Introduction

Hard CoFe2O4/soft CoFe composite has been extensively investigated recently (Quesada et al. 2014; Zan et al. 2013a, b; Ou-Yang et al. 2015) in order to obtain high coercivity (H c ), saturation magnetization (M s ), and the remanence (M r ) to saturation magnetization ratio (M r /M s ) through the exchange–coupling between hard ferrimagnetic CoFe2O4 with high H c and soft ferromagnetic CoFe with high M s (Qin et al. 2009; Zhang et al. 2011; Zehani et al. 2014; Aguirre Mdel et al. 2015; Xu et al. 2015c; Cernea et al. 2016; Ramis Mustafa et al. 2014). Unfortunately, most previous reports revealed that M r /M s was smaller than 0.5 (Quesada et al. 2014; Soares et al. 2014; Soares et al. 2011). This may result from the complex interactions, besides the exchange–coupling interaction, as discussed below, which affects the magnetization reversal and consequently influences on the macroscopic magnetic properties. This issue has not been investigated in detail before for the CoFe2O4/CoFe composite as far as we know.

If the exchange–coupling occurs between hard and soft phases, the magnetization of the soft and hard phases could show an equivalent reversal behavior in the whole temperature region, and thus, the magnetization changes with the external magnetic field smoothly, exhibiting the characteristic of single-phase hard magnet (López-Ortega et al. 2015; Xia et al. 2015; Hamid and Ahmad Khalid 2011). However, some reports observed the exchange–uncoupled (Quesada et al. 2014) or the exchange–spring effect (Zhang et al. 2013) in CoFe2O4/CoFe2 composites, and the hysteresis loops exhibited a jump in the low field region as a result of the broad distribution of reversal fields of hard and soft species (Quesada et al. 2014). Besides the exchange interaction (exchange–coupling and exchange–spring) occurring at the interface between CoFe2O4 and CoFe2, the dipolar interaction between CoFe2O4/CoFe2 particles can lead to the formation of spin-glass state in which the particle moment orients randomly, and the dipolar interaction is suggested to suppress the M r /M s value (Xu et al. 2015a; Geng et al. 2016a, b; Geng et al. 2015; Wang et al. 2012). The strength of dipolar interaction can be estimated by the dipolar field H dip , defined as H dip  = 2 μ/d 3, where μ is the particle moment (μ = M s  × V m ; M s is the saturation magnetization and V m is magnetic grain volume) and d is the distance between particles (center to center). Therefore, the cooperative effects of exchange–spring, exchange–coupling, and dipolar interaction as well as the anisotropy modify the energy barrier distribution, which influence on the magnetization reversal and consequently on the magnetic properties (Kooti and Naghdi Sedeh 2013).

The energy barrier distribution, f (T), can be investigated by the measurements of field cooling (FC) and zero-field cooling (ZFC) magnetizations, i.e., M FC and M ZFC, because f (T) can be calculated by (Pianciola Betiana et al. 2015; Bianco et al. 2002) f (T) − d(M FC − M ZFC)/dT. The energy barrier distribution affects the magnetic properties and magnetic ordering state, as observed in Co3O4 (Mousavand et al. 2009; Benitez et al. 2008), CoFe2O4 (Pianciola Betiana et al. 2015), NiFe2O4 nanoparticles diluted by SiO2 (Nadeem et al. 2014), nanostructure of exchange–coupled Fe core with Fe oxide shell (Bianco et al. 2002), Ni/NiO core–shell nanoparticles (Ji et al. 2015), and ε-Fe3−x Ni x N (Gajbhiye and Bhattacharyya 2008). In the present work, the M FC and M ZFC measured at different magnetic fields from 500 Oe to 20 kOe were investigated on two exchange–spring CoFe2O4/CoFe2 composites with different relative content of CoFe2, throwing light on some aspects of magnetization reversal behavior that to our knowledge were not addressed in previous investigations on CoFe2O4/CoFe2 systems.

Experimental procedure

The synthesis of CoFe2O4 (hard)/CoFe2 (soft) nanocomposites was carried out by two steps: mono-dispersed CoFe2O4 nanoparticles were first synthesized by the thermal decomposition of Fe(acac)3 and Co(acac)2 in organic solvent of benzyl ether, oleic acid, and oleylamine as described elsewhere (Xu et al. 2015a); then, the CoFe2O4 nanoparticles were reduced in the H2 ambient at 300 °C (500 sccm, 96%N2 + 4%H2) for 4 and 8 h to obtain the final samples, which are hereafter referred to as the samples S4H and S8H, respectively.

The crystal structure of the products was determined by X-ray diffraction (XRD) using an X-ray diffractometer (XRD; DX-2000 SSC, Dandong Fangyuan Instrument Company, DanDong, Liaoning, China) with Cu Kα irradiation (λ = 1.5406 Å) in the scanning range 20–80° with a step size of 0.02°. The (high resolution) transmission electron microscopy ((HR)TEM; JEOL JEM-2100, Tokyo, Japan) was used to observe the particle size, morphology, and lattice fringes. The distribution trends of O, Fe, and Co elements were detected by EDS elemental mapping analysis. Magnetic measurements were carried out using a superconducting quantum interference device PPMS system (SQUID, PPMS EC-II, Quantum Design Inc., San Diego, California, USA).

Results and discussion

Crystal structure and morphology

As-prepared CoFe2O4 (Fig. 1b) exhibited the single-phase cubic spinel structure, compared with the powder diffraction file (PDF) of CoFe2O4 (No: 22–1086) in Fig. 1a. After CoFe2O4 was reduced in H2 for 4 h, the obtained sample, i.e., S4H (Fig. 1c), appeared in the reflection of CoFe2 alloy according to the PDF card of CoFe2 (No: 65–4131) in Fig. 1e, due to the reducing reaction: CoFe2O4 + 4H2 → CoFe2 + 4H2O (Soares et al. 2011). For the S8H sample, as shown in Fig. 1d, the diffraction intensity of CoFe2 increases due to the longer duration in the H2/N2 atmosphere.

Fig. 1
figure 1

X-ray diffraction patterns of as-prepared CoFe2O4 (b), S4H (c), and S8H (d); the standard PDF cards of CoFe2O4 (a) and CoFe2 (e)

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As shown in Fig. 2a, the as-prepared CoFe2O4 comprises the well-dispersed nanoparticles. The particle size ranges from 26 to 34 nm, as illustrated in the size histogram in Fig. 2c. The average particle size, defined as the size corresponding to the peak of the Gaussian fitting curve (solid line), is ~30.4 nm. The (HR)TEM image in Fig. 2b shows the clear fringes with the interfringe distance 0.48 nm, corresponding to the (111) crystal plane of CoFe2O4 (Sun et al. 2015). After CoFe2O4 is reduced for 8 h, the particles in the S8H sample aggregate to some extent as shown in Fig. 2g. The (HR)TEM can only detect the fringes from CoFe2, as shown in Fig. 2h, indicating that the reduction of CoFe2O4 occurs first at the surface of particle, i.e., CoFe2 exists at the outer layer while CoFe2O4 exists in the inner of particle. As seen in the EDS spectra of CoFe2O4 and S8H in Fig. 2i, the intensity of O in S8H is obviously lower than that in CoFe2O4 due to the loss of O after reduction of CoFe2O4. From the elemental mapping for O, Fe, and Co, it can be observed that the distribution of O element in CoFe2O4 is more uniform than in S8H, as shown in Fig. 2d, j. Compared with the elemental mapping of Fe and Co in CoFe2O4 (Fig. 2e, f), the S8H sample (Fig. 2k, l) exhibits a clearer contrast, which means a higher concentration of Fe and Co in the S8H sample.

Fig. 2
figure 2

The TEM image (a), HRTEM image (b), size histogram with Gaussian-fitting curve (solid line) (c), and EDS elemental mapping for O (d), Fe (e), and Co (f) of the as-prepared CoFe2O4; the TEM image (g) and HRTEM image (h) of the S8H sample, an energy dispersive spectroscopy (EDS) of CoFe2O4 and S8H (i), and elemental mapping for O (j), Fe (k), and Co (l) of S8H. The inset in h shows the magnified detail of square-marked area

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The magnetic field (H)-dependent magnetization (M) curves, i.e., M(H) loops (−70 kOe < H < + 70 kOe) recorded at 10 and 300 K for the S4H and S8H samples, were shown in Fig. 3. A jump appears in M(H) loop of 10 K around H = 0 for the S4H sample, which can be attributed to the broad distribution of reversal fields of hard CoFe2O4 and soft CoFe2 species (Quesada et al. 2014). The jump is enhanced for S8H because of the more soft CoFe2 component (Sun et al. 2015). Furthermore, the jump also signifies that no exchange–coupling but exchange–spring effect occurs at the interface between CoFe2O4 and CoFe2 because in the exchange–coupled CoFe2O4 and CoFe2 system, their magnetizations could have an equivalent reversal behavior in the whole temperature region, leading to a smooth hysteresis loop which is characteristic of a single-phase hard magnet (López-Ortega et al. 2015). The similar exchange–spring effect was reported before for CoFe2O4/CoFe2 (Zhang et al. 2013) and Fe/Sm-Co (Liu et al. 2011). With increasing temperature, the anisotropy field of CoFe2O4 strongly decreases with increasing temperature, and consequently, the average reversal fields of hard and soft phases may be similar, resulting in the single-phase behavior of loops of 300 K, i.e., the smooth loops. The M s values are 96 emu/g (10 K) and 92 emu/g (300 K) for S4H and 118 emu/g (10 K) and 115 emu/g (300 K) for S8H. S8H has the larger M s value than S4H because of more CoFe2 existing in S8H. The H c values are 11.8 kOe (10 K) and 1.7 kOe (300 K) for S4H and 2.5 kOe (10 K) and 1.2 kOe (300 K) for S8H. H c of S8H is smaller than that for S4H. For the soft and hard composite system, the effective anisotropy constant K is expressed by K = f s K s  + f h K h , where f s and f h are the volume fraction and K s and K h are the anisotropy constant of soft and hard phases with K s  « K h , respectively (Zan et al. 2013a; Geng et al. 2015); S8H has more CoFe2, therefore it has smaller K and hence smaller H c due to H c ∝ K.

Fig. 3
figure 3

M(H) loops for the S4H (a) and S8H (b) samples measured at 10 and 300 K

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Figure 4 shows the field derivative dM/dH of the virgin curves at 10 K for S4H and S8H samples, and the magnetic field at the peak of dM/dH curve is the irreversible magnetization reversal field (H irr ). Two peaks locate at 3.4 and 20 kOe for the S4H sample, and at 2.4 and 16 kOe for the S8H sample, the peaks at low and high field, respectively, corresponding to the irreversible magnetization reversal of CoFe2 and CoFe2O4. CoFe2 is a typical soft magnet with small anisotropy, so it has small H irr . More CoFe2O4 in an individual particle for the S4H sample exerts the pinning effect on the moment of CoFe2, leading to the H irr increase of CoFe2, while more CoFe2 in S8H polarizes the moments of CoFe2O4, resulting in the H irr decrease of CoFe2O4 (Bianco et al. 2002). The appearance of two peaks is also indicative of two-phase feature of magnetization reversal, i.e., exchange–spring rather than exchange–coupling between CoFe2O4 and CoFe2.

Fig. 4
figure 4

The field derivative dM/dH of the virgin curves for S4H and S8H samples at 10 K. The inset shows the local dM/dH data (empty circles) around 16 kOe of the S8H sample with the curve of Lorentz fit (solid line) in order to find the peak position

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Figure 5 shows the zero-field cooling (ZFC) and field cooling (FC) magnetization (M) curves of the sample S4H from 10 to 390 K, recorded at different applied magnetic fields H from 500 Oe to 20 kOe. The FC and ZFC curves for the low fields of H = 500 Oe and 1 kOe do not overlap up to 390 K, and both the ZFC and FC curves decrease with lowering temperature; these behaviors signify the existence of the super-spin-glass (SSG) state as a result of the strong dipolar interaction (Xu et al. 2015a, b, c; Petracic et al. 2006). In the case of H ≥ 2 kOe, the FC and ZFC curves overlap at the irreversibility temperature (T irr ), defined as the temperature where M FC − M ZFC is about 5% (Bianco et al. 2002). Below T irr , the FC and ZFC curves bifurcate. T irr decreases with increasing H, and the variation of T irr with H is plotted in Fig. 11a. On increasing H from 2 to 20 kOe, T irr reduces, but the magnetic irreversibility persists at low temperature even under the largest field of H = 20 kOe. Below T irr , the particle moments are blocking or freezing while they exhibit a ferromagnetic-like trend above T irr . With increasing H, the shape of the ZFC curve depends strongly on the field: M ZFC decreases monotonically with the temperature for H < 3 kOe while it first exhibits a peak and then decreases for H > 3 kOe. M ZFC decreases in the low-temperature region because the unfrozen disordered moments tend to the frozen SSG state at low temperature, in which the moments are pointing randomly into all directions.

Fig. 5
figure 5

ZFC (empty circles) and FC (solid circles) magnetization (M) curves of the S4H sample for different applied magnetic fields

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As shown in Fig. 6, the FC and ZFC curves of the S8H sample exhibit the following features:

  1. 1)

    For all the applied fields, first, the M FC monotonically increases till 50 K, where a peak appears, and then decreases as the temperature is reduced. In order to clearly show the peak position, M FC in Fig. 6 was divided by the maximum of M FC, i.e., normalized M FC, and Fig. 7 representatively shows the normalized M FC curves for H = 2, 5, and 20 kOe. The peak position does not change with H. Such peak is not observed in the S4H sample; so, it can be suggested that the peak relates to more CoFe2 in S8H. The similar peak has been observed in CoFe2 alloy with minimal CoFe2O4 and Fe2O3 (Geng et al. 2016a, b), further confirming that more CoFe2 is responsible for the peak around 50 K. A local maximum or peak in the M FC curve signifies the existence of the SSG state (Mathieu et al. 2013), which typically exhibit glass temperature around 50 K (Petracic et al. 2006). Imaginably, the collective effects of exchange–spring, occurring at the interface of CoFe2O4 and CoFe2, and the dipolar interaction, occurring between CoFe2O4/CoFe2 particles, together with the random anisotropy of CoFe2O4, result in the breakdown of long-range ferromagnetic order in CoFe2 and the frustrated configurations of moments at low temperature, i.e., reentrant spin-glass. The orientation of moments is shown in Fig. 8. Therefore, the S8H sample passes from a paramagnetic, which occur at higher temperature beyond our measuring range, to a ferromagnetic and to a “reentrant” spin-glass phase as the temperature is reduced, as what occurs in ε-Fe3−x Ni x N (0.1 ≤ x ≤ 0.8) (Gajbhiye and Bhattacharyya 2008).

  2. 2)

    T irr of S8H, shown in Fig. 11b, is lower than that of S4H. The S8H sample has more soft CoFe2 with smaller anisotropy than CoFe2O4; so, it has the smaller effective anisotropy K than S4H, leading to the decrease in T irr which can be deduced from KV = 25 k B T irr (Verma and Pravarthana 2011), where V is the volume of the particle and k B is the Boltzmann constant.

Fig. 6
figure 6

ZFC (empty circles) and FC (solid circles) magnetization (M) curves of the S8H sample for different applied magnetic fields

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Fig. 7
figure 7

Normalized M FC by the maximum of M FC with H = 2, 5, and 20 kOe

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Fig. 8
figure 8

Schematic plot for the moment orientation in the S8H sample. Red arrow denotes the moment of CoFe2O4 and blue arrow denotes the moment of CoFe2

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The temperature derivative of the difference between the FC and ZFC magnetization (M FC − M ZFC), i.e., −d(M FC − M ZFC)/dT, has been calculated. The data of −d(M FC − M ZFC)/dT versus temperature T are shown in Fig. 9 for the S4H sample and fitted by a Lorentz function in order to read the peak temperature accurately. In the cases of H = 500 Oe and 1 kOe, −d(M FC − M ZFC)/dT does not exhibit the peak in the temperature region 10~390 K, while a broad peak appears at T 2 = 348 K when H increases to 2 kOe (Fig. 9a) and the peak shifts to lower temperature as H increases, as shown in Fig. 11a. This peak has also been observed in Fe/Fe oxide granular system (Bianco et al. 2002). In the Fe/Fe oxide system, −d(M FC − M ZFC)/dT exhibits two peaks which locate at low-temperature T 1 and at high-temperature T 2. The low-temperature region below T 1 corresponds to the completely frozen state. The region between T 1 and T 2 defines a regime consisting of frozen and relaxing oxide magnetic regions, which coexist with the quasistatic Fe component. However, the S4H sample does not exhibit the quasistatic T 1 peak, maybe indicating that the moments are not fully frozen until 10 K. Fig. 9 The temperature derivative of the difference between the FC and ZFC magnetization (M FC − M ZFC), i.e., the curves of −d(M FC − M ZFC)/dT versus temperature T, for the S4H sample. The solid line is the fitting curve according to the Lorentz function.

figure 9

Furthermore, the broad and relaxing peak at T 2 indicates the existence of a very broad, field-dependent energy barrier distribution. This is supported by the irreversibility below T irr, by the field-dependent M FC − M ZFC at 10 K and by the decrease of T irr with increasing H above 2 kOe. T irr signals the onset of a freezing process with decreasing temperature, i.e., the blocking associated to the highest anisotropy energy barrier (Bianco et al. 2002).

For the S8H sample, the −d(M FC − M ZFC)/dT curves do not appear at a peak for H = 500 Oe and 1 kOe (not shown here). The curves in Fig. 10 with H ≥ 2 kOe exhibit the following characteristics: (1) In the low-temperature region, M FC rapidly rises with decreasing temperature till T 1~15 K, and the shape of curve is not sensitive to the magnetic field, exhibiting the quasistatic characteristic, as what occurred in Fe/Fe oxide (Bianco et al. 2002). The feature of curve around T 1~15 K is not observed in the S4H sample; so, it may be related to the reentrant spin-glass state in S8H with more CoFe2, or in other words, CoFe2 contributes to the quasistatic curve around T 1~15 K. In the Fe/Fe oxide, a quasistatic peak appears at T 1~20 K and a low-temperature region below T1~20 K corresponds to the frozen and disordered magnetic state, characterized by a strong exchange–coupling between the structurally disordered, spin-glass-like oxide matrix, and the Fe nanocrystallites (Bianco et al. 2002). In the S8H sample, the rapid rise of −d(M FC − M ZFC)/dT in the low-temperature region is suggested to have the same origin as that in the Fe/Fe oxide, i.e., below T 1~15 K, there are fully frozen moments including disordered moments at the interface of the exchange–spring CoFe2O4 and CoFe2 and those in reentrant spin-glass state. (2) On increasing the temperature above 15 K, the completely frozen state becomes progressively unfrozen. Between T 1 and T irr, a broad peak appears at T 2 = 224 K for H = 2 kOe, which shifts to lower temperature as H increases, i.e., it is a relaxing peak. The dependence of T 1 and T 2 on H is shown in Fig. 11b. According to the field derivative dM/dH of the virgin curves for S4H and S8H samples at 10 K (see Fig. 4), it can be suggested that the moment reversal of CoFe2 towards the magnetic field direction is almost completed at H = 3.4 kOe for S4H and H = 2.4 kOe for S8H. Therefore, it is reasonable to attribute the shift of T 2 peak occurring at higher field than 2 kOe to the moment reversal of CoFe2O4, which is determined by the cooperative effects of crystalline-anisotropy of CoFe2O4, exchange–spring effect between CoFe2O4 and CoFe2 together with the inter-particle dipolar inter-action. Furthermore, the increase in magnetic field favors the formation of a ferromagnetic network throughout the sample, resulting in the shift of temper-ature for moment freezing or blocking towards a lower value, and consequently the decrease in T2 and T irr Fig. 10 The curves of −d(M FC − M ZFC)/dT versus temperature T for the S8H sample. The solid line is the fitting curve according to the Lorentz function.

figure 10
Fig. 11
figure 11

Dependence of T 1, T 2, and T irr on the applied magnetic field H for S4H (a) and S8H (b). The inset in b shows the T 2 of S4H and S8H versus H

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Summarily, the intra- and inter-particle interaction and anisotropy determine the magnetization reversal in CoFe2O4/CoFe2 granular systems, and consequently affect the magnetic properties, resulting in the different H c, M s, and M r/M s. These can be controlled by changing the content of CoFe2 in CoFe2O4/CoFe2 to obtain the desirable magnetic properties, which is meaningful for the practical applications such as the magnetic record medium and flexi-programmable logic devices [Li et al. 2015]. For example, the magnetic unit in magnetic record medium requires the suitable moment, anisotropy, and inter-particle interaction to stabilize the moment of the magnetic unit. As is well-known, the distribution of hard and soft magnetic phases affects the magnetic properties of hard/soft composites. It deserves the further investigation to synthesize the nanostructures with the metal core/oxide shell, such as CoFe2 (core)/CoFe2O4 (shell) and Fe (core)/Fe2O3 (shell). Furthermore, these nanostructures are expected to be promising materials for various bio-sensing applications because the oxide shell is biocompatible. Further investigations are in process.

Conclusions

The CoFe2O4/CoFe2 composites were synthesized by the reduction of dispersive and uniform CoFe2O4 nanoparticles in H2 ambient for 4 and 8 h in order to increase the relative content of CoFe2, and the temperature-dependent magnetization was measured under different magnetic fields from 500 Oe to 20 kOe. The nature of the interplay between CoFe2O4 and CoFe2 is the exchange–spring which can be observed in the hysteresis loops at 10 K. The magnetic properties of these two composites were determined by the anisotropy, intra-particle exchange–spring, and inter-particle dipolar interaction. The main results are as follows.

With decreasing temperature, a progressive freezing of the moments in two composites occurs at field-dependent irreversible temperature T irr. The sample with more CoFe2 has lower T irr due to smaller anisotropy. In the case of the S4H sample, the moments are not fully frozen till the lowest measuring temperature. In the case of the S8H sample, it contains more CoFe2; the long-range ferromagnetic ordering of CoFe2 is broken down due to the cooperative effects of random anisotropy of CoFe2O4, the exchange–spring between CoFe2O4 and CoFe2, and the inter-particle dipolar interaction, leading to the formation of the reentrant spin-glass state around 50 K. Below T 1~15 K, these disordered moments are fully frozen.

The increase in magnetic field from 2 kOe promotes the formation of a ferromagnetic network throughout the sample and suppresses the freezing or blocking of the moments, leading to the decrease of T 2 and T irr. The shift of T 2 peak towards the lower temperature as H increases from 2 kOe can be attributed to the moment reversal of CoFe2O4, which is determined by the cooperative effects of crystalline-anisotropy of CoFe2O4, exchange–spring effect between CoFe2O4 and CoFe2 together with the inter-particle dipolar interaction.

The results in the present work are meaningful for the practical applications such as the magnetic record medium and flexi-programmable logic devices.