Colossal Reduction in Curie Temperature Due to Finite-Size Effects in

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Colossal Reduction in Curie Temperature Due to Finite-Size Effects in CoFe2O4 Nanoparticles Victor Lopez-Dominguez,† Joan Manel Hernàndez,† Javier Tejada,*,† and Ronald F. Ziolo‡ †

Dept. de Física Fonamental, Universitat de Barcelona, C. Martí i Franqués 1, Barcelona 08028, Spain Centro de Investigación en Química Aplicada, Boulevard Enrique Reyna 140, Saltillo, 25253 Mexico

‡

ABSTRACT: In this work, we show the enormous size effect on the ordering transition temperature, TO, in samples of CoFe2O4 nanoparticles with diameters ranging from 1 to 9 nm. Samples were characterized by HRTEM and XRD analyses and show a bimodal particle size distribution centered at 3 nm and around 6 nm for “small” and “large” particles, respectively. The results and concomitant interpretation were derived from studies of the magnetization dependence of the samples on temperature at low and high magnetic fields and relaxation times using both dc and ac fields. The large particles show a typical superparamagnetic behavior with blocking temperatures, TB, around 100 K and a Curie temperature, TC, above room temperature. The small particles, however, show a colossal reduction of their magnetic ordering temperature and display paramagnetic behavior down to ∼10 K. At lower temperatures, these small particles are blocked and show both exchange and anisotropy field values above 5 T. The order of magnitude reduction in TO demonstrates a heretofore unreported magnetic behavior for ultrasmall nanoparticles of CoFe2O4, suggesting its further study as an advanced material. KEYWORDS: magnetic nanoparticles, Curie temperature

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the so-called anisotropy constant, which depends on the magnetic anisotropy field material, and V being the particle volume, l3. Thus, a particle of a size l < δ is a sufficient condition for the particle to consist of a single domain. The total energy of a single-domain particle depends on the exchange interaction, the crystal field anisotropy, dipolar forces, and on the shape of the particle. In general, single-domain particles are very complex objects because, for example, the exchange interactions at the surface are different from those in the bulk, and in addition, the magnetic anisotropy at the surface differs from the anisotropy in the bulk as a consequence of the different symmetry in the local arrangement of the atoms. In the case of the cobalt iron oxide particles, which are of interest in this work, the energy of the exchange interaction per atom greatly exceeds the energy of the magnetic anisotropy per atom. Consequently, the effective exchange interaction at all atomic sites is sufficiently large to make the particle uniformly magnetized. In this case, the low-energy dynamics of such particles reduces to a uniform rotation of the total magnetic moment.1,14 The magnetic properties of nanoparticles are very much influenced by finite-size and surface effects. These effects can produce a large variety of anomalous magnetic properties, including a reduction in the Curie temperature and the

agnetic nanoparticles are of great interest in many different fields of physics, chemistry, and engineering. At low temperatures, they show magnetic relaxation1 and quantum properties, such as magnetization tunneling,2−5 and at room temperature, their applications cover fields such as data storage,2,6 magnetic resonance imaging,7 magnetic fluids,8 and biomedicine.7,9 Therefore, understanding the fundamental behavior of the magnetic properties of these nanoscale objects is very important. For example, we have the case of the formation of many different types of large agglomerates due to their dipole−dipole interactions with very different magnetic properties between them. Another important aspect of magnetic nanoparticles is the control of their size and shape distributions because both the Curie temperature and the height of the anisotropy energy barriers are strongly affected by the size and shape of the particles.10,11 Among ferrite materials, ferrimagnetic cobalt ferrite nanoparticles with an inverse spinel structure are of high interest due to their ease of synthesis via different methods,12,13 remarkable chemical stability, very high magnetocrystalline anisotropy, and moderate saturation magnetization. It is well-known that large magnetic particles split into magnetic domains in order to decrease their magnetostatic energy. The thickness, δ, of the domain wall where the rotation of spins from one domain to another occurs, is given by δ = a(J/D)1/2, where J and D are the exchange and anisotropy energies per lattice site, respectively, and a is the lattice spacing. For practical reasons, it is assumed that the total anisotropy energy of the particle can also be expressed as KV, with K being © XXXX American Chemical Society

Received: June 22, 2012 Revised: November 14, 2012

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dx.doi.org/10.1021/cm301927z | Chem. Mater. XXXX, XXX, XXX−XXX

Chemistry of Materials

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appearance of magnetic disorder on the surface of the particles.15−17 An interesting and relatively new problem in single-domain particles is the study of their properties when the number of spins on the surface exceeds the number of spins forming the core of the particle. However, we are far from having a good answer to the open question of the size dependence of the exchange energy of the particle as measured by its Curie temperature, TC. Moreover, we may enter in the very interesting regime of values of l, for which the reduction in the value of the Curie temperature is such that the magnetic moment of the particle is blocked due to the magnetic anisotropy at TB = TC. In this case, the effect of spin fluctuations may have a strong influence on the variation of the order parameter M on T. For nanoparticles, the spin fluctuations that affect the Curie temperature are theoretically determined by Monte Carlo simulation.18 Besides fluctuations, TC in very small particles can also be strongly affected by the weak size dependence of the distance between the atoms and exponential dependence of the exchange interaction J on that distance. Experimental evidence of the latter effect is presented in this paper. We report on the preparation, characterization, and magnetic measurements of nanoparticles with a composition of CoFe2O4 having bimodal size distributions defined here as “large” and “small” and ranging in diameter from 1 to 9 nm. While the large particles (centered around 6 nm) show superparamagnetic behavior with the blocking temperature changing with the frequency of the ac field, the smallest particles (centered around 3 nm) show the atomic paramagnetic Curie−Weiss law above the transition temperature of 8.5 K and the magnetic blocked state with out-of-time dependent phenomena at lower temperatures.

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Figure 1. XRD spectrum of the cobalt ferrite sample. The solid lines indicate the expected peak positions for the bulk. Inset: representative EDS spectra of the CoFe2O4 samples showing Co and Fe in an approximately 1:2 ratio. big enough to smear out the contribution of the weakest peaks in the spectrum and is compatible with the existence of very small nanoparticles with diameters below 3−4 nm, as deduced using the Scherrer formula. Moreover, the two observed peaks are slightly shifted to lower diffraction angles, which may indicate that the cell parameters for the smallest nanoparticles are larger than those of the bulk. Particle morphology, shape, and size distribution were examined by a JEOL JEM 2100 transmission electron microscope. Samples for transmission electron microscopy (TEM) analysis were prepared by drying a hexane dispersion of the particles on amorphous carboncoated copper grids. A representative TEM image of the particles is shown in Figure 2. The mean particle size and distribution were

SYNTHESIS AND STRUCTURAL CHARACTERIZATION

The synthesis of the cobalt ferrite particles was carried out via the decomposition of stoichiometric quantities of Fe(acac)3 and Co(acac)2 (acac = acetylacetonate) in high-boiling-point solvents, diphenyl and dibenzyl ether, using a modified procedure after Dai et al.12 Three different sets of cobalt ferrite nanoparticles were prepared to obtain characterizable size distributions of the nanoparticles following two consecutive and separate stages of nucleation and growth, respectively. Accordingly, Co(acac)2 (1 mmol), Fe(acac)3 (2 mmol), 1,2hexadecanediol (10 mmol), oleic acid (6 mmol), oleylamine (6 mmol), and benzyl ether (20 mL) were mixed and magnetically stirred under nitrogen. The mixture was heated to 200 °C for 2 h, and then, under a blanket of nitrogen, heated to reflux (∼290 °C) for 1 h. The black-colored mixture was cooled to room temperature by removing the heat source. Under ambient conditions, ethanol was added to the mixture, and black material was precipitated and separated via centrifugation. The black product was dispersed in hexane and then reflocculated by adding ethanol, followed by centrifugation. Several washings with hexane/ethanol were performed in order to remove any byproducts. Energy-dispersive X-ray spectroscopy (EDX) was used as a local stoichiometry probe. The obtained spectrum is shown in the inset of Figure 1, which clearly shows the presence of Co and Fe in an approximate 1:2 ratio as expected for CoFe2O4. The relatively high intensities of the oxygen and carbon peaks (particles and oleic acid capping agent) were omitted for clarity. X-ray diffraction (XRD) analyses of the synthesized CoFe2O4 powders (see Figure 1) were carried out using Cu Kα radiation. The spectrum shows the presence of only two very broad peaks at positions that approximately correspond to the expected possitions of the most intense peaks for bulk CoFe2O4. The width of the peaks is

Figure 2. Representative HRTEM images of the sample showing both small and large particles (left and right, respectively). Inset: particle size distribution obtained from a set of HRTEM images. The sample is characterized by a bimodal size distribution with two peaks, one centered at about 3 nm and another at about 6 nm. evaluated by measuring the largest internal dimension of at least 100 particles. The result for the particle size histogram shown in the inset of Figure 2 shows the presence of a bimodal size distribution of particles, centered around 3 and 6 nm. This distribution can be fitted to the sum of two log-normal diistributions: one with a mean diameter of 5.4 ± 1.0 nm and σ of 0.2 for bigger particles, and the other one with a mean diameter of 2.6 ± 0.3 nm and σ of 0.15 for the smaller particles. B



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measuring applied field is applied before cooling the sample. The ZFC magnetization curve increases strongly from an initial value at T = 2 K to a maximum at 8.5 K; then it decreases following a paramagnetic C1 + 1/T dependence until about 20 K. C1 is a parameter representing the magnetic contribution of the blocked large particles, which, in this small range of temperatures, may be assumed constant. It then increases again until having a new maximum in the region of T ≈ 90 K, above which it decreases until room temperature. The equilibrium FC magnetization curve, which increases when decreasing the temperature, deviates from the ZFC at around 150 K. In the temperature interval between 20 and 8.5 K, the curve follows a similar paramagnetic dependence as in the case of the ZFC data, which can be described by C2 + 1/T dependence and finally shows a maximum, as the ZFC curve does, at 8.5 K. Figure 5 shows the temperature dependence of the ac susceptibility recorded at different frequencies for the ac field

In Figure 3, we show the calculated spacing between the atomic planes of the family (311), d311, versus the size of the particles. This

Figure 3. Interplanar distance of the (311) family of planes as a function of the particle characteristic size, l. The dotted horizontal line indicates the expected value for bulk samples. distance was calculated selecting the area in the photograph where there was a particle. The Fourier transform was then computed, and the distance between the diffraction peaks was measured. The plotted distances correspond to the (311) family of planes (the most intense of the diffraction peaks of CoFe2O4) for particles of different sizes. The figure indicates that there is a clear variation of the distance between the atomic planes with the size of particle, with an increase of nearly 20% when the size of the particle decreases from 5 to 3 nm. The interplanar spacing calculated for the largest particles coincides with the peak expected for bulk CoFe2O4.

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MAGNETIC STUDIES AND DISCUSSION The magnetic measurements were carried out using a commercial magnetometer.19 The zero-field-cooled (ZFC) and field-cooled (FC) magnetization data, measured with an applied field of 1 mT, are shown in Figure 4. The ZFC measurement protocol is performed as follows: first, the sample is cooled to the lowest temperature (T = 2 K) at zero field; then, the measuring magnetic field is applied and the magnetization is recorded as the sample’s temperature is increased at a constant sweep rate of about 1 K/min. The FC protocol differs from that of the ZFC only in that the

Figure 5. Temperature dependence of the in-phase, m′, and out-ofphase, m″, components of the ac susceptibility measured at different frequencies (squares, circles, and up- and down-pointing triangles: 1, 10, 100, and 1000 Hz, respectively).

ranging from 1 to 1000 Hz. Both the in-phase and the out-ofphase components present two maxima in a similar way as the ZFC magnetization does. From the data in Figure 5, we have deduced that the position of the maxima of the out-of-phase peak corresponds to the inflection point of the temperature dependence of the maxima of the in-phase susceptibility in all the frequency ranges of measurements. The position of the high-temperature peak depends logarithmically on the used frequency. This is clearly seen for the case of the in-phase component peak for all frequencies, as depicted in Figure 6. These two experimental facts are clear signatures that these two peaks correspond to the blocking temperature, TB, of the large magnetic nanoparticles. Moreover, we have fitted this logarithmic dependence to the Arrhenius thermal activation over barrier transition law, Tpeak = KV/log(1/( fτ0)), where τ0 is the attempt time, K is the so-called magnetic anisotropy constant, V is the average volume of the particles, and f is the used frequency. The frequency shift of the in-phase component peak temperature fits pretty well with this logarithmic law using the value of K = 2 × 106 erg/cm3, which corresponds to the case of the bulk, the volume of the biggest particles, and the value of about 10−11 s for the attempt time. The position of the low-temperature peak of both components of the ac susceptibility does not depend on the ac frequency used and

Figure 4. Temperature dependence of the ZFC (lower curve) and FC (upper curve) magnetization curves measured under an applied magnetic field of 1 mT. Two peaks are evident in the ZFC curve at 8.5 K and about 90 K. C



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Figure 6. Frequency dependence of the temperature of the peaks’ inphase component of the ac susceptibility for the low- and hightemperature peaks. Figure 7. ZFC magnetization curves obtained at different magnetic fields (1, 2, 3, 4, and 5 T; lower to upper curves, respectively). The inset shows the ZFC magnetization data at lower fields (10 and 100 mT). The high-temperature peak at about 90 K shifts to lower temperatures as the field increases and disappears for fields higher than 1 T, whereas the peak at low temperatures remains for all the values of the applied fields.

appears always at 8.5 K, which is the same value of the lowtemperature peak in the ZFC magnetization (Figure 6). In other words, the independence of the position of the lowtemperature peak with the frequency of the ac magnetic field is fully compatible with the occurrence of a magnetic phase transition. That is, below 8.5 K, the ordering temperature, the smallest particles are magnetically ordered, whereas above this temperature, they behave paramagnetically. This explains the 1/ T dependence of the ac susceptibility between 20 and 8.5 K for all frequencies. To conclude about these two sets of data (ZFC, FC and ac susceptibility), it can be said that the magnetic signals of both ZFC and ac susceptibility at low and high temperature are the consequence of the independent contribution of the magnetic moments of the small and large nanoparticles, respectively. The main question, therefore, is to elucidate the nature of the magnetic transition occurring at 8.5 K by the small nanoparticles. To go deeper in the understanding of the low-temperature peak associated with the small particles and their phase transition, we performed measurements of ZFC curves at much higher fields, as shown in Figure 7. From this figure, it is clearly seen that the high-temperature peak due to the blocking of the large particles shifts to lower temperatures when increasing the value of the applied magnetic field and disappears for fields larger than 1 T. The case of the low-temperature peak at 8.5 K is completely different. It suffers only a very small shift to lower temperatures for fields of the order of several Tesla. The 1/T behavior of the paramagnetic signal of the small particles is modified as we increase the applied magnetic field. It is remarkable that the magnetic coupling existing below 8.5 K is almost unaffected by the magnetic field, indicating strong exchange coupling inside the small particles. We have also performed isothermal magnetization studies of the samples in the temperature range between 2 and 100 K, as shown in Figure 8. At T > 100 K, the M(H) curve corresponds to the case when the small particles behave paramagnetically and the large particles are superparamagnetic. Consequently, the system exhibits neither remanence nor coercivity. At 10 K, the M(H) curve approaches zero at small fields because the contribution of the paramagnetic signal of the small particles goes to zero, which is the reason for the small coercitivity. At T = 2 K, all particles are blocked and the coercivity is about 0.3 T. The hysteresis cycle is not closed even at 5 T, which may be the

Figure 8. Magnetic hysteresis curves recorded at different temperatures.

consequence of the very high value of the magnetic anisotropy field of the small particles. In Figure 9, we show the temperature dependence of the coercive field, Hc. As expected, the values of Hc increase with lowering the temperature as more and more particles are blocked and there is not enough thermal energy to overcome the barrier heights. The maximum observed at around 30 K and the follow up decreasing until 10 K correspond to the case when both sets of particles, the small, paramagnetic, and the large, are contributing simultaneously to the detected signal. Below 10 K, we are mostly seeing the coercitivity of the smallest particles. To this end, we have explored the metastability of the system by performing relaxation measurements in all of the temperature ranges between 2 and 90 K. The protocol used in these measurements is as follows: First, the sample was put at a temperature much higher than that of the blocking temperature of the largest particles (T = 200 K), where the system was allowed to reach equilibrium. A field of 5 T was then applied to saturate the sample. The sample was then cooled to the desired temperature, the magnetic field switched off, and the system D



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K (not shown), then decreases with decreasing temperature; below 10 K; it is showing a maximum around 6.5 K. The results of the magnetic relaxation can also be presented in a different way to better understand the nature of the physics phenomena observed. The time evolution of magnetization M of the sample depends on time only through the combination T log(t/τ0), where τ0 is a constant of the order of 10−11 s. This means, for example, that, if one observes the log(t) magnetic relaxation due to the barrier distribution, the coefficient in front of log(t) must be proportional to T. This is a very natural feature of complex systems because, as the observation time is running, the system arrives at greater and greater barriers that are more difficult to overcome. The good scaling observed in Figure 10 in all the regimes in the T·log(t/τ0) plot is clear evidence of the thermally activated process of barrier jumping and of the independent relaxation of the two sets of particles. That is, at high temperatures, the data correspond to the relaxation of the largest particles, whereas at temperatures below 10 K, the magnetic moment of the biggest particles is mostly blocked and we only see the relaxation of the magnetic moment of the smallest particles. This low-temperature behavior of the viscosity indicates that, for the smallest particles, both the ordering and the blocking temperatures are very similar. The low-temperature relaxation results point to not very high anisotropy barriers. The size of the smallest particles, therefore, is responsible for both the low value of the ordering temperature of these particles and the small height of the magnetic anisotropy barriers involved in the relaxation phenomena. In the case of the very small particles, the variation detected in the cell parameters suggests that the exchange interaction is smaller than that in the bulk and that it can even change sign. If this were the case, then the lowtemperature peak should correspond to an antiferromagnetic transition with finite magnetic moments due to noncompensation of Neel sublattices. This interpretation agrees well with the fact that, at low temperatures, both the ZFC and the ac susceptibility curves show maxima that shift a little with increasing values of the external field. The results obtained for this sample are similar to those obtained for the other two particle sets that were prepared using the same conditions. In all three cases, the samples presented bimodal size distributions with peaks at approximately the same values and magnetic data showing the same dependencies reported for the present sample. Concerning the effects induced by the interparticle interaction, we may also conclude that the fact that the same magnetic data have been observed in similar samples having different ratios between the number of small and large particles is a clear indication that the interparticle interaction is not playing any role in the data we have analyzed in this paper.

Figure 9. Temperature dependence of the coercive field.

was allowed to relax to the new equilibrium state while the magnetic moment is recorded. In all cases, the time dependence of the magnetization follows very well the time logarithmic law (Figure 10), as expected for a system with a

Figure 10. Results of the magnetic relaxation experiments shown in a T log(t) scale. The different colors indicate the different temperatures (shown in the labels) at which the relaxation experiments are performed. In the T log(t) plot, there are two different thermal regimes. The inset shows the viscosity at low temperatures and a peak at the same temperature as that shown at low temperatures in the ZFC magnetization curve.

wide distribution of energy barriers. In single-domain particles, the intrinsic barriers are typically of the order of KV, with K being the anisotropy constant and V the volume of the particle involved in the relaxation. Consequently, the wide distribution of energy barriers is associated with the broad size distribution of the particles. From these data, we have deduced the value of the magnetic viscosity, S.4 The definition of magnetic viscosity, which is independent of the initial state, and considering that the final equilibrium state corresponds to zero magnetization, is S=−

1 dM M ini d ln t

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CONCLUSIONS In summary, we have reported experimental evidence of lower ordering temperatures of CoFe2O4 nanoparticles with a diameter of about 3 nm. The measured ordering temperature is only 8.5 K, which is 50 times smaller than the Curie temperature of the bulk material. Just below the ordering temperature, these particles are magnetically fully blocked, presenting, therefore, an interesting case where both the paramagnetic-to-ferromagnetic/antiferromagnetic transition and the blocking temperature occur at the same lowtemperature value. On the basis of our data, we suggest that this low-temperature magnetic transition is related to the

(1)

with Mini being the magnetization of the initial state. The temperature dependence of the magnetic viscosity, S, defined by eq 1 is shown in the inset of Figure 8 in the temperature range below the blocking temperature of the large particles. At higher temperature, the viscosity shows a maximum close to 90 E



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interplay of surface effects and the increase of the lattice parameter. This study also shows the value of different magnetic characterization techniques in probing the magnetic behavior of nanoparticle systems with a distribution of particles sizes below 10 nm.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by Spanish Government Project MAT2011-23698. ABBREVIATIONS acac, acetylacetonate; EDX, energy-dispersive X-ray spectroscopy; FC, field-cooled magnetization; XRD, X-ray diffraction; ZFC, zero-field-cooled magnetization

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Colossal Reduction in Curie Temperature Due to Finite-Size Effects in

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