Effects of grain boundary width and crystallite size on conductivity and magnetic properties of magnetite nanoparticles

RESEARCH PAPER

Effects of grain boundary width and crystallite sizeon conductivity and magnetic properties of magnetitenanoparticles

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

� 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. Conduc-

tion 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-field-

cooling 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.

Keywords Magnetite � Nanoparticles � Verwey

transition � Spin-glass � Impedance spectroscopy �Magnetic properties

Introduction

Magnetic nanoparticles (NPs) are subject of continu-

ous and growing interest from fundamental and

K. L. Lopez Maldonado � J. T. Elizalde Galindo (&)

Instituto de Ingenierıa y Tecnologıa, Universidad

Autonoma de Ciudad Juarez, Av. Del Charro 450 norte,

32310 Ciudad Juarez, Mexico

e-mail: [email protected]

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. Fısica de Materiales, Univ. Complutense de Madrid,

Madrid, Spain

M. A. de la Rubia � J. de Frutos

Dpto. Electroceramica, Instituto de Ceramica y Vidrio

(CSIC), Madrid, Spain

M. A. de la Rubia � J. de Frutos

Grupo Poemma, ETSI Telecomunicacion (UPM), Madrid,

Spain

J. A. Matutes Aquino

Centro de Investigacion en Materiales Avanzados, Miguel

de Cervantes 120, 31109 Chihuahua, Mexico

123

J Nanopart Res (2014) 16:2482

DOI 10.1007/s11051-014-2482-3

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 techno-

logical 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 tem-

perature range due to its magnetic properties: high

Curie temperature, large magnetic saturation, large

critical size, etc. Furthermore, magnetite is a half-

metallic 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 coeffi-

cient. 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; Kol-

esnichenko 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 magnetoresis-

tive properties of magnetite are matters of great

importance.

Another interesting structural characteristic appear-

ing in magnetite is Verwey transition. Verwey tran-

sition is reported for bulk magnetite at *125 K, and

during this transformation the structure undergoes

from monoclinic to cubic structure above Verwey

temperature, TV, where the resistance changes by two

orders of magnitude (Garcıa and Subıas 2004; Walz

2002). Although this transition has not been com-

pletely 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;

Verges 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;

Verges 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 bound-

ary width on these properties. Charging energy, and its

dependence on crystallite sizes, is studied by imped-

ance spectroscopy. Besides, magnetic measurements

are used to study Verwey and spin-glass transitions.

Frequency and crystallite size dependences are ana-

lyzed. 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;

Verges 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.

2482 Page 2 of 12 J Nanopart Res (2014) 16:2482

123

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-Karadiation in a PANalytical X’Pert Pro MPD diffrac-

tometer, 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 characteriza-

tion, 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 fre-

quency ranging from 100 to 774 Hz. Magnetization

measurements are carried out using a SQUID Physical

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

with space group Fd�3m, 32 O2? ions arranged in a face

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 (Dezsi 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

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

Fig. 1 XRD patterns for the three samples. All peaks were

identified with #PDF 01-075-0449

J Nanopart Res (2014) 16:2482 Page 3 of 12 2482

123

crystalline phase is achieved in all samples (#PDF01-

075-0449); no secondary phases are observed. Vari-

ation 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 differ-

ences 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.

Cell parameter is close to 8.35 A for all samples, in

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 sam-

ples; 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-spher-

ical particles. This morphological difference is attrib-

uted to a pH variation during chemical reaction

(Verges 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

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 monocrys-

talline; 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,

with interplanar distance 4.71 and 3.03 A, respec-

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 well-

organized 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.

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


123

Fig. 3 HRTEM images of

a planes (111) of a

tetragonal particle and

b planes (111) and (220) of a

polycrystalline quasi-

spherical 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


123

Electrical characterization

After microstructural and crystallinity analysis, and

continuing to achieve a good understanding on the

physical properties of magnetite, the electrical prop-

erties of samples are studied by impedance spectros-

copy 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 differ-

ence between these magnitudes, impedance is a

complex function of frequency:

Z xð Þ ¼ Z 0 xð Þ þ iZ 00 xð Þ 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 phe-

nomena 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. There-

fore, 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 CðxÞis the inverse of RðxÞ. Given the relationship between

impedance, conductance, and resistance, the following

discussion can help to clarify the conduction phenom-

ena and their connection with microstructural and

crystallinity properties.

Figure 4a shows the results for impedance depend-

ing 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

Fig. 4 a Frequency-

dependent 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)


123

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 behav-

ior 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 contri-

bution 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

103 Hz, frequency dependence of impedance is tem-

perature independent.

Now, as theoretically defined for TMR systems,

conductance can be expressed in terms of the potential

barrier and thermal energy as

C / exp �2jd � EC

kBT

� �ð3Þ

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

grains, it may be assumed that EC � e2�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 ¼C0

dð4Þ

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.

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

crystallite sizes


123

In addition, it is important to point out that the inter-

particle 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

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 measure-

ments, 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 (Gonz-

alez-Fernandez et al. 2009; Verges et al. 2008).

In Fig. 9, the derivatives of in-phase susceptibility

at 100 Hz and ZFC at 0 Hz curves for sample M30

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

sample M30

Table 2 Values of the charging energy, EC, and 2jd param-

eter 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)

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


123

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 mono-

clinic to cubic crystal structure due to the lack of long-

range 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 temper-

atures, 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.

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.(Lo-

pez 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 tem-

perature than at 100 Hz, as seen in Fig. 9.

This behavior could be better understood by means

of susceptibility definition:

vðTÞ / v0

1þ ixsð5Þ

where x is related to measuring frequency as 2pf, and

s is the relaxation time described as

s ¼ s0 expðEa=kBTÞ 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

(Zelenakova 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

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)

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


123

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 mea-

sured 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, sec-

ondary 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 Gra-

ham 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

significantly affected; whereas, conduction phenom-

ena 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 tech-

nique 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

Fig. 10 Out-phase susceptibility curves for sample M30. The

sharp peak is observed in all samples and is associated to a spin-

glass-like transition

Fig. 11 Activation energy (Ea) and relaxation time (s) as a

function of field frequency calculated from Eqs. 6 and 7

Fig. 12 Hysteresis loops measured at different temperatures

for sample M30. At the inset, a zoom to the coercivity values of

the sample


123

and particle sizes. A relationship between particle size,

grain boundary width, and charging energy is estab-

lished. The results are in agreement with the expected

behavior. On the other hand, hysteresis loops are not

significantly affected by crystallite/particle size; sat-

uration magnetization is close to the expected theo-

retical 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 con-

firmed 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 magnetore-

sistive responses of magnetite in similar nanostruc-

tured systems. From the point of view of magnetic

properties, only a good control on the magnetic

phase would help to keep the maximum magnetiza-

tion and coercivity values. Our results also suggest

that particle or grain sizes larger than 30 nm have

the magnetic properties of the bulk. Lower magne-

tization 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 signif-

icantly affected by microstructure because of charg-

ing energy that strongly depends on crystallite size

and grain boundaries width, as demonstrated. There-

fore, 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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Effects of grain boundary width and crystallite size on conductivity and magnetic properties of magnetite nanoparticles

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