Magnetic and electronic properties of anisotropic magnetite nanoparticles

Magnetic materials at the nanometer scale can demonstrate highly tunable properties as a result of their reduced dimensionality. While significant advancements have been made in the production of magnetic oxide nanoparticles over the past decades, maintaining the magnetic and electronic phase stabilities in the nanoscale regime continues to pose a critical challenge. Finite-size effects modify or even eliminate the strongly correlated magnetic and electronic properties through strain effects, altering density and intrinsic electronic correlations. In this review, we examine the influence of nanoparticle size, shape, and composition on magnetic and tunneling magnetoresistance (TMR) properties, using magnetite (Fe3O4) as an example. The magnetic and TMR properties of Fe3O4 nanoparticles are strongly related to their size, shape, and synthesis process. Remarkably, faceted nanoparticles exhibit bulk-like magnetic and TMR properties even at ultra-small size-scale. Moreover, it is crucial to comprehend that TMR can be tailored or enhanced through chemical and/or structural modifications, enabling the creation of ‘artificially engineered’ magnetic materials for innovative spintronic applications.


Introduction
The history of magnetic materials began thousands of years ago, around 2000 BC, and since then, magnets have remained intertwined with humanity.For centuries, the magnetic compass served as an indispensable navigation tool for sailors scale [1].The comprehension of magnetism gained traction in the 16th century when William Gilbert conducted various experiments with magnets [2].In the 18th century, Hans Christian Oersted and James Clerk Maxwell made a groundbreaking discovery by establishing the connection between electricity and magnetism [1,2].This pivotal moment marked a significant milestone in the history of magnetism.Subsequently, the utilization of magnets has expanded in numerous ways.Electrical motors, speakers, microphones, permanent magnets, and various other modern devices have contributed to the advancement of society.In the late 19th century, with the emergence of nanotechnology, the exploration of nano-sized magnets, known as 'magnetic nanoparticles,' commenced [3].These nanoparticles present intriguing possibilities for interdisciplinary applications bridging physics, chemistry, and medical sciences.For instance, self-organized assemblies of nanoparticles (such as FePt and FeCo) serve as magnetic storage devices capable of storing nearly a thousand terabits of data per square centimeter [4][5][6][7][8].Moreover, the coupling of biomolecules or medications with magnetic nanoparticles has ushered in a new era in medical diagnostics and therapy [9][10][11][12][13][14][15][16].Consequently, the design and investigation of 'novel' nanoscale magnetic materials have become paramount over the past two decades.
Interestingly, magnetic nanoparticles show several anomalous properties as compared to traditional bulk magnets [17,18].For example, magnetic nanoparticles, unlike their bulk counterparts, attain single-domain structure, hence, ferro and ferrimagnetic materials become superparamagnetic at a few nanometer size scale [1,19].For superparamagnetic particles, thermal energy (few meV at room temperature) is comparable to the sum of all other energies (exchange, anisotropy, dipolar, and Zeeman); therefore, spin reversal is governed by the thermal fluctuations [17,18].Additionally, the effect of surface on the magnetic moment is very strong as the surface always contains vacancies, broken bonds and defects [17,18,20].Therefore, saturation magnetization and susceptibility in nanoparticles decrease as compared to the bulk value for the 'surface disordered layer' [18].In sharp contrast, several non-magnetic metal oxides show ferromagnetism (or anti-ferromagnetism) at the nanoscale due to vacancies and disorders present at the surface [17,21,22].Because the surface has significant contributions at the nanoscale, diverse physical and magnetic properties can arise by changing the size and shape of nanoparticles [20,23].However, there is a threshold for size/shape especially, in applications where superparamagnetism plays a key role, such as contrast agents in magnetic resonance imaging (MRI), and magnetic hyperthermia, etc [10,15].Therefore, optimized magnetization and susceptibility are required in the 'superparamagnetic limit'.
Moreover, for spin device-based applications, nanoparticles with proper stoichiometry and excellent surface coordination are necessary to obtain the desired spin-polarized current [24][25][26][27].To overcome the restrictions with nanoparticulate systems, shape anisotropy could be an imperative parameter to analyse.As compared to conventional spherical nanoparticles having surfaces with higher stress, faceted surfaces such as cubes, and octahedrons possess better surface coordination, and stoichiometry [28][29][30][31].These faceted nanoparticles offer better stoichiometry and higher magnetization because of the lower concentration of surface defects and surface energy [28][29][30][31].Furthermore, due to their uniaxial shape anisotropy and easy magnetization axis along the long axis, rod-shaped geometry is seen as a superior contender for device applications [32,33].Besides, the shape of a particle determines the easy and hard axes of magnetization by modulating the magnetic anisotropy constant, which could design a nanoparticle as a soft or hard permanent magnet [34][35][36].
Therefore, the modulation of magnetocrystalline, surface, and shape anisotropies via the composition, surface, and shape of nanoparticles is not only critical to control the magnetic properties but also produces a number of exciting properties.In this review, we comprehensively examine the role of these three anisotropies in the nano regime.We have primarily focused on Fe 3 O 4 owing to its wide application range.We have included the synthesis processes of anisotropic Fe 3 O 4 nanoparticles and compared their magnetic properties.Further, this review provides an extensive understanding of tunneling magnetoresistance (TMR) in Fe 3 O 4 nanoparticle assemblies.Also, we comprehensively discuss the role of anisotropies on the spin polarization of Fe 3 O 4 .
1.1.Nanoscale magnetism: anisotropy is the key For bulk magnetic materials, small magnetic domains constitute to minimize the associated magnetostatic energy [1,19].As the size reduces, there is a threshold below which the formation of domain wall requires more energy than the reduction in magnetostatic energy [1,19].The threshold diameter for a spherical shaped particle, below which the domain structure does not form, is expressed as [37,38] where J ij is the exchange constant, K m is the magnetocrystalline anisotropy (MCA) constant, m 0 is the free space permeability, and M S is the saturation magnetization.In a single-domain particle ( 22 nm for iron oxide), all spins align in the direction of the applied magnetic field, and the particle magnetizes uniformly [18].
The magnetic anisotropy of nanoparticles is generally divided into four categories, such as magnetocrystalline, surface, shape, and exchange anisotropy [39].MCA arises due to the exchange and spinorbit interactions.The origin of exchange interaction is electrostatic coupling, which leads to long-range ordering of spins [1,19].The exchange interaction is expressed using the Heisenberg Hamiltonian [19] where S i and S j are the spin angular momentum and the J ij is the exchange integral, which signifies the strength of the interaction between i th and j th spin.A positive J ij represents a parallel spin configuration, while a negative J ij depicts an antiparallel spin configuration.Exchange energy is isotropic, i.e., independent of any direction.However, in reality, spins also interact with the crystal lattice, which is known as spin-orbit interaction.Spinorbit interaction breaks the spherical symmetry of exchange interaction, and as a result, the alignment of spins is energetically favorable along a particular crystallographic direction [1,19].This phenomenon brings anisotropy in a magnetic material.The energy required to magnetize a material along the applied magnetic field is called magnetocrystalline energy and is expressed as where V is the particle volume, K m is the magnetocrystalline anisotropy constant, and θ is the angle between the spontaneous magnetization and the easy axis.The energy required for magnetization reversal is K m V [17].When the thermal energy, k B T (k B is Boltzmann constant), exceeds K m V, the magnetization reversal is completely governed by thermal energy.The particles then behave like paramagnets (i.e., no magnetic moment in the absence of an external field) with a large magnetic moment under an applied magnetic field.This phenomenon is called superparamagnetism [19].A superparamagnetic system does not have coercivity as no magnetic energy is stored in the system.The relaxation time of the magnetic moment of a superparamagnetic particle is expressed by the Neel-Arrhenius expression [18,38] where t 0 = 10 −9 s.If the experimental measurement time (τ m ) is longer than the relaxation time (τ), the system remains in superparamagnetic state, while for τ > τ m, the system is in a blocked state.In typical laboratory measurements, τ m ≈ 100 s and τ 0 ≈ 10 −9 s, the blocking temperature (T B ) is expressed as [18,38] = ( ) Therefore, the T B depends on the MCA (different for different materials), and particle volume.
In addition, the size of the nanoparticles also plays an important role in deciding the magnetic properties of nanoparticles, particularly saturation magnetization, coercivity and Curie temperature.
The magnetic behavior of the surface of a nanoparticle is considerably different as compared to the core due to defects, lattice disorders, vacancies, dangling bonds, etc.For magnetic nanoparticles, the surface layer is often referred to as 'the dead layer' because of the reluctance of the surface spins to align along the external magnetic field, and reduces the overall magnetization of a particle [17,18].As the size decreases, the contribution of the surface-disordered layer increases, and as a result, the net magnetization decreases.The saturation magnetization (M s ) and thickness of the spin-disordered layer (t) in nanoparticles with size 'd' are related as [17,18] Therefore, apart from MCA, a second kind of anisotropy arises in nanoparticles due to the surface disorder layer.
In order to take care of the surface effect, Néel first proposed surface anisotropy [2].In the case of ultra-small sized nanoparticles, the surface anisotropy energy often dominates over both the magneto-static and magnetocrystalline anisotropy energies (E a ) [40,41].For spherical particles, the effective magnetic anisotropy (K eff ) can be expressed as [1,19] where K s is the surface anisotropy constant, K m is the magnetocrystalline anisotropy constant, and d is the particle size [19].The surface disorder in nanoparticles generally reduces the M s in ferromagnetic and ferrimagnetic materials [40].However, non-magnetic metal oxides such as cerium oxide, zinc oxide, and aluminum oxide show ferromagnetism (or anti-ferromagnetism) because of the surface disorder [21,22,42].The surface defects result in uncompensated spins in the disordered layer, which leads to magnetization at the surface.Further, oxygen vacancies at the surface also give rise to ferromagnetism.On a broader note, ferromagnetism could be a global property of non-magnetic oxide nanomaterials due to the surface effects [17,21,22,43].
Apart from magnetocrystalline and surface anisotropy, shape anisotropy is also a significant parameter to control the magnetic properties of nanoscale materials.The shape anisotropy of a nanoparticle arises as the demagnetizing field varies in different shapes [19].Spherical nanoparticles do not possess shape anisotropy as the demagnetizing field is isotropic in all directions.In anisotropic shapes, the demagnetizing field is smaller along the longer dimension as the induced poles are far apart [1,19].For example, a spherical shape has a demagnetizing factor of 1/3 in all directions, but a cylindrical shape has a demagnetizing factor of zero along its length (for a long cylinder), and 1/2 perpendicular to that.Shape anisotropy constant can be expressed as where N 2 and N 1 are the demagnetization factors perpendicular and parallel to the magnetic easy axis, respectively.For example, nanorods with a higher aspect ratio (10) have a higher shape anisotropy as the demagnetizing factor along the long axis is nearly zero [44].Therefore, nanorods with a higher length and thinner diameter show a larger coercivity due to the synergistic effects of magnetocrystalline and shape anisotropies [45,46].Besides, nanoparticles with anisotropic shapes, such as rods and octapods, are magnetized with their poles far apart under an applied field and thus have larger magnetic diameters than spherical or cubic nanoparticles of comparable volume [15,47].Further, octahedrons and cubes are faceted with a single crystalline plane, whereas spherical nanoparticles possess all possible crystal planes in their curved surface, which results in higher surface disorder [28][29][30][31].Thus, the shape anisotropy of nanoparticles can largely control the surface anisotropy.The effective magnetic anisotropy of a nanoparticle is constituted as the cumulative result of magnetocrystalline, surface, and shape anisotropy [39].
The exchange coupling interaction between soft/hard or hard/soft core-shell nanoparticles can be considered an effective approach for magnetism control.Kneller and Hawig proposed a model on exchangecoupled nanomagnets, according to the model, the integration of a soft magnetic phase with a high M s to a hard magnetic phase can amplify the magnetization of a composite magnet if the two phases are strongly exchangecoupled via the interphase interface [48][49][50].The exchange-coupled core-shell nanoparticles, as designed, would operate as a single-phase nanomagnet, possessing magnetic anisotropy constant, coercivity, and saturation magnetization values that fall within the range of those exhibited by the individual constituents (see figure 1(a)).Due to the strong coupling of moments at the interface, the demagnetization of the soft magnetization resembles the behavior of a torsional spring.The soft magnetic phase must be thin enough, according to the exchange-spring theory, to prevent the development of domain walls during reversal [51].The domain walls of the soft phase should be about twice as wide as the hard phase domain walls (i.e., ≈ 2 to 4 nm) [52].For example, the T B of Fe 3 O 4 and MnFe 2 O 4 nanoparticles can be greatly increased through integration with a CoFe 2 O 4 nano-shell.We acknowledge that different anisotropies can be adjusted by utilizing various parameters, such as size, shape, and composition, at the nanoscale in order to achieve higher magnetization, susceptibility, coercivity, and spin polarization.Nevertheless, the influence of anisotropies on nanoscale magnetism remains a subject of debate.Further experimental analysis involving anisotropic nanostructures has the potential to yield significant advancements in this field.The transition was named Verwey transition after the name of its discoverer.Verwey transition is explained by the charge localization in the octahedral site of spinel Fe 3 O 4 .At room temperature, electron hopping occurs between Fe 3+ and Fe 2+ cations at the octahedral site [55].Below 120 K, known as the Verwey transition temperature (T V ), long-range order is established among Fe 3+ and Fe 2+ ions at the octahedral sublattice, resulting in the Verwey phase transition [55,60].The Verwey transition is a characteristic feature of stoichiometric Fe 3 O 4 and is no longer observed with even slight changes in stoichiometry.
Figure 3 depicts the electronic band structure of Fe 3 O 4 above and below the T V .Five d (3d) orbital electrons of Fe ions (both Fe 2+ and Fe 3+ ) are subjected to crystal field splitting (Δ cf ) into t 2g and e .g. states due to the effect of the local environment.A further exchange splitting (Δ ex ) between spin-up and spin-down orbitals also takes place due to interaction between Fe cations.Spin-up energy levels exist at/above the Fermi energy (E F ).The sixth electron of Fe 2+ goes to the spin-up t 2g level and provides the semi-metallic nature of Fe 3 O 4 at room temperature [61].When the temperature goes below the T V , the t 2g band is further perturbed by a slight structural distortion, and the extra electron of Fe 2+ occupies the lowest energy state a 1g , which exists below E F .Thus, a gap is formed at E F , and the electrons freeze in an ordered state, which leads to the metal-insulator transition [62].On the contrary, some scientists believe the Verwey transition occurs due to the coulomb interactions between 3d electrons, whereas some scientists consider electron-phonon coupling as the origin of the transition [63,64].However, the origin of the Verwey transition is debatable, and new theories are still evolving.et al reported the Verwey transition in biologically produced Fe 3 O 4 nanoparticles [68].The nanoparticles form chain-like structures that act as individual dipoles with enhanced anisotropy (figure 4(c)).These observations are also reported by Gehring et al in magnetosome chains [69].Observation of the Verwey transition below 20 nm is extremely challenging as the synthesis of stoichiometric Fe 3 O 4 in an ultra-small size regime is very difficult [67].Further, the Verwey transition in ultra-small sized nanoparticles would be very encouraging for memory and spintronics-based applications, as stoichiometric nanoparticles are highly desirable to develop optimized spin-polarized current.

Anisotropic Fe 3 O 4 nanostructures: synthesis and engineering of magnetic properties
In this section, we will discuss how to make monodispersed Fe 3 O 4 nanoparticles that exhibit bulk-like magnetic and electronic properties.The synthesis of nanoparticles follows the LaMer mechanism [70,71] a classical nucleation and diffusion control growth theory.The model is based on three stages: (i) the continuous increase  in the number of monomers (atoms or molecules that serve as the foundational building blocks for nanoparticles), (ii) the aggregation of monomers to form crystal nuclei when the number of monomers exceeds the critical supersaturation (C sat ), and (iii) the decrease in the number of monomers due to the growth termination caused by capping from a stabilizing, two-layer ligand shell (see figure 5(a)).The synthesis parameters, including precursor to surfactant molar concentration, heating rate, nucleation temperature, and growth temperature, can be regulated to synthesize nanoparticles with precise control over the size and shapes.
Among all the methods developed for the synthesis of magnetic nanoparticles, solution-phase chemical synthesis has garnered the most interest because of its unique bottom-up strategy for creating high-quality magnetic nanoparticles with precise size control, even at the scale of 1 nm [72].The synthesis of magnetic nanoparticles via solution-phase reaction involves the use of metal salts, reducing agents, and surfactants [15,28,47,[73][74][75].For example, Fe 3 O 4 nanoparticles synthesized via thermal decomposition of iron pentacarbonyl in the presence of oleic acid and oleylamine have an average size of 10-20 nm.In contrast, Fe 3 O 4 synthesized via thermal decomposition of iron acetylacetonate in the presence of oleic acid and oleylamine have an average size of 5-10 nm.The size range of Fe 3 O 4 synthesized via thermal decomposition of iron (III) acetylacetonate in the presence of oleic acid and oleylamine is 3-10 nm.We have demonstrated a simpler synthesis process using oleylamine as a multifunctional agent, acting as a solvent, surfactant, and reducing agent, to synthesize Fe 3 O 4 nanoparticles with sizes ranging from 3 nm to 32 nm [76].The size of the nanoparticles has been controlled by varying the Fe-precursor to oleylamine concentration, as schematically shown in figure 5(b).Oleylamine is a versatile agent that can be used to synthesize Fe 3 O 4 nanoparticles with a narrow size distribution and high purity.Moreover, high-aspect ratio nanowires with high magnetic coercivity due to the synergistic effects of magnetocrystalline anisotropy and shape anisotropy were realized when they were synthesized via solvothermal processes [77].
Fe 3 O 4 nanoparticles can be synthesized using various methods, including co-precipitation [78,79], reverse micelle [72] hydrothermal [80], sol-gel [81], electro-deposition [82], emulsion precipitation [83] surfactant mediated precipitation [84], microemulsion precipitation [85], and microwave-assisted hydrothermal techniques [86].The choice of synthesis method depends on the desired size, morphology, structure, and magnetic properties of the Fe 3 O 4 nanoparticles.Among these methods, co-precipitation and sol-gel methods are very popular because of their simplicity and cost-effectiveness [87,88].Nevertheless, thermal decomposition offers advantages in terms of achieving uniformity in particle size and shapes, enhancing crystallinity, and yielding superior magnetic properties when compared to alternative methods.In addition, the magnetic properties of Fe 3 O 4 nanoparticles are also related to synthesis conditions, such as precursor-to-surfactant mole concentration, heating rate, nucleation temperature, and growth temperature.The relationship between magnetic properties and synthesis conditions will be discussed in detail in subsequent sections.As the synthesis of Fe 3 O 4 nanoparticles is not the focal point of this review, the authors refer readers who are interested in more details of these synthesis processes to some representative publications [89][90][91][92].

Surface anisotropy: scaling the size
The magnetic properties of nanoparticles are significantly influenced by their size, shape, and composition (including the doping of other metals), as discussed in the section 1.Consequently, researchers have devoted considerable efforts to gaining control over these parameters.Achieving precise control over size allows for the optimization of surface anisotropy, as the surface-to-volume ratio increases significantly with decreasing nanoparticle size.Therefore, the initial challenge was to attain magnetic property optimization through size control.
Sun et al were the first to report the use of thermal decomposition in synthesizing Fe 3 O 4 nanoparticles [93].They employed Fe(acac) 3 as the iron precursor, benzyl ether as the solvent, oleic acid as the surface functionalizing agent, and oleylamine as the reducing agent.In a similar chemical approach, Park et al achieved large-scale synthesis of highly uniform Fe 3 O 4 nanoparticles by using an iron oleate precursor [94].They reported the large-scale synthesis of highly uniform Fe 3 O 4 nanoparticles by a similar chemical approach using iron oleate precursor.They controlled the nanoparticle size by utilizing solvents with varying boiling points.Notably, solvents with higher boiling points led to the formation of larger nanoparticles due to the enhanced reactivity of iron-oleate.Similarly, Lin et al achieved the synthesis of monodisperse Fe 3 O 4 nanoparticles ranging in size from 7.8 to 17.9 nm by pyrolyzing iron oxyhydroxide with oleic acid acting as a reducing and surface functionalization agent [95].Despite the advantages of thermal decomposition, such as precise size control and monodispersity, the procedure has limitations in terms of high reaction temperatures and the use of toxic metal precursors.To address these concerns, a modified thermal decomposition method was reported, eliminating the need for oleic acid.Instead, oleylamine fulfills the dual role of capping and reducing agent [96].Our group reported a synthesis protocol for all spinel ferrite (MFe 2 O 4 where M = Fe, Co Mn, Ni, Zn) nanoparticles, where oleylamine is used as solvent, reducing and surface functionalizing agent at a considerably lower temperature of 200 °C [97].This approach can also be employed to synthesize Fe 3 O 4 nanoparticles with precise control over sizes ranging from 4 nm to 32 nm, as evidenced by the TEM micrographs presented in figure 6 [76].Interestingly, oleylamine capped nanoparticles were found to exhibit better magnetic properties, especially high saturation magnetization and magnetic susceptibility, as compared to oleic acid capped nanoparticles [41].Apart from the above-mentioned synthesis methods, there are several other reports where control of size has been very tight (standard deviation < ∼10%) [18,98].However, the issues such as phase purity, stoichiometry, and crystallinity of nanoparticles have not been addressed properly in most of the synthesis procedures [18,37,93,94].Therefore, further research is essential to fabricate the nanoparticles with better crystallinity and appropriate stoichiometry.
Size control of magnetic nanoparticles provides tailored magnetic properties due to a large variation in surface to volume ratio of the nanoparticles [17,18].Since the surface of the nanoparticles has a higher concentration of vacancies, disorders, and broken bonds in comparison to the core, the ordering of the surface under a magnetic field is drastically different [17,18].Therefore, M S increases with an increase in nanoparticle size as the volume of the disordered layer decreases (equation ( 6)).There are several reports in the literature where an increment of M S is established with an increment of the particle size (figures 7(a) and (b)) [76].In addition to the surface disordered layer, the magnetization of Fe 3 O 4 nanoparticles is also affected by the maghemite layer formed due to surface oxidation.This oxidized layer also decreases with an increase in the size of the nanoparticles [67].An extensive Mössbauer analysis with different sized nanoparticles revealed that if the size of Fe 3 O 4 nanoparticles increased from 6 to 28 nm, the maghemite content decreased (figure 7(c)) [67].In the ultra-small size regime ( 6 nm), an obvious anhysteretic magnetization curve with low magnetic susceptibility is observed [99].Due to the very high surface to volume ratio, the spin disorder layer dominates the magnetic response of ultra-small particles.Whereas the larger sized Fe 3 O 4 nanoparticles, typically above 20 nm, do not exhibit any superparamagnetic features and show reduced spin disorder effects, resulting in M S close to that in bulk magnetite.Apart from M S , T B , which indicates the temperature range for the superparamagnetic state, is directly proportional to the particle size (figure 7(d)) [76,97].Thus, control of size from 3 nm to 24 nm provides control over T B , the T B value increases from 41 to 330 K. Another interesting size dependency attribute is the Verwey transition, which is observed in larger sized Fe 3 O 4 nanoparticles [100,101].As we discussed in the section 1.2, the Verwey transition is highly sensitive to oxidation, and the transition ceases to occur when the Fe 3(1-δ) O 4 off-stoichiometry parameter ( δ ) value is more than 1%.The ultra-small sized nanoparticles exhibit  Reproduced from [76] with permission from the Royal Society of Chemistry.
surface oxidation and spin disorders, resulting in the disappearance of the Verwey transition and low saturation magnetization.The limitations of size control arise when higher magnetization and better surface coordination are required in ultra-small size scale.Therefore, further necessary optimization of magnetic properties can be achieved by scaling shape and composition.

Shape anisotropy: change of shape
Shape anisotropy is one of the most crucial parameters to control the magnetic properties of nanoparticles.In this section, we will discuss how the shape of a nanoparticle offers exciting changes in their magnetic properties.The shape of the nanoparticles is controlled in several ways, such as by using specific surfactants and varying reaction parameters, precursor-surfactant mole concentration, temperature, and heating rate [102][103][104][105][106][107][108].For example, Zhang et al reported the synthesis of truncated octahedral Fe 3 O 4 nanoparticles via thermal decomposition of iron-oleate at 380 °C [109].Octahedral nanoparticles have {111} planes at their facets and {100} planes as their truncations.In another example, Kim et al synthesized Fe 3 O 4 nanocubes via the thermal decomposition technique using Fe(acac) 3 as the iron source at a higher heating rate as compared to the spherical particles [110].Similarly, Sun et al synthesized Fe 3 O 4 nanorods by hydrothermal procedure, using Fe(CO) 5 as the precursor and a mixture of hexadecylamine and oleic acid as the surfactant in n-octanol [107].Our group reported an easier method to synthesize Fe 3 O 4 nanorods wherein, first, FeOOH nanorods are synthesized and then reduced using oleylamine in the next stage to get aspect ratio controlled Fe 3 O 4 nanorods [15,75].In addition, Liu et al synthesized Fe 3 O 4 nanotubes by etching the MgO of core-shell MgO@Fe 3 O 4 nanotubes [111].MgO nanorods were grown on a Si/SiO 2 substrate in the first step, and then a shell of Fe 3 O 4 was grown using the pulsed laser deposition (PLD) technique.Also, Fe 3 O 4 octapod-shaped nanoparticles were synthesized by Zhao et al using iron-oleate precursor in the presence of NaCl as the capping agent in a thermal decomposition method [47].Although there are reports on the synthesis of Fe 3 O 4 with different shapes, as accounted above, obtaining a proper stoichiometry under 50 nm scale is still challenging.Besides, in most of these reports, the reaction process involves complex steps, or the reaction is energetically not favorable.Recently, we explored oleylamine as a multi-functionalizing agent to synthesize nanoparticles with controlled shapes and desired stoichiometry.Figure 8 shows Fe 3 O 4 nanoparticles of different shapes synthesized via the thermal decomposition of iron (III) acetylacetonate and the chemical reduction of FeOOH nanorods using oleylamine as solvent and surfactant [75,112,113].
It has also been clearly illustrated how shape anisotropy affects the magnetic properties of nanoparticles.The zero-field-cooled magnetization (M ZFC ) measurements of Fe 3 O 4 nanoparticles with different shapes are shown in figure 9(a) [75].The spherical and multipod nanoparticles display superparamagnetic T B of 110 and 80 K, respectively.Whereas the other nanoparticles do not exhibit any temperature peak in their M ZFC curves.Interestingly, they exhibit the Verwey transition in the M ZFC curves at 120 K.The Fe 3 O 4 nanoparticles with spherical and multipod shapes have various facets.Consequently, these nanoparticles experience higher surface spin disorder, leading to lower M s values.The octahedral and cubic-shaped nanoparticles, in comparison, have fewer facets, resulting in a reduced degree of spin disorder and consequently higher M s values, as depicted in figure 9(b).In addition, Mössbauer spectroscopy analysis was performed to obtain more insight into why the Ms was so strongly linked to the shape (figures 9(c) and (d)).The Mössbauer data obtained from the cube and wire shaped Fe 3 O 4 nanoparticles shows a good fit with two distinct sextets; the red sextet is attributed to Fe 3+ ions present in the tetrahedral (A) site, whereas the blue sextet is associated with Fe 3+ and Fe 2+ ions located in the octahedral (B) site.
In the case of spherical and multipod-shaped nanoparticles, the superparamagnetic relaxation occurs at a slower rate, resulting in an unresolved magnetic hyperfine structure.This structure comprises broadened, overlapping, and asymmetrical lines, making it challenging to resolve individual components.As an example, the occurrence of doublets in spherical nanoparticles indicates that the Fe atoms may be in either the superparamagnetic or nonmagnetic states.The Mössbauer spectra obtained from Fe 3 O 4 nanowires at 140 K and 120 K, show an excellent fit using two sextets, aligning with the expected spectrum for stoichiometric magnetite.The spectral shape underwent significant changes below the Verwey transition (measured at 70 K), and the data can be best represented by adding one additional sextet.
Further, Alveraz et al reported the magnetic property analysis of similar-sized spherical and cubic maghemite (γ-Fe 2 O 3 ) nanoparticles [114].Spherical particles exhibit larger T B as compared to cubic nanoparticles of the same volume, indicating lesser K eff for cubic particles.Furthermore, Ho et al [29].reported that Fe 3 O 4 nanoparticles with a cubic shape and faceted structure possess a higher concentration of Fe 3+ ions at octahedral sites compared to those with a spherical shape.Additionally, it was found that the {001} facets of Fe 3 O 4 nanoparticles exhibit greater stability for octahedral sites than for tetrahedral sites, indicating a higher Fe 3+ / Fe 2+ ratio on the surfaces of cubic nanoparticles.[115].Furthermore, the flat facets of cubic and octahedral nanoparticles exhibit superior symmetric coordination when compared to the spherical nanoparticles as explained in section 1 [116].Therefore, cubic and octahedral shapes are often found to show the Verwey transition and higher M s value [28,101].Thus, the shape anisotropy of nanoparticles was discovered to be extremely important in controlling nanoparticle stoichiometry and, consequently, the magnetic properties.Noh et al [117] reported a comparison between the spherical and cubic-shaped Zn 0.4 Fe 2.6 O 4 nanoparticles.They demonstrated that surface anisotropy increases in spherical particles while exchange anisotropy increases in cubic particles, resulting in higher M s and H c in cubic particles.Furthermore, simulations showed that the disordered spins effect is greater in the spherical nanoparticles compared to the cubic ones.Interestingly, the density of disordered spins is found to be higher at the corners of the cube, while for spherical particles, disordered spins are distributed homogeneously throughout the surface (figure 10).
The study on shape anisotropy at the nanoscale is still in the infant stage, and there are several opportunities open for applications of anisotropic nanoparticles.In the past two decades, Fe 3 O 4 nanoparticles have been primarily studied for various biomedical applications, storage media, etc, and shape anisotropy renders exciting results in many instances [101,118,119].Anisotropic nanostructures can modulate the effective magnetic anisotropy and therefore control M s and H c. Besides, lower surface energy (for faceted structures) results in a decrease in surface spin disorder and helps to retain perfect stoichiometry.Therefore, for a comparatively new field of spin device-based applications, anisotropic nanoparticles with better stoichiometry and surface coordination have huge potential, as higher M s and lower surface disorder optimize the spin-polarized current in nanoparticle assemblies.

Magnetocrystalline and exchange anisotropy: modulation of composition
Magnetic anisotropy can be further modified by altering material compositions by doping other metals or forming exchange-coupled core-shell structures.3d transition metals such as Mn, Co, Ni, and Zn are the most prominent dopants in Fe 3 O 4 (M x Fe 3-x O 4 where M = Mn, Co, Ni, and Zn).Mn 2+ , Co 2+ , and Ni 2+ ions replace Fe 2+ ions of the octahedral sublattice of the spinel structure.As the magnetic moment of Fe 3 O 4 is given by Fe 2+ ions, magnetization changes as per the magnetic moment of the dopant ions.Manganese has the highest magnetic moment (5μ B ) among all 3d transition metals; therefore, replacing Fe with Mn can result in the highest M s (figure 11(a)) [1,19,97].Cobalt has higher magnetocrystalline anisotropy as compared to iron due to strong spin-orbit coupling, therefore, doping of Co results in magnetic hardening with higher coercivity and remanence (figure 11(b)) [1,19].Apart from doping, magnetic core-shell structures have been studied to modulate the exchange coupling.Magnetic soft/hard, ferromagnetic/antiferromagnetic core-shell exchange-   coupled structures often show exciting new magnetic properties that are not observed in the pristine form of any material [17,18,120,121].There are a few methods for the synthesis of the core-shell particles, among which surface treatment and seed mediated growth are the most popular ones [121].In the surface treatment method, the surface of the nanoparticles is oxidized/reduced to synthesize new material.The seed-mediated growth is a two-step process wherein one kind of nanoparticle is synthesized in the first step and then used as the seed, where the other magnetic material forms a shell.Exchange coupling at the interface of the system provides additional anisotropy to keep magnetic stability in superparamagnetic particles [120].Therefore, core-shell nanoparticles show much better performance in many applications, such as magnetic memory, spintronic devices, biomedical applications, etc [122,123].For example, Lee et al developed exchange coupled soft/hard ferrite nanoparticles and reported a much higher heating effect as compared to simple ferrimagnetic/ superparamagnetic nanoparticles under an AC magnetic field [124].They reported that 9 nm CoFe 2 O 4 nanoparticles and 15 nm MnFe 2 O 4 nanoparticles individually render specific loss power (SLP) of ∼450-500 Wg −1 , but core-shell CoFe 2 O 4 @MnFe 2 O 4 exchange coupled nanostructures render SLP of ∼2200 Wg −1 .The hysteresis loops of iron oxide-manganese oxide core/shell nanoparticles (see figures 11(c) and (d)) exhibit an exchange bias effect with exchange bias field (H E ) of 15 mT when measured along the field axis after field cooling under small fields of 1T.It has also been found that saturation magnetization (see figure 11(e)) of exchange coupled nanoparticles can be precisely tuned by varying size and composition of core-shell structure.Furthermore, core-shell nanoparticles exhibit enhanced effective magnetic anisotropy (see figure 11 [126].Doped nanoparticles and core-shell nanoparticles are ideal for memory-based applications that require both M s and H c .There are some obstacles to miniaturizing devices with these particles, such as low M s , different properties due to polydispersity, uneven shell formation, etc.However, improved synthesis methods, and/or choice of a proper shape can address the existing problems with nanoparticulate device structures.Further, modern technology demands increasing storage capacity in smaller dimensions, which requires assemblies of ultra-small ferromagnetic nanoparticles.Consequently, the modulation in composition becomes essential for modifying the magnetic properties of these ultra-small particles while keeping all other parameters the same. Recently, our group has shown that the Verwey transition in Fe 3 O 4 can be retained at a size scale of 2 nm by synthesizing core-shell Fe 5 C 2 /Fe 3 O 4 nanoparticles (figure 12) [127].Furthermore, an intriguing exchange bias

TMR properties of magnetic nanoparticle assemblies
3.1.Basics of tunneling magnetoresistance and magnetic tunnel junction (MTJ) Magnetoresistance (MR) is defined as the change in electrical resistance under an applied magnetic field.Generally, MR is categorized into different types, such as giant magnetoresistance (GMR), tunneling magnetoresistance (TMR), anisotropic magnetoresistance (AMR), and colossal magnetoresistance (CMR).When the MR effect is observed at magnetic tunnel junctions (MTJ), it is called TMR [128,129].Conventionally, a MTJ consists of two ferromagnetic materials separated by a thin insulating layer.The insulating barrier must be very thin so that with an applied voltage, electrons can tunnel between the two ferromagnetic materials [128,129].In many programmable logic devices and spintronics-based devices such as magnetic random access memory (MRAM), read-head magnetic memory, and various sensors, TMR and GMR play the key roles [130,131].Conventionally, a magnetic tunnel junction (MTJ) consists of two ferromagnetic layers separated by a thin insulating layer.The insulating barrier must be very thin so that with an applied voltage, electrons can tunnel between the two ferromagnetic materials [128,129].TMR is associated with the orientation of magnetization in the two ferromagnetic layers within the MTJ.The tunneling conductance or resistance of a MTJ depends on whether the magnetizations of the two ferromagnetic layers are parallel (P) or anti-parallel (AP).The TMR ratio can be defined as: The TMR effect arises from spin-dependent tunneling, a phenomenon that can be elucidated through the energy band theory.As depicted in figure 13, ferromagnetic material exhibits an imbalance between the numbers of spin-up and spin-down electrons [35].The electrons near the Fermi level are responsible as the spin carriers during spin transport.These electrons preserve their spin characteristics, such as spin-up or spin-down, during the tunneling process as the insulating layer is very thin.The degree of the band imbalance for the ferromagnetic layers are expressed by spin polarization (P), which can be defined as the ratio of the density of states (D) of a particular spin configuration (up or down) to the total density of states at the Fermi level [128].
The TMR effect was first seen by M  where P 1 and P 2 are the spin polarizations of the two ferromagnetic layers.Due to the minimal interlayer coupling between the two ferromagnetic layers in MTJs, a small applied magnetic field can reverse the magnetization direction of one layer, leading to a substantial alteration in tunneling resistance.Consequently, MTJs result in better magnetic field sensitivity, low energy consumption, and consistent performance.The Magnetic Tunnel Junction (MTJ) stands as a crucial component in various spintronics applications, such as the read head of hard disk drives, microwave oscillators, and MRAM.As nanoparticle-based systems are not conventional MTJs, readers interested in more detailed information about conventional MTJs are encouraged to consult representative publications [129,[132][133][134][135].
In this review, we particularly focus on nanoparticulate systems containing an organic surfactant layer at their surface to prevent agglomeration.In terms of electrical conductivity, this surfactant layer acts as the insulating tunnel barrier between the magnetic nanoparticles (figure 14(b)) [38,136,137] and facilitates intergranular tunneling [38,138] These tunnel junctions are often called multiple tunnel junctions.
In terms of conductance (G), magnetoresistance can be expressed as [128], T is transmission coefficient and expressed as [128] where, = - F 2 P is polarization and θ in the angle between two adjacent moments, s is the distances between the grains, m * is the effective mass of an electron, V is the potential barrier and E F is Fermi energy.As the electrostatic charging energy E C (e 2 /2C for the spherical surface where C is capacitance) also interferes with the tunneling of electrons, conductance is written as [128,139]   In a 3D volume, considering conductance in all directions [128,139], In a three-dimensional assembly of Fe 3 O 4 nanoparticles, nanoparticles are magnetized in [111] direction under a magnetic field as [111] is the easy axis for Fe 3 O 4 [28].The average over θ, in the above equation is 〈cos(θ)〉.If we consider θ as the angle between the magnetic moments, then θ relates to relative magnetization m as m 2 = 〈cosθ〉 [128].(Note: when magnetizations in the system align parallel (θ = 0) under a strong magnetic field, m becomes unity).Inoue et al [128].modified the expression for TMR proposed by Julliere for 3d multiple tunnel junctions.After performing the integration, equation ( 14) can be written as where A and G 0 are constants.MR from equation (11) takes a simple form of Therefore, consideration of P = 100% and m = 1 maximizes the TMR value [136].Substituting the maximum achievable value of P and m, a 50% TMR is foreseen using equation (17).The theory proposed by Inoue is equivalent to a circuit composed of parallel resistors.Ziese developed an equation for MR in intergranular tunneling using a modified spin hopping model in discontinuous manganite (La 0.7 Ca 0.3 MnO 3 ) films [140].He considered the multiple tunnel junctions as equivalent circuits of resistors in series.The expression for MR was obtained as The equation (18) demonstrates that TMR can achieve up to 80% if the value of P reaches 1. TMR studies of magnetic nanoparticle assemblies with a layer of organic molecules at the nanoparticle surface have been explored by various research groups [38,93,97,136,137].In addition, researchers have successfully created magnetic core-shell nanoparticles.In this configuration, the core material exhibits an exceptionally high spin polarization, while the shell material functions as a spin valve [126].Spin-dependent tunneling in surfactantcoated nanoparticles was first observed by Black et al where oleic acid functionalized Co nanoparticle assemblies show 7% TMR at 2 K (figure 15(a)) [141].Since then, numerous research groups have reported TMR in various nanoparticle assemblies.The findings presented by these researchers demonstrate that the surface, shape, size, composition, and proximity of nanoparticles play a substantial impact in the TMR properties of such assemblies.We will summarize these findings in the subsequent sections.Specifically, this review will primarily focus on Fe 3 O 4 nanoparticles due to their semi-metallic property, anticipated 100% spin polarization at room temperature, and high Néel temperature.These properties position Fe 3 O 4 as a suitable material for spintronic devices.

Effect of surface anisotropy
As discussed in section 2, the size of nanoparticles plays a crucial role in precisely manipulating their surface anisotropy.This is attributed to the significant influence of the surface-to-volume ratio on the surface anisotropy of nanoparticles.TMR, similar to other magnetic properties such as coercivity, saturation magnetization, and remanent magnetization, can exhibit size dependence.We have demonstrated that as the particle size of Fe 3 O 4 nanoparticles increases, saturation magnetization also increases, and beyond a size of 16 nm, the characteristic Verwey transition is detected.The presence of high saturation magnetization and the stoichiometric magnetite phase is anticipated to enhance TMR.However, there is currently a lack of literature on the investigation of size-dependent TMR in Fe 3 O 4 nanoparticles.Nonetheless, Rinehart et al conducted a study on size and temperature-dependent granular magnetoresistance using CoFe 2 O 4 colloidal nanoparticles (figure 16) [142].The findings reveal a nonlinear relationship between size and magnetoresistance.Smaller particles exhibit a ΔR/R of approximately 18% at 300 K, whereas larger particles experience a threefold decrease.Notably, these results indicate that CoFe 2 O 4 can effectively function as a granular magnetoresistor at room temperature.Moreover, the study demonstrates that high superparamagnetic T B or low resistance are not decisive factors in achieving desirable TMR values for sensing applications.Thus, the findings highlight the potential for further research into unconventional granular structures made up of nanomaterials, moleculebased magnets, and metal-organic frameworks.When considering TMR in granular systems, another crucial aspect of surface anisotropy that needs to be discussed is surface functionalization.It has been observed that the surface chemistry of magnetic nanoparticles, achieved through the attachment of organic molecules to their surfaces, can generate a substantial spin polarization.By synthesizing Fe 3 O 4 nanoparticles through a chemical process and incorporating organic moieties onto their surfaces, the TMR can be tuned accordingly [126,[141][142][143].In order to enhance the spin polarization and magnetoresistance (MR) ratios, the surface magnetism and proximity effect of Fe 3 O 4 nanoparticles have been successfully modulated through surface functionalization using tetrathiafulvalene (TTF)-fused carboxylate (figure 17) [144].By coating the TTF unit around 5 nm Fe 3 O 4 nanoparticles, their assemblies exhibited a remarkable 5% TMR ratio at room temperature.Among the nanoparticle arrays, the one with the shortest chain ligand (referred to as L1-nanoparticles) demonstrated the highest MR ratio.This can be attributed to the closest interparticle spacing, which is controlled by the ligand in the nanoparticle assembly.Additionally, the existence of TTF promotes the formation of a charge transfer layer (through I2-doping) near the Fe 3 O 4 nanoparticles, leading to improved stability and conductivity of the nanoparticle assembly.These findings indicate a promising approach for the rational design of Fe 3 O 4 nanoparticle assemblies with potential applications in spintronics.

Effect of shape anisotropy
Similar to the magnetic characteristics discussed earlier, the TMR properties of nanoparticles are highly influenced by their shape.The shape anisotropy plays a crucial role in determining essential parameters like surface disorder, effective anisotropy constant (K eff ), and demagnetizing factor (N), thus effectively modifying the material properties [28,[145][146][147].The shape dependence of TMR primarily arises owing to (i) the presence of different crystalline planes with different surface energies and defects at the surface of nanoparticles and (ii) the different demagnetizing fields in the different shapes.For example, octahedral nanoparticles with {111} facets have better stoichiometry as compared to spherical nanoparticles which have different crystallographic planes at their surfaces [28].In a study by Pentcheva et al, it was observed that the spin polarization within Fe 3 O 4 experiences a sudden change at surfaces and interfaces, reaching its minimum value for {100} surfaces [148].Similarly, Kurahashi et al reported that the {100} surfaces exhibit the least spin polarization, which can be attributed to the hybridization between oxygen surface states and Fe d x2-y2 surface state.Therefore, improving and engineering the stoichiometry and surface coordination is desirable to obtain an optimized spin-polarized current, and tuning the shape of nanoparticles is one of the most effective ways to achieve that.For example, our group reported a significantly higher TMR value in amine-functionalized octahedral nanoparticles as compared to spherical nanoparticles (figure 18) [145].A 38% TMR was observed at 300 K, which increased to 69% at 180 K for octahedral nanoparticle assemblies.In contrast, 24% and 41% TMR were measured at room temperature and 180 K, respectively, for spherical nanoparticle assemblies.The better stoichiometry of the octahedral particles was confirmed by the Mössbauer spectroscopy analysis.The presence of reduced surface spin disorder and strong amine coupling on the {111} facets of octahedral-shaped Fe 3 O 4 nanoparticles led to increased spin polarization and, consequently, a higher TMR value.
Nanorods have gained significant popularity in spintronics devices due to their magnetic anisotropy and significantly larger interfacial area compared to spherical shapes [149][150][151][152].The enhanced interfacial area of nanorods introduces additional grain boundaries, which can contribute to an increase in TMR.Consequently, nanorods and nanowires offer an added advantage over conventional isotropic shapes [149,150].Our group conducted a study on the TMR characteristics of Fe 3 O 4 nanorod assemblies.At room temperature, we observed a TMR value of 14% in the nanorod assemblies.Intriguingly, when the nanorods were pre-aligned using an external magnetic field (as shown in figures 19(a), (b)), the TMR value increased by a factor of 1.4 [153].Furthermore, we performed a theoretical simulation of magnetization using Comsol Multiphysics to understand the role of alignment on the TMR properties (figures 19(c)-(d)).The simulation results revealed a substantial increase in the average magnetization of nanorods when they align parallel to the external magnetic field, in comparison to the randomly oriented nanorods.In the case of randomly aligned nanorods, it is more challenging to align the spins in the direction of the applied magnetic field due to the lowest demagnetizing field along the long axis of the cylinder.Consequently, there are fewer polarized spins than there are in parallel nanorods.The increased spin polarization in aligned nanorod assemblies contributed to a higher TMR value.Therefore, the shape of the nanoparticles influences the TMR in different ways.The spin transport can be optimized by controlling the stoichiometry, defects, and spin alignment by changing the shape of the nanoparticles.However, more shape-dependent studies with precise control of defects will be beneficial to further realize the role of shape anisotropy.

Effect of magneto-crystalline anisotropy
Fe 3 O 4 nanoparticles hold potential for a broad spectrum of spintronic applications, particularly in memorybased spintronics devices, through the utilization of various ferrite substitutions.Introducing alternative 3d transition metal (such as Ni, Zn, Co, and Mn) as substitutes allows for effective manipulation of spin-orbit coupling in Fe 3 O 4 , thereby enabling significant modulation of magnetization, coercivity, and other relevant properties [154].As an illustration, the incorporation of Mn 2+ (Mn x Fe 3−x O 4 ) results in an elevation of M s since Mn 2+ possesses the highest magnetic moment compared to other 3d transition metals [155].Conversely, within the realm of magnetic memory, the introduction of Co doping (Co x Fe 3−x O 4 ) presents an intriguing prospect by enhancing coercivity (H c ) owing to the strong spin-orbit coupling of Co [156].A number of research groups have investigated the utilization of assembled nanoparticles of substituted ferrites for spintronic applications.Our group reported the preparation and TMR properties of Co x Fe 3−x O 4 nanorods with different concentrations of Co by cation exchange reaction.As compared to CoFe 2 O 4 , the Co x Fe 3−x O 4 system is found to be more advantageous for TMR device applications (figure 20) [157].In the case of CoFe 2 O 4 , complete substitution of Fe 2+ with Co 2+ takes place within the octahedral site, resulting in the absence of t 2g electron hopping.As a consequence, CoFe 2 O 4 exhibits insulating properties [158,159].Conversely, by doping Co 2+ into the octahedral site, complete replacement of Fe 2+ ions does not occur, allowing for electron conduction.The substitution of Fe 2+ with Co 2+ can be represented as CFO1 in the following manner [ [162].The substitution of Co 2+ by Zn 2+ in the shell reduces the magnetic anisotropy, which results in precise control of the TMR switching.These results suggest that substituting other 3d transition metals to modulate the magnetocrystalline anisotropy effectively tunes the TMR behavior of Fe 3 O 4 .Moreover, the magnetic and TMR properties can be accurately tailored by controlling the doping concentrations to meet the desired application.

TMR properties around the verwey transition
The Verwey transition in Fe 3 O 4 is associated with a significant change in the electrical and magnetic properties around 120 K (T V ).Subsequently, the TMR properties of Fe 3 O 4 also substantially change around this temperature.However, the trend of TMR properties below T V reported by different research groups is diverse.Poddar et al found that TMR increased monotonically with a decreasing temperature and reached a maximum just above T V and then decreased with a further decrease in temperature (figure 21(a)) [163].Our investigation using Fe 3 O 4 nanorod assemblies revealed a similar trend; the MR value increased with decreasing temperature and reached a maximum of 31% just above T V (figure 21(b)) [153].With decreasing temperature, the number of polarized spins near the Fermi level increases.Consequently, the spin-dependent tunneling and, subsequently, the magnetoresistance (MR) exhibit an elevation at lower temperatures.However, below the T V , the ordering of electrons significantly reduces the spin polarization, leading to a decrease in the TMR value.This trend in the TMR around 120 K is the most familiar and also observed for Fe 3 O 4 thin-film systems.However, a few different trends have been observed by some research groups.For example, in some instances the TMR of Fe 3 O 4 -based systems has been found to change its sign, i.e., become positive from negative, or vice versa, when the temperature reaches ∼120 K. Lekshmi et al have observed a negative to positive transition of TMR in Fe 3 O 4 superlattice array below the T V [143].The positive MR below T V was explained as the results of the Verwey transition-induced frozen and localized electrons and Zeeman splitting of the localized states, which suppress the spin-dependent transport.A similar observation was reported by Zhang et al [125] they observed a sign change of TMR in FePt@Fe 3 O 4 nanoparticle assemblies below the T V .The defect states of Fe 3 O 4 near the Fermi level were explained to be responsible for the MR inversion at low temperatures.Indeed, several factors influence the trend of TMR around the T V .The surface of Fe 3 O 4 nanoparticles often oxidizes to γ-Fe 2 O 3 .The thickness of the oxidized layer and the defects at the surface of the nanoparticles play a crucial role in determining the spin transport properties, especially at low temperatures when the Fe 3 O 4 electrons become localized.Further, the stoichiometry of Fe 3 O 4 varies drastically at the nanoscale, which also significantly affects spin transport and T V .Therefore, the trend of TMR near T V entirely depends on the stoichiometry, defects, and surface coordination of the nanoparticle assemblies used in the individual studies.The local structural variations significantly influence the electron ordering, electron-lattice interaction, and electron-electron interactions, which lead to the anomalous trend of TMR observed by different researchers.

Conclusions and outlook
This review provides a comprehensive examination of the role of magnetic anisotropies on magnetic and magnetoresistance properties at the nanoscale.We systematically explore how the surface, shape, and magnetocrystalline anisotropies can be successfully engineered by altering the nanoparticles' size, shape, and composition, respectively.These alterations in anisotropies not only lead to fascinating observations but also enable precise control of the magnetic properties.Furthermore, we showcase several unique approaches to achieve pure phase Fe 3 O 4 nanoparticles with controlled size and shape, reaching down to a few nanometers' length scale.Our findings demonstrate that single-crystalline nanoparticles of anisotropic shapes, possessing well-defined nano-facets (such as cube {100}, octahedron {100}, {111}, and wire {100}), exhibit the Verwey metal-insulator transition at approximately 120 K.This transition disappears at the nanoscale due to compositional inhomogeneity, phase instability, and surface disorders.Therefore, our study reveals that anisotropic-shaped nanoparticles possess a stoichiometric superiority owing to their improved surface coordination.This enhancement in stoichiometry and surface coordination leads to superior magnetic properties and spin polarization, ultimately resulting in improved magnetoresistance properties for these nanoparticles.Besides the influence of shape, we also examined the impact of nanoparticle surface, size, and composition on magnetoresistance properties.We showcased how appropriate surface functionalization of nanoparticles can effectively enhance spin transport in granular systems.
The ability to tailor magnetic properties and spin polarization by engineering anisotropies is not only essential from a physics perspective but also opens up exciting possibilities for advanced spintronic applications.Nevertheless, there is still potential for conducting further studies to gain a better understanding and enhance spin polarization even further.One prospective application for granular TMR is in magnetic sensors.These sensors leverage the resistance changes in granular magnetic materials when exposed to external magnetic fields.These sensors have several advantages, including high sensitivity, fast response times, and low power consumption.These characteristics have made them widely used in a range of electronic devices and systems that require precise and efficient magnetic field detection.In addition, nanoparticle-based granular magnetoresistance can be used as the magnetic read head in modern hard disk drives.The read head consists of multiple layers of magnetic and non-magnetic materials, including granular magnetic layers.Moreover, nanoparticle media are being explored as potential recording media and have demonstrated successful application in initial studies of longitudinal contact recording.Researchers devote intense effort to study the light-matter interaction at the nanoscale in magnetic materials, driven by its potential applications in nextgeneration high-density magnetic recording.Laser-assisted switching offers a promising approach to overcome the material limitations of high-anisotropy and high-packing density media.However, there are still many aspects of the switching process dynamics that remain unexplored.
In addition to the practical applications, a significant potential exists for fundamental research studies as well.Similar to Fe 3 O 4 , the bulk materials of highly correlated '3d/4f' electron systems, particularly nickelates, and vanadates, also exhibit metal-insulator transition due to structural phase transition.Moreover, nanoparticles of these materials are especially important for spintronic applications where spins and their charges are modulated to fabricate devices.In addition, non-stoichiometries for the cation and anion are also found in the core of the nanoparticles.Insufficient cations affect the oxygen concentration because the oxygen vacancy stabilizes the insulating phase through the formation of strongly correlated M n+ (n = 2-5) states.Understanding the interplay between cations and anions balancing stoichiometry via computational quantum mechanical modeling is of great importance, as the interplay determines the electronic structure and stabilizes the insulator or metallic phase at the nanoscale.
Overall, while magnetic nanoparticles exhibit promising and attractive TMR properties through anisotropy modulation, considerable research efforts are still required to enable the commercialization of granular magnetoresistance-based devices.Nevertheless, due to the continuous progress in nanomaterial synthesis and characterization technologies, substantial breakthroughs and swift developments are expected to take place in this field in the foreseeable future.

Figure 1 (
b) illustrates a tenfold enhancement in the T B of MnFe 2 O 4 /CoFe 2 O 4 core-shell nanoparticles when the thickness of the CoFe 2 O 4 shell is increased from zero to 2.5 nm [53].

O 4 .
As the temperature goes below 120 K, Fe 3 O 4 undergoes a structural change; the unit cell of Fe 3 O 4 changes from cubic to monoclinic (figures 2(b) and (c)) which is known as the Verwey transition.

Figure 1 .
Figure 1.The exchange coupling between soft and hard magnetic materials gives rise to fascinating magnetic properties.(a) A schematic illustration of magnetic hysteresis loop for soft, hard, and their exchange-coupled nanomagnets.(b) Temperaturedependent susceptibility under 100 Oe field for MnFe 2 O 4 /CoFe 2 O 4 core-shell nanoparticles with CoFe 2 O 4 shell thickness of 0, 0.75, 1.0, 2.0, and 2.5 nm.Reprinted with permission from [53].Copyright (2012) American Chemical Society.

1. 2 . 3 .
Verwey transition in Fe 3 O 4 nanoparticles: stoichiometry is the key In Fe 3 O 4 nanoparticles, the surface disorder layer and oxidized maghemite layer result in stoichiometric defects, which generally prevent the observation of the Verwey transition (figure 4(a)).However, there are few reports where the Verwey transition has been observed in Fe 3 O 4 nanoparticles.Goya et al demonstrated the Verwey transition in nanoparticles with sizes ranging from 50 to 150 nm, where the transition peak in zero-field-cooled (ZFC) magnetization curves decreases with decreasing size and disappears entirely below the 50 nm size scale [65].Arelaro et al reported observations of the Verwey transition for ∼40 nm sized Fe 3 O 4 nanoparticles [66].However, Salazar et al had a profound success and demonstrated the Verwey transition at a lower dimension of 22 nm due to proper stoichiometry of Fe 3 O 4 .Due to an increase in the oxidized maghemite (γ-Fe 2 O 3 ) layer at the surface, the Verwey transition disappears at further lower sizes (figure 4(b)) [67].In similar studies, Prozorov

Figure 2 .
Figure 2. Crystal structure of Fe 3 O 4 ; (a) Spinel cubic structure of Fe 3 O 4 .Fe 3+ ions occupy both tetrahedral, and octahedral sites and Fe 2+ occupy at octahedral sites.(b) Unit cell of Fe 3 O 4 is cubic at a temperature higher than 120 K. (c) The unit cell of Fe 3 O 4 becomes monoclinic below 120 K.This structural change is known as the Verwey transition.

Figure 3 .
Figure 3.The origin of the Verwey transition in Fe 3 O 4 .(a) Electronic band structure of Fe 3 O 4 above 120 K. Adapted figure with permission from [61], Copyright (1972) by the American Physical Society.and (b) below 120 K. Adapted figure with permission from [62], Copyright (1996) by the American Physical Society.Above 120 K, Fe 3 O 4 behaves as a semi-metal but turns into an insulator at 120 K.

Figure 4 .
Figure 4.The Verwey transition is an intrinsic property of stoichiometric Fe 3 O 4 ; however, this transition tends to vanish at the nanoscale due to the presence of stoichiometric defects and surface disorders.(a) Schematic of nanoparticles; the outer shell depicts the spin disorder layer.The brown shell represents the surface oxidized layer, and the inner shell (in black) is the core stoichiometric Fe 3 O 4 .These defects hinder the Verwey transition at the nanoscale.(b) Magnetization versus temperature curves for Fe 3 O 4 nanoparticles of different sizes; particle sizes above 20 nm show the Verwey transition.Reprinted with permission from [67].Copyright (2011) American Chemical Society.(c) Chain-like structure of the Fe 3 O 4 nanoparticle shows Verwey transition as the chain acts like a single dipole.Reprinted figure with permission from [68], Copyright (2007) by the American Physical Society.

Figure 5 .
Figure 5. (a) The La Mer diagram describes the nucleation, and subsequent growth of nanoparticles.The diagram is based on the classical nucleation and diffusion control growth theory and consists of three stages: (i) the continuous increase in the number of monomers, (ii) the aggregation of monomers to form crystal nuclei when the number of monomers exceeds the critical supersaturation (C sat ), and (iii) the decrease in the number of monomers due to the growth of nanoparticles.(b) Schematic view of size control of nanoparticles with variation in metal precursor to oleylamine mole ratio.

Figure 6 .
Figure6.The nanoparticle size can be precisely regulated by adjusting the ratio of precursor to reducing agent.TEM images depict Fe 3 O 4 nanoparticles of varying sizes (ranging from 4 to 32 nm), synthesized using the thermal decomposition technique with different mole ratios of oleylamine and iron precursors.Reproduced from[76] with permission from the Royal Society of Chemistry.

Figure 7 .
Figure 7. Owing to the high surface to volume ratio and the existence of a disordered surface layer, the size of nanoparticles plays a pivotal role in dictating their magnetic properties.Size dependent magnetic properties of Fe 3 O 4 nanoparticles; (a) room temperature field-dependent magnetization curves; and (b) the M S increases as the diameter of nanoparticle increases.(c) Mössbauer spectra of different-sized Fe 3 O 4 nanoparticles recorded at room temperature (i. 4, ii.16 and iii.28 nm).The experimental spectra were fitted with two resolved sextets.The first sextet can be ascribed to Fe 3+ occupying the A site (colored red), while the second sextet corresponds to a combination of Fe 3+ and Fe 2+ occupying the B site (colored blue).Additionally, a singlet (C) was observed, which is recognized to the shorter spin relaxation time of Fe.(d) The ZFC magnetization plot for Fe 3 O 4 nanoparticles of different sizes.Reproduced from[76] with permission from the Royal Society of Chemistry.

Figure 9 .
Figure 9.At the nanoscale, the different shaped particles exhibit significantly varied magnetic properties.(a) M ZFC curves and (b) initial magnetization curves of Fe 3 O 4 nanoparticles with different shapes.(c) The Mössbauer spectra of Fe 3 O 4 nanoparticles with different shapes (multipod, sphere, cube, and wire) at room temperature.(d) Mössbauer spectra of the Fe 3 O 4 nanowires obtained at different temperatures.Reproduced from [75].© IOP Publishing Ltd.All rights reserved.

Figure 10 .
Figure 10.The magnetic anisotropies and spin structure have been observed to vary with the shape of nanoparticles.(a) Exchange and surface anisotropy as a function of size and shape.Simulation of spin structure in (b) cubic and (c) spherical nanoparticles.The result indicates that spherical shape possess more disordered spins (marked as blue).Reprinted with permission from [117].Copyright (2012) American Chemical Society.
(f)) and, consequently, higher coercivity compared to their individual constituents.Estrader et al reported antiferromagnetic coupling between Fe 3 O 4 /Mn 3 O 4 core-shell structure, which has enormous potential in spin filters, spintronics-based sensors, and recording media [123].In another example, FePt@Fe 3 O 4 nanoparticles show sign change in TMR at low temperatures as Fe 3 O 4 becomes an insulator below 120 K and the contribution from FePt dominates the TMR properties [125].Similarly, Anil Kumar et al engineered conventional TMR of Fe 3 O 4 to spin valve magnetoresistance by a thin layer of CoFe 2 O 4 shell over Fe 3 O 4 nanoparticles

Figure 11 .
Figure 11.The magnetic properties can be finely tuned by manipulating magnetocrystalline anisotropy through cation exchange and exchange coupling between soft and hard magnets.(a) Saturation magnetization and (b) T B of different ferrite nanoparticles as function of particle size.Reproduced from [97] with permission from the Royal Society of Chemistry.(c) TEM image (inset of 11c shows the EELS mapping) and (d) exchange bias of manganese oxide deposited on Fe 3 O 4 nanoparticles.Reproduced from [123].CC BY 4.0.(e) Size-dependent saturation magnetization of different ferrites and exchange coupled core-shell nanostructure [124].(f) Magnetic anisotropy values of different ferrites and exchange coupled core-shell nanostructures [124].

Figure 12 .
Figure 12.(a) TEM image of Fe 5 C 2 /Fe 3 O 4 core/shell nanoparticles and (b) the corresponding M ZFC and M FC magnetization curves measured in 100 Oe magnetic field (upper panel) and temperature dependence of exchange bias field (H EB ).Reproduced from[127] with permission from the Royal Society of Chemistry.

Figure 13 .
Figure 13.The schematic illustrates the TMR effect, wherein electrons tunnel from one ferromagnetic layer to another across a thin insulating layer, towards the positive electrode, upon the application of a bias voltage.The density of states of electrons is influenced by the spin orientation in relation to the magnetization of the layer.The tunneling phenomenon is represented for (a) parallel and (b) antiparallel configurations.Reprinted with permission from [35].Copyright (2023) American Chemical Society.

Figure 14 .
Figure 14.The TMR phenomenon is observed in magnetic tunnel junctions (MTJ), yet the concept of MTJs differs between thin films and nanoparticles.Schematic view of the (a) conventional MTJ where two ferromagnets are separated by a thin layer of insulator.(b) Multiple tunnel junctions in surfactant-coated magnetic nanoparticles assemblies.

Figure 15 .
Figure 15.Examples of nanoparticle systems that show a TMR.(a) Spin-dependent tunneling in oleic acid stabilized Co nanoparticles super-lattice.From [141].Reprinted with permission from AAAS.A 7% TMR was observed at 2 K.(b) polystyrene coated Fe 3 O 4 nanoparticles exhibit a 22% TMR at room temperature, which enhances to 40.9% at 110 K. Reprinted figure with permission from [38], Copyright (2006) by the American Physical Society.

Figure16.
Figure16.The size of the nanoparticles has been observed to significantly influence the TMR behavior.(a) TMR of CoFe 2 O 4 at 300 K as a function of magnetic field and particle size (d).(b) Temperature dependence of the resistance of CoFe 2 O 4 nanoparticle pellets in the absence of a magnetic field.Reprinted with permission from [142].Copyright (2018) American Chemical Society.

Figure 17 .
Figure 17.The TMR properties have been observed to be substantially affected by the surface chemistry of the nanoparticles.Schematic illustration of (A) surface modification of oleate (OA)-capped Fe 3 O 4 nanoparticles with TTF-COO-ligands, binding to Fe 3 O 4 surface via the monodentate Fe-O form.(B) Magnetic field MR of L 1 -, L 1 ′-, and OA-nanoparticles at 300 K and (C) Magnetic field MR of L 1-, L 2-, and L 3-nanoparticles at 100 K. Reprinted with permission from [144].Copyright (2015) American Chemical Society.

Figure 18 .
Figure 18.The octahedral Fe 3 O 4 nanoparticles have better surface coordination, which results in superior TMR values compared to their spherical counterparts.Current-voltage characteristics of octahedral and spherical particles obtained under various applied magnetic fields at (a, c) 300 K, and (b, d) 180 K. Reprinted from [145], with the permission of AIP Publishing.

Figure 19 .
Figure 19.The average magnetization of nanorods is enhanced when they align in parallel with an external magnetic field, leading to a higher TMR value compared to randomly oriented nanorods.(a) Fe 3 O 4 nanorods are deposited onto a Si/SiO 2 substrate through drop-casting in a magnetic field.(b) The magnetoresistance (MR) curves for the aligned and randomly oriented nanorods under a magnetic field of ± 20 kOe.The simulated magnetization (in A/m) of (c) magnetically aligned and (b) randomly oriented nanorod assemblies.Reproduced from [153].© IOP Publishing Ltd.All rights reserved.

Figure 20 .
Figure 20.Substituting other 3d transition metals (Ni, Zn, Co, Mn) effectively manipulates spin-orbit coupling in Fe 3 O 4 , allowing notable control of magnetization, coercivity, and hence TMR.(a) The schematic demonstrates the ion exchange process, where Co 2+ ions substitute Fe 2+ ions within the octahedral site of Fe 3 O 4 nanorods.(b) The electronic configurations of ions residing in the octahedral sites of CoFe 2 O 4 and Co x Fe 3−x O 4 are depicted.In Co x Fe 3−x O 4 , the hopping of spin-down electron (indicated in brown) of Fe 2+ within the octahedral sub-lattice leads to enhanced conductivity compared to CoFe 2 O 4 .Magnetic field dependence MR plots for Co x Fe 3−x O 4 nanorod assemblies with (c) x = 0.23 and (d) x = 0.33 at 300 and 150 K. [157] John Wiley & Sons.© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Figure 21 .
Figure 21.Various researchers have investigated the TMR properties near the T V .(a) Fe 3 O 4 nanocrystals.Reprinted figure with permission from [163], Copyright (2002) by the American Physical Society, and (b) nanorods assemblies exhibit the maximum TMR near the T V .Reproduced from [153].© IOP Publishing Ltd.All rights reserved.