Effects of grain boundary width and crystallite size on

J Nanopart Res (2014) 16:2482 DOI 10.1007/s11051-014-2482-3

RESEARCH PAPER

Effects of grain boundary width and crystallite size on conductivity and magnetic properties of magnetite nanoparticles K. L. Lopez Maldonado • P. de la Presa • M. A. de la Rubia • P. Crespo • J. de Frutos • A. Hernando • J. A. Matutes Aquino J. T. Elizalde Galindo

•

Received: 31 March 2014 / Accepted: 23 May 2014 Ó Springer Science+Business Media Dordrecht 2014

Abstract The structural, electrical, and magnetic properties of magnetite nanoparticles, with crystallite sizes 30, 40, and 50 nm, are studied. These crystallite sizes correspond to average particle sizes of 33, 87, and 90 nm, respectively, as determined by TEM. By HRTEM images, it is observed that grain boundary widths decrease as crystallite size increases. Electrical and microstructural properties are correlated based on the theoretical definition of charging energy. Conduction phenomena are investigated as a function of grain boundaries widths, which in turn depend on crystallite size: the calculations suggest that charging energy has a strong dependence on crystallite size. By zero-fieldcooling and susceptibility measurements, it is observed that Verwey transition is crystallite size dependent, with values ranging from 85 to 95 K. In addition, a kink at the out-phase susceptibility curves at 35 K, and a strong change in coercivity is associated to a spin-glass transition, which is independent of crystallite size but

frequency dependent. The activation energy associated to this transition is calculated to be around 6–7 meV. Finally, magnetic saturation and coercivity are found to be not significantly affected by crystallite size, with saturation values close to fine powders values. A detailed knowledge on the effects of grain boundary width and crystallite size on conductivity and magnetic properties is relevant for optimization of materials that can be used in magnetoresistive devices.

K. L. Lopez Maldonado  J. T. Elizalde Galindo (&) Instituto de Ingenierı´a y Tecnologı´a, Universidad Auto´noma de Ciudad Jua´rez, Av. Del Charro 450 norte, 32310 Ciudad Jua´rez, Mexico e-mail: [email protected]

M. A. de la Rubia  J. de Frutos Dpto. Electrocera´mica, Instituto de Cera´mica y Vidrio (CSIC), Madrid, Spain

P. de la Presa  P. Crespo  A. Hernando Instituto de Magnetismo Aplicado (UCM-ADIF-CSIC), PO Box 155, 28230 Las Rozas, Spain P. de la Presa  A. Hernando Dpto. Fı´sica de Materiales, Univ. Complutense de Madrid, Madrid, Spain

Keywords Magnetite  Nanoparticles  Verwey transition  Spin-glass  Impedance spectroscopy  Magnetic properties

Introduction Magnetic nanoparticles (NPs) are subject of continuous and growing interest from fundamental and

M. A. de la Rubia  J. de Frutos Grupo Poemma, ETSI Telecomunicacion (UPM), Madrid, Spain J. A. Matutes Aquino Centro de Investigacio´n en Materiales Avanzados, Miguel de Cervantes 120, 31109 Chihuahua, Mexico

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technological viewpoint. These NPs have remarkable magnetic properties which differ markedly from their parent massive materials; these different properties make them unique physical objects useful for technological and medical applications (Batlle and Labarta 2002; Crespo et al. 2013; Hernando 1999; Knobel et al. 2008). In this field, magnetite (Fe3O4) is a good option for technological applications in a wide temperature range due to its magnetic properties: high Curie temperature, large magnetic saturation, large critical size, etc. Furthermore, magnetite is a halfmetallic ferrimagnet and band structure calculations indicate that 100 % of spin polarization is expected for this structure; this high polarization property leads to a tunnel magneto-resistance effect (TMR) (Coey 1999). Therefore, in the last decades, magnetite has been studied for spintronic applications, trying to get a high degree of spin polarization, and a high TMR coefficient. However, the experimentally observed TMR coefficient on magnetite is found to be far below the expected values. For this reason, many researches focus on the study of the microstructural and physical properties bearing on magnetite magnetoresistance (Mi et al. 2007; Zhang et al. 2007; Zhou et al. 2010). As occurs in other magnetic NPs, surface and interface properties, such as the alignment of moments at grain boundaries, play a key role in applications like magnetoresistive devices. The effects of average crystallite/grain size and particle size distribution on the physical properties are permanently subject to study (Cabrera et al. 2008; Koksharov 2009; Kolesnichenko 2009; Mi et al. 2007). In addition, several studies suggest that the surface effects, like different composition at grain boundaries or low crystallinity degrees, bear on different ways to the interaction between magnetic moments of neighboring grains or between magnetic moments inside grains and surface spins (Mi et al. 2007; Zhou et al. 2010). Kodama et al. (1997) show that surface spin disorder on ferrites NPs is mainly related to their singular magnetic properties. Nowadays, the effects of crystallite and particle sizes and surface effects on the physical and magnetoresistive properties of magnetite are matters of great importance. Another interesting structural characteristic appearing in magnetite is Verwey transition. Verwey transition is reported for bulk magnetite at *125 K, and during this transformation the structure undergoes from monoclinic to cubic structure above Verwey

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temperature, TV, where the resistance changes by two orders of magnitude (Garcı´a and Subı´as 2004; Walz 2002). Although this transition has not been completely understood by now, an effect of crystallite/ particle size on TV in nanostructured systems is expected. Several authors report that TV diminishes at the nanoscale (Goya et al. 2003; Sarkar et al. 2012; Verge´s et al. 2008), suggesting that the transition is strongly correlated to the microstructural effects such as particle and/or crystallite size and surface effects. Consequently, the investigation of TV dependence on particle microstructure is a research matter (Janu˚ et al. 2007; Lopez Maldonado et al. 2013; Sarkar et al. 2012; Verge´s et al. 2008). In this work, the magnetic and electrical properties of magnetite NPs are studied as a function of crystallite and particle size, aiming to understand the influence of particle/crystallite size and grain boundary width on these properties. Charging energy, and its dependence on crystallite sizes, is studied by impedance spectroscopy. Besides, magnetic measurements are used to study Verwey and spin-glass transitions. Frequency and crystallite size dependences are analyzed. Finally, activation energy for the spin-glass to be broken is calculated.

Experimental methodology Synthesis Synthesis of magnetite NPs is carried out based on aging technique (Lopez Maldonado et al. 2013; Verge´s et al. 2008), where a basic solution is prepared in a round bottom flask containing 180 ml of water with NaOH and KNO3 at concentrations in the order of 10-2 and 10-1 M, respectively. Then, a second solution (20 ml) is prepared using 10-2 M H2SO4 and FeSO4 with concentrations varying from 0.11 to 0.34 M in order to achieve different crystallite sizes in the samples (see Table 1). Both solutions are left under N2 flux bubbling during 2 h. Then, ferrous solution is added slowly at a constant rate under stirring into basic one. After 5 min under magnetic stirring, the system is boiled and aged during 2 h; a condenser is used for refluxing. Finally, the mixed solution is cooled down to room temperature (RT). The black precipitated is magnetically decanted and washed several times; then it is left to overnight dry.

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Table 1 Concentration of precursors NOH, KNO3, H2SO4, FeSO4, and pH of particle synthesis Sample

NaOH (M)

KNO3 (M)

H2SO4 (M)

FeSO4 (M)

pH

hDi (nm)

hDparti (nm)

dGB (nm)

M30

7 9 10-2

0.1

0.1

0.114

12.7

30

33

3

M40

7 9 10-2

0.1

0.165

0.342

8

40

87

2

M50

7 9 10-2

0.1

0.165

0.228

8.5

50

90

1

Initial pH values, although pH did not vary considerably during reaction. In addition, average crystallite (hDi) and particle (hDparti) sizes and grain boundary widths (dGB) determined by XRD and HRTEM are shown for samples M30, M40, and M50

Three samples with different crystallite sizes are synthesized by varying OH concentrations. Characterization Crystal structure and average crystallite size, hDi, are measured by X-ray diffraction (XRD) using Cu-Ka radiation in a PANalytical X’Pert Pro MPD diffractometer, with 2h ranging from 25° to 70°. Cell parameters are calculated by means of UNITCELL software (Holland and Redfern 1997). Particle size and morphology are studied by transmission electron microscopy (TEM) using a JEOL JEM-2200FS TEM. For the observation of the sample in the microscope, the particles are dispersed in isobutyl alcohol and a drop of the suspension is placed onto a copper grid covered by a carbon film. For electrical characterization, the samples are shaped into pellets of 6.7 mm of diameter and 1 mm of thickness by applying a 40 kN force. The electrical properties of the pellets are measured by the two probes method with the contacts placed onto both pellets faces. The electrodes are conductive copper tapes AT526 35 Micron Copper Foil Shielding from Advance Tapes. The impedance characterizations are carried out using a Solartron Impedance Analyzer (Model 1260) supplemented with a 1296 dielectric interface modulus that allows determining impedances in the teraohms range. The measurements are carried out at RT with VAC = 0.5 V in a frequency range from 10-1 to 106 Hz. For temperature-dependent impedance measurements, the samples are set in a cryostat Janis Research Co. VNF 100 with temperature varying from 77 to 280 K with 20 K steps. Magnetic susceptibility curves are measured in an Oxford Instrument from 5 to 150 K with 5 K steps, with applied magnetic field HAC = 50 Oe and frequency ranging from 100 to 774 Hz. Magnetization measurements are carried out using a SQUID Physical

Fig. 1 XRD patterns for the three samples. All peaks were identified with #PDF 01-075-0449

Properties Measurement System (PPMS). Hysteresis loops are performed at 5, 50, 90, 120, and 300 K with maximum applied field Hmax = 20 kOe. Zero field cooled (ZFC) curves are measured from 5 to 300 K and 100 Oe applied field.

Results and discussion X-ray diffraction Magnetite has an inverse spinel cubic crystal structure  32 O2? ions arranged in a face with space group Fd 3m, centered cubic lattice, in which 8 of 64 available tetrahedral sites are occupied by Fe3? cations, and 16 of 32 available octahedral sites are equally occupied by Fe3? and Fe2? cations (De´zsi et al. 2008; Ogale et al. 1998; Venkatesan et al. 2003). Figure 1 shows XRD patterns at RT for the three samples. The XRD patterns analysis shows that Fe3O4 single cubic

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Fig. 2 Characteristic TEM images for samples: a M30; b M40; and c M50. Particle size distributions are shown at the inset graphs

crystalline phase is achieved in all samples (#PDF01075-0449); no secondary phases are observed. Variation in mean crystallite size, hDi, as expected from the peak broadening, is calculated using Scherrer’s formula from FWHM of (311) peak; mean hDi values 30, 40, and 50 nm are obtained for the three samples named M30, M40, and M50, respectively. The differences in relative intensity for (311) and (440) planes between M30 and the other two samples are attributed to the morphologies variation, as will be shown later. ˚ for all samples, in Cell parameter is close to 8.35 A agreement with the expected value (Coey 2010). Microscopy In order to understand the differences in relative intensities observed by XRD, morphology and grain size analysis are carried out from TEM micrographies. Figure 2 shows characteristic micrographs for samples; grain size distributions are shown at the insets. As can be seen, M30 sample shows a rather tetragonal morphology; whereas M40 and M50 are quasi-spherical particles. This morphological difference is attributed to a pH variation during chemical reaction (Verge´s et al. 2008) and is responsible for the differences in the relative intensity for (311) and (440) planes between M30 and the other two samples. Average particle sizes hDparti are calculated by measuring more than 600 NPs; the obtained values are 33(2), 87(2), and 90(2) nm for M30, M40, and M50 samples, respectively. Because the NPs are not spherical, the maximum Feret’s diameter is used to compute the size, i.e., the maximum perpendicular distance between parallel lines which are tangent to the perimeter at opposite sides. It is observed that

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particles of M40 and M50 samples are mostly polycrystalline; therefore, mean particle size observed by TEM is much larger than crystallite size determined by XRD. Conduction phenomena of magnetite depend not only on the morphology, but also on the crystallinity degree and grain boundaries width; therefore, a deeper analysis of this dependence is performed in all the samples. Figure 3 shows characteristic high resolution TEM images (HRTEM). From analysis, it is found that M30 NPs are in major part monocrystalline; whereas, particles in samples M40 and M50 are predominately polycrystalline. Analyzing the observed planes on the micrographs by mean of DigitalMicrograph software (Team 1999), planes (111) and (220) are identified to magnetite structure, ˚ , respecwith interplanar distance 4.71 and 3.03 A tively. The amorphous or disordered zones at the crystallite/particle surfaces are indicated in Fig. 3b, c. Since changes in crystalline directions affect conduction phenomena (as will be discussed later), these zones are defined as grain boundaries. By measuring the grain boundaries widths in 200 particles, it is found that amorphous shell decreases from 3 to 1 nm as particle size increases. This behavior could be attributed to the synthesis method, aging method, which produces nucleation, growth, and aggregation of small particles with a wellorganized core and disordered surface in some degree; therefore, it could be expected that when NPs size increases, the crystalline order prevails over disorder at the surface, leading to a decrease of the observed grain boundary width. The calculated values for average grain boundaries widths (dGB) are shown in Table 1.

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Fig. 3 HRTEM images of a planes (111) of a tetragonal particle and b planes (111) and (220) of a polycrystalline quasispherical particle are identified; grain boundaries at the particle surface and between particles are also indicated; c grain boundary observation at the surface of one particle

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Electrical characterization After microstructural and crystallinity analysis, and continuing to achieve a good understanding on the physical properties of magnetite, the electrical properties of samples are studied by impedance spectroscopy in AC electric field. With this analysis, it is possible to determine the different phenomena that contribute to electrical conduction owing to the physical and chemical properties of the samples. When applying an AC field, the impedance is defined as the ratio between applied voltage and generated current intensity. Due to the phase difference between these magnitudes, impedance is a complex function of frequency: Z ðxÞ ¼ Z 0 ðxÞ þ iZ 00 ðxÞ

ð1Þ

where Z 0 and Z 00 are real and complex impedance, respectively, i is the imaginary unit, x ¼ 2pf is the angular frequency in rad/s, and f is ac electric field frequency. In the measured frequency range, the dielectric response is dominated by relaxation phenomena because of the displacement of trapped space charges at the interfaces (Maxwell–Wagner–Sillars relaxation) (Macdonal and Johnson 2005). Using this technique, the system can be resembled mathematically to an equivalent circuit, where the real part referring to loading transfer or polarization and electrode resistance is represented by resistors, and the complex component is given by capacitance. Therefore, the impedance ZðxÞ is defined as follows: ZðxÞ ¼ RðxÞ þ XðxÞ

ð2Þ

where RðxÞis the resistance and XðxÞ is the reactance which is related to capacitance; the conductance CðxÞ is the inverse of RðxÞ. Given the relationship between impedance, conductance, and resistance, the following Fig. 4 a Frequencydependent impedance at RT for all samples. At the inset the Z 00 plots. b Phase difference measured at RT for M30 and M40 (sample M50 behavior is quite similar to M40, thus is omitted for the sake of clarity)

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discussion can help to clarify the conduction phenomena and their connection with microstructural and crystallinity properties. Figure 4a shows the results for impedance depending on frequency obtained at RT for the three samples. The sample with the smallest particle size, M30, shows an impedance value of 1.0 9 107 X almost one magnitude order higher than the values obtained for samples with the bigger particle sizes, M40 and M50 (0.1 and 0.2 9 107 X, respectively). It is observed that impedance increases as frequency decreases and then remains constant for frequencies lower than 103 Hz; however, the frequency range where impedance remains constant (called isoconductance curves) is wider for the largest particles (M40 and M50). The characteristic frequency at which Z 0 becomes constant is called ‘‘relaxation frequency’’ and corresponds to a minimum in the Z 00 versus frequency plots, as can be seen at the inset of Fig. 4a. This frequency-dependent behavior of Z 00 is related to a Debye dielectric relaxation. The results show that the Debye peak is shift to higher frequencies for samples with the largest particle sizes, implying a decrease of relaxation time (s = RC). This behavior is also observed in hollow nanospheres by Sarkar et al. (2012). Besides, Fig. 4b shows the phase versus frequency for samples M30 and M40 (behavior of sample M50 overlaps to M40, it is omitted for the sake of clarity). It is observed that phase is almost zero in a wider frequency range for the samples with the largest particle sizes (M40 and M50), indicating a purer resistive behavior below 103 Hz; whereas, the smallest sample M30, already shows a dielectric (capacitor) behavior at this frequency (phase -908). The real Z 0 and imaginary Z 00 parts of the complex impedance of different samples are analyzed using the Nyquist or Cole–Cole plot (Fig. 5); only one

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103 Hz, frequency dependence of impedance is temperature independent. Now, as theoretically defined for TMR systems, conductance can be expressed in terms of the potential barrier and thermal energy as   EC C / exp 2jd  ð3Þ kB T

Fig. 5 Z0 –Z00 plots at RT for magnetite samples with different crystallite sizes

semicircle or arc is observed throughout the frequency range. The grain boundary resistance (RGB) is obtained at the intercept of the semicircle with the real part of the impedance (Z 0 ). The corresponding resistances to the insulating grain boundaries are very similar to the constant value of the impedance modulus |Z| for lower frequencies. The RGB values for the samples with the larger NP sizes are close to those obtained for magnetite nano-hollow spheres of 100 nm (Sarkar et al. 2012). Moreover, the relaxation time can be estimated from the maximum of the Z 0 –Z 00 plot at which xs *1, x = 2pfmax and, consequently, s *1/ 2pfmax (Psarras et al. 2003). As can be seen from Z 0 –Z 00 graph, relaxation time decreases as crystallite size increases, as deduced from the Debye peak shift in Fig. 4. Additionally, impedance as a function of frequency is measured at different temperatures for all samples. Figure 6 shows impedance frequency dependence at different temperatures for sample M30, similar behavior is observed for the rest of samples (curves are omitted for the sake of clarity). As previously shown in Fig. 4a, impedance has a negligible reactance contribution for frequencies lower than 103 Hz; therefore, from 1 to 103 Hz, impedance is proportional to resistance, which in turn is inversely proportional to conductance. As can be seen from Fig. 6, impedance (conductance) increases (decreases) as temperature decreases for frequencies below 103 Hz, i.e., the sample becomes more resistive at low frequencies as temperature decreases. For frequencies higher than

where j depends on energy barrier height, Fermi energy and electron effective mass; d is the barrier width (grain boundary widths for our samples), kB is the Boltzmann constant, and EC is the charging energy. The latter is the internal energy change due to an electron crossover from one grain to the adjacent one, which at the same time causes the loss of the charge neutrality in the grains generating Coulomb repulsions inside them and increasing internal energy. As EC arises from Coulomb interactions inside the 2 grains, it may be assumed that EC  e r / 1=d , thus it depends on grain size. Therefore, taking into account that amorphous grain boundary width (which in turn depends on crystallite size) acts as conduction barrier for the moving electrons, EC can be expressed as a function of the barrier width as (Inoue 2009) EC ¼

C0 d

ð4Þ

where d is the grain boundary width and C0 is a constant. By mean of Eqs. (3) and (4), EC values are obtained from the isoconductance curves. From this result, the effects of crystallite size on charging energy can be analyzed. It can be deduced from Eq. (4) that EC increases as grain boundary widths decreases. As seen from HRTEM analysis, the larger the crystallite size, the smaller the grain boundary widths (see Table 1); therefore, it is expected that EC increases as grain size increases. The fitting of the isoconductance curves with Eq. (3) (see Table 2) agrees with this scenario giving higher EC values for larger crystallite sizes; these results, at the same time, indicate that conduction is mainly given throughout grain boundaries in this granular system. Furthermore, the obtained 2jd values decreases as increasing crystallite size; however, it seems to have a more pronounced dependence with particle size rather than the grain size, due to similar energy barrier heights in samples M40 and M50.

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Fig. 6 Impedance curves measured from 77 to 280 K for sample M30

Fig. 7 Characteristic in-phase susceptibility curve measured at 464 Hz for sample M40, the other two samples present similar behavior in all frequency range. At the inset, the calculated derivative graph shows temperatures TV and TSG

Table 2 Values of the charging energy, EC, and 2jd parameter calculated from the isoconductance curves Sample

EC (meV)

2jd

M30

166 (5)

9.5 (2)

M40

183 (3)

6.4 (2)

M50

220 (18)

6.6 (8)

In addition, it is important to point out that the interparticle contacts also play a highlighted role; charging energy is affected not only by the grain boundaries and crystallite size, but also by the inter-particle spaces. The latter can lead to an overestimation of ‘‘d’’ in Eq. (4) and to electrical noises due to sample porosity; therefore, a good control of porosity is crucial for technological applications. Magnetic susceptibility and ZFC curves Continuing with the physical properties studies, graphs of in-phase and out-phase parts of AC magnetic susceptibility and ZFC measurements are analyzed. Figure 7 shows a characteristic in-phase susceptibility graph measured at 464 Hz for sample M40; similar results are observed in the other two samples (graphs omitted for sake of clarity). Analyzing the curves derivatives, changes in the in-phase slopes are observed in all samples at two different temperature ranges: 30–40 K and 90–100 K. It is observed that the first slope change, occurring at a temperature TSG around 30–40 K, is a transition

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that depends only on frequency; whereas the contrary occurs for the second transition temperature (TV) which depends on grain size, but is frequency independent. ZFC curves also show two slope changes at similar temperature ranges (within the experimental errors) to those obtained by susceptibility measurements, as can be seen in Fig. 8. At the inset graph a zoom in of the region where TV is observed. The transition observed at TV can be associated to magnetite Verwey transition. The Verwey transition occurs around 120 K for bulk magnetite and is related to atomic reordering in the crystal when transforming from cubic to monoclinic structure; as particle size decreases, this transformation takes place at lower temperatures probably because particle size reduction hinders long-range order (Balanda et al. 2005; Goya et al. 2003). However, the exact connection between the Verwey transition, particle size distribution, and other sample-dependent parameters is still a research challenge. The Verwey transition temperatures for the three samples are shown in Table 3. This transition becomes broader and seems to occur at lower temperature for the smallest particle size M30, whereas for the other two samples, with comparable particle sizes, transition occurs at similar temperatures. Similar behavior is observed in nanostructured magnetite systems (Gonzalez-Fernandez et al. 2009; Verge´s et al. 2008). In Fig. 9, the derivatives of in-phase susceptibility at 100 Hz and ZFC at 0 Hz curves for sample M30

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Fig. 8 ZFC curves obtained for samples M30, M40, and M50. Temperatures TSG and TV are indicated with arrows. TSG is almost constant for the three samples, while TV changes with particle size. The figure shows the curves with arbitrary units and do not reflect the relative magnetization of the samples. This graph is used for a better visualization of the changes of Verwey transition temperature

Table 3 Verwey and spin-glass transition temperatures observed by susceptibility characterization at 100 Hz Sample

TV (K)

TSG (K)

M30

85 (2)

35 (2)

M40

94 (2)

35 (2)

M50

93 (2)

35 (2)

show that Verwey transition takes place at around 85 K in both independent measurements. The shift of TV to lower temperatures can be attributed to small particles sizes. A sample with small particle size requires less thermal energy to transform from monoclinic to cubic crystal structure due to the lack of longrange order and high surface energy; on contrary, larger particles would need more thermal energy to change the crystalline order. On the other hand, the transition at lower temperatures, TSG, can be associated to a spin-glass-like transition, where a change from a state of disordered frozen spins at particle surface undergoes to a ferrimagnetic state with ordered magnetic spins; this yields to an abrupt increase of magnetic susceptibility, as can be seen in Figs. 7 and 8. It is observed that TSG is the same for all samples measured at same frequency, suggesting that this transition is neither affected by crystallite nor particle size. Table 3 shows values of TSG obtained for a frequency of 100 Hz.

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Fig. 9 Derivatives of in-phase susceptibility at 100 Hz and ZFC at 0 Hz curves for sample M30. The vertical lines indicate TV and TSG

In Fig. 10, the out-phase susceptibility curves show that spin-glass transition appears at low temperatures as an intense peak that shifts to higher temperatures as frequency increases, similarly to previous results.(Lopez Maldonado et al. 2013) TSG increases from 35 K at 100 Hz to 39 K at 774 Hz. Likewise, the comparison of derivative curves of in-phase susceptibility and ZFC curves evidences the same behavior: at null frequency (ZFC) the transition occurs at lower temperature than at 100 Hz, as seen in Fig. 9. This behavior could be better understood by means of susceptibility definition: vðTÞ /

v0 1 þ ixs

ð5Þ

where x is related to measuring frequency as 2pf, and s is the relaxation time described as s ¼ s0 expðEa =kB TÞ

ð6Þ

Ea is the activation energy. This activation energy is the energy necessary to break the spin-glass state and let all magnetic moments align ferrimagnetically (Zelenˇa´kova´ et al. 2010). The Ea and s values can be obtained by fitting the in-phase susceptibility curves with Eqs. (5) and (6). As can be seen on Fig. 11, activation energy, with values around 6–7 meV, slightly increases with frequency; whereas the relaxation times decreases almost two orders of magnitude. Due to activation energy increases with frequency, a shift to higher TSG values

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Fig. 10 Out-phase susceptibility curves for sample M30. The sharp peak is observed in all samples and is associated to a spinglass-like transition

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Fig. 11 Activation energy (Ea) and relaxation time (s) as a function of field frequency calculated from Eqs. 6 and 7

with increasing frequencies is expected; this behavior is the peak shifting, observed in the out-phase graphs in Fig. 10. Magnetic hysteresis Figure 12 shows characteristic hysteresis loops measured at different temperatures for sample M30. Similar behavior is observed for M40 and M50 (Lopez Maldonado et al. 2013). Coercive fields and magnetic saturations are found not to be significantly affected by crystallite or particle size, see Table 4; moreover, the magnetic saturation values are close to the reported value for bulk magnetite (84 emu/g); therefore, secondary phases, structural effects or nonmagnetic contributions can be disregard. For temperature higher than 50 K, coercive field and remanence decrease as temperature increases, as expected (Cullity and Graham 2009); however, a substantial drop of coercivity is observed from 5 to 50 K (see inset of Fig. 12). This change can be associated to the spin-glass transition observed in the magnetic susceptibility and ZFC studies. At low temperature, frozen magnetic moments at the grain surfaces give place to a rising in surface anisotropy increasing the coercive field (Lu et al. 2006). As temperature rises, spin-glass is broken leading to a lessening of the superficial anisotropy, consequently, coercivity decreases abruptly. The coercive field values as a function of temperature are shown in Table 4 for all samples. All these results indicate that, for crystallite sizes larger than 30 nm, the magnetic properties are not

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Fig. 12 Hysteresis loops measured at different temperatures for sample M30. At the inset, a zoom to the coercivity values of the sample

significantly affected; whereas, conduction phenomena are strongly influenced by grain boundary size and, consequently, by crystallite size.

Conclusions In this work, microstructural, electrical, and magnetic properties of magnetite NPs prepared by aging technique with crystallite sizes 30, 40, and 50 nm are investigated. By mean of HRTEM, it is found that grain boundaries size decreases as crystallite size increases. This leads to a change in the inter-particle charging energy due to differences in the energy barrier width, bearing on the conduction phenomena of the samples. By using impedance spectroscopy, charging energy is calculated for different crystallite

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Table 4 Values for Coercivity (HC), maximum magnetization (Mmax), and remanence (MR) observed at different temperatures from hysteresis loops for all samples Sample

T (K) 5

M30

M40

90

120

300

HC (Oe)

294 (1)

138 (1)

118 (1)

111 (1)

70 (1)

Mmax (emu/g)

83.7 (5)

83.8 (5)

83.9 (5)

83.8 (5)

80.3 (5)

MR (emu/g)

17.5 (1)

10.9 (1)

9.6 (1)

8.9 (1)

6.0 (1)

HC (Oe)

248 (1)

137 (1)

118 (1)

108 (1)

78 (1)

80 (4)

80 (4)

80 (4)

80 (4)

76 (4) 5.0 (2)

Mmax (emu/g) M50

50

MR (emu/g)

10.9 (4)

7.5 (4)

6.7 (3)

6.3 (3)

HC (Oe)

249 (1)

134 (1)

116 (1)

110 (1)

77 (1)

83 (1)

83 (1)

83 (1)

83 (1)

79 (1)

14.1 (2)

10.0 (1)

9.1 (1)

8.7 (1)

6.9 (1)

Mmax (emu/g) MR (emu/g)

and particle sizes. A relationship between particle size, grain boundary width, and charging energy is established. The results are in agreement with the expected behavior. On the other hand, hysteresis loops are not significantly affected by crystallite/particle size; saturation magnetization is close to the expected theoretical value. In addition to the microstructural effects on the electrical and magnetic properties, two transitions are observed by susceptibility and zero field cooling studies. The first one, the so called Verwey transition is found at 86, 90, and 94 K for samples M30, M40, and M50, respectively. This transition is particle size dependent, as reported by other authors (Goya et al. 2003). The transition occurring at 35 K is associated to a spin-glass-like transition. The activation energy for breaking the spin-glass state is calculated to be around 6 and 7 meV. This activation energy depends on frequency. The spin-glass-like transition is also confirmed by a strong coercivity decrease as temperature increases from 5 to 50 K, supporting the hypothesis that there is a change on the anisotropy due to the canted frozen spins at the surface. These results could help to improve magnetoresistive responses of magnetite in similar nanostructured systems. From the point of view of magnetic properties, only a good control on the magnetic phase would help to keep the maximum magnetization and coercivity values. Our results also suggest that particle or grain sizes larger than 30 nm have the magnetic properties of the bulk. Lower magnetization is expected for smaller sizes due to higher quantity of broken ligands at the surface.

Consequently, for magnetoresistive applications, systems with crystallite sizes above 30 nm could be better for the improvement of magnetic response control. On the other hand, conductivity is significantly affected by microstructure because of charging energy that strongly depends on crystallite size and grain boundaries width, as demonstrated. Therefore, a good control on the microstructure of magnetite would help to have adequate grain boundary conditions to achieve optimal charging energy values; thus, conduction could be enhanced to get a better magnetoresistive response. Acknowledgments This work was partially supported by FONCICYT Project 94682 ‘‘Oxides for Spintronics’’. Also, by Grants from the Spanish Ministry of Science and Innovation MAT2011-23641, MAT2012-37109-C02-01, and Madrid regional government CM (S009/MAT-1726). The authors want to acknowledge CONACYT, CIMAV, and UACJ for their support for making this research possible.

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