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Journal of Alloys and Compounds 653 (2015) 513e522

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Journal of Alloys and Compounds

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Surface and interparticle interactions effects on nano-cobalt ferrites

M. Saidani a, *, W. Belkacem a, A. Bezergheanu b, C.B. Cizmas b, N. Mliki a

a LMOP: LR99ES17, Facult�e des Sciences de Tunis, Universit�e de Tunis El Manar, 2092, Tunisiab D�epartement d'Ing�enierie Electrique et Physique Appliqu�e, Universit�e Transilvania de Brasov, Romania

a r t i c l e i n f o

Article history:Received 1 August 2015Accepted 1 September 2015Available online 7 September 2015

Keywords:Nano-cobalt ferritesSurface affectsInterparticle interaction

* Corresponding author.E-mail address: mohamed1saidani@gmail.com (M

http://dx.doi.org/10.1016/j.jallcom.2015.09.0200925-8388/© 2015 Published by Elsevier B.V.

a b s t r a c t

Cobalt ferrites nanoparticles CoxFe3-xO4 (1� x< 1.8) were synthesized by a solvothermal route. X-raydiffraction, Transmission Electron Microscopy and magnetic measurements show a strong correlationbetween the structural and the magnetic properties. The highest cobalt amount substituted samples(x¼ 1.6 and 1.8) show a jump at low temperature in the hysteresis loops in the range of low applied fields(<10 kOe). This behavior has been explained by surface effects and interparticle interactions. A differencehas been found using two different estimation of the magnetic anisotropy: from the law of approach tosaturation and using the Neel-Brown approach. The last approach leads to an increase of the anisotropyfor x¼ 1.6 and 1.8 coming from finite size effects. Surface effects have been pointed out using the Blochlaw fitting. Zero Filed Cooling (ZFC) measurements exhibit a blocking temperature (TB) range from 294 to240 K. Kneller's law fitting of the coercive field dependence on the temperature exhibits a non-neglectedinterparticle interaction and a wide size distribution according to the difference found between TB andthe Kneller transition temperature TBK.

© 2015 Published by Elsevier B.V.

1. Introduction

Cobalt ferrite nanoscale materials have attracted a greatattention due to the continuous discover of new promising prop-erties which differ from the bulk ones. Reduced sizes may presentinterparticle interactions [1] and surface effects [2]. Cobalt Ferritesnanoparticles are used in a wide variety of applications such asrecording media, microwave, biomedicine, photo-magnetism [3-6]. This can be related to their high cubic magnetic anisotropy,their chemical stability and their high coercive field [7]. Thesesamples have been synthesized by a several chemical and physicalroutes in the purposes to find the suitable one for the requiredproperties.

Cobalt ferrites, of the Spinel structure with AB2O4 formula, canbe described as ðA2þ

1�tB3þt ÞTdðA2þ

t B3þ2�tÞOhO4 where Td, Oh refer to thetetrahedral and octahedral sites respectively and t is the inversiondegree. It is called a normal (inverse) spinel if t is equal to 1 (0).Accordingly, the magnetite Fe3O4 crystallizes in a completely in-verse spinel structure. Fe3þ, occupying the octahedral and tetra-hedral sites by half, are antiferromagnetically coupled through themagnetic superexchange interaction. Fe3þ and Fe2þ cations, located

. Saidani).

in the octahedral sites, are ferromagnetically coupled by means ofthe magnetic double exchange interaction [8]. Thus, the magnitudeof those interactions depends on the cationic distribution and thetype of the tetrahedral and octahedral cations. The substitution ofFe2þ by Co2þ affects the physical properties regarding to thedimension and the difference between their magnetic natures.Swatzky et al found that Fe-OCo superexchange interaction isweaker than FeeCoFe [9].

In this work, we are interested in the effect induced by thesubstitution the iron by cobalt. It is helpful to have knowledge on itsreal structure and on what it depends. CoFe2O4 has an inversespinel structure. Although, it was found that a ratio of Co2þ (2e24%)can occupy tetrahedral sites [10]. This is strongly dependent on thesynthesis method and the heat treatment [11]. Thus, results aregoverned by many parameters as mentioned above and, from asynthesis technique to another, strange and interesting effectscould be observed. The grain size, also, is one of the principal pa-rameters that affects the magnetic properties and was found byRef. [2] to be in relationship with the temperature. In addition, thesubstituted amount has a non-neglected effect on the grain sizegiving rise to different magnetic features [12].

Here, an interesting effect on the hysteresis loops is discussed interms of surface and interparticle interactions resulting from anincrease of the cobalt amount. We investigate, to our knowledge,for the first time the effect of a high cobalt amount substituted iron

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522514

on cobalt ferrite using this synthetic technique on the magneticproperties.

2. Experimental procedure

Samples of CoxFe3-xO4 (x¼ 1 (S1), 1.2 (S2), 1.4 (S3), 1.6 (S4), 1.8(S5)) were synthesized by a solvothermal chemical route [13]. Allsamples were characterized by X-ray diffraction (XRD) using aSiemens D5000 diffractometerworking with Cu Ka radiation in therange of Bragg angles between 20 and 80�. The scanning rate is of0.033� at room temperature. Morphology, grain size and chemicalcompositions of the nanoparticles were determined by Trans-mission Electron Microscopy (TEM), coupled with EDS, using aJEOL2010 FEG microscope operating at 200 kV. Magnetic mea-surements were carried out using a Vibrating Sample Magnetom-eter (VSM) at several temperatures ranging from 10 to 300 K. Zerofield cooling (ZFC) curves were taken at an applied field of 100 Oefrom 40 to 320 K.

3. Structural and magnetic results

3.1. Structural characterization

Fig. 1 shows X-ray diffraction patterns acquired for all sampleswith different cobalt contents which could be indexed in a spinel

Fig. 1. XRD patterns for CoxFe3-xO4 samples (a) and an example of fitted diagram forx¼ 1 (b).

cubic structure. No addition peaks were detected proving a goodhomogeneity of elaborated samples. The lattice parameter wasextracted from Rietveld refinement method of the diagrams usingFullProf software. An example of the fitted one is given in Fig. 1b forx¼ 1 ðc2 ¼ 1:14Þ. Fig. 2 displays the dependence of the latticeparameter on the cobalt content. S1 (CoFe2O4) was found to have alattice parameter of about 8.4 Å which matches the value reportedin the literature [13]. As the cobalt amount increases, the latticeparameter has been found to slightly decrease.

It is worthy to note that when a solid substitution takes place,the lattice parameter follows the known Vegard's law [14,15]. Thisis due to the difference between the atomic radius of cobalt andiron. Nevertheless, a monotonic decrease of the lattice parameter isobserved in this work. This behavior hasto be taken into consid-eration. First of all, it is a deviation from the Vegard's law as it hasbeen observed in several works [16], which could be due to severaleffects. For spinel ferrites, the cell parameter can be calculatedusing the formula [17]:

atheoretic ¼8

3ffiffiffi3

p ��ðrA þ R0Þ þ

ffiffiffi3

pðrB þ R0Þ

�(1)

where rA, rB and R0 are the tetrahedral, the octahedral and theoxygen radius respectively. As it can be seen from the equationabove, the lattice parameter is very sensitive to the cationic dis-tribution. Furthermore, the oxidation state is also an importantparameter that cannot be neglected regarding the fact thatFe3þðCo3þÞ has a less radius than Fe2þðCo2þÞ.

As it has beenmentioned above, an amount of Co2þ (till 24%) canbe located in the tetrahedral sites. When x exceeds 1, this ratio canvary, an oxidation of Co2þ to Co3þ [18] can occur and/or a non-stoichiometry caused by the absence of some oxygen anions as inMgxFe3-xO4 [19]. One concludes that so many important factors areresponsible for determining the structural details.

Table 1 lists the EDS analysis of the cobalt content. A deviationfrom the nominal values for S4 and S5 has been found. This maycome from supersaturating or other parameters which still not wellunderstood. Fig. 3 illustrates TEM images corresponding to S1, S3,S4 and S5 samples. From these images, one notes that the nano-particles have almost spheroid shape. Fig. 4 displays the crystalliteand grain size, estimated using the Scherer's formula and TEMdistributions analysis (see Fig. 5) respectively. It can be seen thatthe sizes are fairly dependent on the cobalt content. S4 and S5 havebeen found to present the smallest sizes. Note that, the

1,0 1,2 1,4 1,6 1,8

8,38

8,40

8,42

Latti

ce c

onst

ant (

)

cobalt content x Fig. 2. Cell parameter as a function of the cobalt content x.

Table 1Mean composition of the CoxFe3-xO4nanoparticles.

Labels x nominal x measured by EDS analysis

S1 1 1S2 1.20 1.19S3 1.40 1.32S4 1.60 1.34S5 1.80 1.50

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522 515

nanoparticles for S4 (see Fig. 3) are rather agglomerated whencompared to the other samples.

The nanoparticles have a spheroid shape except for x¼ 1.8where particles have an irregular shape.

Regarding the low sizes of the particles, the spin reversal dy-namics will be directly affected because both exchange and dipolarinterparticle interactions will be affected [20].

4. Magnetic measurements

The sizes of the nanoparticles are less than 10 nm (see Fig. 4).These sizes may present the superparamagnetic behavior [2]. Wehave performed Zero Field Cooling (ZFC) measurements in thetemperature range between 10 and 320 K under an applied field of100 Oe. Fig. 6 shows the measurements for all cobalt contents. Notethat as the cobalt content increases the maximum of the peaks

Fig. 3. TEM images for CoxFe3-xO4 (x¼ 1:

become more and more broad. This result provides a wide particlesize distribution as confirmed also by TEM analysis.

Fig. 7aee display hysteresis loops for the whole samples recor-ded at 10, 50,150, 250 and 300 K. As the temperature and the cobaltcontent increase, hysteresis shape and parameters (coercive field:Hc, saturation magnetization: Ms and remanence magnetization:Mr) exhibit a noticeable variations. At 300 K (Fig. 7d), CoFe2O4 hasthe typically hysteresis loops behavior for soft ferrimagnetic ma-terials with a coercive field of 263 Oe comparable to the valuefound by Zhang et al. [21] for comparable sizes and a saturationmagnetization Ms¼ 79 emu/g, close to the bulk value (80 emu/g)[17]. The other samples present the superparamagnetism behavior.At 10 K (Fig. 7a), S1, S2 and S3 behave as a ferrimagnetic systemswith an increase of the coercive field due to the decrease of thermalagitation [21]. The samples (S4 and S5) with the highest cobaltamount, exhibit a strange dependence of the magnetization on theapplied magnetic field at low temperatures (Fig. 7b and d); a jumphas been occurred in the field-range from 0 to 0.45 kOe.

5. Discussion

5.1. Hysteresis shape

The behavior (see Fig. 7) found on the hysteresis loops can berelated to different effects. Raghunathan et al [22] have found a

a, x¼ 1.4: b, x¼ 1.6: c and x¼ 1.8: d)

1,0 1,2 1,4 1,6 1,84

6

8

10

Size

(nm

)

cobalt content x

XRD, sherrrer formula TEM

Fig. 4. Crystallite and grain sizes as a function of the cobalt content (from TEM andXRD measurements).

40 80 120 160 200 240 280 320

0,00

0,05

Mom

ent (

emu)

Temperature (K)

x=1 x=1,2 x=1,4 x=1,6 x=1,8

CoxFe3-xO4

Fig. 6. ZFC measurements for samples CoxFe3-xO4.

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522516

similar behavior by applying a compressive stress on electricalsteels. Antunes et al [23] have found this behavior in Er(Co, Mn)O3perovskite systems by a systematic substitution. Using the samechemical synthesis route and changing the temperature, C. Vaz-quezeVazquez et al [2] found this kind of jump. They associated itto surface contribution regarding the sizes of their nano-particles.Nevertheless, Zysler et al. [24] have studied the interpar-ticle interactions effect in ðFe0:2Ni0:74Þ50B50 and they showed that it

4 6 8 10 120

20

40

60

80

num

ber o

f nan

opar

ticle

s

size (nm) (x=1)

(a)

4 6 8 100

20

40

60

80

num

bre

of n

anop

artic

ules

size (nm) (x=1,6)

(c)

Fig. 5. Size distributions for

strongly affects the shape of the hysteresis loop at low temperature.Zhang et al. [21] observed at 10 K for CoFe2O4 a drop in the hys-teresis loop nearby 0 applied fields and they related it to the exis-tence of soft phases. However, their Kneller's law fit showed theexistence of interparticle interaction which can contribute to thedrop as well as additional soft phases.

Note that the drop observed in the work of Zhang et al [21] hasbeen observed for S2 in our work but with a less magnitude. Interms of surface anisotropy magnitude, Kachkachi et al [25] dis-cussed how the strength of this jump would be.

5 6 7 8 9 10 11 120

20

40

60

80

size (nm) (x=1,4)

(b)

4 6 8 100

20

40

size (nm) (x = 1,8)

(d)

different Co contents.

Fig. 7. Hysteresis loops: (a) for S1, S2 and S3 at 10 K (b) for S4 and S5 at 10 K. (c) for S5 at 50, 150 and 250 K. (d) for S1-5 at 300 K and (e) a zoom of S2 (x¼ 1.2) at 10 K.

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522 517

According to the results reported in the literature, our magneticresults with the structural results as TEM images, the low sizes andthe HRTEM analysis for S5 both, interparticle interactions andsurface effects could be the cause of the behavior found for S4 andS5. Furthermore, S4 and S5 present the lowest sizes: 4.8 and 6.2 nmrespectively. These sizes are small enough to exhibit an importantmisalignment surface spin layer [26] which will have an importantrole on the spins reversal dynamic. Comparing hysteresis loops ofS4 and S5, one can conclude that the effect strength is different. Asthe temperature increases, these effects vanish at temperatureshigher than 100 K (see Fig. 7c).

6. Saturation magnetization and magnetic moment

In this part, the saturation magnetization MS, the magneto-cristalline anisotropy deduced from MS, the effective anisotropy

deduced from ZFC measurements are discussed. A comparativestudy will be done between the two kinds of anisotropy in order toaccentuate surface effects.

Even at high applied magnetic field (60 kOe), hysteresis loopsdon't exhibit any saturation. It is a direct consequence of a spinmisalignment at the surface and reflects also that a fraction of thenanoparticles still in a relaxation state even at low temperature[27]. Nevertheless, the magnetization dependence on the magneticfield tends to saturatewhen the temperature increases (Fig. 6c). Thesaturation magnetization Ms can be fitted using the high field partof M (H) chosen between 0.99 Mmax and Mmax using the followingequation [28]:

MðHÞ ¼ Ms��1� b

H2

�(2)

H is the applied magnetic field and b is a fitting constant.

0 100 200 30030

60

90

x = 1,8

x = 1,6

x=1,4 x = 1,2

x = 1

MS (e

mu/

g)

Temperature (K)

symbols : exp-datalines : Bloch's law fit

Fig. 9. Ms dependence on temperature.

Fig. 10. The magnetic moment by formula unit dependence on the cobalt content x.

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522518

Fig. 8 displays the dependence of Mson the cobalt content x.Fig. 9 (symbols) shows the dependence of Msvs the temperature.Ms has been found to decrease with increasing the cobalt content xas well as increasing the temperature for each sample. At 10 K, thehighest and lowest values of Ms were 102 and 49 emu/g for com-positions x¼ 1 and 1.8 respectively (Fig. 8). However, it is notice-able that as x increases the decrease of theMs is getting to be faster.This could be related to the decrease of the particle size [29], thecationic distribution [30] and the oxidation state, Co3þ beingdiamagnetic [31]. Indeed, according to Neel's law, the magnetiza-tion of ferrites by formula unit can be calculated using the relationgiven by Ref. [17]:

m ¼ mB � mA (3)

where mB and mA are the magnetization of the octahedral B and thetetrahedral A sites in units of Bohr magneton mB. From the exper-imental values of the Ms, the magnetization by formula unit can becalculated using the formula [32]:

m ¼ M�Ms

5585(4)

M is the molecular weight.Fig. 10 exhibits the dependence of the magnetic moment by

formula unit m vs x, calculated using the Eq. (4). A perfect antifer-romagnetic alignment for CoFe2O4 in an inverse spinel structureleads to m ¼ 3mB. The normal structure gives m ¼ 7mB. S1 presentsm ¼ 4:27 mB which is a clear confirmation of the existence of mixedspinel structure. At 300 K, the value found is fairly agreed withthose reported in the references [17,32]. The difference from liter-ature could be related to the cationic distribution as a result of thesynthesis technique.

Fig. 11 shows the Mr to Msratio, values are around 0.5. For non-interacting particles, Stoner and Wohlfarth expected a remanenceto be half of the saturation magnetization [33]. S1 has a value of 0.6whereas for S4 and S5 Mr/Ms less than 0.5. For grain sizes smallerthan 20 nm [1], the remanence has been found to be greater ofabout 15% relative to 0.5 (20% in this work). This could be related tothe strength of exchange interactions between neighboring grains[34]. Moreover, S4 and S5 exhibit 0.43 and 0.46 as Mr to Msratiocomparable to Tung and al values [35] obtained for CoFe2O4. As itwas seen in hysteresis loops how surface moments and interpar-ticle interactions manifest, the decrease in the remanence may

1,0 1,2 1,4 1,6 1,8

60

80

100

MS-1

0K [e

mu/

g]

Cobalt content xFig. 8. Ms vs the cobalt content x at 10 K.

become evidence. Indeed, when the applied field shuts to zero(from its maximum value expecting to saturate the whole mo-ments), the maintaining of the spontaneous magnetization in thesystem is ensured by the exchange interactions between neigh-boring moments first, second between grains in the case of highly

1,0 1,2 1,4 1,6 1,8

0,44

0,48

0,52

0,60

MR

/MS-1

0K

Cobalt content x

Fig. 11. Mr to Msratio vs the cobalt content.

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522 519

interacting particles. So, surface moments don't have the sufficientexchange interaction resulting from the lack of neighboring mo-ments resulting of a rapidly decrease relative to the core. That iswhy S4 and S5 present the smallest remanence.

7. Magnetic anisotropy

According toMr toMsratio values, it is permitted to assume thatsamples have an axial anisotropy [35-37]. For cubic anisotropy, thisratio is about 0.85 too high than our results. Hence, for a poly-crystalline assembly of nanoparticles when neighboring magneticexchange interactions can be neglected (Mr/Msy 0.5) the effectiveanisotropy constant K can be deduced from the approach to satu-ration law and it is given by Ref. [31]:

Keff ¼�1058

�b�1=2

�MS (5)

Here b and Ms have the same significance as in Eq. 2. Using thislast equation, the effective anisotropy constant Keff has beendeduced for the whole samples and for each temperature. Fig. 12presents Keff as a function of the temperature for the whole sam-ples. It is clear that Keff is strongly dependent on the temperatureand the cobalt content x. This behavior has been also found byAdolfo et al [38] for nanoparticles prepared by combustion reactionmethod. The difference could be related to the synthesis methodthat has been led to different grain sizes which is an importantparameter governing the magnetic properties for single domainparticle. For all samples, the highest anisotropy constant has beenobserved at low temperature then it is reduced to its half value at300 K. In the work of Adolfo et al [38], a much more sensitivity totemperature has been found,: for example in CoFe2O4, Keff de-creases from ~40*106 erg/cm3 at 4 K to ~8*106 erg/cm3 at 272 K for agrain size about 48 nm, higher than in this work (~7 nm for S1). Itwas reported in the literature [39] that CoFe2O4 in its bulk stateexhibits an anisotropy constant being in the range of2.1e3.9 * 106 erg/cm3 at room temperature. Nevertheless, anenhancement of Keff has been observed (2e3 times larger) and wasdiscussed as the resulting from exchange interactions betweenneighboring grains [40]. In this work, S1 shows much moreenhancement of K (1.027*107 erg/cm3) at room temperature rela-tive to the bulk value and it is in the order of 10 times larger thanvalues reported on [38,39]. Hence, it becomes evidence that

0 40 80 120 160 200 240 280

8,0x106

1,2x107

1,6x107

2,0x107

2,4x107

K(e

rg/c

m3 )

Temperature (K)

x= 1x=1,2x=1,4x=1,6x=1,8

Fig. 12. effective anisotropy constant for CoxFe3-xO4 samples as a function of thetemperature.

reduction grain size would affect inter-particle interactions andmanifests on the macroscopic magnetic properties as the anisot-ropy energy and the coercive field.

Unlike in Ref. [38], where the highest anisotropy constant isfound for CoFe2O4, our data grants the highest value for Co1.2Fe1.8O4when temperature changes from 10 to 300 K. This can be explainedas follow: first of all, it may advisable to know that the magneto-cristalline anisotropy is affected by two competing factors: thespineorbit coupling and the distortion of the octahedral symmetryproduced by oxygen anions [31]. It has been reported byRefs. [41,42] that Co2þ located on octahedral sites might ensure thedominant contribution to the anisotropy energy. So, one can believethat S2 presents the highest Co2þ amount which has been lead tothe highest anisotropy constant. Moreover, when replacing Fe3þ byCo2þ one affects the spineorbit coupling strength according to thezero orbital moment of Fe3þ [43]. As x increases, the anisotropyconstant drops after reaching its maximum value for S2 (x¼ 1.2). Itis worthy to note that the decrease of the lattice parameter hasbeen reported to be due to the presence of Co3þ, the possiblemigration of Co2þ from B to A sites and the possible existence ofvacancies. These causes will have a remarkable effect on the crystalfield (shrinkage of the lattice parameter leads to a distortion of theoctahedral crystal field). Then a decrease of the strength of the spinorbit coupling, originates from the diamagnetic behavior of Co3þ

ð0 mBÞ [31], takes place.For monodomainenanoparticles, the magnetocristalline anisot-

ropy constant can be deduced from ZFC measurements usingTBvalues and the Neel-Brown relaxation law written as follow:

KZFC ¼ 25KBTBV

(6)

where KB is the Boltzmann constant and V is is the mean volume[44]. Fig. 13 shows KZFC vs x. When increasing x, KZFC shows aweakly variation till x¼ 1.4 and a rapid increase for x¼ 1.6 and 1.8.This dependence has been found in our group by Ajroudi et al [45].One comparing the kinds of estimation, the second one is muchmore sensitive to the size of the system. This dependence of KZFC onx is a clear evidence of finite size effects. Probably, using the law ofapproach to saturation the additional anisotropies as shape, strainand surface anisotropies were underestimated. For the two kinds ofanisotropies, values are close but with two different behaviors.

At this stage, one can predict that the behavior found on thehysteresis shape for x¼ 1.6 and 1.8 is due to the existence of surfaceeffects.

1,0 1,2 1,4 1,6 1,8

7,0x106

1,4x107

KEF

Fer

g/cm

3

cobalt content x

Fig. 13. Effective anisotropy deduced from ZFC measurements.

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522520

8. Surface effects

For ordered magnetic systems, the temperature dependence ofthe magnetization is related to the presence of low energy collec-tive excitations known as magnons [46]. This phenomenon mani-fests by a decrease of the spontaneous magnetization as thetemperature increases. Thus, it allowed the development of a po-wer law that describes the dependence of the saturation magne-tization on the temperature known as Bloch T3=2 law and given byRefs. [35,47]:

MSðTÞ ¼ MSð0Þð1� B�TaÞ (7)

whereMSð0Þ is the saturation magnetization estimated at 0 K and Band a are the Bloch constant and exponent which are size andstructure dependent [48,49]. It was reported in literature that Bincreases as the size decreases and Bsurface may be in order ofmagnitude 10 times larger than BBulk. For bulk CoFe2O4, NiFe2O4and Fe3O4 [2] a is equal to 2 and fits well the experimental data.Nevertheless, a value of 1.5 has been found to also fit Ms (T) inMgxFe3�xO4 [48] for sizes range from 35 to 50 nm which is higherthan in this work. Hence, it is clear that Bloch's law parameters arestrongly structure and atomic features dependent as well as theexchange energy [9] which has been extracted from Bloch constantand found to be dependent on the Mg content [48].

Fig. 9 displays the fitting of the Ms using the Eq. (5). Fig. 14shows the dependence of a and B on x: as x increases, a de-creases. The highest value, 1.75, is assigned to S1 (CoFe2O4) and thelowest value, 1.39 to S5 (Co1.8Fe1.2O4). B has been found to increasewith increasing x. S1 has a value of 9.97 10�6 K�1.75, S5 has a valueof 9 10�5 K�1.39. So, a decreases and BeS5 is about 10 times largerthan BeS1. From these results, we believe that the observed jumpin S4 and S5 is mainly due to surface effects and are more pro-nounced in S5. The dependence of a on the particle's diameter hasbeen studied by Ngo et al [50] and the results are similar to ourresults; an increase of a with increasing particle size.

12 x=1

9. Coercive field and interparticle interactions

From M (H) curves, the coercive field HC has been extracted andthe data are plotted in Fig. 15 (symbols). It can be shown that HCdepends on both the temperature and the cobalt content. Suchbehavior has been observed for CoFe2O4 nanoparticles [2] and formanganese-substituted cobalt ferrite by Melikhov et al [42]. HCincreases when the temperature decreases for all the samplesexcept S4 (1.6) which exhibits a weak value relative to the other

Fig. 14. Bloch's law constants dependence on x.

samples even at 10 K. This out of range value is due to the presenceof aggregated nanoparticles as shown by TEM image (Fig. 3c).

The main parameters influencing the coercive field are the grainsize [51] and the microstructural features, although, the magneticexchange interactions [52] which depend on the cationic distri-bution. Sample's sizes are found to be weakly dependent on thecobalt amount whereas the dependence of the coercive field on thesize seems to be not totally affected at 10 K. Samples S1, S2 and S3exhibit very similar values 10.7, 9.5 and 11 kOe respectively, at 10 Kand found to be higher than those reported by Refs. [2,21]. Refer-ring to M (H) curves recorded at 300 K (Fig. 7d), S2, S3, S4 and S5have no hysteresis. This feature is the footprint of the super-paramagnetism [51] behavior at room temperature. The depen-dence of the coercive field on the grain size will be governed by thevolume and the anisotropy energy as it was described by Neel [51].Fig. 16 shows HC dependence of the cobalt content x at 300 K. It isclear that the cobalt content has affected the coercive field throughthe anisotropy energy unlike the behavior found for 10 K.

Fig. 17 presents the blocking temperature (TB) as a function ofthe cobalt content x. It is estimated as the maximum of ZFC curvesfor single non-interacting mono-domain nanoparticles [2]. TBalmost decreases with x originate from the overcoming of thebarrier anisotropy energy KV by the thermal fluctuations. Thedecrease of TB is mainly related to the decrease of the anisotropyeffective constant K.

For non-interacting single domain magnetic nanoparticles, thedependence of the coercive field on the temperature has beenfound to follow an empirical law known as the Kneller's law [52]given by:

HC ¼ HC0� 1�

�TTBK

�0:5!

(8)

HC0and TBK are the coercive field at 0 K and the superparamagnetic

blocking temperature. From this fit, the Kneller's blocking tem-perature (TBK) has been extracted and the results are plotted inFig. 17. One can note that the results are in fairly agreement withvalues estimated using ZFC for all cobalt content except for x¼ 1.6where Kneller's law fit value deviates from the value estimatedform ZFC value. This discrepancy reflects the strength of theinterparticle interaction [21]. Because S1-ZFC's curve presents thesharper peak, the difference between the value estimated from ZFCcurve and the value extracted from the Kneller's law fit is the

0 100 200 300

0

6

HC

(kO

e)

Temperature (K)

fit x=1 x=1,2 fit x=1,2 x=1,4 fit x=1,4 x=1,6 fit x=1,6 x=1,8 fit x=1,8

Fig. 15. Coercive field dependence on the temperature for CoxFe3�XO4.

1,0 1,2 1,4 1,6 1,8

0,0

0,1

0,2

0,3H

C-3

00 K

(kO

e)

Cobalt content x

Fig. 16. HC dependence on the cobalt content x at 300 K.

1,0 1,2 1,4 1,6 1,8

240

260

280

300

320

Tem

pera

ture

(K)

Cobalt content x

TB from ZFC measurment

TB from Kneller's law fit

Fig. 17. Blocking temperature versus cobalt content x for CoxFe3�xO4 samples.

M. Saidani et al. / Journal of Alloys and Compounds 653 (2015) 513e522 521

minimum. One notices the existence of a non-neglected disparityfor x¼ 1.2 (S2). 10 K hysteresis loop for S2 displays a drop nearby0 applied filed (see Fig. 7E). This result confirms the discrepancybetween TB and TBK and it originates from interparticle interactionsas discussed above. S1, S3 and S5 display weak deviation relative toS2 and S4 reflecting neglected or very weakly interparticleinteractions.

10. Conclusions

We have studied the effect induced by the substitution of cobaltby iron following the formula CoxFe3�xO4 (1� x< 1.8) using a sol-vothermal route. We have found that the higher cobalt content(x¼ 1.6 and 1.8) samples (S4 and S5) is the subject of finite sizes andsurface effects. At low temperature, themoments at the surface actson the magnetization by a jump on the hysteresis loops, a rapiddecrease of the magnetization nearby zero applied fields. We haveconfirmed the surface effects by the magnetic anisotropy estimatedfrom ZFC measurements and the fitting of the saturation magne-tization dependence on the temperature to the power Bloch T3/2

law. B and a, which are the Bloch's law constants, have been foundto be very dependent on x. The blocking temperature and themagnetocristalline anisotropy energy have been found to decreasewith increasing x. This has been related to the presence of Co3þ as

diamagnetic cations which act on the exchange energy CoeOeFe.An agglomerated particles like have been observed for S4 (x¼ 1.6)by TEM. The magnetic response has been confirmed by its effect onthe coercive field, the aggregated nanoparticles have allowed tohigh interparticle interactions. The interparticle interactions havebeen confirmed by means of the discrepancy found between theKneller blocking temperature, estimated from the Kneller's law fitof the coercive field dependence on the temperature, and theblocking temperature TB.

In the future, we plan to study the surface effects, the cationicdistribution by means of the 57Fe Mossbauer Spectroscopy.

Acknowledgment

This work was supported by the ‘‘Minist�ere de l'EnseignementSup�erieur, de la Recherche Scientifique’’, Tunisia and l'AgenceUniversitaire de la Francophonie (AUF) via the scholarship program“Eugen Ionesco”. We thank also the Sectoral Operational Pro-gramme Human Resources Development (SOP HRD), financed fromthe European Social Fund and by the Romanian Government underthe project number POSDRU/159/1.5/S/134378 and by the struc-tural founds project PRO-DD (POS-CCE, O.2.2.1., ID 123, SMIS 2637,ctr. No 11/2009) for providing the infrastructure used in this work.

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