductance ac susceptometer. The powders used in the magnetic measurements were com-pressed in a cylindrical glass sample holder to block the ro-tation of the particles. Each of the randomly packed poly-crystalline grains contains a large number of nanoparticles, yielding an overall random anisotropy system.
III. RESULTS AND DISCUSSION
The XRD of the FexAg100−x granular alloys produced by the ICR technique revealed a higher degree of purity than the ones prepared by sol-gel. For comparison, Fig. 1 shows the XRD of the Fe10Ag90 sample prepared by these two pro-cesses in a similar H2atmosphere. It can be observed that the sample prepared by the sol-gel process 共upper curve兲 pre-sents the Fe3O4phase while the sample prepared by the ICR technique 共lower curve兲 does not. Besides, their diffraction peaks are more intense and better defined, indicating good crystallization and homogeneity in the samples prepared by the ICR process. In short, the ICR technique revealed a great efficiency in producing high-quality samples of the FeAg granular alloys.
Figures 2共a兲 and 2共b兲 show the XRD for the Fe30Ag70 sample in two different stages of preparation:共a兲 the precur-sor powder and共b兲 the reduced powder. It can be observed
where that peak has its largest intensity, we calculated the Fe particle average diameters Dm using the Scherrers formula.
The average sizes of those particles range from 30 to 32 nm. Thus, even with the Fe concentration variation of 2% for 50% in these samples, Dmremains practically unchanged. A
Rietveld refinement was also carried out in order to obtain the average diameter of the particles and the Fe concentra-tion. We obtained the Fe particle average diameters as calcu-lated by the Scherrer’s formula and by the stoichiometric relations. This suggests that there was no formation of ag-glomerates of the Fe particle. These results are of great im-portance because they made it possible to study the magnetic interaction evolution among particles as a function of the Fe concentration.
Figure 3 shows the TEM for the Fe10Ag90 sample. It can be observed from this image that the Fe共darker spots兲 and Ag共brighter spots兲 particle sizes are close to 30 nm in good agreement with the results obtained from the XRD. The TEM did also indicate that the FeAg granular alloys are in-deed homogeneous.
Figure 4 shows the hysteresis curves for five iron concen-tration, namely, Fe10Ag90, Fe20Ag80, Fe30Ag70, Fe40Ag60, and Fe50Ag50. This kind of hysteresis curves are usually assigned to materials composed by blocked single domain particles, as is the case in the samples used in the present work. As shown
FIG. 1. X-ray diffractogram for the Fe10Ag90granular alloy
pre-pared 共a兲 by a sol-gel process 共Ref. 35兲 and 共b兲 by an ICR technique.
FIG. 2. 共a兲 XRD for the precursor powder of the Fe30Ag70 granular alloy. 共b兲 XRD for the
Fe30Ag70 powder sample after being reduced in 400 °C in a H2 atmosphere. Both intensity axes
were chosen in such a way that allowed us to emphasize the presence of the ␥−Fe2O3 and
previously, the average size of the iron particles in the samples is within 30 and 32 nm. This value is two times larger than the critical superparamagnetic diameter共Dc兲 for a
spherical Fe particle that is 16 nm. Dc separates the
super-paramagnetic state from the blocked state. Moreover, the process used in the preparation of these samples generates a narrow particle size distribution. Thus, it can be deduced that practically all particles are in the blocked state. The inset of Fig. 4 shows the behavior of remanent magnetization Mras a
function of the Fe concentration共%Fe兲. Mrincreases linearly
with the content of Fe in FexAg100−x for 5 %艋x艋50%, in-dicating a progressive increase in the number of Fe particles in the blocked state.
Figure 5共a兲 shows the behavior of coercive field Hcas a
function of the Fe concentration. Hcshows quite interesting
behavior. First, it increases from Hc= 226 Oe for x = 2% up to
Hc= 456 Oe for x = 10%. Next, it stays close to this high
value up to a Fe concentration of 16%. Finally, Hcdecreases
to 324 Oe for x = 20% and it stays unchanged for higher Fe concentrations. This behavior cannot be accounted for by variations in the size of particles because, as shown previ-ously, their size varies very little with the iron concentration. A possible scenario that explains this particular behavior of
Hccan be drawn from the study of the evolution of magnetic
interaction between Fe particles as a function of the Fe con-centration. This scenario is presented next.
In Fig. 5共b兲 it is shown the Mr/ MS ratio as a function of
the Fe concentration. It is known that when randomly ori-ented noninteracting particles undergoing coherent rotation,
Mr/ MS= 0.5.40Also, for particles exhibiting dipolar
interac-tions the Mr/ MSratio decreases,41as is observed in Fig. 5共b兲
for concentrations of Fe between 2% and 10%. For higher concentrations, the Mr/ MSratio remains unchanged, in good
agreement with the Hcbehavior. Thus, if other interactions
between particles of Fe are present in the samples with con-centrations above 20%, they do not cause a significant varia-tion in Hceither in the Mr/ MSratio.
The nature of the Fe interparticle interactions were inves-tigated using the thermoremanent magnetization 共TRM兲 measurements data. A typical TRM versus time curve is shown in Fig. 6 for a Fe5Ag95sample. The symbols are the experimental data while the solid line is a fit to the equation43
M共t兲 = M0+ M1e−t/. 共1兲
The fitting parameters were M0= 0.341± 0.001 emu/ g, M1 = 0.506± 0.0005 emu/ g, and = 3.29± 0.02 s. The insets in
FIG. 3. TEM image for the Fe10Ag90sample. The iron and the silver particles are shown as the darker and the brighter spots, respectively.
FIG. 4. Room temperature hysteresis curves of the FexAg100−x
granular alloy for 10%艋x艋50%. The inset shows the remanent magnetization as a function of the Fe concentration.
FIG. 5. Coercive field versus Fe concentration measured at room temperature.
Fig. 6 shows the data and the corresponding fit for the time-dependent TRM curves for the following samples: Fe5Ag95, Fe10Ag90, Fe20Ag80, Fe30Ag70, Fe40Ag60, and Fe50Ag50. In those curves one can see three dynamical regimes. The first one共samples with 5% and 10% of Fe兲 is characterized by a dynamical behavior where the ln TRM decreases almost lin-early with time, with some upturn deviation for t close to 15 s. In the second regime 共%Fe=20% and 30%兲, it decreases with time in a similar way to the first one but the deviation goes to the other side 共down兲. Finally, in the third regime, however, the time decay of the TRM start to deviate from the linear behavior in lower values of time共10 s兲 and the devia-tion is in the same direcdevia-tion, as observed in the first regime 共upturn兲. This type of behavior may be related to three types of couplings between the Fe particles.
Henkel and ␦m plots37,38 have also been carried out to further understand the Fe interparticle magnetic interactions. These plots use the remanence mr and the inverse of the
remanence mddata obtained from the same hysteresis curves.
Figure 7 shows the Henkel plots for Fe5Ag95, Fe10Ag90, Fe20Ag80, and Fe30Ag70. It can be observed from there that, for the sample with 5% of Fe, md共H兲 vs mr共H兲 shows a
lin-ear behavior indicating that there are no interparticle interac-tions. For this low value of Fe concentration, the Fe particles are far away from each other. However, for the sample with 10% of Fe, the behavior deviates from the linear one. This may be so because with more Fe the mean distance between the Fe particles diminishes, giving rise to interactions among them. The interaction reaches its maximum in the Fe20Ag80
sample. Further increasing the Fe concentration, as in Fe30Ag70, the deviation from the linear behavior start to de-crease, indicating a new regime. Henkel plots are good to indicate that there exist some Fe interparticle interactions in the samples, but they are not good enough to identify the nature of the interaction. Thus,␦m plots were used to
com-plete the scenario.
From the Wohlfarth relationship, md共H兲=1−2mr共H兲, a ␦m关=md共H兲−1+2mr共H兲兴 can be defined. It helps one to
ana-lyze both the magnitude and the kind of Fe interparticle in-teractions, as will be shown next. In Fig. 8,␦m was shown,
plotted as a function of the applied magnetic field for six values of the Fe concentration. The sample with 5% of Fe has a ␦m plot that does not present in its magnetic field
dependence on any peak structure for fields up to 1 T. How-ever, for 20% of Fe, a positive peak is present in the␦m plot,
indicating an exchange-type interparticle interaction as ob-served in FePt.39The Fe
10Ag90and Fe30Ag70samples, on the other hand, showed positive peaks. Further, for Fe40Ag60the peak height diminishes and it practically disappears in Fe50Ag50.
FIG. 6. Time decay of the room temperature TRM for
H = 1 kOe for the Fe5Ag95 sample. Within our time window, the decay can be nicely fitted by Eq.共1兲 共solid line兲. The inset shows the fit for the time decay of the TRM for共a兲 Fe5Ag95共solid tri-angles兲 and Fe10Ag90共open triangles兲; 共b兲 Fe20Ag80共solid squares兲
and Fe30Ag70 共open squares兲; 共c兲 Fe40Ag60 共solid cicles兲 and Fe50Ag50共open cicles兲.
FIG. 7. Inverse remanence as a function of the direct remanence for several samples of a FeAg granular alloy.
The results of the Henkel and␦m plots are consistent with
the results we obtained from the time decay of the TRM and from the Mr/ MS ratio measured at room temperature. The
samples with values of Fe concentration up to 5% may be described as an ensemble of noninteracting or weakly inter-acting共dipolar兲 randomly oriented particles. For Fe concen-tration in the range 10%–30%, the particles presented a sig-nificant difference in Mrand Md indicating the existence of
interactions between them with the particles randomly ori-ented. An onset to a long-range order occurs for higher con-centrations of Fe, namely, 40% and 50%, where the ␦m
peaks diminish.
An exchange interaction also has been observed in thin films of FeAg with a high concentration of Fe and the ap-proach to saturation at room temperature was described by a correlated spin glass 共CSG兲 state predicted by the random anisotropy 共RA兲 model.42 In the RA model, the disordered CSG state is weak and by the application of a small magnetic field induces a transition to a ferromagnet state with wander-ing axes 共FWA兲. In this FWA state the magnetization ap-proaches to saturation following a square-root law:44,45
MS− M MS =⌬M MS ⬀
冑
1 H. 共2兲Figure 9 shows a plot of the⌬M /MS data versus 1 /
冑
H.There, one can see a good agreement with what is expected from Eq.共2兲, even though there are some clear deviations. As pointed out in Refs. 44 and 45, besides the 1 /
冑
Hcontribu-tion an important 1 / H2 magnetic field dependence is also expected when one approaches saturation. By using the high magnetic field part of our data, we found that most of the deviation from the 1 /
冑
H can indeed be accounted for byincluding the 1 / H2contribution in our analyses. By adjusting the function 1 + A /
冑
H + B / H2to the high magnetic field partof the⌬M /MSdata, one finds that for the samples with 5%
and 10%, the 1 / H2contribution is smaller than the 1 /
冑
H one 共A⬇1.07 T1/2 and B⬇−0.02 T2 for these two sample con-centrations兲. For samples with a higher amount of iron, the 1 / H2contribution became ten times larger共A⬇1.29 T1/2andB⬇−0.26 T2兲 in the same magnetic field regime. Even so, it is important to notice that we are not going to very high values of magnetic fields and we are not too close to satura-tion yet. The samples with concentrasatura-tions between 20% and 40% of Fe follow a linear behavior at low fields, but it de-viates from this behavior at higher fields. Therefore, based on these results, the sample with 50% of Fe shows a behav-ior at low magnetic fields that is close to the FWA state. The onset to LRMO start to appear in the Fe30Ag70sample, cul-minating in a kind of superferromagnetic order in Fe50Ag50. The above results are in agreement with the Henkel and␦m
plots: the decrease in the peaks in the␦m plots is an
indica-tion that a LRMO is being developed.
In order to study the LRMO in these samples, we per-formed magnetic susceptibility measurements as a function of temperature. The data for the 40%–50% of Fe samples are shown in Fig. 10. We found that for the sample Fe40Ag60 there exists a typical transition from a blocked state to a superparamagnetic state at 376 °C. However, the ac suscep-tibility curve obtained for the sample with 50% of Fe shows a typical transition from a ferromagnetic to paramagnetic state. Although, taking in consideration that the particles of Fe are ultrafine, of the order of 30 nm, and that the tempera-ture of the transition is 396 °C, this behavior can also be interpreted as due to a transition from a long-range ordered blocked state to a superparamagnetic one. Therefore, it seems that the long-range correlations increase from the sample with 30% of Fe and reaches a maximum in the Fe50Ag50 sample.
In summary, the results presented in this work are consis-tent with the following scenario: in the investigated sample compositions there exists three distinct coupling regimes of interaction between Fe particles. The samples with a Fe con-centration of up to 5% of Fe may be described as an en-semble of noninteracting or weakly interacting共dipolar兲
ran-FIG. 9. Variation of the magnetization relative to the saturation magnetization as a function of the square-root of H, for several FeAg samples.
FIG. 10. ac susceptibility measured as a function of the tempera-ture for the Fe40Ag60and Fe50Ag50samples.
that magnetic interaction among the Fe particles varies sig-nificantly. A detailed study of the nature of these interactions was done using the Henkel and the␦m plots. By means of
the time decay of the thermoremanent magnetization, we found three dynamical regimes that are in agreement with
The TEM micrographs were obtained at LIKA-UFPE and we thank Professor José Luiz de Lima Filho for kindly help-ing us. This work was partially supported by the Brazilian agencies CNPq, FINEP, CAPES, and FACEPE.
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