Nanoscale

PAPER

Cite this: Nanoscale, 2015, 7, 17764

Received 2nd July 2015,Accepted 26th September 2015

DOI: 10.1039/c5nr04424c

www.rsc.org/nanoscale

Superparamagnetic versus blocked statesin aggregates of Fe3−xO4 nanoparticlesstudied by MFM†

Carlos Moya,*‡a Óscar Iglesias-Freire,‡b,c Xavier Batlle,a Amilcar Labartaa andAgustina Asenjob

Magnetic domain configurations in two samples containing small aggregates of Fe3−xO4 nanoparticles of

about 11 and 49 nm in size, respectively, were characterized by magnetic force microscopy (MFM). Two

distinct magnetic behaviors were observed depending on the particle size. The aggregates constituted of

nanoparticles of about 11 nm in size showed a uniform dark contrast on MFM images, reflecting the pre-

dominant superparamagnetic character of these particles and arising from the coherent rotation of the

spins within the aggregate as the latter align along the tip stray-field. By applying a variable in-plane field,

it is possible to induce magnetic polarization yielding an increasing dark/bright contrast as the strength of

the applied field overcomes the stray-field of the tip, although this polarization completely disappears as

the remanent state is recovered when the magnetic field is switched off. On the contrary, for aggregates

of NPs of about 49 nm in size, dark/bright contrast associated with the existence of magnetic domains

and magnetic polarization prevails in MFM images all along the magnetic cycle due to the blocking state

of the magnetization of these larger particles, even in the absence of an applied field. All in all, we un-

ambiguously demonstrate the capabilities of magnetic force microscopy to distinguish between blocked

and superparamagnetic states in the aggregates of magnetic nanoparticles. Micromagnetic simulations

strongly support the conclusions stated from the MFM experiments.

Introduction

Magnetite nanoparticles (NPs) have been the focus of a lot ofinterest due to their easy production by chemical methods,1

remarkable magnetic properties2,3 and relatively low toxicity,4

all of which make these NPs suitable candidates for potentialapplications in biomedicine, such as contrast agents in mag-netic resonance imaging (MRI),5 drug delivery6 and hyperther-mia7 among others,8 and in technology, such as in magneticrecording.9,10 In addition, they are ideal systems to studyfinite-size effects, yielding new phenomena and enhanced pro-perties with respect to their bulk-counterparts.11 One of the

most common finite-size effects is superparamagnetism (SPM)which not only depends on the particle volume but it is also atime-dependent phenomenon due to the stochastic nature ofthe thermal activation energy.11,12 Thus, for non-interactingparticles, the observed magnetic behavior depends on the rela-tive characteristic value of the acquisition time, τm, of thespecific experimental technique with respect to the relaxationtime, τ, associated with the probability of the spins to over-come the energy barriers for magnetic anisotropy.11,12 Inaddition, the SPM regime limits the use of NPs in severalbioapplications and magnetic recording.11 Consequently,special attention has been paid to obtain an accurate dynami-cal magnetic characterization in order to distinguish betweenthe SPM and blocked regimes of the net magnetization of NPensembles. The majority of these studies have been performedby measuring both DC (τm = 100 s) and AC susceptibilities(τm = 10−1–10−5 s for typical experiments), Mössbauer spec-troscopy (τm = 10−7–10−9 s) and neutron scattering (τm = 10−8–10−12 s).13,14 A common downside of all these standard charac-terization techniques lies on the fact that they only provideaverage information over a very large number of NPs. On thecontrary, the direct observation of either a single particle orsmall clusters of NPs is available by magnetic force microscopy

†Electronic supplementary information (ESI) available: PDF material containsTEM images for samples R11 and R49 (Fig. S1), thermogravimetric curves forsamples R11 and R49 (Fig. S2) and the calculated relaxation time from Arrheniuslaw for a single Fe3−xO4 NP following Néel relaxation (Fig. S3). See DOI: 10.1039/c5nr04424c‡These two authors contributed equally.

aDepartament de Física Fonamental, Institut de Nanociència i Nanotecnologia,

Universitat de Barcelona, Barcelona, 08028, Spain. E-mail: cmoya@ffn.ub.esbInstituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, Madrid

28049, SpaincDepartment of Physics, McGill University, Montreal, H3A 2T8, Canada

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(MFM).15–19 MFM has proved to be a versatile technique, bymeans of which it is possible to study the real time evolutionof the magnetic domains by variable-field MFM (VF-MFM)20 orto characterize the evolution of MFM contrast versus the tip–sample distance by the 3D mode, allowing a complete charac-terization of the small structures.21,22 In addition, micro-magnetic simulations performed with the Object OrientedMicromagnetic Framework (OOMF) code constitutes an idealtool to interpret the experimental MFM images.23

Within this framework, we have addressed the study of SPMand blocked regimes of aggregates by MFM experiments ontwo samples of Fe3−xO4 NPs with mean diameters of 11 nm(R11) and 49 nm (R49), respectively, that were synthesized bythermal decomposition of organic precursors.24,25 SPMs andferrimagnetic blocked NPs were independently observed andwere fully differentiated for samples R11 and R49, respectively.Interestingly enough, the 3D mode and VF-MFM experimentswere carried out, aiming at studying the influence that thestray field emerging from the MFM tip has on the magneticstate of the sample, so as to avoid artifacts and misinterpreta-tion of data when images corresponding to the SPM andblocked regimes were compared. Finally, micromagnetic simu-lations were used to gain some insight into the differentmechanisms taking place during magnetization reversal.

Sample preparation

Fe3−xO4 NPs were prepared by high-temperature decompo-sition of Fe(III)–acetylacetonate with decanoic acid as thecapping ligand in an organic solvent, as reported else-where.25,26 It has been shown that a wide range of mono-disperse particle sizes can be obtained depending on therelative concentration of the reactants and the temperatureprofile of the reaction.25,26

Sample R11. For 11 nm NPs, 5 mmol of decanoic acid weremixed with 1 mmol of Fe(III)–acetylacetonate in 25 mL ofdibenzyl-ether. First of all, the solution was heated up to200 °C at a constant rate of 6.5 °C min−1 under a nitrogenatmosphere with vigorous stirring. After 2 h at 200 °C, the reac-tion mixture was heated up to 270 °C and maintained at thistemperature for 1 h. Finally, the solution was cooled down toroom temperature, washed three times with ethanol and theNPs were collected by centrifugation at 9000 rpm.

Sample R49. NPs of 49 nm in size were obtained by follow-ing the same method explained before but with a larger molarratio of decanoic acid to Fe(III)–acetylacetonate (1 : 4) andsetting the temperature profile to 3.5 °C min−1 for the lastreaction stage.

Samples were stored in ethanol until final use.

Structural and magnetic characterization

The samples were prepared for transmission electronmicroscopy (TEM) (MT80-Hitachi microscope) by placing onedrop of a dilute NP suspension onto a carbon-coated coppergrid and drying at room temperature. The size distribution wasanalyzed by measuring at least 2000 particles and the resultinghistograms were fitted to log-normal functions (see Fig. 1dand e and S1a and b, ESI†). The particles in both samples werefound to be the faceted (see Fig. 1a and b) and single-crystaldomains of 11 and 49 nm in mean size, respectively. The stan-dard deviation of the size distribution was 6 nm for R11 and30 nm for R49.

The crystalline phase of the iron oxide particles was identi-fied by powder X-ray diffraction. The patterns were collectedbetween 5° and 120° in 2θ using a PANalytical X’Pert PROMPD diffractometer by using Cu Kα radiation, and they wereindexed to an inverse spinel structure (Fig. 1f). The mean par-

Fig. 1 (a) and (b) HRTEM images of samples R11 and R49, respectively. (c) Hysteresis loops of Fe3−xO4 NPs at 300 K. Blue circles: sample R49, blackcircles: sample R11. Inset: details of the low field region, (d) and (e) show the particle size distribution for R11 and for R49, respectively, (f ) X-raydiffraction pattern with the indexation of the Bragg peaks to an inverse structure for R11 (black line) and for R49 (blue line).

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ticle diameters obtained from the XRD data (DXRD) were 11 ±0.5 nm for R11 and 45 ± 2 nm for R49, which are in goodagreement with the estimations from TEM. This also confirmsthe high crystalline quality of the samples and their single-crystal domain features.

The organic fraction of the samples was evaluated bythermogravimetric analysis (TGA). The measurements wereeffected using a TGA-SDTA 851e/SF/1100 (Mettler Toledo) at aheating rate of 10 °C min−1 from room temperature up to800 °C under a nitrogen atmosphere (see Fig. S2, ESI†).

Hysteresis loops M(H) were measured using a QuantumDesign SQUID magnetometer at 300 K (see Fig. 1c) to studythe coercive field (Hc) and saturation magnetization (Ms) undera maximum magnetic field of ±50 kOe. Ms was obtained byextrapolation of the high-field region of M(H) curves to zeromagnetic field, assuming the high-field behavior, M(H) = Ms +χH, where χ is a residual susceptibility.3 Ms values were nor-malized to the magnetic content by subtracting the organicfraction evaluated by TGA analyses from the sample mass. Thevalues obtained at RT were Ms = 78.0 ± 0.7 emu g−1 for R11and Ms = 84.3 ± 0.1 emu g−1 for R49. These values are justslightly smaller than the bulk one, indicating an almostperfect ferrimagnetic order throughout the whole NPs, as pre-viously observed in samples with very high crystal quality syn-thesized by the thermal decomposition method.2,3,13,26

Besides, Hc was defined as Hc = (|Hc+|+|Hc

−|)/2, where Hc+ and

Hc− are the interceptions of the hysteresis loop with the posi-

tive and negative sides of the H-axis, respectively. A magnifi-cation of the field range where these interceptions take placeis shown in the inset of Fig. 1c. The obtained values of thecoercive field are 0.8 ± 0.3 mT for R11 and 4.3 ± 0.5 mT forR49. This very small value of Hc for R11 suggests that themajority of the particles in this sample are SPMs at RT, in con-trast with the case for R49 where the magnetization of most ofthe particles remains blocked.

Magnetic force microscopy

Characterization of the aggregates by MFM. Fig. 2 showsthe topography and MFM images at remanence (zero field) ofseveral aggregates containing a few particles of samples R11(Fig. 2a–d) and R49 (Fig. 2e and f) and the corresponding topo-graphic and frequency shift profiles. The aggregates of thesmaller R11 NPs give rise to a homogeneous attractive inter-action between the tip and the sample, displayed as a uniformdark contrast in Fig. 2a–d, which is consistent with a coherentrotation of the spins within the NPs induced by the tip stray-field. This reflects the relatively low value of the net anisotropyenergy arising from the small size of the R11 NPs and, conse-quently, their predominant SPM character.

This kind of attractive tip-induced interactions is expectedto occur in either SPM NPs or very soft magnetic nano-structures, the two cases not being unambiguously dis-tinguishable by recording solely the conventional MFMimages. Therefore, care must be taken to avoid misinterpreta-tion of the MFM data, as has been previously reported.15,16,27,28

In order to confirm the SPM character of the aggregates of R11

NPs, a study of the dependence of the frequency shift on thetip–sample distance was carried out and the results are shownin Fig. 3.21,22 To perform this sort of experiments, the sameprofile across the aggregate is repeatedly scanned while the liftheight is varied from 30 to 180 nm. As shown in Fig. 3d, thefrequency shift decreases with the distance from (−1.23 ± 0.6)Hz at 30 nm to (−0.06 ± 0.42) Hz at 180 nm, accordingly with amonotonous reduction of the attractive interaction until thesignal becomes comparable to the experimental noise. Thelatter reveals that the net magnetization of the R11 aggregatesorients along the vertical direction even for very small valuesof the stray field emerging from the tip,15 which in turn con-firms the SPM character of these aggregates. However, theaggregates of R49 NPs yield MFM images with well-definedmagnetic polarity because of the blocked state of their netmagnetization at RT (see Fig. 2e and f).

The characterization by MFM imaging of these aggregateshas revealed two situations with regard to the interactionbetween the stray-fields of the tip (Btip) and that generated by

Fig. 2 The remanent state. (a)–(f ) Topographic AFM (left row) and MFMimages (center row) of six different clusters of Fe3−xO4 NPs (R11: (a)–(d),R49: (e) and (f )), measured at remanence after in-plane magnetic satur-ation along the horizontal axis of the images. Right-most column:height (red solid line) and frequency shift (blue solid line) profiles of thestudied clusters (R11 and R49, respectively).

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the sample (Bsample). For sample R11, Btip > Bsample and aggre-gates are observed to be in a SPM regime, while for sampleR49, Btip < Bsample and a blocked state of the sample magneti-zation with well-defined magnetic polarity is clearly displayedin the MFM images.

Variable field MFM study

A deeper insight into the magnetic nature of these particleaggregates can be gained by recording VF-MFM images as afunction of an in-plane applied magnetic field. The results areshown in Fig. 4 for three cases recorded, respectively, at zerofield and with a field of 82 mT applied in opposite in-planedirections. Similar magnetic domain structures with oppositepolarities can be observed when comparing images at theopposite values of the applied field for R11 aggregates (seeFig. 4a–d). Considering that these aggregates are SPMs at zerofield, the observed magnetic polarization can be understood asjust induced by the action of the external magnetic field, sincethe associated dark/bright contrast progressively disappearsbecoming only a dark contrast as the magnitude of the field isdecreased to zero (see the central panels in Fig. 4a–d). So thein-plane polarization is imprinted in the aggregates when thestrength of the applied field is large enough to overcome theattractive interaction between the sample and the stray-field ofthe tip. On the contrary, magnetic domains within the R49aggregates are not totally saturated at 82 mT and non-sym-metric states of the magnetization polarization are observedon both sides of the magnetic cycle (see Fig. 4e and f). At thesame time, the dark/bright contrast prevails along the wholemagnetic cycle since the net magnetization of these large par-ticles remains blocked during the acquisition time of theMFM images.

A detailed sequence depicting the reversal processes of themagnetic domains for the R49 aggregates shown in Fig. 4e is

presented in Fig. 5a. A single domain configuration isobserved on both sides of the magnetic cycle and along muchof the way down to remanence, indicating that the aggregatebehaves predominantly like a macro-spin. Interestingly, as thefield direction is reversed from negative values a multi-domain

Fig. 3 (a) Topography of a cluster of NPs for R11. (b) Height profile ofthe studied cluster. (c) MFM image of the cluster in (a). (d) Variation ofthe frequency shift from 30 to 180 nm lift height in a 3D experiment.

Fig. 4 The domain polarity. Topographic (left) and MFM images (right)of the same NPs in Fig. 2(a)–(f ) [(a)–(d) for R11 and (e) and (f ) for R49],in the presence of in-plane horizontal magnetic fields with oppositedirection (±82 mT) and at zero magnetic field.

Fig. 5 (a) MFM images of the aggregate shown in Fig. 4e in the pres-ence of horizontal in-plane magnetic fields with variable magnitudesand directions. (b) Results of the micromagnetic simulations, for acluster of (3 × 3) 50 nm NPs with an additional cluster on the top of themiddle, showing various stages of the magnetization reversal, comparedto the MFM images squared in (a) by color frames. The arrows and colorcode indicate the correspondence between the MFM images and thesnapshots of the micromagnetic simulations.

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structure is observed, where a domain wall seems to bepresent. This multi-domain structure defines the reversalprocess until a single domain configuration is reached again,with an uncompleted reversal of the magnetization polaritybecause the magnitude of the maximum applied field is notenough to achieve complete saturation. Therefore, the largervolume of these aggregates and their multi-particle natureresult in a domain wall-mediated reversal of the magnetiza-tion, as compared to the coherent rotation of spins takingplace in isolated NPs, as reported elsewhere.18

Micromagnetic simulations

In order to gain further knowledge on the processes involvedin magnetization reversal, micromagnetic simulations werecarried out using the OOMMF free source software.23 The 3DOxsii mode was used with the following parameters: saturationmagnetization, Ms = 4.66 kA m−1 (obtained from the hysteresisloop shown in Fig. 1b); exchange stiffness constant for magne-tite,29 A = 13.2 × 10−12 J m−1; magneto-crystalline anisotropyconstant for bulk magnetite,13 k1 = 12 kJ m−3 and a cubic cellsize of (2 × 2 × 2) nm3. One should recall here that micromag-netic simulations are known to reproduce with highly reliableexperimental results in a qualitative manner, lacking ingeneral quantitative reproducibility of experiments. Thereasons for this can be attributed to thermally activated pro-cesses, the influence of structural and/or surface effects.

Fig. 5b presents a simulated distribution of the magnetiza-tion during the reversal process in a cluster of (3 × 3) 50 nmNPs with an additional cluster on the top of the middle of thesquare cluster. The external field was applied in-plane alongthe horizontal axis of the images. The apparent broadening oflateral dimensions intrinsic to AFM experiments mentionedabove might cause such a cluster to appear with similardimensions to the ones displayed in Fig. 4. The directionof the local magnetization is represented by arrows in ablue–red scale which indicates an outbound–inbound com-ponent (with respect to the image plane); the simulated MFMimage is shown in a black–white scale which stands for anegative–positive divergence of the magnetization (thus,causing the appearance of the magnetic charges to whichMFM is sensitive). The sample was initially saturated alongthe direction of negative polarity and magnetization reversalwas studied.

The snapshots of the most relevant steps within the reversalprocess are shown in Fig. 5b. A single-domain phase is againfirst observed all the way from saturation to remanence (leftimage in Fig. 5b) and even for low fields applied upon reversalof the field direction. However, the relatively large lateraldimensions of this cluster of NPs allow for the magnetizationto adopt a configuration with increasing in-plane curling. At acertain field value, a magnetic vortex is formed and magnetiza-tion reversal then takes place as the vortex moves across thecluster. The simulated MFM contrast emerging from this con-figuration reproduces up to a good extent the experimentalresults highlighted in Fig. 5a by green/yellow frames. Note thatthe exact orientation and shape of the experimental cluster

may differ from that of the simulated one. Finally, a single(but reversed) domain is again obtained.

Therefore, our simulations suggest that magnetizationreversal is mediated by nucleation and propagation of a vortexdomain wall. Additional simulations were performed in largerclusters of (4 × 4) NPs with another cluster on the top and thesame mechanism was observed.

Conclusions

MFM characterization of small aggregates of Fe3−xO4 NPs atRT reveals two distinct magnetic behaviors depending on theparticle size. The aggregates constituted of NPs of about11 nm in size show a homogeneous attractive tip–sample inter-action, displayed as a uniform dark contrast on the MFMimages, and arising from the coherent rotation of the spinswithin the aggregate as they align along the tip stray-field. Thisreflects the predominant SPM character of those small par-ticles observed within the characteristic acquisition time of theMFM technique and at zero applied field. Interestinglyenough, by applying a variable in-plane field, it is possible toinduce a magnetic polarization yielding an increasing dark/bright contrast as the strength of the applied field increasesand overcomes the stray-field of the tip. However, this inducedpolarization completely disappears as the remanent state isrecovered when the applied field is switched off. On the con-trary, for aggregates of NPs of about 49 nm in size, dark/brightcontrast associated with the existence of magnetic domainsand magnetization–polarization prevails in the MFM imagesall along the magnetic cycle, since the net magnetization ofthese large particles remains blocked during the acquisitiontime of the MFM images even at zero applied field. Therefore,the larger volume of these aggregates and their multi-particlenature yield a domain-wall mediated reversal of the magnetiza-tion, as compared to the coherent rotation of spins takingplace in either aggregates of SPM NPs or even isolated particleswith blocked magnetization. Micromagnetic simulationssuggest such walls to be formed by an in-plane magneticvortex moving across the cluster.

Experimental section

MFM measurements were carried out at RT using a VF-MFMset-up from Nanotec Electrónica.30 All experiments were per-formed using the lift mode (lift height: 40 nm), in which thetopographic profile is retraced at a tip–sample distance forwhich magnetostatic interactions become dominant. TheMFM data arise from the change in the resonance frequency ofthe oscillating cantilever induced by such magnetostatic coup-ling between the tip and sample. In all the experiments per-formed, a phase-locked loop (PLL) was used to maintain aconstant phase lag between the driving signal and the cantile-ver oscillation, so that the MFM data have units of Hz. Budget-Sensors Multi75-G tips were used with nominal values of

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the spring constant k ≈ 3 N m−1 and resonance frequencyf0 ≈ 75 kHz.

Samples for MFM observations were prepared by placingone drop of a dilute suspension of NPs onto a carbon–siliconwafer and letting it dry in an oven at 348 K for 1 h in order toremove all the remaining solvent. All images were collected at0.5 lines per s and with a resolution of 256 × 256 pixels, sothat the acquisition time was 7.8 ms per pixel. Taking this intoaccount, an estimation of the maximum size for an isolatedparticle showing SPM behavior can be calculated by assuminga typical Néel relaxation of the magnetization with a relaxationtime of about τ0 = 10−9–10−11 s and an anisotropy constant ofKv = 2−4 × 105 erg cm−3, within the typical values found inmagnetite NPs.31,32 As a result, a critical particle size of11–16 nm is estimated for the observation of the SPM regimein our MFM data (see S3, ESI†). Thus, NPs with smallerdimensions will exhibit SPM behavior and, consequently,internal magnetic domain configurations will not be observableby MFM.

It is worth noting that AFM techniques are very accurate inmeasuring vertical distances, whereas lateral dimensions ofprotruding nanostructures are unavoidably overestimated dueto the convolution of tip–sample interactions over the tip apexvolume.18 As a consequence, NPs appear wider than their realsize, whereas this convolution effect is not present in verticaldisplacements of the tip, which yields particle heights (seeFig. 2e–h) in outstanding agreement with the TEM size histo-gram shown in Fig. 1d and e. The corresponding topographicand MFM images display exactly the same location; however,magnetic features may appear offset from the topographicones, as different regions of the tip are sensitive to the inter-actions with the sample during either AFM or MFM imaging(see Fig. S4, ESI†).

Acknowledgements

This work was supported by Spanish MINECO (MAT2012-33037, CSD2010-00024 and MAT2013-48054-C2) and CatalanDURSI (2014SGR220).

Notes and references

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Paper Nanoscale

17770 | Nanoscale, 2015, 7, 17764–17770 This journal is © The Royal Society of Chemistry 2015

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