Influence of dipolar interactions on hyperthermia properties offerromagnetic particlesD. Serantes, D. Baldomir, C. Martinez-Boubeta, K. Simeonidis, M. Angelakeris et al. Citation: J. Appl. Phys. 108, 073918 (2010); doi: 10.1063/1.3488881 View online: http://dx.doi.org/10.1063/1.3488881 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v108/i7 Published by the American Institute of Physics. Related ArticlesFe3O4-citrate-curcumin: Promising conjugates for superoxide scavenging, tumor suppression and cancerhyperthermia J. Appl. Phys. 111, 064702 (2012) Integrated intravital microscopy and mathematical modeling to optimize nanotherapeutics delivery to tumors AIP Advances 2, 011208 (2012) In vitro cytotoxicity of Selol-loaded magnetic nanocapsules against neoplastic cell lines under AC magnetic fieldactivation J. Appl. Phys. 111, 07B335 (2012) Magnetically driven spinning nanowires as effective materials for eradicating living cells J. Appl. Phys. 111, 07B329 (2012) Experimental characterization of electrochemical synthesized Fe nanowires for biomedical applications J. Appl. Phys. 111, 056103 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Influence of dipolar interactions on hyperthermia propertiesof ferromagnetic particles

D. Serantes,1 D. Baldomir,1,a� C. Martinez-Boubeta,2,a� K. Simeonidis,3 M. Angelakeris,3

E. Natividad,4 M. Castro,4 A. Mediano,5 D.-X. Chen,6 A. Sanchez,6 LI. Balcells,7

and B. Martínez7

1Departamento de Física Aplicada, Instituto de Investigacións Tecnolóxicas, Universidade de Santiagode Compostela, 15782 Santiago de Compostela, Spain2IN2UB and Departament d’Electrònica, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona,Spain3Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece4Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Sede Campus Río Ebro,María de Luna 3, 50018 Zaragoza, Spain5Grupo de Electrónica de Potencia y Microelectrónica (GEPM), Instituto de Investigación en Ingenieríade Aragón, Universidad de Zaragoza, María de Luna 3, 50018 Zaragoza, Spain6Departament de Física, ICREA, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain7ICMAB-CSIC, Campus UAB, 08193 Bellaterra, Spain

�Received 23 June 2010; accepted 4 August 2010; published online 8 October 2010�

We show both experimental evidences and Monte Carlo modeling of the effects of interparticledipolar interactions on the hysteresis losses. Results indicate that an increase in the intensity ofdipolar interactions produce a decrease in the magnetic susceptibility and hysteresis losses, thusdiminishing the hyperthermia output. These findings may have important clinical implications forcancer treatment. © 2010 American Institute of Physics. �doi:10.1063/1.3488881�

I. INTRODUCTION

About half a century ago, the search of a method topasteurize the nodes which contain cancer metastases missedat surgical interventions, motivated investigations on themagnetic properties of iron oxide nanoparticles �NPs� whichwould heat appreciably at radio frequencies after injectioninto lymphatic channels.1 Since then, in vitro experimentswith magnetic fluids have confirmed their excellent powerabsorption capabilities.2 In vivo experiments have docu-mented the feasibility of this treatment in animal models ofmelanoma,3 breast tumors,4 and prostate cancer.5 Dependingon the applied temperature and the duration of heating thistreatment either results in direct tumor cell killing or makesthe cells more susceptible to concomitant radio—or chemo-therapy, thus increasing therapeutic efficiency.

The heating power of magnetic NPs is determined byseveral factors including particle type, the frequency of theradiated alternating magnetic field and the magnetic field in-tensity. Namely, there are two mechanisms to account forheat generation of magnetic of NPs less than about 30 nm indiameter: �a� Néel relaxation, that is, the fluctuation of acrystal’s magnetic moment over an anisotropic energy barrierand �b� Brown relaxation to viscous losses due to particlereorientation in solution.6 Given that, for clinical practice,7

Brownian contributions to ac losses are eliminated in thecase of immobilized particles,8 larger particles �showing fer-romagnetic hysteresis� seem a better choice for these appli-cations using alternating magnetic fields below the mega-hertz range.6

On the other hand, the losses due to magnetization reori-

entation in ferromagnetic particles depend on the type ofremagnetizing process which, besides the intrinsic magneticproperties—like magnetocrystalline anisotropy—is deter-mined in complicated ways by particle size, shape and mi-crostructure. Modeling of the performance of magnetic NPsin hyperthermia has been previously reported.9,10 However, ithas not been clarified yet if an increase in the concentrationof particles leads to an increase in the heating capacity, or toa decrease as recently suggested by Urtizberea et al.11 There-fore, the use of Monte Carlo �MC� simulation methods couldbe of valuable help to analyze the performances of ferromag-netic NPs for hyperthermia applications. Our previous resultsdemonstrated that nanostructured Fe NPs coated with a uni-form MgO epitaxial shell may act as high performancetherapy vectors with similar heating power of existing mate-rials but at much more lower doses.12 It was anticipated thata ferromagnetic coupling between NPs might result in a de-creased hysteresis and hence in a diminished heating ability.We shall report here the effect of particle concentration onthe magnetic hysteresis of the monodisperse NP assembliesby comparing our own experimental data with MC simula-tions. This study aims in the explanation of the role playedby interparticle dipolar interactions and the optimization ofthe solution properties for hyperthermia applications.

II. EXPERIMENTAL RESULTS

The studied nanostructures consist of spherical zero-valence ferromagnetic Fe particles ��75 nm� with a MgOcoating for biocompatibility. Figure 1 shows a ferromagneticbehavior well above room temperature �RT�. The effectiveanisotropy constant �K�4.5�104 J /m3� and saturationmagnetization �MS=210 emu /g� values are very close toa�Electronic addresses: daniel.baldomir@usc.es and cboubeta@el.ub.es.

JOURNAL OF APPLIED PHYSICS 108, 073918 �2010�

0021-8979/2010/108�7�/073918/5/$30.00 © 2010 American Institute of Physics108, 073918-1

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that of bulk bcc Fe. A detailed structural, morphological andmagnetic characterization of the samples has been alreadypublished.12,13 At low concentrations, particles are prone toappear in the form of interconnected chainlike structures,thus demonstrating strong dipolar interactions.14

In order to assess the effects of dipolar interactions onthe NP intrinsic magnetic properties, particles were diluted atdifferent concentrations into distilled water or ethanol. Mag-netic hyperthermia experiments were carried out under vari-ous ac magnetic fields by means of a water cooled inductioncoil of 23 mm diameter consisting of three turns, and a com-mercial generator with a power of 4.5 kW.12 The heatingefficiency is quantified by the specific absorption rate �SAR�,actually by measuring the initial slope of the temperature risebefore the effect of heat conduction becomes important.15

Adiabatic SAR measurements were performed on particlesdispersed in an epoxy matrix by a calorimetric method de-scribed in Ref. 16. Such experiments allowed quantifyingaccurately the small heating powers generated at low concen-tration and low ac fields. It is widely believed that the heat-ing effect is a result of energy absorption from the alternatingmagnetic field and its transformation into heat by means ofthe hysteresis loss during reversal of magnetization. For thatreason, and for the sake of comparison, the loss power wasalso determined from hysteresis losses in powder samplesmeasured by using a superconducting quantum interferencedevice magnetometer, by taking into account the proportion-ality of power with frequency.17 Please note that in magnetichyperthermia applications, the frequencies of the alternatingmagnetic fields are several orders of magnitude higher thanthose frequencies applied by the magnetometer to measurethe energy dissipation per cycle.

Alternative methods for quantifying SAR were also ap-plied. Still, the ac susceptibility �=��−j�� of magnetic liq-uids was measured as a function of ac field amplitude andfrequency, by using a home-made high-field acsusceptometer.18 Although a linear frequency dependence isusually assumed, in real magnetic liquids one may observedeviations from the ideal Debye-like behavior. In our case,the imaginary part of the susceptibility exhibits a maximumbelow 10 mT, where particle interactions cause a slight fre-

quency dependence in the position of the maximum. Theseeffects, illustrated in Fig. 2, are in agreement with the con-clusion drawn by Morozov et al.19 on the frequency depen-dence of the susceptibility of colloid suspensions with differ-ent particle concentrations. Such deviations have usuallybeen attributed to interparticle interactions.20

In other words, susceptibility measurements indicate aninteraction exists,21 and this interaction increases with par-ticle volume fraction. In addition, the very low relative re-manence �MR�0.2� in Fig. 1, compared to an assembly ofnoninteracting randomly oriented particles �MR=0.5�,22 ex-plains the reduction in SAR values on increasing the par-ticles’ concentration �Fig. 2�a��. It appears that increasingconcentration reduces the magnetic hysteresis due to dipolarcoupling effects, as has also been suggested in previousworks reporting similar SAR versus magnetic fieldevolution.11,23 However, the cause of such decrease remainsstill unclear, being also conjectured to originate from a broadsize distribution. Thus, with the purpose of studying the roleof magnetic dipolar interactions on the hyperthermia proper-

400 nm

-10000 -5000 0 5000 10000-240

-160

-80

0

80

160

240

M(e.m.u.perFegram)

H (Oe)

-200 -100 0 100 200

-10

0

10

FIG. 1. �Color online� Field dependent magnetization curve at room tem-perature of the Fe core/MgO shell NPs. Inset on the left shows an electronmicroscopy image of the NPs arranged in a chain resembling a magneto-some �Ref. 29�. The inset on the right exhibits minor hysteresis loops.

100 101 102

10-3

10-2

10-1

100

101 (a)

mg/ml (conditions)0.06 (non-adiabatic)0.56 (non-adiabatic)1.00 (non-adiabatic)560 (adiabatic)16 Χ103 (susceptometer)40 Χ103 (SQUID data)

SAR/f(J/kg)

Hmax (kA/m)

10-1 100 101 1020.0

0.2

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Hmax (kA/m)

30 Hz90 Hz270 Hz

FIG. 2. �Color online� �a� Magnetic hysteresis losses �SAR� in dependenceon the magnetic field amplitude for different experimental conditions andconcentrations. Adiabatic conditions refer to experiments performed follow-ing Ref. 16; nonadiabatic conditions refers to conventional hyperthermiameasurements in ferrofluids at different concentrations, and susceptometerrefers to experiments performed following Ref. 18. �b� Susceptibility mea-sured at RT as functions of ac field amplitude �Hmax� and frequency.

073918-2 Serantes et al. J. Appl. Phys. 108, 073918 �2010�

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ties of the NP system, we performed MC simulations to treatthe influence of particle concentration and field dependenceon the SAR.

III. MODELIZATION AND DISCUSSION

The physical model employed for our numerical simula-tions considers the usual approximation of single-domainmagnetic NPs with an effective uniaxial magnetic anisotropyK� ef f which may be of magnetocrystalline or shape origin. Wealso assume that every i-particle has uniform magnetizationand composition, and all its atomic moments rotate coher-ently, so that the magnetic moment of each particle is ��� �=MSV and K� ef f =KVn̂, with n̂ the unit vector along the easy-axis direction and V the particle’s volume. The spatial distri-bution of the particles resembles a frozen ferrofluid withoutaggregations, the positions of the particles are kept fixed andthe easy axes are chosen randomly. Aiming to focus on therole of the dipolar interparticle interactions we have simpli-fied the system in order to set very ideal conditions, assum-ing �i� temperature-independent K, V, and MS and �ii� a per-fectly monodisperse system. The energy model is the sameas in Ref. 24 so that the energy of each particle in this idealscenario is regarded to have three main sources: anisotropy�EA�, Zeeman �EH� and dipolar interaction �ED�. Theuniaxial-type anisotropy of each i-particle is given byEA

�i�=−KV��� i · n̂i / ��� i��2, the influence of the external mag-netic field H� is treated in the usual way EZ

�i�=−�� i ·H� , and themagnetic dipolar interaction energy among two particles i , jlocated at positions r�i ,r� j is given by ED

�i,j�=�� i ·�� j /rij3

−3��� i ·r�ij���� j ·r�ij� /rij5 , with rij the distance between both par-

ticles. The total energy of the system is therefore the sum-mation of these energies extended to all particles.

In our simulations, we reproduce M�H� curves at differ-ent sample concentrations �c� and for different values ofmaximum applied field Hmax, using the parameter values ex-tracted from the MgO-coated Fe NPs as described above.The process to simulate a M�H� curve starts by first thermal-izing the system at zero field from a very high temperature tothe desired chosen temperature. Next, the magnetic field isapplied and increased in small intervals until a certain Hmax

value; then it is decreased down to −Hmax, and increasedagain up to Hmax so that the cycle is complete. To simulatethe time-dependence of the magnetization between two fieldconditions we use the Metropolis algorithm with localdynamics,24 i.e., the particles are allowed to change theirconfiguration a certain amount of trials. In each step, a neworientation of the magnetic moment is generated inside acone of radius �� around the actual orientation.25 The energyvariation �E is calculated and the change to the new orien-tation is then accepted with probability min�1,exp�−�E /kBT��, with kB the Boltzmann constant. For a systemof N-particles, the repetition of this process N times by ran-domly picking the particles defines one MC step. The mag-netization of the system is recorded after a certain amount ofMC steps as the projection of the magnetic moments alongthe field direction.

With the purpose of illustrating the overall working ofthe program, Fig. 3�a� shows the M�H� curve for the very

diluted sample c=0.0001 �0.01% volume fraction�. We haveconsidered a system of N=1000 particles and magnetizationresults are obtained from averaging the magnetization of allthe particles in the system over five different configurations,and for all simulations the field variation ratio was kept con-stant as �H=10 Oe every 400 MC steps. This ratio waschosen so that both the remanence and the coercive field�HC� in the ideal noninteracting case at very low tempera-tures reproduce the expected values MR�0.50 and HC

�0.48 Ha,19 where Ha=2 K /MS is the anisotropy field of

the particles. Since the Ha-value is of primary importance indetermining the magnetic properties of particle systems, be-cause it weights the relative importance of the Zeemanenergy,26 in our simulations we emphasize the value of theexternal field in relation with Ha.

Some M�H� curves at higher temperatures �treated bymeans of usual computational reduced temperature units t=kBT /2 KV� �Ref. 24� are plotted in Fig. 3�b� showing thereduction in the hysteresis area with larger temperatures, asexpected: the higher thermal energy promotes larger fluctua-tions in the orientation of the magnetic moments, until at

-1.0 -0.5 0.0 0.5 1.0-1.0

-0.5

0.0

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1.0

-1

0

1

-1 0-1

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1

-1 0 1

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

0.5

1.0

1.5

2.0

-8 -6 -4 -2 0 2 4 6 8-1.0

-0.5

0.0

0.5

1.0

0.48

M/M

S

0.50

t = 0.40t = 0.20

t = 0.10

t = 0.001

t = 0.05

(c)

(b)

(a)

HC/Ha

initial

t = kBT/2KV

H/Ha

t = kBT/2KV0.0010.0100.0500.1000.2000.3000.400

FIG. 3. �Color online� �a� Magnetization vs magnetic field curve in the idealdiluted limit at low temperatures, used as control for setting the amount ofMC steps reproducing the Stoner–Wohlfarth conditions, as indicated by thearrows. �b� M�H� curves at increasing temperatures �reduced units t=kBT /2 KV� that illustrate the decrease in hysteresis and HC with tempera-ture. �c� M�H� curves at different temperatures showing the common satu-ration behavior at very high fields. Inset shows the temperature dependenceof the initial dM /dT susceptibility �upper curve, full squares�, and of thecoercive field HC /Ha �lower curve, empty squares�.

073918-3 Serantes et al. J. Appl. Phys. 108, 073918 �2010�

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high enough temperatures the anisotropy energy wells of theparticles are completely overcome and the particles reach thesuperparamagnetic �SPM� state. This process is analyzed inmore detail on the inset of Fig. 3�c�, where it is plotted thetemperature dependence of the initial susceptibility �uppercurve, full square symbols� and coercive field �lower curve,empty square symbols�. The initial susceptibility first growsuntil a maximum is reached, and decays afterwards. Thisbehavior agrees with the tendency observed in zero fieldcooling processes,24 as could be expected since the processstarts after thermalization of the magnetic moment in zerofield. In fact, paramagnetic-like decay of the initial suscepti-bility seems to be indicated in the high-temperature regime,as corresponds to the SPM behavior. This reasoning is alsosupported by the trend followed by the coercive field as afunction of the temperature, decreasing HC with growingtemperature until it disappears when reaching the SPM-statetemperature range. The data shown in the main panel of Fig.3�c� illustrates the occurrence of saturation of the M�H�curves at the different temperatures for large fields wellabove the anisotropy field of the particles.

In Fig. 4�a� simulated M�H� curves are shown as a func-tion of the sample concentration. A decrease in the initialsusceptibility with increasing c is observed, so that the stron-ger the interaction between particles, the lower the hyper-thermia response. Our results partially agree with those pub-lished by Wang et al.27 but run contrary to the findings inpolydisperse ferrofluids reported by Jeun et al.,28 althoughwe think that the different system analyzed in the latter�sample concentration is described as related to the size dis-tribution, whereas in our case a monodisperse system is as-sumed� may be responsible for such discrepancy. Figure 4�b�shows magnetization curves as a function of the amplitude ofthe magnetic field for c=0.007, where the importance of thefield with respect to Ha is underlined: for fields H�Hc

=0.48 Ha there is almost no noticeable effect in the area ofthe cycle, whereas for values Hc�H�Ha large increases areobserved. No noticeable variations are found for HHa.

IV. CONCLUSIONS

Modeling of the hysteresis losses of a magnetic fluidwith alternating magnetic field reveals that heating is depen-dent on the particle concentrations. This dependence is ana-

lyzed in detail in Fig. 5. The results show a well definedlinear dependence on the field amplitude for the concentratedsamples �c=0.07, 0.15�, and a more complex behavior forthe more diluted one �c=0.007�. As expected, the model pre-dicts that SAR saturates to a constant value for large fields,and despite its simplicity, gives a good quantitative accountof the measured data shown in Fig. 2 and also reported inother works �see, for instance, Fig. 3 in Ref. 23�, the satura-tion taking place at larger values for larger concentrations.Our results also emphasize the importance of taking intoaccount the characteristic Ha-field of the particles to set ourhyperthermia experimental conditions: it seems that Ha

�larger the higher the concentration� gives an estimation ofthe upper limit for the field amplitude for larger SAR.

In summary, MC simulations of an assembly of mono-disperse single domain magnetic particles—liquid likearranged—in thermal equilibrium have shown that interpar-ticle interactions modify the energy barrier, changing the glo-bal magnetic behavior of the particle systems. We observethat dipolar interactions between NPs significantly affect themagnetic susceptibility and hysteresis losses, thus implying aconsiderable reduction in specific heating power for hyper-thermia applications.

FIG. 4. �Color online� �a� Field dependent magnetiza-tion curves for increasing sample concentration; insetshows the initial susceptibility. �b� Magnetizationcurves as a function of the magnetic field amplitude fora selected sample concentration �c=0.007�. In bothcases arrow indicates magnitude increasing direction.

FIG. 5. �Color online� Field-dependence of the SAR for different concen-trations �c=0.007, 0.070, 0.150�. Field data is also expressed in real units inorder to make easier the comparison with the experimental values plotted inFig. 2.

073918-4 Serantes et al. J. Appl. Phys. 108, 073918 �2010�

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ACKNOWLEDGMENTS

This work was supported by the Greek Secretariat ofResearch and Technology—Contract No. 03EΔ667 and theSpanish MICINN and FEDER �Project Nos. MAT2009-08024, MAT2009-08165, MAT2007-61621, and CON-SOLIDER CSD2007-00041�. Xunta de Galicia is acknowl-edged for project INCITE under Project No.08PXIB236052PR and for the financial support of D. Se-rantes �María Barbeito program�. C. Boubeta credits supportthrough the Ramón y Cajal program.

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