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Particle size, spin wave and surface effects on magnetic properties of MgFe2O4 nanoparticles
Journal of Magnetism and Magnetic Materials 422 (2017) 7–12
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Particle size, spin wave and surface effects on magnetic properties of MgFe2O4 nanoparticles B. Aslibeiki a,n, G. Varvaro b, D. Peddis b, P. Kameli c a
Department of Physics, University of Tabriz, Tabriz 51666-16471, Iran Istituto di Struttura della Materia, National Research Council, Monterotondo Scalo, Roma 00015, Italy c Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran b
art ic l e i nf o
a b s t r a c t
Article history: Received 28 March 2016 Received in revised form 6 July 2016 Accepted 19 August 2016 Available online 21 August 2016
Magnesium ferrite, MgFe2O4, nanoparticles with a mean diameter varying from ∼6 to ∼17 nm were successfully synthesized using a simple thermal decomposition method at different annealing temperatures ranging in between 400 and 600 °C. Pure spinel ferrite nanoparticles were obtained at temperatures lower than 500 °C, while the presence of hematite (α-Fe2O3) impurities was observed at higher temperatures. Single-phase samples show a superparamagnetic behavior at 300 K, the saturation magnetization (Ms) becoming larger with the increase of particles size. The temperature dependence of Ms was explained in terms of surface spin-canting as well as spin wave excitations in the core. Using a α modified Bloch law, [Ms(T)¼ Ms(0)(1 βT )], we observed a size dependent behavior of the Bloch constant β and the exponent α, whose values increase and decrease, respectively, as the particle size reduces. & 2016 Elsevier B.V. All rights reserved.
Keywords: Magnesium ferrite Annealing temperature Surface spins Bloch law Coercivity
1. Introduction Understanding the properties of magnetic nanoparticles have been a long-standing topics of interest for both fundamental studies and potential applications including transformers, microwave devices, magnetic storage media, ferrofluids, catalysts and biomedical devices [1–10]. Most of the physical properties of magnetic nanoparticles, such as the coercivity (Hc), the saturation magnetization (Ms), and the magnetic anisotropy (K), strongly depend on the particles size. It is well known that reducing the size below a threshold value, the magnetic multi-domain configuration, typical of bulk materials, is no more energetically favorable and a single-domain state is observed [11,12]. The magnetic moment of single-domain particles can be considered as a “superspin” with a magnitude in the range of 103–105 Bohr magnetons (μB) depending on the particle volume (V) [13,14]. Below a critical volume thermally activated magnetization reversal processes take place, thus resulting in a continuous flip of magnetization between its antiparallel easy directions separated by the energy barrier ΔE ¼KV for a uniaxial system (superparamagnetic state) [15–17]. Nanosized spinel ferrites, MeFe2O4 (Me2 þ : Mn, Fe, Ni, Co, Mg, Cu, etc.), have been intensively investigated in recent years because of their potential application in many fields including
biomedicine, microwaves and environmental safety [18–21]. In our previous studies we showed that both the saturation magnetization and the coercivity of MnFe2O4 nanoparticles reduce with the decrease of particles size [22]. The reduction of Ms is usually attributed to the higher surface/volume ratio of small particles [22– 25]. Indeed, the surface of nanoparticles often shows a non-collinear spin structure (i.e. spin-canting) due to broken bands and crystalline deficiencies, which results in a reduction of net magnetization, this effect being larger as the surface/volume ratio decreases with the reduction of particle size. On the other hand, far from the absolute zero, the core spins are not necessarily aligned because of thermally activated spin wave excitations [15,26], which also contributes to the reduction of the net magnetization [26,27]. To the best of our knowledge, only in a few papers the spin waves excitation mechanism is proposed to explain the dependence of the saturation magnetization on the particles size [26,27]. In addition, there is no a deep study on spin wave effects in magnesium ferrite (MgFe2O4) nanoparticles, as an important ferrite. Start to this frame, in this work we carefully discussed the effect of particle size on the magnetic properties of MgFe2O4 by considering both surface and the spin waves excitation effects.
2. Experimental and data treatment n
Corresponding author. E-mail address: [email protected] (B. Aslibeiki).
http://dx.doi.org/10.1016/j.jmmm.2016.08.057 0304-8853/& 2016 Elsevier B.V. All rights reserved.
MgFe2O4 nanoparticles were prepared using a simple thermal
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B. Aslibeiki et al. / Journal of Magnetism and Magnetic Materials 422 (2017) 7–12
crystalline structure was analyzed using a Philips X′Pert Pro MPDX-ray diffractometer with Cu-Kα (λ ¼0.154 nm) radiation. Microstructure was investigated by a JEM-2100 transmission electron microscope (TEM) with an accelerating voltage of 200 kV. A deep study of the magnetic properties was carried out by a Model-10 MicroSense vibrating sample magnetometer with a maximum applied field of 20 kOe.
3. Results and discussion
Fig. 1. TGA (dot line) and DTA (solid line) of the initial mixture of metal nitrates and citric acid.
Fig. 2. XRD patterns of the MgFe2O4 nanoparticles annealed at different temperatures.
Table 1 Lattice parameter (a), volume of unit cell (Vu.c.) and crystallites size (DXRD) of MgFe2O4 nanoparticles synthesized at different temperatures. Parameter
Mg400
Mg450
Mg500
Mg600
a (Å) Vu.c. (Å3) DXRD (nm)
8.37(3) 586(6) 6.4(0.3)
8.38(6) 588(8) 7.6(2)
8.39(0.05) 590(10) 8.8(3)
8.35(0.03) 582(6) 16.7(6)
decomposition method based on solid-state ball milling and calcination of metal nitrates and citric acid. The synthesis process can be summarized as follows: magnesium nitrate (Mg(NO3)2 6H2O, Merck, 99%), iron nitrate (Fe(NO3)3 9H2O, Merck, 99%), and citric acid (C6H6O7, Merck, 99.5%) powders were mixed by an equal molar ratio of total metal nitrates to citric acid. The powders were ball milled in a planetary ball mill for 1 h using agate balls. Finally, the ball milled powders were annealed in air at different temperatures, i.e. 400 °C (sample Mg400), 450 °C (sample Mg450), 500 °C (sample Mg500) and 600 °C (sample Mg600) for 1 h to obtain MgFe2O4 nanoparticles with different sizes. Thermogravimetry (TGA) and simultaneous differential thermal analysis (DTA) of the initial precursors were carried out on a BAHR STA 503 instrument with a heating rate of 10 °C min 1 in air. The
Thermal analysis (TGA and DTA) of the initial mixture of reactants (Fig. 1) was performed to investigate the thermal evolution of chemical reaction, allowing the appropriate annealing temperatures to be determined. The first endothermic peak around 100 °C, associated with small weight loss, is due to water evaporation in the reactant. In addition, different weight losses are visible in the TGA curve, being accompanied with exothermic peaks, around 110 °C, 165 °C, 310 °C and 390 °C. These positions are in good agreement with the boiling (or decomposition) point of iron nitrate (125–150 °C) [28,29], citric acid (∼175 °C) [30], magnesium nitrate (∼330 °C) [31] and the removal of residual carbon (∼400 °C). The arrows in Fig. 1 show the thermal decomposition temperature of each component. Furthermore, a small peak around 600 °C, not associated with weight loss, is visible in the DTA curve, which can be attributed to the decomposition of spinal ferrite to other compounds like α–Fe2O3 and MgO [32]. X-ray diffraction (XRD) patterns of all the samples are shown in Fig. 2. The observed reflections correspond to a cubic spinel phase with Fd-3m space group (JCPDS Card no. 73-1960). However, reflection peaks corresponding to the hematite phase (α–Fe2O3) appear in the XRD pattern of the Mg600 sample, being in agreement with the observed peak in the DTA curve around 600 °C. In most of the ferrites, the spinel structure is unstable at temperatures higher than 600 °C and typically decomposes to metal oxide phases [32,33]. The average crystallite size (DXRD) calculated by using the Scherrer's formula increases from ∼6 to ∼17 nm by enhancing the annealing temperature from 400 °C to 600 °C (Table 1). The lattice parameter a and volume of unit cell Vu.c ¼ a3 were determined using Eq. (1) where s is the spacing between the planes in the atomic lattice and the h,k,l are Miller indices. The obtained a values were almost identical for all the samples being also very close to the bulk value (8.36 Å) thus proving the high degree of crystallinity of the nanoparticles.
1 h2 + k 2 + l2 = 2 s a2
(1)
XRD results are also confirmed by the TEM investigation. As an example, Fig. 3a shows the TEM image of a selected area of the Mg500 sample. Nanoparticles are uniform in size and well distributed with some aggregation occurring. The size dispersion histogram reported in the inset is well fitted with a log-normal function leading to a mean diameter 〈d〉¼8.0(2). The measured particle size is in good agreement with the value obtained from the XRD pattern (DXRD ¼8.8(3)). In addition, the HRTEM image (Fig. 3b) where the lattice planes are clearly visible, confirms the high crystalline degree of the MgFe2O4 samples. Dynamics of the superspins has been recently investigated [34]: AC magnetic susceptibility shows broad peak (TP) increasing by increasing the annealing temperature, in the range 170–250 K. Frequency dependence of AC magnetic susceptibility shows features typical of superspin glass magnetization dynamics. Starting from this landscape, quasi static magnetic properties have been investigated in the range 120–290 K.
B. Aslibeiki et al. / Journal of Magnetism and Magnetic Materials 422 (2017) 7–12
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Fig. 3. (a) TEM image of the Mg500 sample. Inset shows the particles size distribution fitted with a log-normal function (solid line). (b) HRTEM image of MgFe2O4 nanoparticles prepared at 500 °C.
Fig. 4 shows the field-dependent magnetization loops of all the samples measured at 290 and 120 K. The maximum applied field (20 kOe) is not high enough to saturate the samples, both because of the presence of magnetic disorder at the particle surface and for the presence of a fraction of superparamagnetic particles [35,36]. Single phase ferrite samples are superparamagnetic at 290 K (i.e. zero coercivity and remanence magnetization), while the Mg600 sample shows an Hc ¼ 68(1) Oe (see inset in Fig. 4). At 120 K all the samples consist of blocked particles and the coercivity increases from 42(1) to 293(3) Oe by enhancing the annealing temperature from 400 °C to 600 °C, as a result of the increase of particles size and the energy barrier that must be overcome in the magnetization reversal process. Enhancing the annealing temperature also leads to an increase of the magnetization corresponding to the maximum applied field (M2T) from 8.1 emu/g to 16.9 emu/g at 290 K and from 11.6 emu/g to 23.1 emu/g at 120 K, being in any case smaller that the bulk saturation value (27 emu/g at 293 K [37]). The lower saturation value as well as its enhancement with the increase of particle size can be attributed, to a first approximation, to the surface effects, i.e. to the reduction of the surface/ volume ratio and then of the surface spin contribution to the total magnetization. This effect was investigated by fitting the fielddependent magnetization loops measured at 290 K with a modified Langevin function [38,39]:
⎛ μ H⎞ M = Ms L⎜ P ⎟ + χH ⎝ kBT ⎠
(2)
where μp is the average (superspin) moment, kB is the Boltzmann constant, L(x)¼coth(x) 1/x is the Langevin function, and χ is the high-field susceptibility that arises from the paramagnetic surface spins contribution [38–40]. The obtained values for μp, Ms and χ are collected in Table 2. The average moment μp is found to increase with the enhancement of the annealing temperature as a consequence of the increase of particle size. The high-field susceptibility shows a small initial increase and then remains almost constant with the increase of the annealing temperature, suggesting a similar paramagnetic behavior of surface spins in all the samples. To estimate the thickness of the surface layer, also referred as dead-layer, the following formula was used [41]:
Fig. 4. Field-dependent magnetization loops of all the samples measured at (a) 290 K and (b) 120 K. Solid curves in (a) show the fitting of experimental data with a modified Langevin function (Eq. (2)). Inset in (b) shows the low field magnetization behavior.
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⎛ 6t ⎞ ⎟ Ms = Ms⎜ 1 − ⎝ d⎠
(3)
where Ms is the bulk saturation magnetization, t the dead-layer thickness and d the particle diameter. The fitting was performed using the Ms value obtained from Eq. (2) and the crystallite size Table 2 Average moment (μp), saturation magnetization (Ms) and high-field susceptibility (χ) obtained by fitting the M–H curves at 290 K with Eq. (2). Parameter
Mg400
Mg450
Mg500
Mg600
μP(μB) Ms (emu/g) χ (emu/gOe)
704 4.77(0.05) 1.96(0.03)
799 6.69(0.06) 2.37(0.05)
831 8.5 2.28(0.02)
1328 13 2.17(0.05)
Table 3 Shell thickness and physical parameters of the MgFe2O4 nanoparticles as obtained from Eqs. (3) and (5). Parameter
Mg400
Mg450
Mg500
Mg600
t (nm) Ms(0) emu/g β ( 10 4 K α) α
0.88(3) 14.9 (8) 41(4) 0.83(2)
0.95(2) 18.4(0.4) 24(1) 0.91(1)
1.00(3) 21.1(0.4) 6.6(1) 1.14(1)
1.44(4) 25.3(2) 0.79(1) 1.47(4)
DXRD as a measure of the particle diameter. The estimated values of t are collected in Table 3. Pure ferrite samples present a similar dead-layer thickness ( 1 nm), thus indicating a reduction of the surface/volume ratio with the increase of particle size, which can explain, to a first approximation, the increase of saturation magnetization. The higher value of t ( 1.45 nm) observed in Mg600 sample can be ascribed to the presence of a small quantity of αFe2O3 that induces a reduction of Ms. Since the spin-wave excitations in the core can also affect the value of the saturation magnetization, their dependence on the particle size was investigated by studying the temperature dependence of the saturation magnetization in the 120–290 K range, where core spin effects are dominant being negligible the surface spins contribution, which is predominant at low temperatures (typically in the 30–50 K range) [42]. For this purpose, a series of field-dependent magnetization curves were measured at different temperatures in the 120–290 K range (Fig. 5) from which the temperature dependence of M2T was evaluated (Fig. 6a). The observed trend can be described by the Bloch law based on the presence of low energy collective spin-wave excitations (or magnons):
Ms(T ) = Ms(0)(1 − β T 3/2)
(4)
where Ms(0) is the saturation magnetization at absolute zero and β is Bloch constant. Because of the finite size effects, a deviation from the T3/2 dependence behavior could occur in nanoparticle
Fig. 5. M–H curves of all the samples measured at different temperatures.
B. Aslibeiki et al. / Journal of Magnetism and Magnetic Materials 422 (2017) 7–12
Fig. 6. Temperature dependence of M2T for MgFe2O4 samples annealed at different temperatures. (Symbols): experimental data; (Solid line): best fit of experimental data using Eq. (5).
systems [26,43]. As a consequence, a general formula, in which the exponent is given by a variable parameter α, depending on the particles size, was used [26]:
Ms(T ) = Ms(0)(1 − β T α )
(5)
Fig. 6(a) shows the best fits of experimental data with Eq. (5) and the obtained values for Ms(0), β and α are collected in Table 3. The values of the fitting parameters β and α increase and decrease, respectively, as the particles size reduces, thus confirming the sizedependent behavior of the spin-wave excitations. The β value depends on the Curie temperature (β∝1/Tc), which is affected by thermal fluctuations that are larger for surface than core spins. Therefore, increasing the size of particles and consequently decreasing the surface⁄volume ratio leads to a reduction of β. The observed increase of the α value with the increase of particles size was already reported in the literature for different nanoparticle systems [26,43], being related to a different temperature dependence behavior of the magnetization. The obtained value of α ¼1.47(4) for the Mg600 sample is close to the bulk one (1.5), suggesting that the strong increase of the particle size induces a bulk like behavior. The presence of a small quantity of hematite seems to not affect the magnetic behavior of the Mg600 sample.
4. Conclusion MgFe2O4 nanoparticles with a mean diameter varying from ∼6 to ∼17 nm were successfully synthesized using a simple thermal decomposition method at different annealing temperatures ranging in between 400 and 600 °C. Pure and high crystalline spinel ferrite nanoparticles were obtained up to a temperature of 500 °C, while hematite impurities were observed at 600 °C. The increase of particle size with increasing the annealing temperature results in an enhancement of saturation magnetization and coercivity, the former being attributed to both the surface effects and the sizedependent spin-wave excitations. Temperature dependent magnetic hysteresis loops revealed the size-dependent behavior of the spin-wave excitations.
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Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Particle size, spin wave and surface effects on magnetic properties of MgFe2O4 nanoparticles B. Aslibeiki a,n, G. Varvaro b, D. Peddis b, P. Kameli c a
Department of Physics, University of Tabriz, Tabriz 51666-16471, Iran Istituto di Struttura della Materia, National Research Council, Monterotondo Scalo, Roma 00015, Italy c Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran b
art ic l e i nf o
a b s t r a c t
Article history: Received 28 March 2016 Received in revised form 6 July 2016 Accepted 19 August 2016 Available online 21 August 2016
Magnesium ferrite, MgFe2O4, nanoparticles with a mean diameter varying from ∼6 to ∼17 nm were successfully synthesized using a simple thermal decomposition method at different annealing temperatures ranging in between 400 and 600 °C. Pure spinel ferrite nanoparticles were obtained at temperatures lower than 500 °C, while the presence of hematite (α-Fe2O3) impurities was observed at higher temperatures. Single-phase samples show a superparamagnetic behavior at 300 K, the saturation magnetization (Ms) becoming larger with the increase of particles size. The temperature dependence of Ms was explained in terms of surface spin-canting as well as spin wave excitations in the core. Using a α modified Bloch law, [Ms(T)¼ Ms(0)(1 βT )], we observed a size dependent behavior of the Bloch constant β and the exponent α, whose values increase and decrease, respectively, as the particle size reduces. & 2016 Elsevier B.V. All rights reserved.
Keywords: Magnesium ferrite Annealing temperature Surface spins Bloch law Coercivity
1. Introduction Understanding the properties of magnetic nanoparticles have been a long-standing topics of interest for both fundamental studies and potential applications including transformers, microwave devices, magnetic storage media, ferrofluids, catalysts and biomedical devices [1–10]. Most of the physical properties of magnetic nanoparticles, such as the coercivity (Hc), the saturation magnetization (Ms), and the magnetic anisotropy (K), strongly depend on the particles size. It is well known that reducing the size below a threshold value, the magnetic multi-domain configuration, typical of bulk materials, is no more energetically favorable and a single-domain state is observed [11,12]. The magnetic moment of single-domain particles can be considered as a “superspin” with a magnitude in the range of 103–105 Bohr magnetons (μB) depending on the particle volume (V) [13,14]. Below a critical volume thermally activated magnetization reversal processes take place, thus resulting in a continuous flip of magnetization between its antiparallel easy directions separated by the energy barrier ΔE ¼KV for a uniaxial system (superparamagnetic state) [15–17]. Nanosized spinel ferrites, MeFe2O4 (Me2 þ : Mn, Fe, Ni, Co, Mg, Cu, etc.), have been intensively investigated in recent years because of their potential application in many fields including
biomedicine, microwaves and environmental safety [18–21]. In our previous studies we showed that both the saturation magnetization and the coercivity of MnFe2O4 nanoparticles reduce with the decrease of particles size [22]. The reduction of Ms is usually attributed to the higher surface/volume ratio of small particles [22– 25]. Indeed, the surface of nanoparticles often shows a non-collinear spin structure (i.e. spin-canting) due to broken bands and crystalline deficiencies, which results in a reduction of net magnetization, this effect being larger as the surface/volume ratio decreases with the reduction of particle size. On the other hand, far from the absolute zero, the core spins are not necessarily aligned because of thermally activated spin wave excitations [15,26], which also contributes to the reduction of the net magnetization [26,27]. To the best of our knowledge, only in a few papers the spin waves excitation mechanism is proposed to explain the dependence of the saturation magnetization on the particles size [26,27]. In addition, there is no a deep study on spin wave effects in magnesium ferrite (MgFe2O4) nanoparticles, as an important ferrite. Start to this frame, in this work we carefully discussed the effect of particle size on the magnetic properties of MgFe2O4 by considering both surface and the spin waves excitation effects.
2. Experimental and data treatment n
Corresponding author. E-mail address: [email protected] (B. Aslibeiki).
http://dx.doi.org/10.1016/j.jmmm.2016.08.057 0304-8853/& 2016 Elsevier B.V. All rights reserved.
MgFe2O4 nanoparticles were prepared using a simple thermal
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crystalline structure was analyzed using a Philips X′Pert Pro MPDX-ray diffractometer with Cu-Kα (λ ¼0.154 nm) radiation. Microstructure was investigated by a JEM-2100 transmission electron microscope (TEM) with an accelerating voltage of 200 kV. A deep study of the magnetic properties was carried out by a Model-10 MicroSense vibrating sample magnetometer with a maximum applied field of 20 kOe.
3. Results and discussion
Fig. 1. TGA (dot line) and DTA (solid line) of the initial mixture of metal nitrates and citric acid.
Fig. 2. XRD patterns of the MgFe2O4 nanoparticles annealed at different temperatures.
Table 1 Lattice parameter (a), volume of unit cell (Vu.c.) and crystallites size (DXRD) of MgFe2O4 nanoparticles synthesized at different temperatures. Parameter
Mg400
Mg450
Mg500
Mg600
a (Å) Vu.c. (Å3) DXRD (nm)
8.37(3) 586(6) 6.4(0.3)
8.38(6) 588(8) 7.6(2)
8.39(0.05) 590(10) 8.8(3)
8.35(0.03) 582(6) 16.7(6)
decomposition method based on solid-state ball milling and calcination of metal nitrates and citric acid. The synthesis process can be summarized as follows: magnesium nitrate (Mg(NO3)2 6H2O, Merck, 99%), iron nitrate (Fe(NO3)3 9H2O, Merck, 99%), and citric acid (C6H6O7, Merck, 99.5%) powders were mixed by an equal molar ratio of total metal nitrates to citric acid. The powders were ball milled in a planetary ball mill for 1 h using agate balls. Finally, the ball milled powders were annealed in air at different temperatures, i.e. 400 °C (sample Mg400), 450 °C (sample Mg450), 500 °C (sample Mg500) and 600 °C (sample Mg600) for 1 h to obtain MgFe2O4 nanoparticles with different sizes. Thermogravimetry (TGA) and simultaneous differential thermal analysis (DTA) of the initial precursors were carried out on a BAHR STA 503 instrument with a heating rate of 10 °C min 1 in air. The
Thermal analysis (TGA and DTA) of the initial mixture of reactants (Fig. 1) was performed to investigate the thermal evolution of chemical reaction, allowing the appropriate annealing temperatures to be determined. The first endothermic peak around 100 °C, associated with small weight loss, is due to water evaporation in the reactant. In addition, different weight losses are visible in the TGA curve, being accompanied with exothermic peaks, around 110 °C, 165 °C, 310 °C and 390 °C. These positions are in good agreement with the boiling (or decomposition) point of iron nitrate (125–150 °C) [28,29], citric acid (∼175 °C) [30], magnesium nitrate (∼330 °C) [31] and the removal of residual carbon (∼400 °C). The arrows in Fig. 1 show the thermal decomposition temperature of each component. Furthermore, a small peak around 600 °C, not associated with weight loss, is visible in the DTA curve, which can be attributed to the decomposition of spinal ferrite to other compounds like α–Fe2O3 and MgO [32]. X-ray diffraction (XRD) patterns of all the samples are shown in Fig. 2. The observed reflections correspond to a cubic spinel phase with Fd-3m space group (JCPDS Card no. 73-1960). However, reflection peaks corresponding to the hematite phase (α–Fe2O3) appear in the XRD pattern of the Mg600 sample, being in agreement with the observed peak in the DTA curve around 600 °C. In most of the ferrites, the spinel structure is unstable at temperatures higher than 600 °C and typically decomposes to metal oxide phases [32,33]. The average crystallite size (DXRD) calculated by using the Scherrer's formula increases from ∼6 to ∼17 nm by enhancing the annealing temperature from 400 °C to 600 °C (Table 1). The lattice parameter a and volume of unit cell Vu.c ¼ a3 were determined using Eq. (1) where s is the spacing between the planes in the atomic lattice and the h,k,l are Miller indices. The obtained a values were almost identical for all the samples being also very close to the bulk value (8.36 Å) thus proving the high degree of crystallinity of the nanoparticles.
1 h2 + k 2 + l2 = 2 s a2
(1)
XRD results are also confirmed by the TEM investigation. As an example, Fig. 3a shows the TEM image of a selected area of the Mg500 sample. Nanoparticles are uniform in size and well distributed with some aggregation occurring. The size dispersion histogram reported in the inset is well fitted with a log-normal function leading to a mean diameter 〈d〉¼8.0(2). The measured particle size is in good agreement with the value obtained from the XRD pattern (DXRD ¼8.8(3)). In addition, the HRTEM image (Fig. 3b) where the lattice planes are clearly visible, confirms the high crystalline degree of the MgFe2O4 samples. Dynamics of the superspins has been recently investigated [34]: AC magnetic susceptibility shows broad peak (TP) increasing by increasing the annealing temperature, in the range 170–250 K. Frequency dependence of AC magnetic susceptibility shows features typical of superspin glass magnetization dynamics. Starting from this landscape, quasi static magnetic properties have been investigated in the range 120–290 K.
B. Aslibeiki et al. / Journal of Magnetism and Magnetic Materials 422 (2017) 7–12
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Fig. 3. (a) TEM image of the Mg500 sample. Inset shows the particles size distribution fitted with a log-normal function (solid line). (b) HRTEM image of MgFe2O4 nanoparticles prepared at 500 °C.
Fig. 4 shows the field-dependent magnetization loops of all the samples measured at 290 and 120 K. The maximum applied field (20 kOe) is not high enough to saturate the samples, both because of the presence of magnetic disorder at the particle surface and for the presence of a fraction of superparamagnetic particles [35,36]. Single phase ferrite samples are superparamagnetic at 290 K (i.e. zero coercivity and remanence magnetization), while the Mg600 sample shows an Hc ¼ 68(1) Oe (see inset in Fig. 4). At 120 K all the samples consist of blocked particles and the coercivity increases from 42(1) to 293(3) Oe by enhancing the annealing temperature from 400 °C to 600 °C, as a result of the increase of particles size and the energy barrier that must be overcome in the magnetization reversal process. Enhancing the annealing temperature also leads to an increase of the magnetization corresponding to the maximum applied field (M2T) from 8.1 emu/g to 16.9 emu/g at 290 K and from 11.6 emu/g to 23.1 emu/g at 120 K, being in any case smaller that the bulk saturation value (27 emu/g at 293 K [37]). The lower saturation value as well as its enhancement with the increase of particle size can be attributed, to a first approximation, to the surface effects, i.e. to the reduction of the surface/ volume ratio and then of the surface spin contribution to the total magnetization. This effect was investigated by fitting the fielddependent magnetization loops measured at 290 K with a modified Langevin function [38,39]:
⎛ μ H⎞ M = Ms L⎜ P ⎟ + χH ⎝ kBT ⎠
(2)
where μp is the average (superspin) moment, kB is the Boltzmann constant, L(x)¼coth(x) 1/x is the Langevin function, and χ is the high-field susceptibility that arises from the paramagnetic surface spins contribution [38–40]. The obtained values for μp, Ms and χ are collected in Table 2. The average moment μp is found to increase with the enhancement of the annealing temperature as a consequence of the increase of particle size. The high-field susceptibility shows a small initial increase and then remains almost constant with the increase of the annealing temperature, suggesting a similar paramagnetic behavior of surface spins in all the samples. To estimate the thickness of the surface layer, also referred as dead-layer, the following formula was used [41]:
Fig. 4. Field-dependent magnetization loops of all the samples measured at (a) 290 K and (b) 120 K. Solid curves in (a) show the fitting of experimental data with a modified Langevin function (Eq. (2)). Inset in (b) shows the low field magnetization behavior.
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⎛ 6t ⎞ ⎟ Ms = Ms⎜ 1 − ⎝ d⎠
(3)
where Ms is the bulk saturation magnetization, t the dead-layer thickness and d the particle diameter. The fitting was performed using the Ms value obtained from Eq. (2) and the crystallite size Table 2 Average moment (μp), saturation magnetization (Ms) and high-field susceptibility (χ) obtained by fitting the M–H curves at 290 K with Eq. (2). Parameter
Mg400
Mg450
Mg500
Mg600
μP(μB) Ms (emu/g) χ (emu/gOe)
704 4.77(0.05) 1.96(0.03)
799 6.69(0.06) 2.37(0.05)
831 8.5 2.28(0.02)
1328 13 2.17(0.05)
Table 3 Shell thickness and physical parameters of the MgFe2O4 nanoparticles as obtained from Eqs. (3) and (5). Parameter
Mg400
Mg450
Mg500
Mg600
t (nm) Ms(0) emu/g β ( 10 4 K α) α
0.88(3) 14.9 (8) 41(4) 0.83(2)
0.95(2) 18.4(0.4) 24(1) 0.91(1)
1.00(3) 21.1(0.4) 6.6(1) 1.14(1)
1.44(4) 25.3(2) 0.79(1) 1.47(4)
DXRD as a measure of the particle diameter. The estimated values of t are collected in Table 3. Pure ferrite samples present a similar dead-layer thickness ( 1 nm), thus indicating a reduction of the surface/volume ratio with the increase of particle size, which can explain, to a first approximation, the increase of saturation magnetization. The higher value of t ( 1.45 nm) observed in Mg600 sample can be ascribed to the presence of a small quantity of αFe2O3 that induces a reduction of Ms. Since the spin-wave excitations in the core can also affect the value of the saturation magnetization, their dependence on the particle size was investigated by studying the temperature dependence of the saturation magnetization in the 120–290 K range, where core spin effects are dominant being negligible the surface spins contribution, which is predominant at low temperatures (typically in the 30–50 K range) [42]. For this purpose, a series of field-dependent magnetization curves were measured at different temperatures in the 120–290 K range (Fig. 5) from which the temperature dependence of M2T was evaluated (Fig. 6a). The observed trend can be described by the Bloch law based on the presence of low energy collective spin-wave excitations (or magnons):
Ms(T ) = Ms(0)(1 − β T 3/2)
(4)
where Ms(0) is the saturation magnetization at absolute zero and β is Bloch constant. Because of the finite size effects, a deviation from the T3/2 dependence behavior could occur in nanoparticle
Fig. 5. M–H curves of all the samples measured at different temperatures.
B. Aslibeiki et al. / Journal of Magnetism and Magnetic Materials 422 (2017) 7–12
Fig. 6. Temperature dependence of M2T for MgFe2O4 samples annealed at different temperatures. (Symbols): experimental data; (Solid line): best fit of experimental data using Eq. (5).
systems [26,43]. As a consequence, a general formula, in which the exponent is given by a variable parameter α, depending on the particles size, was used [26]:
Ms(T ) = Ms(0)(1 − β T α )
(5)
Fig. 6(a) shows the best fits of experimental data with Eq. (5) and the obtained values for Ms(0), β and α are collected in Table 3. The values of the fitting parameters β and α increase and decrease, respectively, as the particles size reduces, thus confirming the sizedependent behavior of the spin-wave excitations. The β value depends on the Curie temperature (β∝1/Tc), which is affected by thermal fluctuations that are larger for surface than core spins. Therefore, increasing the size of particles and consequently decreasing the surface⁄volume ratio leads to a reduction of β. The observed increase of the α value with the increase of particles size was already reported in the literature for different nanoparticle systems [26,43], being related to a different temperature dependence behavior of the magnetization. The obtained value of α ¼1.47(4) for the Mg600 sample is close to the bulk one (1.5), suggesting that the strong increase of the particle size induces a bulk like behavior. The presence of a small quantity of hematite seems to not affect the magnetic behavior of the Mg600 sample.
4. Conclusion MgFe2O4 nanoparticles with a mean diameter varying from ∼6 to ∼17 nm were successfully synthesized using a simple thermal decomposition method at different annealing temperatures ranging in between 400 and 600 °C. Pure and high crystalline spinel ferrite nanoparticles were obtained up to a temperature of 500 °C, while hematite impurities were observed at 600 °C. The increase of particle size with increasing the annealing temperature results in an enhancement of saturation magnetization and coercivity, the former being attributed to both the surface effects and the sizedependent spin-wave excitations. Temperature dependent magnetic hysteresis loops revealed the size-dependent behavior of the spin-wave excitations.
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