Eur. Phys. J. B 64, 211–218 (2008)DOI: 10.1140/epjb/e2008-00294-6 THE EUROPEAN

PHYSICAL JOURNAL B

Effective anisotropy field variation of magnetite nanoparticleswith size reduction

J.M. Vargas1,a, E. Lima Jr1, R.D. Zysler1, J.G.S. Duque2, E. De Biasi2, and M. Knobel2

1 Centro Atomico Bariloche and Instituto Balseiro, 8400 S. C. de Bariloche, RN, Argentina2 Instituto de Fısica “Gleb Wataghin”, Universidade Estadual de Campinas, Campinas (SP) 13081-970, Brazil

Received 28 February 2008 / Received in final form 9 June 2008Published online 25 July 2008 – c© EDP Sciences, Societa Italiana di Fisica, Springer-Verlag 2008

Abstract. Size effect on the internal magnetic structure has been investigated on weakly interacting mag-netite (Fe3O4) nanoparticles by ferromagnetic resonance experiments at 9.5 GHz as a function of tempera-ture (4–300 K). A set of three samples with mean particle size of 2.5 nm, 5.0 nm and 13.0 nm, respectively,were prepared by chemical route with narrow size distribution (σ < 0.27). To minimize the dipolar interac-tion, the particles were dispersed in a liquid and a solid polymer matrix at ∼0.6% in mass. By freezing theliquid suspension with an applied external field, a textured was obtained. Thus, both random and texturedsuspensions were studied and compared. The ferromagnetic resonance experiments in zero-field-cooled andfield-cooled conditions were carried out to study the size effect on the effective anisotropy field. The dcmagnetization measurements clearly show that the internal magnetic structure was strongly affected bythe particle size.

PACS. 75.50.Tt Fine-particle systems; nanocrystalline materials – 75.30.Gw Magnetic anisotropy –75.60.Ch Domain walls and domain structure – 76.50.+g Ferromagnetic, antiferromagnetic, and ferri-magnetic resonances; spin-wave resonance

1 Introduction

Although many nanostructured systems (i.e., systemswith particle sizes of the order of nanometers) have beenreported as superparamagnetic, in general the experimen-tal data show deviations from the standard superpara-magnetic theory. These differences are usually ascribedto the intrinsic particle size distribution, anisotropies ofdifferent origins, and interactions among magnetic par-ticles. An ideal superparamagnetic system is composedby magnetic single-domain nanoparticles whose atomicmagnetic moments rigidly align through exchange interac-tion. All the individual magnetic moments add to form amagnetic supermoment, usually of the order of thousandsBohr magnetons (μB). The description of superparamag-netism, following the Langevin formalism, considers a neg-ligible anisotropy for each particle and neglects the effectof interparticle interactions [1–3]. More recently, Kodamaet al. [4,5] suggested that the modification of the structuraland electronic properties near to the particle surface wouldgive rise to site specific surface anisotropy and weakenedexchange coupling, which would lead to surface spin mis-alignment with respect to the ordered core spins and frus-tration. Such disorder would propagate from the surfaceto the particle core, actually making no longer valid the

a e-mail: vargasjm@ifi.unicamp.br

picture of the particle as a perfectly ordered single-domainnanoparticle [6–8].

Among many publications on magnetic nanoparticles,there is a considerable number of studies performed bymeans of ferromagnetic resonance (FMR) due to the factthat it yields relevant information regarding the dynam-ics of the system, and it allows one to discriminate thedifferent internal magnetic contributions. For exampleKoksharov et al. [9], studied ferrite nanoparticles embed-ded in polyethylene matrix by ferromagnetic resonancetechnique, where the coexistence of both ferromagneticand antiferromagnetic phases were clearly determined.Berger et al. [10], studied the effect of annealing on thenucleation and growth of nanoparticles in borate glassesdoped with low concentration of iron oxide, where anew resonance component was observed when the anneal-ing temperature increased, ascribed to superparamagneticnanoparticles of a crystalline iron-containing compound.From the viewpoint of finite size effect, Gazeau et al. [11],studied the internal fields in colloidal maghemite nanopar-ticles with particle size between 5–10 nm, where twocontributions to the internal fields were determined, oneanisotropic and other isotropic. In the effort to better un-derstand the evolution of the magnetic properties from theatomic level to a bulk solid, De Biasi et al. [12,13] consid-ered the internal magnetic structure for isolated particles.In their model the site-to-site spin was followed by Monte

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Carlo simulations considering different spin-spin couplingfor the core, shell and between them. Thus, the observedferromagnetic resonance quantities (line shape, line widthand resonant field) were interpreted in terms of the parti-cle parameters (magnetic moment, anisotropy) [13–15].

Undoubtedly, a major challenge to better understandthe internal magnetic structure in nanosystems and testthe existing models is to produce good quality samples. Infact, the limited knowledge of nanoparticle shape, compo-sition gradient, size distribution, or even the existance oftouching nanoparticles can hinder an accurate picture ofthe whole system. We have contributed to overcome thisproblem by producing nanosized magnetite nanoparticlesof approximately cubic-faceted shape and narrow size dis-tribution by chemical synthesis method. The presence oforganic insulating capping on the surface of the magneticparticles prevents the formation of agglomerates or chains.Furthermore, the particles have been dispersed in polymerand solvent in order to minimize the inter-particle dipo-lar interactions, allowing us to systematically study thefinite size effect on the internal magnetic structure of suchsystems.

2 Experimental procedure

The magnetite nanoparticles were prepared by chemi-cal synthesis as described in reference [16]. Briefly, ina reaction vessel a metallic precursor, iron (III) acety-lacetonate, in presence of 1,2-hexadecanediol and oleicacid-oleylamine surfactant were vigorously stirred inphenyl-ether solvent under inert gas flux. The reactionwas carried out at high temperature (∼270 ◦C) and themean size of the particles was tuned by the molar ratiobetween metallic precursor and surfactant (rp:s), with-out size-selection process. This method leads to colloidalmagnetite nanoparticles with characteristics close to idealnanoparticle systems, i.e. particles with excellent mor-phological (size and shape) and crystalline homogeneity.The determination of the spinel oxide phase is a difficulttask due to the oxygen stoichiometry variations and thesmall size of the particles. It is well established that smallchanges in the oxygen stoichiometry results in variationsin the Verwey transition temperature [17]. Therefore, inour nanoparticles, we expect a smoothing in the Verweytransition. In this aspect, Mossbauer Spectroscopy (MS)is a suitable technique since it probes the local environ-mental and the oxidation state of the Fe atoms. MS anal-ysis in similar systems showed that the samples usuallypresent both Fe+2 characteristic of magnetite and a lackof the expected stoichiometry of the particles [18]. Ac-tually, as we are interesting in the magnetic behaviourof the “spinel structure” our results are independent ofthe oxygen stoichiometry. The as-made nanoparticles werecoated by surfactant molecules to avoid the agglomerationand the direct exchange-like interactions among particles.We have obtained three samples with different mean grainsizes, L, when rp:s was fixed at the values: 1:20 (2.5 nm),1:10 (5 nm) and 1:2 (13 nm), respectively. The sampleswere labeled as SI, SII and SIII, respectively.

The morphological characterization was performed bytransmission electron microscopy (TEM), in a Philips CM200 UT-TEM (200 kV). Samples for TEM analysis wereprepared by drying a high-concentrated solution of the as-made nanoparticles, on amorphous carbon cooper grids.The crystalline characterization was performed by X-raydiffraction (XRD), in a Philips W1700 diffractometer un-der Cu-Kα radiation source. The ferromagnetic resonance(FMR) measurements were performed using a Bruker ESP300 spectrometer operating at 9.5 GHz (X-band), modu-lation field frequency at 100 kHz and amplitude 10 Oe.A commercial gas flow cryostat was used which allowedto achieve temperatures in the range of 1.4–300 K. Thecavity itself was kept at room temperature and its qual-ity factor was not changed upon cooling. The dc magne-tization curves as functions of temperature M(T ) (4 K< T < 300 K, under zero-field-cooling and field-coolingconditions, H = 20 Oe) and applied field M(H) (H ≤ 50kOe) were measured in a MPMS XL7 SQUID magnetome-ter (Quantum Design).

3 Results and discussions

Figure 1 shows the TEM images (Figs. 1a–1c) and diffrac-tion patterns (Figs. 1d–1f) for the samples SI, SII and SIII,respectively. As the mean size increases, the crystalline de-gree rises from amorphous-like to well-crystalline pattern,with narrower peaks owing to the increment of sizes [19].From several TEM images, the particle size histogram hasbeen built by counting more than 300 particles for eachsample. The cubic-faceted shape particles display a rathernarrow Lognormal size distribution, with σ ∼ 0.27. For thewell-crystalline samples SII and SIII, the volume averagecrystalline domain size (Lv) was calculated by the Scherrerformula [20] applied to the principal (113) peak (see pat-terns in Figs. 1e–1f). Table 1 summarizes the crystallinedomain size and their comparison with the TEM particlesize characterization. Since the diffraction analysis givesa volume average value for the mean crystalline domainsize, the volume-average particle sizes (LTW ) were esti-mated from the TEM histograms [21]. Therefore, an ex-cellent agreement was obtained between both crystallineand morphological mean particle size for the samples SIIand SIII. For the dc magnetic measurements, the particleswere dispersed in a polymer (PEI) at 0.6%wt., to minimizethe dipolar interaction. Roughly, the calculated mean dis-tance between particles (ζ), correspond to ζ/L > 8 [22].Figure 2 shows the temperature variation of the magneti-zation measurement for the samples SI, SII and SIII un-der zero-field-cooling (ZFC) and field-cooling (FC) condi-tions, for applied fields of H = 20 Oe. The irreversibilitytemperature, Tirr, is defined as the threshold temperatureabove which FC and ZFC curves coincide. Therefore, asthe mean size increases, the Tirr rises from 4 K to nearlyroom temperature (see values in Tab. 2). Interestingly,the shape of the ZFC-FC magnetization curves is similarto the one expected for ideal weakly interacting and ran-domly oriented particle systems [23]. On the other hand,the FC magnetization curve of sample SIII suggests the

J.M. Vargas et al.: Effective anisotropy field variation of magnetite nanoparticles with size reduction 213

Fig. 1. TEM images for the samples SI (a), SII (b) and SIII (c); and the diffraction patterns SI (d), SII (e) and SIII (f).

Table 1. Mean size values obtained from TEM and XRD char-acterization.

sample L (nm) L3 (nm3) Lv (nm) LTW (nm)SI 2.5 15.6 — 2.8SII 5.0 125.0 5.5 5.5SIII 13.0 2197.0 12.7 14.4

appearance of dipolar interactions [24]. The main blockingtemperature, TB, is defined as the maximum value in theenergy barrier distribution occurs. For weakly-interactingnanoparticles, according to the Neel-Brown model for asingle superparamagnetic particle, the blocking temper-ature distribution function (f (T )) can be obtained fromthe ZFC and FC magnetization curves as, d[MZFC(T ) –MFC(T )]/dT ∝ Tf(T ) [25]. Then, the K value of eachsample was estimated by using the TB value and the Ar-rhenius law. As is commented below, although for samplesSI and SII the Arrhenius law is not completely satisfieddue to the complex internal magnetic structure, it waspossible to estimate a rough value for K for each sam-ple. Figure 3 shows the magnetization loops for the threesamples at room temperature and T = 4 K. At room tem-perature (Figs. 3a–3c) the three samples are in the ther-mal equilibrium i.e., loops without hysteretic or memoryeffects, showing reversible magnetization. Moreover, fromthe slope of the magnetization curves it was possible to ob-serve that the curve is more pronounced as the particle sizeincreases, in good agreement with the Langevin formalism[1–3]. At T = 4 K (Figs. 3d–3f), as the particle size in-creases the hysteretic loops show striking variation: fromwasp-waisted-like shape for the sample SI to square-likeshape for the sample SIII. Comparing the three samples,the maximum value of HC was achieved for the sampleSII, probably due to the strong interaction between thecore and shell magnetic regions. Moreover, in agreementwith the theoretical predictions, the sample SI shows thebiggest Hirr ∼ 10 kOe (where Hirr correspond to the high-field value where both ascending and descending magne-tization curves splitting), associated to the strong surface

Fig. 2. Temperature variation of the dc magnetization mea-sured under ZFC and FC conditions for the samples SI (a),SII (b) and SIII (c), with H = 20 Oe. The open circle corre-spond to the ferromagnetic resonance susceptibility (∝IF MR),measured in the ZFC condition.

Table 2. Values and parameters from the dc magnetic char-acterization.

ZFC-FC hysteresis loopssample Tirr (K) TB (K) K (erg/cm3) HC (Oe) Hirr (Oe)

SI 6 <2 <5.0 × 105 23 10 000SII 50 19 5.8 × 105 310 5200SIII 272 86 1.5 × 105 274 2400

anisotropy contribution, which leads to magnetic frustra-tion in surface at low temperature [15]. Table 2 summarizethe dc magnetic results.

214 The European Physical Journal B

Fig. 3. Magnetization loops at room temperature for the samples SI (a), SII (b) and SIII (c); and T = 4 K for the samples SI(d), SII (e) and SIII (f).

Fig. 4. Temperature variation of the magnetic resonance spectra at (i) 300 K, (ii) 250 K, (iii) 110 K, (iv) 50 K, (v) 4 K in theZFC condition for the samples SI (a), SII (b) and SIII (c). The dotted lines correspond to the computer simulated spectra.

In the FMR experiments the particles were dispersedin toluene (with freezing temperature ∼180 K), where thevolume ratio between the as made colloidal solution andsolvent was 1:20. Approximately, for this dilution, themean distance between nanoparticles was ζ/L > 8 [22].Figure 4 shows the temperature variation of the FMRspectra in the ZFC condition for the samples SI, SII andSIII. From the absorption-derivative spectra, two charac-teristic parameters were defined: the resonant field H0 asthe point where the spectrum equals to zero; and the peak-to-peak line width ΔHpp. Therefore, the following featureswere observed in the FMR-ZFC experiments:

• The spectrum of the sample SI (Fig. 4a) shows a nar-row symmetric line, with a Lorentzian-like shape, cen-

tered at H0 = 3379 Oe and ΔHpp ∼ 110 Oe. Asthe temperature decreases the H0 does not change,although a small continuous broadened effect is ob-served. The integrated FMR absorption intensity,IFMR, was calculated through the double integrationof the absorption-derivative spectra at each tempera-ture. Previous normalization by the dc magnetic sus-ceptibility at room temperature, the IFMR does notshow appreciable temperature variation. This featurecould be explained by a strong surface anisotropy con-tribution, with spin-glass-like characteristics.

• The spectrum of the sample SII (Fig. 4b) consists in anasymmetric line that can be described as a sum of twolines: a broad line with the ΔHpp ∼ 380 Oe, associatedwith the particle-core contribution, and a narrow one

J.M. Vargas et al.: Effective anisotropy field variation of magnetite nanoparticles with size reduction 215

Fig. 5. The H‖ and H⊥ resonance fields obtained from the simulated ZFC curves at temperatures 4 K < T < 110 K for thesamples SI (a), SII (b) and SIII (c). These values are compared with the respective ones measured in the FMR-FC spectra. Thetemperature variation of the center field, H0(T ), is plotted for comparison (values obtained from the FMR-ZFC spectra).

with ΔHpp ∼ 50 Oe, associated with the particle-shellcontribution [9,10]. Cooling the sample, the narrowline decreases steeply, and the broad line shifts towardslower fields and its width increases. The temperaturevariation of IFMR for the broad line was calculated(previously discounting the narrow line, i.e., the shellmagnetic contribution) and it is plotted in Figure 2b.At T > 150 K, a good agreement is observed betweenboth dc and IFMR susceptibilities. Interestingly, thisagreement was predicted for ideal paramagnetic sys-tems, where IFMR is proportional to the paramag-netic susceptibility [26], i.e., the temperature variationof the broad line follows the superparamagnetic-corecharacteristics. At lower temperatures IFMR(T ) in-creases monotonically, although it is not enough tofollow the dc susceptibility.

• The spectrum of sample SIII (Fig. 4c) shows a broadand symmetric line, ΔHpp ∼ 420 Oe, without the nar-row line component. As the temperature decreases, theline shifts toward lower fields and its width increases.Moreover, IFMR(T ) slows down as the temperatureincreases (see Fig. 2c), as it would be expected in thenanoparticle FMR model [13].

Therefore, as the particle size increases, the sharp line fea-ture in the FMR-ZFC spectra was gradually replaced bythe broad one, and the two line-component coexist at in-termediate sizes. Actually, similar trends were observed incomputer-generated spectra by Berger et al. [30], for idealnanoparticles with size and shape distribution. The FMR-ZFC spectra were simulated at temperatures lower than110 K, where the ferrofluid was frozen, with randomly ori-ented easy magnetization axis. The theoretical absorptionexpression for a randomly oriented anisotropy axis systemcan be written as [28]:

A(H) ∝∫ H⊥

H‖K(H ′)F (H ′)dH ′, (1)

where F (H ′) = 1/((H − H ′)2 + ΔH20 ) is the Lorentzian

function and K = (H2‖ + H ′2)/H2

‖ is the weight prob-ably factor. The H‖, H⊥ and ΔHpp are the parametersof the fitting. In particular, in the linear model [13], thecorrelation between both resonant fields and the effectiveanisotropy field HA can be written as:

32HA = H⊥ − H‖. (2)

Figure 5 shows the temperature variation of the calculatedparameters H‖ and H⊥. Whereas the mean particle sizeincreases, the difference between both resonance fields in-creases. Interestingly, the calculated parameter ΔHpp forthe three samples not show an appreciable temperaturevariation between 4–300 K, where for the sample SI theΔHpp ∼ 300 Oe, and for the samples SII and SIII theΔHpp ∼ 800 Oe.

The FMR spectra measured in the FC condition(FMR-FC), i.e., after the ferrofluid was frozen in an ap-plied field (H = 10 kOe) and the easy magnetizationaxes became more aligned along the external field direc-tion, provide fundamental information about the differ-ent anisotropy contributions. From the FMR-FC spectra,the measured parallel and perpendicular resonance fieldswere compared with the calculated ones parameters (seeFig. 5). Whereas for the samples SI and SIII an excel-lent agreement is observed, the disagreement observed forthe sample SII at low temperatures can be associated to acore-shell magnetic structure (60/40%), which in this casehas not been considered. From the angular variation of theFMR-FC spectra it is evident that as the mean particlesize increases, the amplitude of the angular variation ismore accentuated (Fig. 6). Moreover, the angular varia-tion is well fitted with the cos2β dependence, expected foruniaxial anisotropy systems [11].

As is mentioned above, the shape spectrum in theFMR-FC condition is very sensitive to the coexistence ofthe different anisotropy contributions. Figure 7 shows thetemperature variation (4 K < T < 110 K) of the FMR

216 The European Physical Journal B

Fig. 6. The angular variation of the center field H0 at 4 K, 50 K and 110 K for the samples SI (a), SII (b) and SIII (c), afterfreezing the fluid with an applied field (H = 10 kOe).

Fig. 7. Temperature variation of the magnetic resonance spec-tra measured in the FC condition at (i) 4 K, (ii) 10 K, (iii) 20 K,(iv) 30 K, (v) 50 K, (vi) 110 K, for the sample SI. The spectrado not show angular variation.

spectra measured in the FC condition for the sample SI.At low temperatures (T < 27 K), a very broad line isobserved. For temperatures higher than 27 K, the broadline is steeply narrowed, centered at H0 = 3379 Oe. Also,the IFMR calculated from the FMR-FC spectra reachesa maximum at Tfz = 27 K, where Tfz is defined as thefreezing temperature of surface contribution. Remarkably,the dc magnetization vs temperature measured after cool-ing with H = 50 kOe (M50 kOe (T ) (figure not shown) iscorrelated to magnetic variation observed in the FMR-FCspectrum at low-temperatures. The M50 kOe (T ) curverises at T < 27 K, owing to the formation of a cluster-glass-like phase at low temperatures [32]. Concomitantly,the shape of the FMR-FC spectra becomes more asym-metric as the mean particle size increases (see Figs. 7and 8), due to the relative increase of the crystallineanisotropy contribution and the vanishing of the surface

anisotropy contribution. Generally speaking, for an idealcrystal with cubic symmetry two maxima are expectedin the angular variation, fact that does not occur in thestudied samples [11]. Therefore, the shape anisotropy isthe most important factor to the effective anisotropy inthe present case. To check whether the asymmetric lineshape of the FMR-FC experiments is related to the coexis-tence of the shape and crystalline magnetic contributions,we simulated the spectra with both contributions, i.e., theshape uniaxial anisotropy and the magnetocrystalline withcubic-distortion symmetry [34]. The inset of Figure 8b,shows the good agreement between the experimental andsimulated shape spectra. The effective anisotropy fieldHA(T ) was calculated from equation (2) and it is shownin Figure 9 for the three studied samples. In particular, forthe smaller particle size (2.5 nm), without angular varia-tion, HA ∝ H⊥ − H‖ = 0. In this case, the difference ob-served in the FMR experiments between the ZFC and FCconditions evidences the shell magnetic contribution withstrong surface anisotropy field. Thus, at low temperatures,in the FMR-ZFC experiments the disordered spin configu-ration leads to a small amounts of accessible states for theresonance condition, with narrow anisotropy field distri-bution. On the other hand, in the FMR-FC experiments,all spins are quasi-aligned and in the resonance condition,with a subsequent broad anisotropy field distribution. Inthe case of intermediary (5.0 nm) and bigger (13.0 nm)particles, HA = 800 Oe at T = 4 K, and both follow sim-ilar trends. However, for the sample SII (particles withintermediate sizes) the variation is more accentuated dueto the surface contribution. Similar values were reportedby Barker et al. [33], for the case of uniaxial anisotropy.

4 Conclusions

In summary, the present study shows that the FMR tech-nique in association with the dc magnetic measurementsyields an effective tool for exploring the shape, crys-talline and surface magnetic contributions of the magneticnanoparticles. In particular, such combination sheds somelight into the effect of size on the magnetic structure of the

J.M. Vargas et al.: Effective anisotropy field variation of magnetite nanoparticles with size reduction 217

Fig. 8. The parallel and perpendicular ferromagnetic resonance lines at 4 K, 50 K and 110 K for the samples SII (a) and SIII(b). The continuous and dotted lines correspond to the parallel and perpendicular measurements, respectively. The inset in (b)correspond to the computer simulated parallel and perpendicular curves.

Fig. 9. The temperature variation of the effective anisotropyfield, HA, for the samples SI (a), SII (b) and SIII (c).

nanoparticle. In the present study, a set of three samplesof magnetite nanoparticles were systematically preparedand investigated. The mean particle size was tuned in thesynthesis process and samples with mean sizes of 2.5 nm,5.0 nm and 13.0 nm were obtained with corresponding sur-face to volume ratios of 90%, 40% and 10%, respectively.

The degree of spin fluctuations was expected to de-crease with increasing the particle size [11,12,32]. Thiseffect was confirmed by FMR and dc magnetic measure-ments in the present study. For the sample with smallernanoparticles (SI) the magnetic properties are absolutelydominated by surface magnetism, where the surface spinis strongly disordered. It was shown that the surface spinfluctuation decreases as the temperature is diminished,leading to a frozen disordered state of the surface spins atlow temperatures, which the effective HA = 0. In the otherextreme, for the sample with bigger particles (SIII), themagnetic properties are completely dominated by the vol-ume contribution, following the Stoner-Wohlfarth model,where the internal magnetic structure of the nanoparti-

cle nearly corresponds to a ferromagnetic single-domainstate. In this case the effective HA = 800 Oe at 4 K andslowly down as the temperature increase. In the samplewith intermediate grain sizes (SII), the coexistence of bothsurface and volume contribution was clearly observed andthe HA slowly down as the temperature increase (whereHA = 800 Oe at 4 K). However, compared with the sam-ple SIII, the temperature variation is more accentuateddue to the surface contribution.

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