This chapter focuses on the relationship between structural and magnetic properties of cubic spinel ferrite MFe2O4 (M = Mg, Mn, Fe, Co, Ni, Cu and Zn) nanoparticles (NPs). First, a brief overview of the preparation methods yielding well‐developed NPs is given. Then, key parameters of magnetic NPs representing their structural and magnetic properties are summarized with link to the relevant methods of characterization. Peculiar features of magnetism in real systems of the NPs at atomic, single‐particle, and mesoscopic level, respectively, are also discussed. Finally, the significant part of the chapter is devoted to the discussion of the structural and magnetic properties of the NPs in the context of the relevant preparation routes. Future outlooks in the field profiting from tailoring of the NP properties by doping or design of core‐shell spinel‐only particles are given.
- cubic spinel ferrite nanoparticles
- magnetic properties
- core‐shell structure
- particle size
- spin canting
- Mössbauer spectroscopy
- magnetic susceptibility
- size effect
- magnetic anisotropy
Spinel ferrite nanoparticles (NPs) are in the spotlight of current nanoscience due to immense application potential. Very interesting aspects of the spinel ferrite NPs are their excellent magnetic properties often accompanied with other functional properties, such as catalytic activity. Moreover, the magnetic response of the NPs can be tuned by particle size and shape up to some extent. Consequently, various spinel ferrite NPs are suggested as universal and multifunctional materials for exploitation in biomedicine [1–4], magnetic recording, catalysis [5–8] including magnetically separable catalysts [9–12], sensing [13–16] and beyond (MgFe2O4 in Li ion batteries [17, 18], or investigation of dopamine ). Thus it is of ultimate interest to get control over their functional properties, which requires in‐depth understanding of the correlation between their structural and magnetic order. For example, the particle size and shape are extremely important both in biomedical imaging using Magnetic Resonance Imaging (MRI)  and therapies by means of magnetic field‐assisted hyperthermia .
The chapter aims to summarize the most important aspects of magnetism of cubic spinel ferrite nanoparticles (
2. Brief overview of preparation methods of spinel ferrite nanoparticles
In this section, selected methods of the NP preparation are summarized. Explicitly, the wet methods yielding well‐defined NPs, either isolated or embedded in a matrix, are accented. The reason is that only such samples can be sufficiently characterized and the factors defined within the “three level” concept can be disentangled. Outstanding reviews on the specific method(s) with further details and references are also included [22–25].
Coprecipitation method is the archetype route, which can be used for preparation of all cubic spinel ferrite NPs: Fe3O4/γ‐Fe2O3 [24, 26], MgFe2O4 , etc. In general, two water‐soluble metallic salts are coprecipitated by a base. The reaction can be partly controlled in order to improve characteristics of the NPs [26, 28, 29]; however, it is generally reported as a facile method yielding polydispersed NPs with lower crystallinity and consequently less significant magnetic properties.
The family of decomposition routes includes wet approaches based on decomposition of metal organic precursors in high‐boiling solvents, typically in the presence of coating agents (all , Fe3O4/γ‐Fe2O3 [24, 31], CoFe2O4 [32, 33], NiFe2O4 , ZnFe2O4 ). The most common organic complexes used for decomposition are metal oleates and acetylacetonates. The decomposition methods yield highly crystalline particles close to monodisperse limit with very good magnetic properties. However, the reaction conditions must be controlled in correspondence of the growth model suggested by Cheng et al. . They can be also tailored to produce NPs of different shapes (CoFe2O4 [36, 37], Fe3O4/γ‐Fe2O3 [38, 39]). Higher‐order assemblies of the NPs can be also achieved by varying the ratio of the precursor and reaction temperature (CoFe2O4 ). Alternatively, the decomposition takes place in high‐pressure vessel (autoclave) [41, 42].
A large group of preparation protocols is based on solvothermal treatments, in aqueous conditions termed as hydrothermal. The preparation can be carried out either in a simple single‐solvent system (MgFe2O4 , NiFe2O4 [44, 45]), mixture of solvents (MnFe2O4 , ZnFe2O4 ), surfactant‐assisted routes (ZnFe2O4 ), or in multicomponent systems, such as water‐alcohol‐fatty acid (Fe3O4/γ‐Fe2O3 , CoFe2O4 ). The solvothermal routes are often carried out at elevated pressure and can be also maintained in supercritical conditions (MgFe2O4 ). The NPs prepared by this class of methods are in general of very good crystallinity, in some cases competitive to the NPs obtained by the decomposition routes.
Spinel ferrite NPs can be also obtained with the help of normal or reverse micelle methods, often referred as microemulsion routes (all [52, 53], Fe3O4/γ‐Fe2O3 , MgFe2O4 [55–57], CoFe2O4 , NiFe2O4 , CoFe2O4 and MnFe2O4 , ZnFe2O4 ). This approach takes advantage of the defined size of the micelle given by the ratio of the microemulsion components (water‐organic phase‐surfactant) according to the equilibrium phase diagram . The micelles serve as nano‐reactors, which exchange the constituents dissolved in the water phase during the reaction and self‐limit the maximum size of the NPs. The as‐prepared NPs are often subjected to thermal posttreatment, which improves the NP crystallinity and enhances magnetic properties. However, such NPs are no more dispersible in liquid phase and their applications are thus limited. On the other hand, the microemulsion technique can be used for preparation of the NPs of a defined shape  and mixed ferrites .
A modified polyol method is also used for preparation of spinel ferrite NPs [22, 24, 65–67]. While in the standard route the polyol acts as a solvent and sometimes reducing or complexing agent for metal ions, for preparation of the ferrite NPs, the reaction of 1,2‐alkanediols and metal acetylacetonates in high‐boiling solvents is the most common variant.
Sol‐gel chemistry is a handy approach to produce spinel ferrite NPs. The common tactic is the growth of the NPs in porous silica matrix yielding well‐developed NPs embedded in the transparent matrix. The route requires annealing of the gel; however, the particle size can be sufficiently varied by the annealing temperature. Different spinel ferrites can be prepared (Fe3O4/γ‐Fe2O3 , CoFe2O4 [69–71], MnFe2O4 , NiFe2O4 [73–75]).
NPs of spinel ferrites are also prepared with assistance of microwaves [76, 77], ultrasound (CoFe2O4 , MgFe2O4 ), combustion routes (MgFe2O4 ), or mechanical treatments (MgFe2O4 , MnFe2O4 , NiFe2O4 ); however, the as‐prepared NPs often require heat treatment, and the resulting samples with sufficient crystallinity are better classified as fine powders. Less common methods such as the use of electrochemical synthesis for the γ‐Fe2O3 NPs  or NiFe2O4  and synthesis employing ionic liquids for cubic magnetite NPs  were recently reported. NPs with size in the multicore limit were obtained by disaccharide‐assisted seed growth . Recently, combination of stop‐flow lithography and coprecipitation was reported . Typical TEM images of spinel ferrite NPs prepared by the most common routes are shown in Figure 1.
The preparation methods described above can be successfully applied to preparation of core‐shell NPs: CoFe2O4@
3. Characterization of magnetic nanoparticles: parameters and methods
In this section, the most important parameters characterizing structural and magnetic properties of NPs are introduced. Overview of the key experimental methods used for their evaluation is also included. For straightforwardness, details on the theoretical models and related formalism are not given, but relevant references are included. More details on the topic can be found in a comprehensive work by Koksharov .
3.1. Basic structural and magnetic characterization
The most important parameter is the particle size itself, usually attributed to the diameter of a single NP. The first‐choice technique for determination of the particle size is the transmission electron microscopy (TEM), which gives the real (or physical) particle size,
Particle size can be also determined using powder X‐ray diffraction (XRD). The profile of the diffraction peak contains information about the so‐called crystallite size,
The physical profile is the convolution of the two dominant contributions caused by the small
Other important parameters characterizing magnetic NPs are related to formation of a single‐domain state. In order to decrease the magnetostatic energy that is associated with the dipolar fields, the ferromagnetic (or ferrimagnetic)‐ordered crystal is divided into the magnetic domains. Within each of the domain, the magnetization,
In the magnetic NPs, the typical dimensions are comparable with the thickness of the domain; thus, at some critical size, it is energetically favorable for the NP to become single domain. The critical dimension ranging from 10-7 to 10-8 m is strictly specific to each magnetic spinel ferrite .
In small magnetic NPs reaching the single‐domain regime, the paramagnetic‐like behavior can be observed even below the Curie temperature,
Another important parameter is the relaxation time,
A very important parameter characterizing the blocked state is the coercivity,
The typical magnetic measurements of the NP magnetic parameters yielding the above‐described parameters can be summarized as follows: temperature dependence of the magnetization in low external applied field, the so‐called zero field cooled curve (ZFC) and field cooled curve (FC); field dependence of the magnetization at fixed temperatures, the so‐called magnetization isotherm (or hysteresis loop in the blocked state); and the a.c. susceptibility measurement. The ZFC‐FC protocol reveals the value of the
A unique tool used in characterization of spinel ferrite NPs is the Mössbauer spectroscopy. It is a dual probe both for structure and magnetism at local level based on recoilless resonant absorption of γ radiation. In general, information on coordination surroundings of the iron cations, their valence, degree of inversion of the spinel structure, and orientation of spins on the cubic spinel sub‐lattices can be obtained [108, 109].
The small spinel ferrite NPs exhibit relaxation time in order of 10-9 s that is close to the time window of the MS (10-8 s) allowing the study of relaxation of the NPs by means of MS [109, 110]. Furthermore, the big advantage of the MS is that it is not restricted to the well crystalline samples; thus, a non‐well crystalline NP can be also investigated using MS. Finally, the so‐called spin canting angle, usually attributed to the presence of the surface spins, can be estimated .
3.2. Real effects in magnetic nanoparticles
3.2.1. Size distribution
All real systems of the NPs exhibit an intrinsic size distribution, which must be considered in evaluation and interpretation of structural and magnetic data. The most common is the log‐normal distribution (see Figure 1); however, Gaussian distribution has been also reported [112–114]. In the case of the TEM observation for the
Typical examples of magnetization isotherms and ZFC‐FC curves influenced by the particle‐size distribution are shown in Figure 2, presenting unhysteretic magnetization isotherms (Langevin curves) for different values of
3.2.2. Spin canting phenomenon and surface effects
Decreasing the NP size, the number of atoms located at the surface dramatically increases. Thus the surface spins become dominant in the magnetic properties of the whole NP. The atoms at the surface exhibit lower coordination numbers originating from breaking of symmetry of the lattice at the surface.
Moreover, the exchange bonds are broken resulting in the spin disorder and frustration at the surface leading to the undesirable effects such as low saturation magnetization of the NP and the unsaturation of the magnetization in the high magnetic applied field . To explain these effects, J. M. D. Coey proposed the so‐called core‐shell model in which the NP consists of a core with the normal spin arrangement and the disordered shell, where the spins are inclined at random angles to the surface, the so‐called spin canting angle  (see Figure 3). The spin canting angle in general depends on the number of the magnetic nearest neighbors connecting with the reduced symmetry and dangling bonds. Other effects such as the interparticle interactions play role . The spin canting angle can be determined with the help of in‐field Mössbauer spectroscopy (IFMS); an example is given in Figure 4.
However, the spin canting is not a unique property of the surface spins, and several works point to the volume nature of the effect [125–127]. Thus the surface effects in the NPs together with the origin of the spin canting angle are still discussed within the scientific community [109, 128–130].
Another consequence of the increased number of the surface atoms is the dominance of surface term to the anisotropy energy, usually expressed as a sum:
3.2.3. Interparticle interactions
The interparticle interactions play a very important role in the magnetic response of the NPs, because they are usually not enough spatially separated to follow the behavior of an ideal SPM system. In general, two types of interaction can be observed: 1) the exchange interaction that affects mainly the surface spins of the NPs in close proximity thus can be neglected in most cases and 2) the long-range order dipolar interaction that is the dominant due to the high magnetic moment of the NPs .
The NP systems can be tentatively divided into the weakly interacting systems (the representatives are much diluted ferrofluids or NPs embedded in matrix in small concentration) and strongly interacting system with the powder samples as representatives. The strength of the interparticle interactions is given by the magnitude of the superspins and interparticle distance, in reality by the concentration of the NPs in ferrofluids, thickness of the NP coating, or matrix‐to‐NP ratio. The interparticle interactions affect all parameters characterizing the single‐domain state. Furthermore, the strong interparticle interactions can result in the collective magnetic state at low temperature that resembles the typical physical properties of spin glasses , termed as superspin glasses in the case of strongly interacting SPM species [132–134].
In weakly interacting system, the dipolar interaction is treated as a perturbation to the SPM model within the Vogel‐Fulcher law , the NP relaxation time is then written as:
The effect on the
In the case of strong interactions, the collective state of the NP condensates below a characteristic temperature—the so‐called glass‐transition temperature,
The heart of the problem of calculating the
The presence of interparticle interactions (as well as the particle‐size distribution) is usually evidenced on the ZFC‐FC curves; typical examples of medium and strongly interacting ensembles of NPs in comparison to the ideal noninteracting case are given in Figure 5. In real samples, all effects are present with variable contribution, and in some cases, both the size distribution and interparticle interactions must be addressed to describe the magnetic response of the samples properly [141, 142] (Figure 5).
4. Synergy of structural and magnetic probes
In order to provide complete insight into properties of magnetic NPs, synergy of structural and magnetic probes is essential. At the atomic and single‐particle level, the complementarity of the (HR) TEM and XRD provides information on phase composition, the presence and type of defects, and particle sizes:
At the mesoscopic level, the influence of interparticle interactions should not be neglected. For that purpose, morphology of the NP ensembles observed by the TEM gives estimate of mutual interparticle distance. The relevance of the interaction regime can be corroborated by a.c. susceptibility experiments, which yields characteristic relaxation times of the superspins, τ. As discussed above, those are strongly reformed because of the interactions. Finally, the effect of the
5. Impact of preparation and strategies of tuning magnetic properties
The intrinsic NP parameters at all levels are imprinted during the preparation process. In this section, a brief discussion of this issue is given in the view of the “three‐level” concept considering the structural and spin order in the unit cell and coordination polyhedra, single‐particle, and NP ensemble level. Strategies profiting from the control over the imprint of the real effects by substitution or formation of artificial core‐shell structures are also mentioned.
The degree of inversion,
The presence of defects, mainly by means of oxygen vacancies, is believed to be another important factor driving magnetic properties of the NPs. It was shown that they dominate the properties of the NPs obtained by mechanochemical processes , and it was also demonstrated that the level of defects can be influenced by vacuum annealing [149–151]. A specific issue is related to the presence of the Verwey transition in the Fe3O4 NPs  as the topotactic oxidation from magnetite to maghemite is a rapid process in common environments. Consequently, experimental investigations of the iron oxide NPs with size below 20 nm do not evidence the transition [26, 153]. Recently, the Verwey transition was observed in the NPs with a size of 6 nm, which were kept under inert atmosphere, and thus their oxidation was prevented .
The most significant and discussed issue is the spin order at single‐particle level and its surface to volume nature. Most works report the dominance of surface spin frustration and suggest the presence of the magnetically dead layer. The increased contribution of the frustrated spins is attributed mainly to size effect, low crystallinity, and surface roughness, dominating in the NPs obtained by coprecipitation method [26, 155–165]. The spin canting in the surface layer was also observed in diluted ferrofluids, which confirms the nature of the effect on single‐particle level . However, the surface spin structure can be reformed when the NPs are in close proximity . Significant increase of the amount of disordered spins was reported for hollow NPs of NiFe2O4 thanks to the additional inner surface . On the other hand, the spin canting was also considered as volume effect, which occurs due to ion order‐disorder in the spinel structure [127, 168] or pinning of the spins on internal defects in single NPs .
Focusing on the mesoscopic effects, the NP size distribution and interparticle interactions will be addressed. The particle‐size distribution is found to be very sensitive to the preparation method used. The NPs with almost monodisperse character are obtained by the decomposition route; however, the parameters of the reaction must be carefully controlled. For example, the prolongation of the reaction time leads both to larger NPs but also increased size distribution [33, 169]. Similar effect was observed for increasing concentration of the oleic acid or oleylamine . Other techniques provide NPs with PDI over 0.2, and the size distribution must be then considered in analysis of the magnetic measurements [69, 116, 142]. However, it is worth mentioning that the narrow‐size distribution of the
In spite of the fact that the surface effects, defects, and interparticle interactions are believed to be contra‐productive factors as they in general decrease the value of saturation magnetization , they were recognized as potential enhancers of effective magnetocrystalline anisotropy, reflected, for example, in increase of the hysteresis losses . Consequently, attempts to prepare smart NPs based on artificial core‐shell structure, e.g., NiFe2O4@γ‐Fe2O3 , ZnFe2O4@γ‐Fe2O3 , and Co,Fe2/Ni,Fe2O4 , appeared recently. Tri‐magnetic multi‐shell structures prepared by high‐temperature decomposition of the metal oleates were also reported .
Alternative strategy is the tuning of magnetic properties of the spinel ferrite NPs via site‐specific occupation of the spinel lattice. This is a straightforward approach as the relevant metal ions can substitute each other in the spinel structure easily. In this case, however, the site occupation must be carefully evaluated and controlled. Successful preparation and basic investigation of structure and magnetic properties of the NPs of Mn‐doped CuFe2O4 ferrite , Zn‐doped MnFe2O4  and NiFe2O4 [193, 194], Co‐doped NiFe2O4  and ZnFe2O4 , and Cr‐doped CoFe2O4  were reported. Recently, doping of spinel ferrites by large cations was suggested as a promising way to increase the effective magnetic anisotropy. La‐doped CoFe2O4 , Sr‐doped MgFe2O4 , and Ce‐doped NiFe2O4  or ZnFe2O4  were prepared. For the doped samples, the most promising are the polyol, sol‐gel, or microemulsion methods as they do not require identical decomposition temperatures of metal precursors like the organic‐based routes, allow rather good control over homogeneity of doping, and yield samples with sufficiently low particle‐size distribution.
6. Conclusions and outlooks
The core message of the chapter is to emphasize the importance of structural and spin order mirrored in magnetic properties of well‐defined spinel ferrite nanoparticles (NPs). The correlation between the specific preparation route to the typical structural and magnetic parameters of the particles is given, and the suitability of the resulting NPs in the context of possible applications is evaluated. Explicitly the meaning of different particle sizes obtained by different characterization methods, related to the degree of structural and spin order, is emphasized in the context of the magnetic properties. In order to wrap up the given subject, let's outline future outlooks in the field. The research of fine magnetic particles is progressively developing thanks to high demand on their practical exploitation, mainly in biomedicine. The forthcoming trend in customization of the magnetic NPs is obviously converging to control of the required magnetic properties at single‐particle level by adjustment of the synthetic protocols, which lead to fine tuning of the particle size, shape, and degree of order [169, 202]. For example, enhancement of the specific absorption rate in NPs can be achieved in natural or arbitrary core‐shell structures , via coupling of magnetically soft and hard ferrites for maximization of hysteresis losses  or by doping‐driven enhancement of heat generation . Finally, smart self‐assembling strategies leading to superstructures , which can be even induced by magnetic field , seem to be a powerful tool for managing the magnetic response of the NPs at mesoscopic level.
The authors gratefully acknowledge Dr. Puerto Morales from the Instituto de Ciencia de Materiales de Madrid for her generous support and for sharing his expertise in synthesis of uniform iron oxide nanoparticles and Prof. Carla Cannas from the Università degli studi di Cagliari for sharing her knowledge in synthesis of core‐shell spinel ferrite nanoparticles. The research was carried out thanks to the support of the Czech Science Foundation, project no. 15‐01953S, and 7FP program project MULTIFUN (no. 262,943), cofinanced by the Ministry of Education, Youth, and Sports (project no. 7E12057). Magnetic measurements were performed in MLTL (http://mltl.eu/), which is supported within the program of Czech Research Infrastructures (project no. LM2011025).