Investigating Exchange Bias and Coercivity in Fe3O4–γ-Fe2O3 Core–Shell Nanoparticles of Fixed Core Diameter and Variable Shell Thicknesses

We have carried out extensive measurements on novel Fe3O4–γ-Fe2O3 core–shell nanoparticles of nearly similar core diameter (8 nm) and of various shell thicknesses of 1 nm (sample S1), 3 nm (sample S2), and 5 nm (sample S3). The structure and morphology of the samples were studied using X-ray diffraction (XRD), transmission electron microscopy (TEM), and selected area electron diffraction (SAED). The direct current (DC) magnetic measurements were carried out using a superconducting quantum interference device (SQUID). Exchange bias and coercivity were investigated at several temperatures where the applied field was varied between 3 and −3 T. Several key results are obtained, such as: (a) the complete absence of exchange bias effect in sample S3; (b) the occurrence of nonconventional exchange bias effect in samples S2 and S1; (c) the sign-change of exchange bias field in sample S2; (d) the monotonic increase of coercivity with temperature above 100 K in all samples; (e) the existence of a critical temperature (100 K) at which the coercivity is minimum; (f) the surprising suppression of coercivity upon field-cooling; and (g) the observation of coercivity at all temperatures, even at 300 K. The results are discussed and attributed to the existence of spin glass clusters at the core–shell interface.


Introduction
Magnetic nanoparticles (MNPs) are of great interest due to their energy and bio-medical applications [1][2][3][4][5][6][7][8][9], e.g., data storage systems. Coercivity and exchange bias are among the most important magnetic parameters that could influence the magnetization of MNPs. Core-shell ferromagnetic (FM)-antiferromagnetic (AFM) and ferrimagnetic (FIM)-antiferromagnetic (AFM) MNPs have drawn large attention due to their applications in permanent magnets and high-density recording media [10,11]. Shifting of the magnetization versus applied magnetic field (M-H) hysteresis loops along the magnetic field axis (horizontal direction) was observed in such core-shell MNPs. This shifting of the magnetization hysteresis loop is called the exchange bias effect and was attributed to exchange coupling at the core-shell interfaces [1,12,13]. Exchange bias can provide an extra source of anisotropy, leading to stable magnetization [14]. However, the origin of the exchange bias is yet to be fully understood. According to earlier reports, the exchange coupling between the FIM-AFM and The sizes of the nanoparticles were inferred from the XRD data by using Scherrer's formula: where DP is the average crystallite size, λ is the x-ray wavelength, β is the full width of half maximum (FWHM) of the XRD line, and θ is the Bragg's angle. The average sizes calculated from Scherrer's formula were 9, 11, and 13 nm for samples S1, S2, and S3, respectively.

Morphological Analysis
The morphology of the phase pure samples was studied using transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) techniques. Figure 2 displays the TEM images and the particle size histograms of the three samples. The TEM images show that the particles in all samples are almost spherical in shape. The particle size histograms, which were obtained from TEM measurements on many particles, show narrow size distributions with average sizes of 9, 11, and 13 nm, for samples S1, S2, and S3, respectively. Some aggregations can be observed in the TEM images. Figure 3 displays the HRTEM of all samples. The sizes of the nanoparticles were inferred from the XRD data by using Scherrer's formula: where D P is the average crystallite size, λ is the X-ray wavelength, β is the full width of half maximum (FWHM) of the XRD line, and θ is the Bragg's angle. The average sizes calculated from Scherrer's formula were 9, 11, and 13 nm for samples S1, S2, and S3, respectively.

Morphological Analysis
The morphology of the phase pure samples was studied using transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) techniques. Figure 2 displays the TEM images and the particle size histograms of the three samples. The TEM images show that the particles in all samples are almost spherical in shape. The particle size histograms, which were obtained from TEM measurements on many particles, show narrow size distributions with average sizes of 9, 11, and 13 nm, for samples S1, S2, and S3, respectively. Some aggregations can be observed in the TEM images. Figure 3 displays the HRTEM of all samples.
The average core and shell dimensions were obtained from several HRTEM images. The core-shell structure is well displayed where the core appears darker than the shell. The average dimensions of the cores and shells were calculated form several HRTEM images. All the samples were found to have the same average core diameter of approximately 8 nm. The average shell thicknesses for samples S1, S2, and S3 were found to be 1, 3, and 5 nm, respectively. In the insets of Figure 3, the dotted lines were drawn at the core-shell interface as well as the surface of the nanoparticle as guides for the eye. The average core and shell dimensions were obtained from several HRTEM images. The core-shell structure is well displayed where the core appears darker than the shell. The average dimensions of the cores and shells were calculated form several HRTEM images. All the samples were found to have the same average core diameter of approximately 8 nm. The average shell thicknesses for samples S1, S2, and S3 were found to be 1, 3, and 5 nm, respectively. In the insets of Figure 3, the dotted lines were drawn at the core-shell interface as well as the surface of the nanoparticle as guides for the eye.   The average core and shell dimensions were obtained from several HRTEM images. The core-shell structure is well displayed where the core appears darker than the shell. The average dimensions of the cores and shells were calculated form several HRTEM images. All the samples were found to have the same average core diameter of approximately 8 nm. The average shell thicknesses for samples S1, S2, and S3 were found to be 1, 3, and 5 nm, respectively. In the insets of Figure 3, the dotted lines were drawn at the core-shell interface as well as the surface of the nanoparticle as guides for the eye.   Selected area electron diffraction (SAED) patterns as shown in Figure 4 confirmed the Fe 3 O 4 -γ-Fe 2 O 3 core-shell structure of the nanoparticles. Figure 4 shows the SAED pattern for sample S2, which is a representative of the SAED patterns of all samples. The ring-type pattern confirms the polycrystalline nature of the sample. The figure also clearly confirms the presence of Fe 3 O 4 and γ-Fe 2 O 3 crystal planes forming the core-shell structure. The highest intensity peaks (311) for both Fe 3 O 4 and γ-Fe 2 O 3 phases were for d = 0.253 and 0.252 nm, respectively. Hence, the (311) plane shown in Figure 3b corresponds to the superimposed planes of both the phases. The existence of (511), (422), (311), and (220) planes of Fe 3 O 4 corresponding to d = 0.161 nm, 0.171 nm, 0.253 nm, and 0.296 nm, respectively, are confirmed. The presence of the (321) and (221)  Selected area electron diffraction (SAED) patterns as shown in Figure 4 confirmed the Fe3O4-γ-Fe2O3 core-shell structure of the nanoparticles. Figure 4 shows the SAED pattern for sample S2, which is a representative of the SAED patterns of all samples. The ring-type pattern confirms the polycrystalline nature of the sample. The figure also clearly confirms the presence of Fe3O4 and γ-Fe2O3 crystal planes forming the core-shell structure. The highest intensity peaks (311) for both Fe3O4 and γ-Fe2O3 phases were for d = 0.253 and 0.252 nm, respectively. Hence, the (311) plane shown in Figure 3b corresponds to the superimposed planes of both the phases. The existence of (511), (422), (311), and (220) planes of Fe3O4 corresponding to d = 0.161 nm, 0.171 nm, 0.253 nm, and 0.296 nm, respectively, are confirmed. The presence of the (321) and (221) planes of γ-Fe2O3 corresponding to the d = 0.253 and 0.278 nm, respectively, are verified as pointed out in the figure. This clearly confirmed that the core-shell nanoparticles are Fe3O4/γ-Fe2O3 nanoparticles.  Figure 5 shows the Mössbauer spectra (dots) at 78 K for the different samples, and the fitting is represented by the solid curves. It is clear from this figure that the spectra of all the samples show magnetically split components. The spectra are fitted with four six-line patterns: one component for the -Fe2O3 (ferromagnetic), two components (with ratios of 2:1 for the Octahedral and the Tetrahedral sites) for the Fe3O4 (Ferrimagnetic), and the fourth one with very small percentage, which might be due to the interface. Table 1 presents the Mössbauer parameters for the different components without the interface, which has the values of δ = 0.37 mm/s, Bhf = 43 T, w = 0.50-0.54 mm/s, and very small relative intensity of A= 2.3-3.3%. One aim of the Mössbauer study is to determine the percentages of -Fe2O3 and Fe3O4, which can be done using the percentage area (relative intensity) of each subspectra. The isomer shift (δ) and the hyperfine magnetic field (Bhf) are the main parameters which are used to distinguish between the -Fe2O3 and Fe3O4 in the Mössbauer spectra.   Figure 5 shows the Mössbauer spectra (dots) at 78 K for the different samples, and the fitting is represented by the solid curves. It is clear from this figure that the spectra of all the samples show magnetically split components. The spectra are fitted with four six-line patterns: one component for the γ-Fe 2 O 3 (ferromagnetic), two components (with ratios of 2:1 for the Octahedral and the Tetrahedral sites) for the Fe 3 O 4 (Ferrimagnetic), and the fourth one with very small percentage, which might be due to the interface. Table 1 presents the Mössbauer parameters for the different components without the interface, which has the values of δ = 0.37 mm/s, B hf = 43 T, w = 0.50-0.54 mm/s, and very small relative intensity of A= 2.3-3.3%. One aim of the Mössbauer study is to determine the percentages of γ-Fe 2 O 3 and Fe 3 O 4 , which can be done using the percentage area (relative intensity) of each subspectra. The isomer shift (δ) and the hyperfine magnetic field (B hf ) are the main parameters which are used to distinguish between the γ-Fe   From the density of 5.24 g/cm 3 and the molar mass of 159.688 g/mol for -Fe2O3, and from the density of 5.17 g/cm 3 and the molar mass of 231.533 g/mol for Fe3O4, we can estimate the percentage of iron (or the number of Fe-atoms) in equal volumes of -Fe2O3 and Fe3O4. By dividing the molar mass over the density for -Fe2O3, we get 32.81x10 -3 mol/cm 3 , and for Fe3O4 we get 22.32x10 -3 mol./cm 3 , since the mol of the material contains Avogadro's number (NA) of the molecules; then for -Fe2O3 we get 2 × 32.81 × 10 −3 = 65.63 × 10 −3 of NA Fe-atoms/cm 3 , and for Fe3O4 we get 3 × 22.32 × 10 −3 = 66.9 × 10 −3 of NA Fe-atoms/cm 3 . These values show that the number of Fe-atoms in the same volume of -Fe2O3 and Fe3O4 is about the same (i.e., if we divide 65.63 by 66.9 we get the ratio of 0.981). Accordingly, from the percentage area (relative intensity) of each subspectra of the Mössbauer spectra, we can find the ratio of the -Fe2O3 to that of Fe3O4 in each sample. Table 2 shows these ratios and the calculated ratio for the volumes occupied by Fe3O4 in the core and for -Fe2O3 in the shell. It can be seen from the last two columns of Table 2 that these ratios are almost the same, which confirms the occupancy of Fe3O4 in the core and -Fe2O3 in the shell.

Mössbauer Analysis
From this Mossbauer data we confirm that the ratio of the -Fe2O3 phase is equal to the shell-to-core volumes ratio regardless of the shell thickness. Thus, the core and shell phases do not change with the change of shell thickness.
The quadrupole shifts (=2ε) for all the samples were very small 2ε= 0.02 ± 0.01 (mm/s). The ratio of the line widths for the first three lines relative to the line width of the inner lines (W in (mm/s ± 0.02)) of each subspectra were fixed to the values of 1.2, 1.1, 1 in all the samples. From the density of 5.24 g/cm 3 and the molar mass of 159.688 g/mol for γ-Fe 2 O 3 , and from the density of 5.17 g/cm 3  we get the ratio of 0.981). Accordingly, from the percentage area (relative intensity) of each subspectra of the Mössbauer spectra, we can find the ratio of the γ-Fe 2 O 3 to that of Fe 3 O 4 in each sample. Table 2 shows these ratios and the calculated ratio for the volumes occupied by Fe 3 O 4 in the core and for γ-Fe 2 O 3 in the shell. It can be seen from the last two columns of Table 2 that these ratios are almost the same, which confirms the occupancy of Fe 3 O 4 in the core and γ-Fe 2 O 3 in the shell.
From this Mossbauer data we confirm that the ratio of the γ-Fe 2 O 3 phase is equal to the shell-to-core volumes ratio regardless of the shell thickness. Thus, the core and shell phases do not change with the change of shell thickness.

Magnetic Properties
Magnetization versus applied magnetic field hysteresis loops (M-H) were measured at several temperature values, 2, 50, 100, 200, and 300 K. In each loop cycle, the magnetization was recorded while the applied field was changing between the maximum values of −3 T and 3 T. In the field-cooled (FC) protocol, for each loop measurement, the temperature of the sample was brought to room temperature followed by the application of a magnetic field of a specific value (the FC value). The sample was then cooled down from room temperature to one of the above mentioned temperatures while the field remains applied. At each temperature, the M-H was measured at the FC values H FC of 0.5, 1, 2, and 3 T, respectively.
Selected M-H hysteresis loops for samples S1 and S2 are shown in Figure 6. For sample S1, the M-H hysteresis loops are shown at 2 K at field-cooling values of 0.5 and 1 T. For sample S2, the M-H hysteresis loops are shown at field cooling value of 3 T at 2 and 300 K. Typical hysteresis loops were obtained at other temperatures and H FC values for all samples.

Magnetic Properties
Magnetization versus applied magnetic field hysteresis loops (M-H) were measured at several temperature values, 2, 50, 100, 200, and 300 K. In each loop cycle, the magnetization was recorded while the applied field was changing between the maximum values of -3 T and 3 T. In the field-cooled (FC) protocol, for each loop measurement, the temperature of the sample was brought to room temperature followed by the application of a magnetic field of a specific value (the FC value). The sample was then cooled down from room temperature to one of the above mentioned temperatures while the field remains applied. At each temperature, the M-H was measured at the FC values HFC of 0.5, 1, 2, and 3 T, respectively.
Selected M-H hysteresis loops for samples S1 and S2 are shown in Figure 6. For sample S1, the M-H hysteresis loops are shown at 2 K at field-cooling values of 0.5 and 1 T. For sample S2, the M-H hysteresis loops are shown at field cooling value of 3 T at 2 and 300 K. Typical hysteresis loops were obtained at other temperatures and HFC values for all samples. From the insets of Figure 6, it was observed that both samples display horizontal loop shifting. The horizontal shift of the loops was defined as the exchange bias field, HEB. From these From the insets of Figure 6, it was observed that both samples display horizontal loop shifting. The horizontal shift of the loops was defined as the exchange bias field, H EB . From these magnetization hysteresis loops, the exchange bias field, H EB , and the coercivity, H C , were calculated for all samples at several conditions. H C and H EB were calculated using the formulas: where H C1 and H C2 are the coercive fields (including their signs) at the descending and the ascending branches of the M-H hysteresis loop, respectively. Figure 7 shows the exchange bias field versus temperature in sample S2 at several field-cooling values. It can be seen in this figure that at very low temperatures (below 50 K), H EB is negative with an absolute value at 2 K that increases with H FC . This absolute value decreases with temperature up to a temperature T 0 , at which it becomes zero. Above A similar trend of the temperature dependence of H EB up to 200 K in our samples was reported in spin-glass-ferromagnet bilayers [43] under several H FC . This trend was also reported in polycrystalline Fe-Cr bilayers [44] under only one field-cooling value of H FC = 1 kOe. The temperature-driven sign reversal of H EB was attributed to Fe-Cr spin glass. In [43], T 0 and T M were found to decrease with increasing H FC , whereas H EB at T M was found to increase. These observations are almost similar to what we have observed in our core-shell nanoparticle system. However, there are some discrepancies, where in their spin-glass-ferromagnet bilayers system, H EB at 2 K decreased with increasing H FC and T M increased with increasing H FC . These differences could be due to the different systems studied. The sign change of H EB was also observed in a ferromagnet-spin-glass Co-CuMn bilayer system [45]. Up to our knowledge, such sign-change in H EB has not been reported in core-shell nanoparticles. The similarity of the temperature dependence of H EB in our sample S2 with those reported in layered structures which include spin-glass (SG) hints for the SG phase in our samples.
At H FC = 1 T, H EB does not change its positive sign but oscillates with temperature. In our core-shell nanoparticles, the temperature dependence of H EB strongly depends on field-cooling. This point is clearly seen in Figure 8, which displays the field-cooling dependence of H EB at several temperatures. It is worth mentioning that H EB has a peak value at 1 T at almost all of the temperatures. magnetization hysteresis loops, the exchange bias field, HEB, and the coercivity, HC, were calculated for all samples at several conditions. HC and HEB were calculated using the formulas: where HC1 and HC2 are the coercive fields (including their signs) at the descending and the ascending branches of the M-H hysteresis loop, respectively. Figure 7 shows the exchange bias field versus temperature in sample S2 at several field-cooling values. It can be seen in this figure that at very low temperatures (below 50 K), HEB is negative with an absolute value at 2 K that increases with HFC. This absolute value decreases with temperature up to a temperature T0, at which it becomes zero. Above T0, HEB becomes positive and increases until it reaches a maximum at a temperature TM. Above TM, HEB decreases until it becomes zero again at the blocking temperature, TB (which is 100 or 200 K, depending on the HFC). Above TB, HEB becomes positive and increases up to 300 K. A similar trend of the temperature dependence of HEB up to 200 K in our samples was reported in spin-glass-ferromagnet bilayers [43] under several HFC. This trend was also reported in polycrystalline Fe-Cr bilayers [44] under only one field-cooling value of HFC = 1 kOe. The temperature-driven sign reversal of HEB was attributed to Fe-Cr spin glass. In [43], T0 and TM were found to decrease with increasing HFC, whereas HEB at TM was found to increase. These observations are almost similar to what we have observed in our core-shell nanoparticle system. However, there are some discrepancies, where in their spin-glass-ferromagnet bilayers system, HEB at 2 K decreased with increasing HFC and TM increased with increasing HFC. These differences could be due to the different systems studied. The sign change of HEB was also observed in a ferromagnet-spin-glass Co-CuMn bilayer system [45]. Up to our knowledge, such sign-change in HEB has not been reported in core-shell nanoparticles. The similarity of the temperature dependence of HEB in our sample S2 with those reported in layered structures which include spin-glass (SG) hints for the SG phase in our samples. At HFC = 1 T, HEB does not change its positive sign but oscillates with temperature. In our core-shell nanoparticles, the temperature dependence of HEB strongly depends on field-cooling. This point is clearly seen in Figure 8, which displays the field-cooling dependence of HEB at several temperatures. It is worth mentioning that HEB has a peak value at 1 T at almost all of the temperatures.   The occurrence of unconventional exchange bias in samples S1 (with a maximum value of 5 Oe) only at 2 K and at 10 K at particular field-cooling values. At 2 K, the exchange bias was observed only at the smallest field-cooled values of 0.5 T, and 1 T whereas at 10 K, it was observed only at 0.5 T. (c) The occurrence of unconventional exchange bias in samples S2 (with a maximum value of 20 Oe) at all temperatures and all field-cooling values. The exchange bias effect appears after field-cooling from room temperature (300 K) which is much lower than both the Tc of the shell (which is above 820 K) and the TC of the core (which is around 850 K) [46,47]. (d) The exchange bias in sample S2 has a nonmonotonic behavior with temperature as well as with field-cooling. This is opposite to the familiar exchange bias behavior in other systems where exchange bias decreases with temperature and increases with the increase of the field-cooling value. (e) The exchange bias in sample S2 did not vanish at 300 K at all field-cooled values. (f) Negative as well as positive exchange bias were observed in sample S2. The switch from negative to positive exchange bias in this sample occurred at temperature of 50, 30, and 21 K, for field-cooling values of 0.5, 2, and 3 T, respectively. Hence, we can state that in this FIM-FIM core-shell structure, a shell thickness of 3 nm represents a critical thickness at which the exchange bias occurs nearly at all temperatures and at all field-cooling values. In addition, 1 T is a critical field-cooling value in sample S2, where only positive exchange bias occurs and the exchange bias displays a peak or a dip at nearly all temperatures. Figure 9 shows the coercivity as a function of temperature for all samples in the zero-field-cooling (ZFC) state and in the FC state at several field-cooling values. Figure 10 shows the coercivity as a function of shell thickness at several temperatures in the ZFC state and in the FC state at several field-cooling values. At zero-field-cooling, no exchange bias was observed in all samples at all temperatures. After field-cooling, the main results (as displayed in Figures 7 and 8) are as follows. (a) The complete disappearance of the exchange bias effect in the sample S3 at all field-cooling values and at all temperatures. (b) The occurrence of unconventional exchange bias in samples S1 (with a maximum value of 5 Oe) only at 2 K and at 10 K at particular field-cooling values. At 2 K, the exchange bias was observed only at the smallest field-cooled values of 0.5 T, and 1 T whereas at 10 K, it was observed only at 0.5 T. (c) The occurrence of unconventional exchange bias in samples S2 (with a maximum value of 20 Oe) at all temperatures and all field-cooling values. The exchange bias effect appears after field-cooling from room temperature (300 K) which is much lower than both the Tc of the shell (which is above 820 K) and the T C of the core (which is around 850 K) [46,47]. (d) The exchange bias in sample S2 has a nonmonotonic behavior with temperature as well as with field-cooling. This is opposite to the familiar exchange bias behavior in other systems where exchange bias decreases with temperature and increases with the increase of the field-cooling value. (e) The exchange bias in sample S2 did not vanish at 300 K at all field-cooled values. (f) Negative as well as positive exchange bias were observed in sample S2. The switch from negative to positive exchange bias in this sample occurred at temperature of 50, 30, and 21 K, for field-cooling values of 0.5, 2, and 3 T, respectively. Hence, we can state that in this FIM-FIM core-shell structure, a shell thickness of 3 nm represents a critical thickness at which the exchange bias occurs nearly at all temperatures and at all field-cooling values. In addition, 1 T is a critical field-cooling value in sample S2, where only positive exchange bias occurs and the exchange bias displays a peak or a dip at nearly all temperatures. Figure 9 shows the coercivity as a function of temperature for all samples in the zero-field-cooling (ZFC) state and in the FC state at several field-cooling values. Figure 10 shows the coercivity as a function of shell thickness at several temperatures in the ZFC state and in the FC state at several field-cooling values. Nanomaterials 2017, 7, 415 10 of 17     The key results displayed by these two figures are as follows. (a) Coercivity, with appreciable magnitudes, has been detected in all samples at all temperatures at zero-field-cooling as well as at all field-cooling values. (b) The coercivity in all samples behaves in a systematic manner with temperature at zero-field-cooling as well as at all field-cooling values. (c) As function of temperature, coercivity in all samples (at zero-field-cooling and at all field-cooling values) was observed to initially decrease monotonically and sharply with increasing temperature, reaching a non-zero minimum value at 100 K for samples S1 and S2 and at 200 K for sample S3. (d) As the temperature increases above 100 K (for samples S1 and S2) and above 200 K (for sample S3), a surprising and interesting slow (and almost linear) increase of coercivity with temperature takes place and continues up to 300 K. (e) After field cooling, coercivity displayed the same behavior but with different magnitudes. The increase of coercivity with temperature after reaching a minimum value and the non-vanishing of coercivity at room temperature in all samples (at zero-field-cooling and at all field-cooled values) are novel and very important observations in this FIM-FIM core-shell structure. This behavior of coercivity is opposite to that in other systems where coercivity keeps decreasing with temperature. (f) In the zero-field-cooled state (at a particular temperature), the shell thickness has a noticeable role on coercivity, where it increased at some temperatures and decreased at others. (g) In the field-cooled state (at particular field-cooling value and temperature), shell thickness does not have any noticeable effect on coercivity. (h) The largest coercivity measured in our study occurred in sample S2 at 2 K in the zero-field-cooling state. (i) At zero-field-cooling, the magnitude of coercivity in each sample is the largest at 2 K. (j) After field-cooling at 0.5 T, the magnitudes of coercivity decrease in all samples at all temperatures (except at 2 K in sample S1). No significant additional changes in the magnitudes of coercivity occurred at higher field-cooling values in all the samples. However, after field-cooling, the magnitude of coercivity in each sample remains the largest at 2 K. Hence, field-cooling has a negative effect on coercivity in all samples and at all temperatures. This behavior of coercivity is opposite to that in other systems, where coercivity increases with the increase of the field-cooling values. (k) In sample S1, the field-cooling value of 0.5 T enhances coercivity at 2 K. Larger field-cooled values showed no significant additional enhancement. (l) At temperatures below 100 K (at zero-field-cooling as well as after field-cooling), the magnitudes of coercivity are different in different samples. (m) At temperatures above 100 K, the magnitudes of coercivity are nearly the same in all samples in the field-cooled state, whereas they are different in different samples in the zero-field-cooled state. (n) At zero-field-cooling, the rate of decrease of coercivity with temperature (below 100 K) has different values in different samples, where it is the slowest in sample S1 and the fastest in sample S3. (o) After field-cooling at 0.5 T, the rate of decrease of coercivity with temperature (below 100 K) becomes nearly the same in all samples. No observable additional changes of this behavior occurred at higher field-cooling values. (p) At zero-field-cooling, the rate of increase of coercivity with temperature (above 100 K) has different values in different samples. (q) After field-cooling at 0.5 T, the rate of increase of coercivity with temperature (above 100 K) becomes nearly the same in all samples. No significant additional changes in the behavior of coercivity occurred at larger field-cooling values. (r) Although in the field-cooled state, the rate of increase of coercivity with temperature (above 100 K) is nearly the same in all samples, it is slower than that in the zero-field-cooled case. Hence, we can consider 0.5 T as a critical field-cooling value at which coercivity starts decreasing in all samples at all temperatures.

Discussion
The existence of the exchange bias effect in some samples at some conditions after field-cooling from 300 K, which is much lower than the T C of the shell (which is above 820 K) and the T C of the core (which is around 850 K) [1,17], is unconventional. In systems where the shell material was AFM and field-cooling occurred from temperatures below the T N of the shell material, this behavior was attributed to the spontaneous exchange bias mechanism [18,19].
We believe that the Fe 3 O 4 core and γ-Fe 2 O 3 shell materials are not in good contact due to large interface defect concentration. This can be seen in HRTEM images where the interface is not well-ordered. The interface defects could result in large interface strain, which lowers the interfacial exchange coupling and thus lowers the exchange bias field. The interface defects also could lead to a magnetic disorder at the interface, which results in the existence of interfacial uncompensated spins. These interfacial spins could freeze at low temperatures causing spin-glass clusters (SGCs) with random spin orientations. In addition, the spin-glass phase could exist at the core-shell interface due to interfacial canted spins. It is well-established that the spin-orbit coupling is responsible for the magnetocrystalline anisotropy. Lattice parameters and distortion (which decrease symmetry) have significant influence on the magnetocrystalline anisotropy. Broken exchange bonds at the surface result in the reduced coordination of surface cations, which leads to changes in their spin-orbit energy, resulting in changes in the local magnetocrystalline anisotropy [20,21]. In addition, low symmetry near the surface produces large contribution to the local magnetic anisotropy, resulting in spin canting [22]. This is the expected case also at the core-shell interface where these interfacial canted spins can freeze into SGCs. Randomly spread spin-glass-like phases at the layered FM-AFM and core-shell nanoparticle interfaces were proposed to significantly influence the exchange bias properties [1,23,24]. The interfacial strain also could lead to a spin-glass phase. Because of the small size of nanoparticles, the radius of curvature is very small. For core-shell nanoparticles, lattice mismatching between the shell and core materials is expected. Hence, a large degree of interfacial structural disorder is expected to occur in such nanoparticle systems. The smaller the core diameter, the larger is the interfacial structural disorder [7]. Although the core was fixed at 8 nm in our core-shell nanoparticles, the shell thickness was varied, which results in varied stress values on core leading to different interfacial defects and, hence, different quantities of spin-glass clusters. In addition, it was reported that surface spins in γ-Fe 2 O 3 nanoparticles are more magnetically disordered than in Fe 3 O 4 nanoparticles of the same size [25][26][27], and thus we expect larger amount of interfacial spin-glass as the shell thickness increases.
The interfacial SGCs prevent the direct exchange coupling of the core and shell spins. Each of these SGCs has a fixed direction, which is the direction of the net spins composing the cluster. The directions of net spins of all clusters are randomly oriented. Their temperature behavior is not well-defined because of the unknown pining strengths and orientations of these spins.
We suggest that the interfacial spin-glass phase is composed of several SGCs, where each SGC has a net spin (magnetic moment) and the spins in the SGCs are randomly oriented. These SGCs are coupled to each other and to the core and shell surfaces. The pinning strength of the spin of each SGC is determined by its exchange interactions with nearby spins (of other SGCs), the core spins, and shell spins near the interface. At high temperatures, these SGC spins are weakly coupled and can be considered as free. At low temperatures, they freeze in random directions with strong couplings.
Several signatures of the spin-glass behavior in these core-shell nanoparticles were obtained (and will be reported in a separate paper). Hence, this model of interpretation could be reasonable for our samples and other core-shell nanoparticles with similar core-shell materials and similar interfacial structure. For core-shell nanoparticles with good core-shell contact, less (or no) concentrations of interfacial defects might occur with the absence of interfacial SGCs, leading to a different behavior of exchange bias field and coercivity with temperature and field cooling. It is worth mentioning that the amount of the interfacial SGCs can be experimentally determined using X-ray magnetic circular dichroism (XMCD) [28,46,47]. Another method that was applied to layered FM-AFM structures uses the so-called blocking temperature distribution from magnetic hysteresis loops at several conditions [34,35]. We have not conducted any study on quantifying the SG phase in our core-shell nanoparticles.
In FM-AFM core-shell nanoparticles, H EB was shown to increase with increasing the field-cooling value and then saturates for field-cooling values above 2 T [48]. This behavior was attributed to the polarization of the uncompensated spins as the cooling field is increased. In [49], exchange bias with small values was observed in very small FeO nanoparticles of average diameters of 3.3 nm.
The occurrence of exchange bias in these nanoparticles was attributed to the limited existence of antiferromagnetically compensated spins with in each particle. In FM-AFM systems involving spin-glass-like behavior or spin disorder, with increasing the field-cooling value, H EB decreased after reaching a maximum without saturation [15,35,50]. Our exchange bias results for sample S2 do not contain any of these behaviors. The common observation in our data is that H EB increases with increasing the field-cooling value reaching a maximum and then decreases. With further increase of field-cooling value, H EB keeps decreasing, reaches saturation, or increases slightly.
The nearly similar magnitudes of coercivity along with its systematic behavior with temperature in all samples at all field-cooled values are clear indications of the insignificant role of shell thickness on coercivity. Hence, it might be concluded that the coercivity in our core-shell nanoparticles is mainly determined by core effects and the exchange coupling between the core spins near the interface and the interfacial SGCs. The different behavior of coercivity with temperature in these samples was displayed only in the zero-field-cooled case, where slightly different magnitudes and different rates of decrease (below 100 K) or increase (above 100 K) are observed in different samples. At temperatures below 100 K, the fast and monotonic decrease of coercivity with temperature in all samples is attributed to the thermal activation effects of the blocked core moments (spins) over the anisotropy barriers. However, the different rates of decrease of coercivity with temperature (below 100 K) is not a core effect. Because all these particles have nearly the same core size, we believe that this different behavior in coercivity is due to the different nature of the interfacial SGCs. A field-cooled value of 0.5 T is large enough to align the spins of each cluster and thus eliminate the different identities of each SGC in each sample. In the field-cooling process, the spins within each SGC will be aligned in the same direction and thus behave similarly. The temperature provides the interfacial SGCs with the energy needed to unpin the spins within each cluster and hence decrease the exchange coupling with the nearby core spins, regardless of the initial field-cooling. The small and linear increase of coercivity above the critical temperature could be attributed to an enhanced interaction between the core spins near the interface and the interfacial spin-glass clusters. As the temperature is raised above 100 K, the SGC will start to vanish and the initially pinned spins within each cluster will start to become unpinned and rotate in the direction of the applied magnetic field. Hence, an enhanced exchange coupling starts to occur between these well-directed spins and the nearby core spins, leading to the small increase in coercivity with temperature.
The different behaviors of coercivity and exchange bias with temperatures at all field-cooled values hint for different mechanisms of interaction of these effects in such FIM-FIM core-shell structure. The variations of exchange bias with shell thickness is a clear indication on the role of the whole shell material on exchange bias. The nonmonotonic behavior of exchange bias with temperature in sample S2 (especially the enhanced exchange bias at 300 K) is an indication of the role of the interfacial SGCs. Hence, we propose that the exchange bias effect in our core-shell nanoparticles is mainly due to the indirect exchange coupling between the core and shell spins. The layer of interfacial SGCs mediates the exchange coupling between the core and shell spins. The exchange bias vanishes in the sample S3 (with the thickest shell) because the shell spins are under-coupled, and the samples behave as if they do not possess shells. The vanishing of exchange bias (in most conditions) in sample S1 (with the thinnest shell) occurs because the core and shell spins are over-coupled, causing the shell spins to be completely locked to the core spins and rotate with them, and hence giving no exchange bias. The core and shell spins in sample S2 are coupled enough such that the rotation of the core spins will be opposed by the shell spins, producing exchange bias effect. Temperature and an applied magnetic field might influence the spin-glass interfacial clusters in a particular region more than in others, depending on the strength of spin coupling (pinning) within these SGCs and their coupling with the core and shell spins. The different and unpredicted responses of the spin-glass interfacial clusters to the temperature and applied field lead to unpredicted temperature and field dependence of the indirect exchange coupling between the core and shell spins, and hence of the exchange bias as observed in sample S2. The small exchange bias magnitudes in all samples could be attributed to the weak exchange coupling between the core and shell spins that is mediated by the interfacial SGCs. The nonmonotonic behavior attributed to the unpredicted behavior of these spin-glass clusters with temperature and field-cooling. The enhanced exchange bias at 300 K could be attributed to the enhanced indirect core-shell coupling due to the directed spins in these clusters. The positive exchange bias could be due to an antiferromagnetic nature of the exchange interaction at the interface, whereas the negative exchange bias could be due to a ferromagnetic nature of the exchange interaction at the interface.

Materials and Methods
The key and novel result here is the successful control of the core and shell dimensions, where the core diameter was fixed at nearly 8 nm while the shell thickness was varied from 1 to 5 nm. We have synthesized iron oxide (Fe 3 O 4 -γ-Fe 2 O 3 ) nanomaterials with different particle sizes by the usual co-precipitation method. The FeCl 3 ·6H 2 O (0.1 M) and FeCl 2 ·4H 2 O (0.05 M) were used as precursor materials. Both the precursor materials were dissolved in deionized water separately and mixed at room temperature. Ammonium hydroxide solution (25%) was added drop by drop until PH became 10. The mixed solution was kept at 80 • C for the reaction to occur. The reaction was carried out in atmospheric pressure, and the reaction times were 1, 2, and 3 h to get nanoparticles with different sizes. Finally, a black precipitation was formed, collected, and dried at 120 • C in vacuum. It was reported that a reaction mechanism involving inward anionic diffusion was responsible for the γ-Fe 2 O 3 phase [51]. The atomic oxygen plays a major role in inducing the γ-Fe 2 O 3 phase. This is due to the direct logarithmic kinetic diffusion with a logarithmic relation between γ-Fe 2 O 3 thicknesses versus oxygen exposure time. Hence, instead of keeping the nanoparticles in vacuum, they were allowed to oxidize in ambient atmosphere for different time spans. The smaller particles are allowed to oxidize in oxygen atmosphere for shorter time, and the largest particles are allowed to oxidize for longer time to get thicker shells with the same core dimensions. The nanoparticle with 1 h reaction time in open air had the smallest γ-Fe 2 O 3 shell thickness, whereas nanoparticles with 3 h reaction time in open air had the largest γ-Fe 2 O 3 shell thickness. All the samples were found to have the same core diameter of 8 nm. The samples, which were prepared with reaction times of 1, 2, and 3 h, were found to have shell thickness of 1 nm (sample S1), 3 nm (sample S2), and 5 nm (sample S3), respectively.
In order to confirm the corresponding phase, X-ray diffraction characterization was performed using a PANalytical X'Pert Pro X-ray diffractometer (Almelo, The Netherlands). The morphology of the nanoparticles was confirmed by several microscopic tools such as high-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED). The transmission electron microscopy (TEM) measurements were performed using an FEI, TECNAI G 2 F30, S-TWIN microscope GG Eindhoven, The Netherlands) operating at 300 kV equipped with a GATAN Orius SC1000B CCD camera. Mössbauer spectra were collected using a standard constant acceleration Mössbauer spectrometer (Wissel, Stamberg, Germany) over 1024 channels. The samples for Mössbauer studies were circular disks of diameter 1.3 cm, prepared by sprinkling a thin layer of the finely powdered alloys on a piece of Scotch tape. The γ-ray source was a 50 mCi Co 57 in a rhodium matrix. Isomer shifts were measured relative to the centroid of the α-iron spectrum at room temperature, and α-iron spectrum was also used for calibration. The magnetic measurements were conducted using a superconducting quantum interference device (SQUID) (San Diego, CA, USA) from Quantum Design. Magnetic moment versus applied field up to 3 T was measured for the three samples at several temperatures after cooling the samples in zero field and in several applied fields.

Conclusions
The Fe 3 O 4 -γ-Fe 2 O 3 core-shell nanoparticles with fixed core diameter and three different shell thicknesses were prepared by the usual chemical precipitation method. The X-ray diffraction and transmission electron microscopy images showed that particles are nearly spherical with diameters of 9, 11, and 13 nm, respectively. The Mossbauer spectroscopy and selected area electron diffraction ascertained that the core-shell particles mainly consisted of Fe 3 O 4 core and γ-Fe 2 O 3 shell. Several key results on exchange bias and coercivity were obtained and attributed to the existence of spin glass clusters at the core-shell interface. These interfacial spin glass clusters were suggested to mediate the exchange interaction between the core and shell spins.