From core/shell to hollow Fe/γ-Fe₂O₃ nanoparticles: evolution of the magnetic behavior

Figures 1(a)–(c) show conventional bright-field TEM images of the 12 nm core/shell, core/void/shell, and hollow nanoparticles (scale bars are 20 nm), along with a representative histogram of the particle size population as observed from the TEM image of the core/shell nanoparticles (inset of figure 1(a)). The size distribution results for the other nanoparticles are very similar. Contrast variation in the center of the core/shell nanoparticles clearly indicates that with increasing time, the core of the nanoparticles becomes progressively smaller until it finally disappears. A clear transformation in the morphology from core/shell to core/void/shell and to hollow is seen in the TEM images of figures 1(a)–(c). The average particle diameter, core diameter, and shell thickness of the 12 and 8 nm core/shell nanoparticles before and after transforming into the core/void/shell and hollow structures are listed in table 1. It is worth noting herein that both the core size and the shell thickness were altered during the core/shell to hollow transformation process. For both the 8 and 12 nm nanoparticles, the average particle diameter increases considerably when transforming from the core/shell to hollow morphology. Under this transformation, the shell thickness increases significantly for the case of the 12 nm particles, while it remains almost unchanged for the case of the 8 nm particles. These morphological changes are shown below to significantly influence the static and dynamic magnetic properties of the nanoparticles.

Zoom In Zoom Out Reset image size

The SAED pattern of the 12 nm hollow nanoparticles is presented in the inset to figure 1(c), and is indexed to be fcc iron-oxide. HRTEM images of core/shell, core/void/shell, and hollow nanoparticles are respectively displayed in figures 1(d)–(f). These HRTEM images reveal the crystalline structure of both core and shell with lattice spacing of 2.02 Å for the core and 2.52 Å for the shell corresponding to (110) planes of bcc iron and (311) planes of fcc iron oxide phase, respectively. The Fe core is single crystalline, however, the shell of γ-Fe₂O₃ is composed of small crystallites which are oriented randomly, as described in figure 1(f). In addition, we have recently performed x-ray absorption near edge spectroscopy (XANES) on these samples, and the fitting results (not shown here) corroborate that the shell is mostly formed by maghemite, while the core is composed of Fe.

In this section we first present and discuss the magnetic data of the 12 nm core/shell, core/void/shell, and hollow nanoparticles. The temperature dependence of magnetization (M–T) was measured under the zero-field-cooled (ZFC) and field-cooled (FC) protocols in a field of 100 Oe for all samples investigated. Figure 2(a) shows the ZFC M–T curves measured for the three samples. These curves have been normalized to M_max for comparison. Clearly, the ZFC M–T curves exhibit a typical peak, T_P-ZFC, which displaces towards a lower temperature when the morphology changes from core/shell to core/void/shell and hollow (table 2). During this process, the mass normalized magnetization progressively decreases, and the ZFC and FC magnetization branches become more separated, with the irreversibility, T_irr, taking place at increasingly higher temperatures (see figure 2(b) and its inset). At low temperatures T < T_P-ZFC, the FC M–T curves show different behaviors; for the core/shell sample the FC magnetization first decreased with lowering temperature just below T_P-ZFC and then became almost unchanged, while for the hollow sample the FC magnetization first increased and then remained constant. These results clearly indicate that the thermal dependent magnetic behavior of the 12 nm particles was largely altered as the core/shell morphology became progressively hollow.

Zoom In Zoom Out Reset image size

It is generally accepted that for an ensemble of non-interacting, monodisperse nanoparticles, the peak in a ZFC M–T curve (T_P-ZFC) is referred as to the mean blocking temperature (T_B), and is defined as the temperature at which the relaxation time of the nanoparticles, τ, is equal to the measurement time of the system, t_m. For SPM non-interacting nanoparticles, the relaxation time is given by the Néel expression τ = τ₀ exp(KV/k_BT), being K the anisotropy constant of the nanoparticles, V the volume of each nanoparticle, and ${{\rm{\tau }}}_{0}$ is related to the gyromagnetic precession (10⁻⁹ − 10⁻¹⁰ s). In the particular case of a VSM, the measurement time can be considered to be t_m ∼ 100 s and therefore T_B ≈ KV/25k_B. In this kind of system, T_irr often takes place near T_P-ZFC, and the FC magnetization continuously increases with decreasing temperature. This clearly differs from the behavior observed for our nanoparticles (figure 2), suggesting that the energy barrier is being significantly affected by the different nature of the core and the shell, inter-particle and intra-particle interactions, surface disorder, and finite-size distribution [16]. Therefore, T_P-ZFC may not represent the true blocking temperature of the presently studied nanoparticles. To be more precise, we have defined the mean blocking temperature, 〈T_B〉, as the temperature at which the maximum number of nanoparticles enters a blocked state as temperature decreases. Taking this into account, 〈T_B〉 can be easily determined from the peak position in the d(M_FC-M_ZFC)/dT [40], as illustrated in figure 2(b). The values of 〈T_B〉 of the samples are summarized in table 2. According to the Neel–Arrhenius magnetic relaxation model, 〈T_B〉 of a particle system is proportional to the average anisotropy and volume of the nanoparticles, 〈T_B〉 = KV/25k_B. This would lead to a general expectation that 〈T_B〉 increases as the nanoparticles transform from the core/shell to hollow morphology, since the total volume effectively increases (from 800 to 1400 nm³). But, unlike the case of nanoparticles made up of one kind of material, for our nanoparticles we have to consider the individual core (Fe) and the nanograins (γ-Fe₂O₃) in the shell as different magnetic entities with different blocking temperatures [16, 26]. Since the nanograins in the shell are not spherical and possess a considerable size distribution (figure 1(d)), an accurate determination of the average grain size is not easy [26, 34, 35]. However, we can suppose, in a first approximation, that the average grain size is close to the shell thickness. Using these values and the previously obtained 〈T_B〉, the effective anisotropy of the γ-Fe₂O₃ hollow nanoparticles is estimated to be ∼9.5×10⁶ erg cm⁻³, which is two orders of magnitude higher than that of bulk maghemite (4.5×10⁴ erg cm⁻³) and compares well with the values reported for these kinds of systems [35, 41]. It is also noted that the anisotropy axis in each individual crystallite can lead to a formation of multiple magnetic domains in the shell. For the core/shell and core/void/shell nanoparticles, the analysis becomes even more cumbersome, because of the presence of the core, with its own anisotropy constant, that will also affect the effective anisotropy of the shell due to core/shell interactions. For the core/shell and core/void/shell nanoparticles, if we assume that, due to the higher magnetization of the Fe core, we are mostly seeing the blocking of the Fe cores at 〈T_B〉, the effective anisotropy is determined to be ∼1.5×10⁶ erg cm⁻³ and ∼4.1×10⁶ erg cm⁻³, respectively, which is one order of magnitude larger than that of bulk Fe (∼5×10⁵ erg cm⁻³). Since we are not considering the contribution of the shell grains to the anisotropy, these values should be regarded as purely qualitative estimations.

As we noted above, there are some distinct differences in the FC M–T behavior between the core/shell and hollow nanoparticles (figure 2(b)). For the hollow nanoparticles, a large separation between the ZFC and FC magnetization branches can be related to the size distribution of the nanograins inside the shell, the presence of large exchange anisotropy, and the effects of inter-particle and intra-particle interactions. For the core/shell nanoparticles, the FC magnetization abruptly decreases (ΔFC = 23%) from T_P-ZFC down to 50 K, below which it remains almost constant. This decrease of the FC magnetization in systems of interacting solid nanoparticles at low temperatures has been attributed to the onset of a collective glassy behavior and/or to the freezing of surface spins [31, 42, 43]. On the other hand, for the hollow nanoparticles the FC magnetization keeps increasing below T_P-ZFC and reaches a maximum around 40 K, below which it experiences a much smaller decrease (ΔFC = 0.5%). This behavior is more similar to that reported for non-interacting SPM systems.

The strength and nature of magnetic interactions in the present nanoparticles can be further analyzed by fitting the ZFC−FC curves for T > T_P-ZFC to a Curie–Weiss model. It is well known that in the SPM regime (T > 〈T_B〉), the magnetic susceptibility of a particle system can be typically described by a Curie–Weiss law:

$$\begin{eqnarray}&&\chi =\displaystyle \frac{C}{T-{T}_{{\rm{C}}}},\end{eqnarray} \tag{ 1 }$$

where C is a constant, which depends on the magnetic moment of the nanoparticles, and T_C is a temperature whose absolute value can be considered as a measure of the strength of interparticle interactions. As can be seen in figure 2(c), reasonable fits have been obtained for all three samples in the high temperature range. The T_C values are determined to be 59, 11, and −320 K, for the core/shell, core/void/shell, and hollow nanoparticles, respectively. The change in sign of T_C could suggest some considerable change in the magnetic behavior of the nanoparticles when the core/shell morphology was changed into the hollow structure. For the core/shell nanoparticles, the positive sign indicates that ferromagnetic (FM) interactions are established between the nanoparticles, probably of dipolar nature since the nanoparticles are not in contact due to the surfactants on their surfaces, and mainly mediated by the Fe cores. Since the size of the core diminishes for the core/void/shell nanoparticles, the strength of these interactions also diminishes, consistent with the observation that T_C decreased from 59 K for the core/shell nanoparticles to 11 K for the core/void shell nanoparticles. For the hollow nanoparticles, however, we have obtained a high negative value of T_C (−320 K). Given the very small size and high anisotropy of the randomly oriented nanograins inside the shell, it is reasonable to attribute this to the relative orientation of the anisotropy axes of the shell nanograins with respect to the magnetic field [44], rather than to the existence of very strong antiferromagnetic (AFM) inter-grain interactions, although the latter cannot be completely ruled out.

To further probe this, we have compared our experimental ZFC results with the theory. For simulations, we have used an expression derived from the Stoner–Wohlfarth model [40]. In principle this model was designed for non-interacting uniaxial nanoparticles, but, in a first approximation, it can be considered that the presence of interparticle interactions will mainly affect the effective anisotropy constant, K. According to this model, the ZFC magnetization is given by:

$$\begin{eqnarray}&&{M}_{{\rm{ZFC}}}=\displaystyle {\int }_{0}^{{V}_{{\rm{c}}}}{M}_{{\rm{ZFC}}}^{{\rm{SPM}}}f(V){\rm{d}}V+\displaystyle {\int }_{{V}_{{\rm{C}}}}^{\infty }{M}_{{\rm{ZFC}}}^{{\rm{bl}}}f(V){\rm{d}}V,\end{eqnarray} \tag{ 2 }$$

where the first and second terms correspond to the un-blocked SPM (V < V_C) and the blocked nanoparticles (V > V_C), respectively, being:

$$\begin{eqnarray}&&{M}_{{\rm{ZFC}}}^{{\rm{SPM}}}={M}_{{\rm{o}}}L(\displaystyle \frac{{\mu }_{0}{M}_{{\rm{s}}}VH}{{k}_{{\rm{B}}}T})\\ &&{M}_{{\rm{ZFC}}}^{{\rm{bl}}}={M}_{{\rm{o}}}\displaystyle \frac{{\mu }_{0}{M}_{{\rm{s}}}H}{3K}.\end{eqnarray} \tag{ 3 }$$

L(x) corresponds to a Langevin function, L(x) = cotanh(x)-1/x, M_o is the saturation magnetization of the system of nanoparticles (given by the M–H loops), and M_S is the saturation magnetization of each nanoparticle according to their composition (e.g. M_S = 392 emu cm⁻³ for bulk maghemite). The function f(V) or f(D) is the particle size distribution; in our case a log-normal function defined by two parameters ($\alpha$ and $\beta )$ has been used, as shown below:

$$\begin{eqnarray}&&f(D)=\displaystyle \frac{1}{D\beta \sqrt{2\pi }}\cdot \mathrm{exp}(-\displaystyle \frac{{(\mathrm{ln}\;D-\;\mathrm{ln}\;\alpha )}^{2}}{2{\beta }^{2}}).\end{eqnarray} \tag{ 4 }$$

In this distribution the mean diameter and standard deviation are given by:

$$\begin{eqnarray}&&\bar{D}=\alpha \mathrm{exp}({\beta }^{2}/2),\quad {\sigma }^{2}={\bar{D}}^{2}(\displaystyle \frac{{\bar{D}}^{2}}{{\alpha }^{2}}-1).\end{eqnarray} \tag{ 5 }$$

As observed in figure 2(d), a good fit with this model has been obtained only for the core/shell nanoparticles. The main problem with the fittings for the core/void/shell and hollow nanoparticles is the slower decay of the magnetization above T_P-ZFC, which can be related to the broader distribution of energy barriers of the shell nanograins. For the core/shell nanoparticles, the average size is estimated to be D = 7.0 nm, which is close to the core size determined from the TEM image (figure 1(a)), and the obtained value of K = 1.5 × 10⁶ erg cm⁻³ is also close to that estimated above. This indicates that at T ∼ 55 K, the magnetic behavior of the core/shell system can be understood in terms of an ensemble of interacting nanoparticles, with an effective size close to that of the Fe core, which starts to become collectively blocked at T ∼ 100 K. Since the interactions are mainly of dipolar nature, we can estimate the dipolar temperature, T_dip = E_dip/k_B, for the core/shell nanoparticles. The value of the dipolar energy E_dip is given by:

$$\begin{eqnarray}&&{E}_{{\rm{dip}}}=\;\displaystyle \frac{{\mu }_{0}{\mu }^{2}}{4\pi {L}^{3}}.\end{eqnarray} \tag{ 6 }$$

Since the nanoparticles in our study are packed together, though not in direct contact due to the presence of surfactants (see figure 1), L can be considered to be close to the diameter of the particle (L ∼ 12–13 nm). Accordingly, the value of T_dip for the core/shell nanoparticles is calculated to be ∼95 K, which is close to T_P-ZFC (111 K), corroborating the dipolar nature of the interactions in this system. For the hollow nanoparticles, however, T_dip is close to 0 K, suggesting that as the nanoparticles become hollow, dipolar interparticle interactions become less relevant.

To probe the magnetic field evolution of the magnetization in the core/shell, core/void/shell, and hollow morphologies, we have measured and analyzed the magnetic hysteresis (M–H) loops at low (5 K) and high (300 K) temperatures. As can be seen in figure 3(a), the M–H curves measured at 5 K under ZFC protocol show a clear hysteresis and a non-saturating behavior. The loops have been normalized to M_50kOe for comparison. The overall shape of the M–H loops changes slightly when going from the core/shell to core/void/shell morphology, with a small increase of the high field slope and a decrease of the saturation magnetization. The decrease of the coercivity when going from the core/shell to core/void/shell morphology has been attributed to the detachment of the core from the shell [45]. For the hollow nanoparticles, however, the shape of the M–H loops changes drastically, presenting an elongated shape with a pronounced increase of the coercivity and the high field slope. As summarized in table 3, as the nanoparticles become hollow, the normalized remanence decreases, while the coercivity greatly increases. The M–H loop for the hollow nanoparticles, especially at low temperatures, resembles those of frustrated and disordered random anisotropy magnets, and the same features have also been observed in similar hollow maghemite nanoparticles with strong shell anisotropy [35]. This suggests that there is a higher frustration for the spins in the shell of the hollow nanoparticles in comparison with the core/shell and core/void/shell ones. On the other hand, for the core/shell and core/void/shell nanoparticles, the presence of the Fe core and the reduced volume of the shell (V_sh ∼ 650 nm³ for the core/shell and core/void/shell nanoparticles, while V_sh ∼ 1400 nm³ for the hollow nanoparticles) give a behavior more similar to the one expected in interacting nanoparticle systems.

Zoom In Zoom Out Reset image size

To understand the relative contributions of the disordered surface and interface spins to the magnetization of the nanoparticles, we have analyzed the M–H loops measured at 300 K. As observed in figures 3(b)–(d), all the M–H curves present no hysteresis, meaning null coercivity and remanence, and a linear contribution at high fields that tends to increase when going from the core/shell to hollow morphology. This linear contribution can be associated with the presence of an increasing amount of surface and interface spins which behave in a paramagnetic (PM) way. To quantify this, we have fitted the M–H loops using two contributions: (i) a SPM contribution corresponding to the magnetization of the cores and shell grains, and (b) a PM contribution associated with uncompensated spins:

$$\begin{eqnarray}&&M(H)={M}_{{\rm{o}}}\displaystyle {\int }_{0}^{\infty }L(\displaystyle \frac{\mu H}{{k}_{{\rm{B}}}T})f(D){\rm{d}}D+{\chi }_{{\rm{PM}}}H,\end{eqnarray} \tag{ 7 }$$

where χ_PM is the PM susceptibility. As can be seen in figures 3(b)–(d), good fits have been obtained for the three samples, indicating that the average estimated size decreases when the morphology changes from core/shell to hollow, but the size distribution becomes bigger. This agrees with our previous analysis on the ZFC M–T curves. For the core/shell and core/void/shell nanoparticles, the estimated size is similar to the core of the nanoparticles, indicating that the SPM behavior originates mainly from the Fe cores. For the core/shell nanoparticles, the Fe core occupies 23% of the total volume of the particle, but since the magnetization of Fe (1710 emu cm⁻³) is much higher than γ-Fe₂O₃ (392 emu cm⁻³), the magnetic contribution (emu) per particle represents nearly a 60%. For the hollow nanoparticles, however, the average size is close to the shell thickness and can be associated with the grains inside the shell, that present a considerable size distribution. In addition, the PM contribution, which is minimal for the core/shell nanoparticles, 7%, becomes much more important for the core/void/shell nanoparticles, 30%, due to the detachment of the core from the shell, which originates from the apparition of additional uncompensated spins at the inner and outer surfaces of the shell and the core, respectively. On the other hand, for the hollow nanoparticles, taking into account the disappearance of the core and the increase in the shell thickness, the relative number of uncompensated spins, and thereby the PM contribution, would be expected to diminish. Instead, it remains almost the same ∼30%. Together with the M–H data at 5 K, this suggests that for the hollow nanoparticles, the number of uncompensated spins must increase and be related to the increase in the thickness of the shell observed for these nanoparticles. This can be understood if we consider that each shell nanograin is composed of central and surface spins, following the model presented by Cabot et al [35]. According to this model, in the hollow nanoparticles (thickness ∼3.2 nm) we have an exchange coupling between the irreversible outer (surface) spins and the ferrimagnetically ordered and reversible inner (core) spins. This can result in an additional source of frustration which is not observed when the shell is thinner, such as in the case of the core/void/shell nanoparticles (at a shell thickness ∼2.2 nm).

A striking consequence of the different orientation of the surface and core spins, as well as the large number of uncompensated spins at the shell of the nanoparticles is the observation of EB (i.e. a horizontal shift in the M–H loop and an increase in coercivity after cooling in a magnetic field). Figure 4(a) shows the M–H loops measured at 5 K under the FC (50 kOe) protocol. As can be seen in this figure, the shapes of these M–H curves are similar to those measured under the ZFC protocol, but with higher coercivity and the M–H loops being shifted along both the horizontal and vertical directions. It is noted that for the hollow nanoparticles the maximum applied field is smaller than the irreversibility field, so the shift observed in the M–H loop may not represent a real EB effect, but just a minor hysteresis loop. Nevertheless, we will also be referring to it as EB. Another interesting feature is the presence of a sharp change or a jump in the magnetization at low fields, ΔM, in the M–H loop as indicated by an arrow, which appears both in the core/shell and hollow nanoparticles. A noticeable difference in this jump is observed between these two samples. For the core/shell nanoparticles, this jump only appeared at 5 K after FC and during the negative field sweep. For the hollow nanoparticles, however, the jump was observed below 25 K in both the positive and negative field sweeps and under both the FC and ZFC protocols. For the core/shell nanoparticles, the jump can be easily related to the unidirectional alignment of frozen interfacial spins with FC, which provides a maximum exchange coupling between the core and the shell. As the field drops, this core/shell coupling is overcome by the random crystalline anisotropies in the shell, resulting in a demagnetization of the shell [26]. This would also explain why no jump was observed for the core/void/shell nanoparticles. However, for the hollow nanoparticles (with the absence of interface spins between the core and the shell), the appearance of a jump below 30 K must be related to the coupling between the central layer and surface spins in the nanograins, as explained before. Moreover, for these hollow samples an asymmetrical magnetization reversal has been observed in the FC M–H loops measured below ∼30 K; the descending branch of the M–H loops shows a much slower approach to saturation than the ascending one, which has been attributed to the competing anisotropy and spin orientation in the shell [46, 47]. This again suggests that ∼30 K marks the onset for a spin freezing phenomenon at the shell nanograins of the hollow nanoparticles.

Zoom In Zoom Out Reset image size

Figures 4(b) and (c) show the temperature dependence of the coercivity, H_C, and the EB field, H_EB, for the three samples after field cooling in 50 kOe. It can be observed that for all the samples both H_C and H_EB progressively decrease with increasing temperature. H_EB becomes close to zero above ∼30 K, while H_C is still non-zero above this temperature. This indicates that for the three samples, below ∼30 K, surface and interface atoms at the shell start to freeze, as supported by the increase in coercivity, behaving as pinning centers for the development of EB. Above this temperature, these 'melted' spins no longer contribute to the EB, but they are still exchange coupled with the nearby atoms from the core and/or the shell grains, thus contributing to the coercivity [25]. It can be seen that while the H_C values of the core/shell and core/void/shell nanoparticles are similar, a slight increase in H_EB is observed for the core/void/shell sample. As discussed before, for the core/void/shell sample the number of uncompensated spins greatly increased in comparison with the core/shell ones, due to the detachment and decrease in size of the core. This is also confirmed by the increase in the vertical shift of the hysteresis loops (see figure 4(d)), which has been defined as:

$$\begin{eqnarray}&&{M}_{{\rm{vert}}}=\displaystyle \frac{1}{2}({M}_{{\rm{max}}}-{M}_{{\rm{min}}}).\end{eqnarray} \tag{ 8 }$$

This value of M_vert is proportional to the number of frozen spins that cannot be reversed by the magnetic field [27], and, in principle, H_EB should depend linearly on the ratio of number of frozen spins to reversible spins:

$$\begin{eqnarray}&&{H}_{{\rm{EB}}}\propto \displaystyle \frac{{M}_{{\rm{vert}}}}{{M}_{{\rm{max}}}}.\end{eqnarray} \tag{ 9 }$$

Hence, the increase in H_EB for the core/void/shell sample can be interpreted in terms of an increase in the number of frozen spins at the inner and outer surface of the shell, which act as pinning centers for the EB phenomenon. However, although hollow nanoparticles present a similar relative number of uncompensated spins as core/void/shell nanoparticles (∼30%), H_EB is much larger for these, reaching values of ∼7 kOe at low temperatures. This indicates that the coupling between the central and surface atoms in each nanograin, together with the strong anisotropies and big size distribution of the nanograins in this shell, give rise to a remarkable EB effect that is not observed in the case of the core/shell and core/void/shell nanoparticles having a thinner shell. This indicates that the hollow nanoparticles are very promising for EB-based spintronics applications and that the shell thickness is crucial in order to enhance the EB effect in these systems.

To probe the spin dynamics of these nanoparticles, ac susceptibility measurements were systematically performed on the samples by applying a 10 Oe ac field within the frequency range 10 Hz to 10 kHz. By changing the frequency, we are deliberately changing the probe time, τ = 1/ω = 1/2πf, which allows us to probe the relaxation of the magnetic moments in different time windows. Figure 5 shows the real, χ', and imaginary, χ'', components of the ac susceptibility. It can be observed that for all the samples a clear maximum is obtained in both components. The position of χ' maximum, T_m', has been typically associated with the collective freezing temperature of the system. With increasing frequency, this peak becomes smaller and its position displaces towards higher temperatures, as it is typical in disordered systems such as spin glasses [48]. Above this maximum, the χ'(T) curves overlap and there is a continuous decay of the susceptibility. On the other hand, the imaginary part, χ'', has been associated with the appearance of dissipative processes in the system, with its position given by T_m''. It can be seen that there are some interesting differences in the evolution of χ'' for the core/shell on one hand, and the core/void/shell and hollow nanoparticles on the other hand. For the core/shell nanoparticles, χ'' increases with increasing frequency, as is conventional in systems of magnetic nanoparticles, but there is a change below ∼80 K, where it decreases. On the other hand, for the core/void/shell and hollow nanoparticles, χ'' slightly decreases with increasing frequency. This behavior indicates a more frustrated state for the core/void/shell and hollow nanoparticles (see for example, Frey et al [49]). In addition, the change in the evolution of χ'' for the core/shell nanoparticles reveals two different freezing processes taking place, as already hinted by dc ZFC−FC measurements; one starting around 100 K associated with the collective freezing of the nanoparticles and mediated by dipolar inter-particle interactions, and the second one at lower temperatures, which for its similarity with the core/void/shell and hollow nanoparticles, must be associated with the freezing of the nanograins inside the shell. Above the maximum, χ'' falls towards zero in the three cases, indicating that at high temperatures the system enters into a SPM-like state [50].

Zoom In Zoom Out Reset image size

In order to obtain more quantitative information about the different collective magnetic behaviors at low temperatures, we have analyzed the displacement of the χ' peak as a function of the frequency. The peak shift can be quantified by

$$\begin{eqnarray}&&{\rm{\Gamma }}\;=\;\displaystyle \frac{{\rm{\Delta }}{T}_{{\rm{m}}^{\prime} }}{{T}_{{\rm{m}}^{\prime} }{\rm{\Delta }}\;\mathrm{log}\;\omega }.\end{eqnarray} \tag{ 10 }$$

The obtained values of Γ (table 4) are close to those of spin glass-like systems (Γ < 0.06). Γ increases as the morphology changes from core/shell to hollow, which can be related to the weakening of the interactions [51]. An attempt to fit the T_m' versus f dependence using a Neel–Arrehnius expression, typical of SPM systems, yielded unphysical values. Thus, we have extended our analysis to the Vogel–Fulcher model, which is actually a phenomenological modification of the Neel–Arrhenius model to include the effect of the interactions in the form of a change to the energy barrier, as given by an additional temperature, T_VF. According to this model, the relaxation of the magnetic moments in our systems is assessed by:

$$\begin{eqnarray}&&\tau ={\tau }_{{\rm{VF}}}\mathrm{exp}(\displaystyle \frac{{E}_{{\rm{a}}}}{{k}_{{\rm{B}}}(T-{T}_{{\rm{VF}}})}),\end{eqnarray} \tag{ 11 }$$

where E_a = KV is the anisotropy energy barrier and τ_VF is the relaxation time of each magnetic nanoparticle. T_VF is in principle related to the strength of the interactions. As can be seen in figure 6(a), good fits have been obtained in all the cases. The obtained τ_VF values are within the typical limits of the relaxation times of individual nanoparticles or clusters (10⁻⁸ − 10⁻¹² s). As the nanoparticles become hollow, the energy barrier progressively increases. The decrease in T_VF is related to the decrease in 〈T_B〉, which suggests a weakening of the inter-particle interactions for the core/void/shell and hollow nanoparticles.

Zoom In Zoom Out Reset image size

Since the Γ values and the FC M–T features suggested the presence of a glassy freezing at low temperatures, we have employed a critical power law, which is mostly associated with spin-glass systems:

$$\begin{eqnarray}&&\tau ={\tau }_{{\rm{C}}}{(\displaystyle \frac{T}{{T}_{{\rm{g}}}}-1)}^{-zv}.\end{eqnarray} \tag{ 12 }$$

Here T_g marks the onset of the collective glassy behavior, τ_C corresponds again with the relaxation time of each magnetic nanoparticle, and zv is a critical exponent related to the correlation length that diverges at T_g. Again, very good fits have been obtained for the three samples (figure 6(b)). The obtained values of T_g are close to those of 〈T_B〉 for the core/void/shell and hollow nanoparticles, and close to T_P-ZFC for the core/shell nanoparticles. This indicates that we are probing the freezing of the shell grains in the first two cases and the collective blocking of the nanoparticles in the last one. As the particles become hollow, both zv and τ_C increase. Higher zv values have been reported in the case of cluster-glass systems and can be attributed to the increased disorder of the spins in the shell.

In short, we have observed a clear change in the magnetic behavior of the 12 nm core/shell nanoparticles as they become hollow. The core/shell nanoparticles behave like an ensemble of interacting nanoparticles, with a collective freezing of spins into a SSG-like state below 100 K, mediated by inter-particle dipolar interactions. The shell becomes frozen at around 30 K and the EB effect is observed below this temperature, due to the freezing of core–shell interface spins. As the core detaches from the shell and the morphology transforms into core/void/shell, the magnetization of the system decays, inter-particle interactions become weaker, and the effective anisotropy increases due to an increase in the number of uncompensated spins both at the inner and outer surfaces of the shell and the core, respectively. A slight increase of the EB is achieved as a result. The changes are more drastic when the nanoparticles become completely hollow. In this case, the magnetic behavior is only associated with the spins in the nanograins forming the polycrystalline shell. Due to the increase of the shell thickness, a coupling between the ferrimagnetic central spins layer and the disordered surface spins is established inside these nanograins. This gives rise to a highly frustrated magnetic state, which greatly increases the EB effect, indicating that the morphology of the shell plays a crucial role in this kind of exchange-biased systems. Below the freezing temperature of the shell, 30 K, the system presents a spin glass like behavior.

In addition the effect of disordered surface spins, the finite-size effect has been reported to be important in ferrimagnetic nanoparticle systems [27]. This effect arises mainly from an unbalanced number of spins in an antiparallel arrangement, which usually differs from the bulk material and is expected to vary significantly as the particle size is reduced below a critical size. In comparison with the case of the 12 nm nanoparticles (with particle size larger than the critical size, 10 nm), we have also studied the magnetic properties of 8 nm nanoparticles, that is, below the critical size. The main results are shown in figures 7 and 8. Figure 7(a) shows the ZFC−FC M–H curves measured in a field of 100 Oe for the 8 nm core/shell and hollow nanoparticles. It can be observed that the curves are very similar for both samples, except for a slight displacement of the maximum position, T_P-ZFC. Here we note that the Fe core only occupies 6% of the whole volume of the nanoparticle, which is nearly four times less than in the case of the 12 nm nanoparticles. As a result, a similar magnetic behavior can be expected for both the core/shell and hollow nanoparticles. Weaker dipolar inter-particle interactions are also expected for these nanoparticles, as compared to the 12 nm nanoparticles. Above T_P-ZFC, the magnetization decays progressively, approaching zero at high temperatures. The values of 〈T_B〉 are estimated using the same method employed before for the 12 nm nanoparticles. It is interesting to note that in contrast to the case of the 12 nm nanoparticles, 〈T_B〉 increases when the morphology changes from core/shell to hollow for the case of the 8 nm nanoparticles: from 45 K for the core/shell morphology to 54 K for the hollow ones. This increase in 〈T_B〉 cannot be solely attributed to the enhancement in the surface anisotropy in the particles with hollow morphology, as suggested in the previous work [34], but must be also related to the finite-size effect of the nanoparticles. This finding points towards the importance of the finite-size effect in these systems, which fully agrees with our previous observation of a critical particle size (mean size, ∼10 nm) for the Fe/γ-Fe₂O₃ core/shell nanoparticles, above which the interface spin effect contributes mainly to the EB, but below which the surface spin effect is dominant. On the other hand, both samples show a small and similar decrease in the FC magnetization below T_P-ZFC, which can be attributed to the presence of a SG-like state of the shell at low temperatures. It is noted that we no longer obtain the high temperature irreversibility that was observed in the case of the 12 nm hollow nanoparticles' ZFC−FC magnetization curves (see the inset to figure 2(b)). This suggests a smaller size distribution of the nanograins in the 8 nm hollow nanoparticles than in the 12 nm hollow nanoparticles. Except at very high temperatures, a strong deviation of the Curie–Weiss law is observed for the 8 nm samples, which has been typically found in SG systems [48].

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We have also measured the M–H loops at 5 and 300 K for the 8 nm core/shell and hollow nanoparticles. As can be seen in figure 7(b), at 5 K the M–H loops are very similar for both samples. The H_C of both 8 nm nanoparticles is ∼1250 Oe, which is smaller than that of the 12 nm hollow nanoparticles (∼1870 Oe) but larger than that of the 12 nm core/shell nanoparticles (690 Oe). On the other hand, the room-temperature M–H loops present a Langevin-type non-hysteretic behavior (figures 7(c) and (d)), with a PM contribution of 27% and 36% for the core/shell and hollow nanoparticles, respectively. These results indicate that by decreasing the particle size from 12 to 8 nm, the number of uncompensated spins increases. In particular, if we compare the volume occupied by inner and outer surface spins, given the same thickness of approximately 1 atomic layer (0.8 nm), then we obtain that for the 12 nm nanoparticles the relative volume occupied by the atoms on the surfaces of the shell is 45%, while for the 8 nm samples it is about 80%.

To examine if such an increase of the volume occupied by surface spins gives rise to EB in the 8 nm nanoparticles, the thermal evolution of the EB and coercivity after FC at 50 kOe were studied, as shown in the inset to figure 7(d) for the hollow nanoparticles. H_C at low temperatures is ∼3500 Oe, which keeps practically constant up to 15 K and then starts to decrease at higher temperatures. On the other hand, H_EB rapidly increases below 25 K, and reaches the highest value of ∼5000 Oe at 5 K. Similar results have been obtained for the 8 nm core/shell nanoparticles. As the shell thickness in both cases is almost equal (∼2 nm), the morphology of the crystallites inside the shell should not vary appreciably. However, these values of H_EB are still smaller than those obtained for the 12 nm hollow nanoparticles (∼7000 Oe at 5 K). This can be understood by considering the fact that the origin of the EB in hollow nanoparticle systems is also associated with the exchange coupling between the irreversible surface spins and the reversible central spins in the shell nanograins. As the particle size of the hollow nanoparticles decreases from 12 to 8 nm, the volume occupied by the central spins is significantly reduced, leading to the weakening of the exchange coupling. As a result, a smaller EB effect is obtained for the 8 nm hollow nanoparticles. This is fully consistent with the M–T data (figure 7) and analysis that suggest a low temperature SG-like behavior for the 8 nm hollow particles.

To further elucidate this intriguing feature, we have performed ac susceptibility measurements for the 8 nm core/shell and hollow samples. The main results are presented in figure 8 and the fit parameters summarized in table 5. The evolution of χ' and χ'' is similar to the one obtained for the 12 nm hollow nanoparticles: both χ' and χ'' displace towards higher temperatures with increasing frequency, but the amplitude only changes noticeably for χ'. The obtained values of Γ are of the same order of magnitude of SG-like systems. Again, fits to the Neel–Arrhenius model give unphysical parameters. However, the Vogel–Fulcher model yields a similar anisotropy barrier for both samples, and indicates that the intrinsic relaxation time is appreciably smaller for the hollow nanoparticles than for the core/shell nanoparticles. A similar result is also obtained from the critical power law analysis. It can be seen however that the value of the relaxation time is always smaller for the hollow nanoparticles, and that the critical exponent increases. This can be related to the absence of the core and the increased number of uncompensated spins, which gives rise to a more spin glass-like behavior in the case of the hollow nanoparticles. Similar τ_C and zν values have been reported in the case of spin glass systems [50]. A final note is that the relaxation time, determined from both the Vogel–Fulcher model and the critical exponent law, is much smaller for the 8 nm hollow nanoparticles than for the 12 nm nanoparticles. This once again suggests a more conventional glassy behavior for the 8 nm particles.