# A Short Review on Verwey Transition in Nanostructured Fe3O4 Materials

Authors: Murtaza Bohra; Nishit Agarwal; Vidyadhar Singh
Journal: Journal of Nanomaterials
 (2019)

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## Abstract

Verwey transition (VT) of Fe3O4 has been extensively investigated as this results in sharp changes in its physical properties. Exploitation of VT for potential applications in spin/charge transport, multiferroicity, exchange bias, and spin Seebeck effect-based devices has attracted researchers recently. Although hundreds of reports have been published, the origin of VT is still debatable. Besides, not only the size effects have a significant impact on VT in Fe3O4, even the conditions of synthesis of Fe3O4 nanostructures mostly affect the changes in VT. Here, we review not only the effects of scaling but also the growth conditions of the Fe3O4 nanostructures on the VT and their novel applications in spintronics and nanotechnology.


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## Body

## 1. Introduction

The metal-insulator transition also known as Verwey transition (VT) in strongly correlated magnetite (Fe3O4) system is vital for its potential applications in nanoelectronics, spintronics, and mottoronix [1]. From a scientific point of view, the VT provides information to understand the extraordinary crystal lattice (regarding the freezing-in fluctuating lattice) and electronic structure (charge, spin, and orbital) order of Fe3O4 [2, 3]. However, owing to the many competing degrees of freedom, the close energetic proximity of the different phases (presence of twining) often obscures the exact nature of the VT as they are probed in thermal equilibrium. Technologically, the resistive switching behaviour in Fe3O4 thin films at VT shows high potential for alternative memory applications, such as gate voltage-driven resistive switching in field-effect transistors [4]. On the other hand, the large change observed in magnetoresistance and spin Seebeck coefficient around VT makes it useful for sensors and solid-state energy conversion devices [5–7]. Thus, ever since then Fe3O4 and in particular the VT has been an object of extensive research and great debate. Although experimental and theoretical progress has recently been made on Fe3O4, the origin of the VT is still under discussion.Fe3O4 is a cubic ferrimagnetic oxide with the highest magnetization M=4.2 μB below Curie temperature, TC=858K. Band structure calculations predict half-metallic (-100% spin polarization) character of Fe3O4 with room temperature conductivity, σ=200 (Ω·cm)-1 [8, 9]. Stoichiometric Fe3O4 shows VT wherein first-order structural phase transformation occurs around 124 K (TV) [10]. In the low-temperature phase, Fe3O4 is an insulator, has a monoclinic structure connected to the charge ordering, and exhibits an orbital order on the Fe2+ sites [11]. Also, it was found that localized electrons are shared between three Fe ions on octahedral B-lattice sites which can be termed as trimerons [8]. This transition also has manifestations in resistivity, heat capacity, magnetization, and many other properties [3]. Therefore, VT, which has a potential in cutting-edge technologies, provides an external tuning competency of the properties by changing the temperature. Despite the tremendous progress in nanostructured Fe3O4, it is still an open question how the VT changes in the nanoregime. The most critical difficulty in the size-dependent characterization of VT is the synthesis of uniform and stoichiometric nanostructured Fe3O4 because VT is reported to be extremely sensitive to the oxygen stoichiometry [12]. The size of nanostructure having the VT varies in different reports, as stoichiometry commonly depends on growth conditions. Furthermore, at the nanoscale, the VT is difficult to technically observe because diffraction methods suffer from severe peak broadening due to the small crystallite size [9]. The occurrence of superparamagnetism hampers the observation in magnetometry, and measurements of the conductivity are difficult to interpret in the case of ensembles of nanoparticles, since the path of the electric current may simply change [9].Thus, the understanding of VT in nanostructured Fe3O4 is the main focus of this review. Here, we shall discuss the best growth methods and characterization techniques which are being currently employed to investigate nanostructured Fe3O4 material and their potential applications. Before presenting the results on nanostructured Fe3O4, some basic properties of Fe3O4 shall be summarized.


## 2. Material Properties of Fe3O4

### 2.1. Crystalline Properties

Fe3O4 possesses an inverse spinel structure AB2O4 (space group Fd3m; a=8.39Å) (Figure 1(a)), wherein oxygen anions form a cubic face-centred (fcc) lattice, and the large interstices between O2- are partially occupied by iron cations. Tetrahedral A positions are occupied by Fe3+ cations, while octahedral B positions are equally occupied by Fe3+ and Fe2+ cations ([FeTd3+]A[FeOh3+FeOh2+]BO4) [8, 9]. In Fe3O4, ferrimagnetism exists through two main mechanisms, as shown in Figure 1(c). The first is the antiferromagnetic superexchange interactions between the FeOh3+ and FeTd3+ cations through the O2− anions [13, 14]. The spin-up 5d electrons in the FeOh3+ couple with the overlapping 2p orbitals in the O2− making them spin down. The other 2p electron is thus spin-up which makes the FeOh3+5d electrons spin down. Thus, FeOh3+ and FeOh3+ are antiparallel and cancel out each other’s unpaired spin magnetic moments. The second factor is related to the double-exchange interaction [15] in which the spin-down electron can only hop from FeOh2+ to FeOh3+ if the majority spins are the same. Hence, they are coupled and aligned parallel. Therefore, all the Fe2+ cations contribute to the magnetic moment while all Fe3+ cations cancel each other out, resulting net magnetic moment (9−5=4) μB (see Figure 1(d)). Because of the strong antiferromagnetic A-B superexchange interaction, A-A and B-B superexchange interactions become ferromagnetic resulting in the ferrimagnetic structure of Fe3O4. The extra electron of FeOh2+ ions is transferred to the empty orbitals of FeOh3+ by displacing electrons from the intervening O2- ions in a double-exchange process: FeOh2+ to O2- and O2- to FeOh3+. The room temperature conductivity of Fe3O4 is, thus, attributed to this hopping of electrons (Fe2+⇋Fe3++e−) at octahedral B-sites. The extra electron of the Fe2+ ion occupies the minority t2g band, which is the only band located at Fermi level Ef, giving rise to half-metallicity as predicted by band structure calculation, shown in a simplistic form in Figure 1(e) [8, 9].Figure 1
Cubic inverse spinel structure of Fe3O4 with tetrahedral and octahedral sites above TV (a) and distorted monoclinic crystal structure below the TV (b). The double and superexchange interaction mechanisms (c) [13]. Sketch of the localized structure of the spins at tetrahedral and octahedral sites (d). The density of states occupied by electrons of Fe+2 ions at octahedral sites (e).


### 2.2. Verwey Transition

Upon cooling of Fe3O4 below the TV, the electron hopping between Fe2+ and Fe3+ ions freezes, and the combination of 2+ and 3+ species then arranges themselves in a regular pattern without moving (charge ordering). In this nonconducting state, the stagnant Fe2+ ions are Jahn-Teller (J-T) active [8]; this means that the extra electron in Fe2+ has a choice between occupying any one of the three available half-filled orbitals dxy or the two dxz/yz, as they all have the same energy (see the top of Figure 2(a)). Electrons prefer to occupy the orbit with the least energy. To break this choice, an effective energy separation between dxy and dyz/dzx is created in the four Fe–O bonds (depicted by red arrows in the bottom of Figure 2(a)) in the xy plane that are elongated or contracted. The negative value of Δt2g signifies that the energy of dxy is lower than that of dyz/dzx, that is, tetragonal distorted Fe2+O6 octahedra with elongated Fe–O bonds in the xy plane. On top of this, an additional structural distortion in which B-site Fe-Fe distances within linear Fe3+-Fe2+-Fe3+ units (depicted by the grey ellipsoid in the bottom of Figure 2(a)) is anomalously shortened showing that electrons are not fully localized as Fe2+ states but are instead spread over the three sites resulting in highly structured three-site polarons defined as a single trimeron [8]. The J-T distortion in Fe2+O6 octahedra mentioned earlier directly couples to the neighbouring Fe3+O6 octahedra constituting the trimerons, although they are J-T inactive in the first approximation. Due to trimeron formation, distances from Fe2+ states to their two B-site neighbours in the local orbital ordering plane are anomalously shortened. The cumulative effect of this trimeron shortening penetrates throughout the crystal in the various trimeron locations to significantly perturb the cubic Fe3O4 structure to the complex overall distortion. The cubic spinel- (a=b=c) type structure of Fe3O4 distorts to a monoclinic superstructure with Cc space group symmetry (a=b≠c) (2,2,2), as shown in Figure 1(b). This structural transformation was first found by Verwey in 1939 and was named after him [16, 17]. The charge, orbital, and trimeron orders of Fe3O4 stand out perhaps as the most complex electron-ordered ground state known.Figure 2
Energy separation due to Jahn-Teller distortion (up) and depiction of trimeron concept in single Fe+2O6 octahedra (down) (a) [8]. Changes in magnetic susceptibility, resistance, and specific heat at TV (b) [10, 17]. For clarity, the temperature scale for R and χ′ was shifted concerning the true temperature scale. With an increasing number of vacancies or doped atoms, the VT shifts to low temperatures (c) [18].
(a)
(b)
(c)Because of this structural transformation in Fe3O4, many physical properties (specific heat, magnetic susceptibility, and resistance) show abrupt change around TV [3] (see Figure 2(b)). It has been reported that several factors can affect VT of bulk Fe3O4 negatively, such as oxygen off-stoichiometry and cation substitution. The TV gradually decreases from 124 to 80 K and finally vanishes completely with increasing oxygen off-stoichiometry or cation substitution (Ti2+, Zn2+, etc.) (see Figure 2(c)) [18].Even after an intense research, there still exist two major schools of interpretation: the first one interprets the VT as a transition driven by charge/orbital ordering and the second one exploits the mechanism of a lattice distortion-driven charge ordering leading to metal-insulator behaviour.


## 2.1. Crystalline Properties

Fe3O4 possesses an inverse spinel structure AB2O4 (space group Fd3m; a=8.39Å) (Figure 1(a)), wherein oxygen anions form a cubic face-centred (fcc) lattice, and the large interstices between O2- are partially occupied by iron cations. Tetrahedral A positions are occupied by Fe3+ cations, while octahedral B positions are equally occupied by Fe3+ and Fe2+ cations ([FeTd3+]A[FeOh3+FeOh2+]BO4) [8, 9]. In Fe3O4, ferrimagnetism exists through two main mechanisms, as shown in Figure 1(c). The first is the antiferromagnetic superexchange interactions between the FeOh3+ and FeTd3+ cations through the O2− anions [13, 14]. The spin-up 5d electrons in the FeOh3+ couple with the overlapping 2p orbitals in the O2− making them spin down. The other 2p electron is thus spin-up which makes the FeOh3+5d electrons spin down. Thus, FeOh3+ and FeOh3+ are antiparallel and cancel out each other’s unpaired spin magnetic moments. The second factor is related to the double-exchange interaction [15] in which the spin-down electron can only hop from FeOh2+ to FeOh3+ if the majority spins are the same. Hence, they are coupled and aligned parallel. Therefore, all the Fe2+ cations contribute to the magnetic moment while all Fe3+ cations cancel each other out, resulting net magnetic moment (9−5=4) μB (see Figure 1(d)). Because of the strong antiferromagnetic A-B superexchange interaction, A-A and B-B superexchange interactions become ferromagnetic resulting in the ferrimagnetic structure of Fe3O4. The extra electron of FeOh2+ ions is transferred to the empty orbitals of FeOh3+ by displacing electrons from the intervening O2- ions in a double-exchange process: FeOh2+ to O2- and O2- to FeOh3+. The room temperature conductivity of Fe3O4 is, thus, attributed to this hopping of electrons (Fe2+⇋Fe3++e−) at octahedral B-sites. The extra electron of the Fe2+ ion occupies the minority t2g band, which is the only band located at Fermi level Ef, giving rise to half-metallicity as predicted by band structure calculation, shown in a simplistic form in Figure 1(e) [8, 9].Figure 1
Cubic inverse spinel structure of Fe3O4 with tetrahedral and octahedral sites above TV (a) and distorted monoclinic crystal structure below the TV (b). The double and superexchange interaction mechanisms (c) [13]. Sketch of the localized structure of the spins at tetrahedral and octahedral sites (d). The density of states occupied by electrons of Fe+2 ions at octahedral sites (e).


## 2.2. Verwey Transition

Upon cooling of Fe3O4 below the TV, the electron hopping between Fe2+ and Fe3+ ions freezes, and the combination of 2+ and 3+ species then arranges themselves in a regular pattern without moving (charge ordering). In this nonconducting state, the stagnant Fe2+ ions are Jahn-Teller (J-T) active [8]; this means that the extra electron in Fe2+ has a choice between occupying any one of the three available half-filled orbitals dxy or the two dxz/yz, as they all have the same energy (see the top of Figure 2(a)). Electrons prefer to occupy the orbit with the least energy. To break this choice, an effective energy separation between dxy and dyz/dzx is created in the four Fe–O bonds (depicted by red arrows in the bottom of Figure 2(a)) in the xy plane that are elongated or contracted. The negative value of Δt2g signifies that the energy of dxy is lower than that of dyz/dzx, that is, tetragonal distorted Fe2+O6 octahedra with elongated Fe–O bonds in the xy plane. On top of this, an additional structural distortion in which B-site Fe-Fe distances within linear Fe3+-Fe2+-Fe3+ units (depicted by the grey ellipsoid in the bottom of Figure 2(a)) is anomalously shortened showing that electrons are not fully localized as Fe2+ states but are instead spread over the three sites resulting in highly structured three-site polarons defined as a single trimeron [8]. The J-T distortion in Fe2+O6 octahedra mentioned earlier directly couples to the neighbouring Fe3+O6 octahedra constituting the trimerons, although they are J-T inactive in the first approximation. Due to trimeron formation, distances from Fe2+ states to their two B-site neighbours in the local orbital ordering plane are anomalously shortened. The cumulative effect of this trimeron shortening penetrates throughout the crystal in the various trimeron locations to significantly perturb the cubic Fe3O4 structure to the complex overall distortion. The cubic spinel- (a=b=c) type structure of Fe3O4 distorts to a monoclinic superstructure with Cc space group symmetry (a=b≠c) (2,2,2), as shown in Figure 1(b). This structural transformation was first found by Verwey in 1939 and was named after him [16, 17]. The charge, orbital, and trimeron orders of Fe3O4 stand out perhaps as the most complex electron-ordered ground state known.Figure 2
Energy separation due to Jahn-Teller distortion (up) and depiction of trimeron concept in single Fe+2O6 octahedra (down) (a) [8]. Changes in magnetic susceptibility, resistance, and specific heat at TV (b) [10, 17]. For clarity, the temperature scale for R and χ′ was shifted concerning the true temperature scale. With an increasing number of vacancies or doped atoms, the VT shifts to low temperatures (c) [18].
(a)
(b)
(c)Because of this structural transformation in Fe3O4, many physical properties (specific heat, magnetic susceptibility, and resistance) show abrupt change around TV [3] (see Figure 2(b)). It has been reported that several factors can affect VT of bulk Fe3O4 negatively, such as oxygen off-stoichiometry and cation substitution. The TV gradually decreases from 124 to 80 K and finally vanishes completely with increasing oxygen off-stoichiometry or cation substitution (Ti2+, Zn2+, etc.) (see Figure 2(c)) [18].Even after an intense research, there still exist two major schools of interpretation: the first one interprets the VT as a transition driven by charge/orbital ordering and the second one exploits the mechanism of a lattice distortion-driven charge ordering leading to metal-insulator behaviour.


## 3. Observation of Verwey Transition in Various Fe3O4 Nanostructures

Recently, a lot of work has been carried out to study the effect of various nanostructured Fe3O4 morphologies on VT, which include single crystals, epitaxial and polycrystalline thin films, particles, arrays of colloidal nanocrystals, heterostructures, and also in the form of nanocontacts. The eventual utilization of these morphologies is to develop novel VT-based devices, and this is a critical issue for further investigations.


### 3.1. Nanoparticles (1nm<ParticleSize<100nm)

The recent advancement in the synthesis of uniform and size-controllable Fe3O4 nanocrystals has enabled the size-dependent physical property characterization and their applications [21]. Recently, Lee et al. [20] have successfully synthesized stoichiometric and uniform-sized Fe3O4 nanocrystals with sizes ranging from 5 to 100 nm. These nanocrystals show the VT in the conductance, magnetization, and heat capacity measurements (see Figures 3(a)–3(c)). The VT is generally masked in magnetization data of superparamagnetic nanocrystals below the blocking temperature; therefore, it was reassured that the heat capacity of nanocrystals shows a lambda-like anomaly similar to the single crystal Fe3O4, confirming a truly thermodynamic transition. 57Fe nuclear magnetic resonance (NMR) of Fe3O4 nanocrystals (7 nm-7 μm) was also measured [19]. The line width of NMR spectra changes drastically around 120 K (see Figure 3(d)), showing microscopic evidence of the Verwey transition. The inset shows the NMR spectral intensity for one of the representative samples (25 nm) obtained at temperatures around the TV. In the region above the transition temperature, the line width of the spectrum increases and the spin-spin relaxation time decreases as the nanocrystal size decreases. The line width broadening indicates the significant deformation of magnetic structure and reduction of charge order compared to bulk crystals, even when the structural distortion is unobservable. The VT is weakly size-dependent (see Figure 3(e)) and gets suppressed in nanocrystals smaller than 20 nm before completely disappearing for a size less than 6 nm, which is a clear yet highly interesting indication of a size effect of this well-known phenomenon.Figure 3
Size-dependent characterization of the VT: temperature dependence of the first derivative of conductance (a), magnetization data measured at 100 Oe (b), and total heat capacity divided by temperature (c). The full width at quarter maximum (FWQM) of the Fe NMR spectra versus temperature [19]. The inset shows the Fe NMR spectral intensity of the 25 nm sample obtained at temperatures around TV (d). Size dependence of VT from combined data (e) [20].
(a)
(b)
(c)
(d)
(e)


### 3.2. Nanocrystalline Thin Films (1nm<GrainSize<100nm)

Considering the spintronic applications concerning magnetoresistance (MR) that depends on the spin polarization of the materials being used, an in-depth study of the growth of nanocrystalline Fe3O4 thin films is of interest. A relatively large low-field MR (-6% at 300 K to -10.0% at 200 K at the field of 5 kOe) was indeed found in nanocrystalline films [22]; however, in most cases, large MR could only be obtained at a high field and especially at low temperatures. The MR response in Fe3O4 seems to be very sensitive to the preparation conditions, and the reason for low or inconsistent MR response could be because of the nonstoichiometry grain boundaries and surface spin arrangement. In literature, nanocrystalline Fe3O4 thin films have been grown by a range of deposition techniques, such as evaporation, sputtering, molecular beam epitaxy, and pulsed laser deposition (PLD) [23–25].Previously, the author has worked extensively on oxide films, and we consider that the PLD [26–28] is the most suitable technique for stoichiometric growth of complex oxides. The deposition of Fe3O4 has been performed in a reducing atmosphere (under the vacuum of 1×10−5 mbar and substrate temperature, TS: RT-850°C) from the α-Fe2O3 target on an amorphous quartz substrate [26]. This regime can produce Fe3O4 in a limited TS window of 350-500°C (see Figure 4(a): Fe/O phase diagram). These films were followed by two different annealing processes, namely, (1) vacuum annealing and (2) wet H2 annealing, in that the wet H2 annealing only produces single-phase Fe3O4 films with grain sizes ranging 30-60 nm. The normalized M vs. T curve shows noticeable VT (see Figure 4(b)) which is a useful indicator for the stoichiometry of the samples, except for a higher TS film showing a broad transition due to slight Fe/O off-stoichiometry.Figure 4
Various Fe/O phases at differentTS before and after reduction treatments (a), MT/M (5 K) (at the fixed field of 5 kOe) and ρ vs. T curves for wet H2 annealed films at different TS (b) [26].
(a)
(b)The electric transport properties of the nanocrystalline Fe3O4 thin films are not well defined as compared to the magnetic properties, particularly the absence of VT (see Figure 4(b)). To understand this contradictory behaviour, we plotted M/M (300 K) vs. T curves at different fields for one of the representative samples (TS=500°C), as shown in Figure 5(a). We see that the magnitude of the drop in magnetizations at VT has severely reduced from 40% to 0.4% with the increasing field from 0.5 to 20 kOe [27]. This raises a question if this drop in magnetization is due to a change of the magnetic moment of Fe3O4 or is it just a manifestation of the increased anisotropy. The M-H loops (inset) support our arguments that the nonsaturation of magnetization at high fields and coercivity have increased significantly below VT. We fitted the high-field part of M-H loops to the approach to saturation formula, 4πM=Q1−H∗/H1/2, where Q is the magnetization at the infinite field and H∗ is related to the magnetocrystalline anisotropy [27]. The Q vs. T curve (Figure 5(b)) does not show any drop in magnetizations around VT as was seen in Figure 5(a) for low fields. We can conclude that the intrinsic saturation magnetic moment does not show any drop while cooling across VT, and whatever drop in magnetization we observed in Figure 5(a), it is just because of inadequate saturation field and there is nothing to do with any magnetic interaction change. This transition can also happen even if there is no structural transition but if there is a change in anisotropy. We now argue that charge order is triggered by the structural transition and it has nothing to do with magnetic ordering, as discussed by us elsewhere [28]. So the absence of VT in electronic transport may have a different origin like grain boundary volume, and defects/vacancies induced intergranular strain in nanocrystalline Fe3O4 films that suppress the resistivity change caused during VT [28].Figure 5
M vs. T curves under various fixed fields (a). The inset shows M-H loops below and above VT. The Q vs. T curves deduced from Chikazumi’s formula (b) [27] and δS vs. T curves for in situ and ex situ annealed Fe3O4 films (c) [29].Another interesting feature comes from large magnetocaloric effect observed in these nanocrystalline Fe3O4 films around VT, as shown in Figure 5(c). The fitting of M-H loops in Maxwell equations [29],δSM=∫HiHf∂M/∂TdH, yield large positive entropy change δS=2-12 J/kg K at VT under the field of 10 kOe. The magnitude of δS depends upon the detail microstructures of nanocrystalline films produced by different thermal treatments. This result is significant for cooler on-chip devices for next-generation nano-/microelectromechanical systems (NEMS/MEMS).


### 3.3. Epitaxial Films (1nm<Nanothick<200nm)

Despite the remarkable amount of work devoted in preparing Fe3O4 thin films in the last two decades, the VT even in epitaxial thin films is extremely broad and occurs at substantially lower temperatures as compared to the high-quality bulk single crystals. A systematic study on the influence of oxygen stoichiometry on epitaxial Fe3O4 films found that even for the optimal oxygen composition, the transition remains broad [22]. The study also discovered that the microstructure of the films has an important role; particularly, a larger domain size distribution results in a broader transition and a small domain size gives lower transition temperatures. The transition itself is still first order as it shows hysteresis, and there are indications that each domain has its transition temperature. Various substrates have been used in the literature to grow epitaxial Fe3O4 thin films, e.g., MgO, MgAl2O4, Al2O3, SrTiO3, and BaTiO3 [30]. These studies suggest that the larger the lattice mismatch, the broader the transition and the lower the average transition temperature.Recently, Liu et al. [30] succeeded in making a particular class of spinel substrates that allows the growth of Fe3O4 thin films with the VT as sharp as in bulk. The key principle was to obtain sufficiently large domain sizes of Fe3O4 thin films with small domain size distribution. Figure 6(a) shows ρ vs. T curves of 40 nm thick Fe3O4 (001) films grown on MgO and spinel substrates (Co2TiO4, Co1.75Mn0.25TiO4, and Co1.25Fe0.5Mn0.25TiO4), along with bulk Fe3O4 single crystal. We can see that the bulk sample has a sharp VT at 124 K, whereas the film on MgO shows the typical broad transition at lower temperatures. In contrast, the thin films grown on the spinel substrates all show a very sharp transition, almost as sharp as the bulk with a hysteresis value of 0.7 K. The most exciting feature is that now the transition temperatures of thin films grown on spinel substrates (127 K on Co2TiO4 (lattice mismatch +0.66%), 133 K on Co1.75Mn0.25TiO4 (+0.98%), and 136 K on Co1.25Fe0.5Mn0.25TiO4 (+1.11%)) are even higher than those of the bulk [31–35]. Figure 6(b) shows that TV gradually increases with the film thickness and, again, that it is larger for the spinel substrates with the larger lattice constant mismatch between the film and the substrate. Although films with the thicknesses of 5 nm and less do not show a VT, we can see a well-defined transition for films when they are 10 nm or thicker. Thus, using tensile strain, one can increase the transition temperature into considerably higher values than bulk. The occurrence of the VT in the highly anisotropic strained films raises a new question on the intricacies of the interplay between the charge and orbital degrees of freedom of the Fe ions in Fe3O4, adding another aspect to the elusiveness of this quantum material.Figure 6
ρ vs. T curves for 40 nm epitaxial Fe3O4 films grown on MgO (001), Co2TiO4 (001), Co1.75Mn0.25TiO4 (001), and Co1.25Fe0.5Mn0.25TiO4 (001) substrates along with single-crystal Fe3O4 (a). Corresponding TV vs. thickness curves (b) [30].
(a)
(b)The anisotropic magnetoresistance (AMR) of high-quality epitaxial Fe3O4 films on MgO (100) and Al2O3 (0001) substrates [36] was investigated in charge-ordering state, as shown in Figure 7(a). It was found that the Verwey transition contains two processes, a fast charge-ordering process and a continuous formation of trimeron process. In the Fe3O4 (100) film, the twofold AMR at 104K<116K comes from the uniaxial magnetic anisotropy, whereas the fourfold AMR at T=104K can be ascribed to the in-plane trimerons (Figure 7(b)). However, AMR in the Fe3O4 (111) film maintains twofold symmetry (Figure 7(c)). By comparing the AMR below TV between two oriented films, it shows the maxima when the trimerons are parallel to the magnetic field. A uniaxial magnetic anisotropy might appear in the trimeron, and the easy axis is along the trimeron. Thus, in-plane trimerons play an important role in the complex AMR behaviour below the TV.Figure 7
Sketch map of the sample, magnetic field, and current arrangement in the left corner (a). The structure of trimeron is shown in the right corner (a). AMR at 80 K and 50 kOe of Fe3O4 (100) film and the in-plane trimeron distribution at the corresponding angle (b). AMR at 110 K and 10 kOe of Fe3O4 (111) film and the in-plane trimeron distribution at the corresponding angle (c) [36].
(a)
(b)
(c)


### 3.4. Other Nanostructured Fe3O4 Geometries

While a lot of work has been done in thin film form, little is known about the potential use of Fe3O4 for device applications in nanoparticle morphology. Also, the VT is very sensitive to stoichiometry, and it is hardly observed in superparamagnetic length scale; an alternate approach to optimize the stoichiometry is to tailor the shape of the particles, since anisotropy plays a crucial role in deciding the magnetic characteristics of the magnetic nanocrystals. Recently, Mitra et al. [1] investigated the VT in shape-controlled small amine-coated Fe3O4 nanoparticles (6–14 nm). The VT of Fe3O4 near 120 K is seen in octahedral particles (Figure 8(a)), but it is not observed in their spherical particles (Figure 8(b)) in the FC- (field cooled-) ZFC (zero field cooled) measurements. The facets of octahedral particles consist of energetically most stable {111} planes which are protected against surface oxidation. The surface anisotropy is substantially reduced since the flat surface of octahedron has fewer broken bonds and oxygen vacancies. A lower concentration of defects and almost no oxidized layer at the surface provide a better stoichiometry to octahedral particles, which is the cause of the VT in octahedral nanoparticles.Figure 8
FC and ZFC magnetizations for different sizes of spherical and octahedral Fe3O4 nanoparticles (a, b) [1]. FC and ZFC magnetization of epitaxial Fe3O4 nanorods (along in- and out-of-plane directions) (c) and nanocubes (d) [37]. Insets (a–d) show the surface morphology of nanostructured Fe3O4 materials [38].
(a)
(b)
(c)
(d)Unfortunately, the crystal quality of spherical nanoparticles suffers from surface spin disorder and uncompensated bonds; epitaxial Fe3O4 nanorods with well-defined magnetic anisotropy are very promising as building blocks in spintronic devices. Chandra et al. [37] demonstrated the epitaxial growth of highly oriented Fe3O4 nanorods on SrTiO3 substrates by hydrothermal synthesis, as depicted in Figure 8(c). The epitaxial nanorods show biaxial magnetic anisotropy with an order of magnitude difference between the anisotropy field values of the easy and hard axes along with sharp VT. The interplay of epitaxy and enhanced magnetic anisotropy at room temperature, concerning randomly oriented Fe3O4 powder, and the nanorods are useful materials for magnetic data storage. Differently, Fe3O4 nanocubes [38] synthesized by the oxidation of Fe1−xO/Fe3−δO4 core-shell nanocubes (see in Figure 8(d)) show a kink at 110 K in the ZFC curve which can be attributed to the VT; however, it is not that much sharp as observed in nanorods and octahedral particles of Fe3O4.


## 3.1. Nanoparticles (1nm<ParticleSize<100nm)

The recent advancement in the synthesis of uniform and size-controllable Fe3O4 nanocrystals has enabled the size-dependent physical property characterization and their applications [21]. Recently, Lee et al. [20] have successfully synthesized stoichiometric and uniform-sized Fe3O4 nanocrystals with sizes ranging from 5 to 100 nm. These nanocrystals show the VT in the conductance, magnetization, and heat capacity measurements (see Figures 3(a)–3(c)). The VT is generally masked in magnetization data of superparamagnetic nanocrystals below the blocking temperature; therefore, it was reassured that the heat capacity of nanocrystals shows a lambda-like anomaly similar to the single crystal Fe3O4, confirming a truly thermodynamic transition. 57Fe nuclear magnetic resonance (NMR) of Fe3O4 nanocrystals (7 nm-7 μm) was also measured [19]. The line width of NMR spectra changes drastically around 120 K (see Figure 3(d)), showing microscopic evidence of the Verwey transition. The inset shows the NMR spectral intensity for one of the representative samples (25 nm) obtained at temperatures around the TV. In the region above the transition temperature, the line width of the spectrum increases and the spin-spin relaxation time decreases as the nanocrystal size decreases. The line width broadening indicates the significant deformation of magnetic structure and reduction of charge order compared to bulk crystals, even when the structural distortion is unobservable. The VT is weakly size-dependent (see Figure 3(e)) and gets suppressed in nanocrystals smaller than 20 nm before completely disappearing for a size less than 6 nm, which is a clear yet highly interesting indication of a size effect of this well-known phenomenon.Figure 3
Size-dependent characterization of the VT: temperature dependence of the first derivative of conductance (a), magnetization data measured at 100 Oe (b), and total heat capacity divided by temperature (c). The full width at quarter maximum (FWQM) of the Fe NMR spectra versus temperature [19]. The inset shows the Fe NMR spectral intensity of the 25 nm sample obtained at temperatures around TV (d). Size dependence of VT from combined data (e) [20].
(a)
(b)
(c)
(d)
(e)


## 3.2. Nanocrystalline Thin Films (1nm<GrainSize<100nm)

Considering the spintronic applications concerning magnetoresistance (MR) that depends on the spin polarization of the materials being used, an in-depth study of the growth of nanocrystalline Fe3O4 thin films is of interest. A relatively large low-field MR (-6% at 300 K to -10.0% at 200 K at the field of 5 kOe) was indeed found in nanocrystalline films [22]; however, in most cases, large MR could only be obtained at a high field and especially at low temperatures. The MR response in Fe3O4 seems to be very sensitive to the preparation conditions, and the reason for low or inconsistent MR response could be because of the nonstoichiometry grain boundaries and surface spin arrangement. In literature, nanocrystalline Fe3O4 thin films have been grown by a range of deposition techniques, such as evaporation, sputtering, molecular beam epitaxy, and pulsed laser deposition (PLD) [23–25].Previously, the author has worked extensively on oxide films, and we consider that the PLD [26–28] is the most suitable technique for stoichiometric growth of complex oxides. The deposition of Fe3O4 has been performed in a reducing atmosphere (under the vacuum of 1×10−5 mbar and substrate temperature, TS: RT-850°C) from the α-Fe2O3 target on an amorphous quartz substrate [26]. This regime can produce Fe3O4 in a limited TS window of 350-500°C (see Figure 4(a): Fe/O phase diagram). These films were followed by two different annealing processes, namely, (1) vacuum annealing and (2) wet H2 annealing, in that the wet H2 annealing only produces single-phase Fe3O4 films with grain sizes ranging 30-60 nm. The normalized M vs. T curve shows noticeable VT (see Figure 4(b)) which is a useful indicator for the stoichiometry of the samples, except for a higher TS film showing a broad transition due to slight Fe/O off-stoichiometry.Figure 4
Various Fe/O phases at differentTS before and after reduction treatments (a), MT/M (5 K) (at the fixed field of 5 kOe) and ρ vs. T curves for wet H2 annealed films at different TS (b) [26].
(a)
(b)The electric transport properties of the nanocrystalline Fe3O4 thin films are not well defined as compared to the magnetic properties, particularly the absence of VT (see Figure 4(b)). To understand this contradictory behaviour, we plotted M/M (300 K) vs. T curves at different fields for one of the representative samples (TS=500°C), as shown in Figure 5(a). We see that the magnitude of the drop in magnetizations at VT has severely reduced from 40% to 0.4% with the increasing field from 0.5 to 20 kOe [27]. This raises a question if this drop in magnetization is due to a change of the magnetic moment of Fe3O4 or is it just a manifestation of the increased anisotropy. The M-H loops (inset) support our arguments that the nonsaturation of magnetization at high fields and coercivity have increased significantly below VT. We fitted the high-field part of M-H loops to the approach to saturation formula, 4πM=Q1−H∗/H1/2, where Q is the magnetization at the infinite field and H∗ is related to the magnetocrystalline anisotropy [27]. The Q vs. T curve (Figure 5(b)) does not show any drop in magnetizations around VT as was seen in Figure 5(a) for low fields. We can conclude that the intrinsic saturation magnetic moment does not show any drop while cooling across VT, and whatever drop in magnetization we observed in Figure 5(a), it is just because of inadequate saturation field and there is nothing to do with any magnetic interaction change. This transition can also happen even if there is no structural transition but if there is a change in anisotropy. We now argue that charge order is triggered by the structural transition and it has nothing to do with magnetic ordering, as discussed by us elsewhere [28]. So the absence of VT in electronic transport may have a different origin like grain boundary volume, and defects/vacancies induced intergranular strain in nanocrystalline Fe3O4 films that suppress the resistivity change caused during VT [28].Figure 5
M vs. T curves under various fixed fields (a). The inset shows M-H loops below and above VT. The Q vs. T curves deduced from Chikazumi’s formula (b) [27] and δS vs. T curves for in situ and ex situ annealed Fe3O4 films (c) [29].Another interesting feature comes from large magnetocaloric effect observed in these nanocrystalline Fe3O4 films around VT, as shown in Figure 5(c). The fitting of M-H loops in Maxwell equations [29],δSM=∫HiHf∂M/∂TdH, yield large positive entropy change δS=2-12 J/kg K at VT under the field of 10 kOe. The magnitude of δS depends upon the detail microstructures of nanocrystalline films produced by different thermal treatments. This result is significant for cooler on-chip devices for next-generation nano-/microelectromechanical systems (NEMS/MEMS).


## 3.3. Epitaxial Films (1nm<Nanothick<200nm)

Despite the remarkable amount of work devoted in preparing Fe3O4 thin films in the last two decades, the VT even in epitaxial thin films is extremely broad and occurs at substantially lower temperatures as compared to the high-quality bulk single crystals. A systematic study on the influence of oxygen stoichiometry on epitaxial Fe3O4 films found that even for the optimal oxygen composition, the transition remains broad [22]. The study also discovered that the microstructure of the films has an important role; particularly, a larger domain size distribution results in a broader transition and a small domain size gives lower transition temperatures. The transition itself is still first order as it shows hysteresis, and there are indications that each domain has its transition temperature. Various substrates have been used in the literature to grow epitaxial Fe3O4 thin films, e.g., MgO, MgAl2O4, Al2O3, SrTiO3, and BaTiO3 [30]. These studies suggest that the larger the lattice mismatch, the broader the transition and the lower the average transition temperature.Recently, Liu et al. [30] succeeded in making a particular class of spinel substrates that allows the growth of Fe3O4 thin films with the VT as sharp as in bulk. The key principle was to obtain sufficiently large domain sizes of Fe3O4 thin films with small domain size distribution. Figure 6(a) shows ρ vs. T curves of 40 nm thick Fe3O4 (001) films grown on MgO and spinel substrates (Co2TiO4, Co1.75Mn0.25TiO4, and Co1.25Fe0.5Mn0.25TiO4), along with bulk Fe3O4 single crystal. We can see that the bulk sample has a sharp VT at 124 K, whereas the film on MgO shows the typical broad transition at lower temperatures. In contrast, the thin films grown on the spinel substrates all show a very sharp transition, almost as sharp as the bulk with a hysteresis value of 0.7 K. The most exciting feature is that now the transition temperatures of thin films grown on spinel substrates (127 K on Co2TiO4 (lattice mismatch +0.66%), 133 K on Co1.75Mn0.25TiO4 (+0.98%), and 136 K on Co1.25Fe0.5Mn0.25TiO4 (+1.11%)) are even higher than those of the bulk [31–35]. Figure 6(b) shows that TV gradually increases with the film thickness and, again, that it is larger for the spinel substrates with the larger lattice constant mismatch between the film and the substrate. Although films with the thicknesses of 5 nm and less do not show a VT, we can see a well-defined transition for films when they are 10 nm or thicker. Thus, using tensile strain, one can increase the transition temperature into considerably higher values than bulk. The occurrence of the VT in the highly anisotropic strained films raises a new question on the intricacies of the interplay between the charge and orbital degrees of freedom of the Fe ions in Fe3O4, adding another aspect to the elusiveness of this quantum material.Figure 6
ρ vs. T curves for 40 nm epitaxial Fe3O4 films grown on MgO (001), Co2TiO4 (001), Co1.75Mn0.25TiO4 (001), and Co1.25Fe0.5Mn0.25TiO4 (001) substrates along with single-crystal Fe3O4 (a). Corresponding TV vs. thickness curves (b) [30].
(a)
(b)The anisotropic magnetoresistance (AMR) of high-quality epitaxial Fe3O4 films on MgO (100) and Al2O3 (0001) substrates [36] was investigated in charge-ordering state, as shown in Figure 7(a). It was found that the Verwey transition contains two processes, a fast charge-ordering process and a continuous formation of trimeron process. In the Fe3O4 (100) film, the twofold AMR at 104K<116K comes from the uniaxial magnetic anisotropy, whereas the fourfold AMR at T=104K can be ascribed to the in-plane trimerons (Figure 7(b)). However, AMR in the Fe3O4 (111) film maintains twofold symmetry (Figure 7(c)). By comparing the AMR below TV between two oriented films, it shows the maxima when the trimerons are parallel to the magnetic field. A uniaxial magnetic anisotropy might appear in the trimeron, and the easy axis is along the trimeron. Thus, in-plane trimerons play an important role in the complex AMR behaviour below the TV.Figure 7
Sketch map of the sample, magnetic field, and current arrangement in the left corner (a). The structure of trimeron is shown in the right corner (a). AMR at 80 K and 50 kOe of Fe3O4 (100) film and the in-plane trimeron distribution at the corresponding angle (b). AMR at 110 K and 10 kOe of Fe3O4 (111) film and the in-plane trimeron distribution at the corresponding angle (c) [36].
(a)
(b)
(c)


## 3.4. Other Nanostructured Fe3O4 Geometries

While a lot of work has been done in thin film form, little is known about the potential use of Fe3O4 for device applications in nanoparticle morphology. Also, the VT is very sensitive to stoichiometry, and it is hardly observed in superparamagnetic length scale; an alternate approach to optimize the stoichiometry is to tailor the shape of the particles, since anisotropy plays a crucial role in deciding the magnetic characteristics of the magnetic nanocrystals. Recently, Mitra et al. [1] investigated the VT in shape-controlled small amine-coated Fe3O4 nanoparticles (6–14 nm). The VT of Fe3O4 near 120 K is seen in octahedral particles (Figure 8(a)), but it is not observed in their spherical particles (Figure 8(b)) in the FC- (field cooled-) ZFC (zero field cooled) measurements. The facets of octahedral particles consist of energetically most stable {111} planes which are protected against surface oxidation. The surface anisotropy is substantially reduced since the flat surface of octahedron has fewer broken bonds and oxygen vacancies. A lower concentration of defects and almost no oxidized layer at the surface provide a better stoichiometry to octahedral particles, which is the cause of the VT in octahedral nanoparticles.Figure 8
FC and ZFC magnetizations for different sizes of spherical and octahedral Fe3O4 nanoparticles (a, b) [1]. FC and ZFC magnetization of epitaxial Fe3O4 nanorods (along in- and out-of-plane directions) (c) and nanocubes (d) [37]. Insets (a–d) show the surface morphology of nanostructured Fe3O4 materials [38].
(a)
(b)
(c)
(d)Unfortunately, the crystal quality of spherical nanoparticles suffers from surface spin disorder and uncompensated bonds; epitaxial Fe3O4 nanorods with well-defined magnetic anisotropy are very promising as building blocks in spintronic devices. Chandra et al. [37] demonstrated the epitaxial growth of highly oriented Fe3O4 nanorods on SrTiO3 substrates by hydrothermal synthesis, as depicted in Figure 8(c). The epitaxial nanorods show biaxial magnetic anisotropy with an order of magnitude difference between the anisotropy field values of the easy and hard axes along with sharp VT. The interplay of epitaxy and enhanced magnetic anisotropy at room temperature, concerning randomly oriented Fe3O4 powder, and the nanorods are useful materials for magnetic data storage. Differently, Fe3O4 nanocubes [38] synthesized by the oxidation of Fe1−xO/Fe3−δO4 core-shell nanocubes (see in Figure 8(d)) show a kink at 110 K in the ZFC curve which can be attributed to the VT; however, it is not that much sharp as observed in nanorods and octahedral particles of Fe3O4.


## 4. Applications

### 4.1. Multiferroic Properties

In addition to all its acclaimed fame, Fe3O4 is also probably one of the first multiferroics, which shows the ferroelectric effect (FE) in its insulating state below VT [39–48]. However, the microscopic nature of the FE in Fe3O4 is still a matter of debate. Probably, it is related to the coexistence of bond-centred and charge-centred charge ordering. In the proposed structural and charge pattern, besides the site-centred charge ordering, one also notices the alternation of the formal Fe2+ and Fe3+ valence states and strong modulation of the Fe-Fe distances (the bond lengths). In the structure shown in Figure 9(a) [49], one sees that, e.g., along the Fe chains running in the (110) direction (in cubic setting), i.e., in the xy chains, there is an alternation of Fe2+ and Fe3+ (open and filled circles), but simultaneously there is an alternation of short and long Fe-Fe bonds. This direction corresponds to the monoclinic b-direction, in which the polarization is observed. In this framework, each of such (110) mixed bond- and site-centred charge-ordering chains gives a nonzero contribution to the electrical polarization.Figure 9
Sketch of the possible origin of ferroelectricity in Fe3O4 and emphasis on the Fe chains running in the (110) direction of Fe3O4 []. In the xy chains, there is an alternation of Fe2+ and Fe3+ ions (open and filled circles). Concurrently, there is an alternation of short and long Fe-Fe bonds; shifts of Fe ions are shown by black arrows. The resulting polarization is indicated by the red arrows (a) [49]. Electric saturation polarization of the Fe3O4 films made by pulsed laser deposition and sputtering (b) [50].
(a)
(b)Firmly, the proof for the existence of FE order (as shown in Figure9(b)) in 150 nm thick Fe3O4 films synthesized by pulsed laser deposition and magnetron sputtering on Nb-doped SrTiO3 substrates has been investigated recently [50]. The appearance of ferroelectric order below 38 K was explained by the existence of spontaneous electric polarization in the noncentrosymmetric monoclinic Cc structure, which arises from an alternation of charge states and bond lengths [51, 52]. However, it is surprising that the electric polarization does not already develop at the VT. This is because in between 40 K and TV, the electric polarization is suppressed by relaxation processes due to electron tunnelling and electron hopping processes [53], glassy polar degrees of freedom [54], or thermally activated structural processes [55]. Since the easy-axis direction is generally stabilized by the film-substrate strain, it would be easier to observe a ferroelectric polarization in thin films than in bulk. Indeed, the polarization values measured in Fe3O4 films tend to be larger than in single crystals. This scenario explains the close relation between magnetoelectric effects and relaxation processes observed both in the electric and magnetic susceptibilities. In contrast to conventional relaxor ferroelectrics [56], the relaxor behaviour in Fe3O4 is not driven by chemical heterogeneity but by the dynamical structural disorder.Conventionally, the multiferroics are single-phase materials with the coexistence of ferromagnetism, ferroelectricity, or ferroelasticity, which can result in novel functionalities. Because of advancement of the thin-film growth techniques and computational capabilities, the coupling in multiferroics that was predicted in 1894 has developed rapidly [57, 58]. In the class of single-phase multiferroic materials, magnetism occurs independently from ferroelectricity. Some multiferroic heterostructures have been produced by compound ferromagnetics (Fe3O4) with ferroelectrics BaTiO3 [59], Pb(Mg1/3Nb2/3)O3-PbTiO3(PMN-PT) [60], PdZrxTi1-xO3 (PZT) [61], BiFeO3 [62], HoMnO3, and YMnO3 [63]. These multiferroic heterostructures show the strong interfacial magnetoelectric effects [64–69], which can be used in multifunctional spintronic, nanoelectronic, and optoelectronic devices.Electric-field-controlled magnetism and VT in highly correlated Fe3O4 materials have generated great interest recently both scientifically and technologically [51]. Ferroelastic strain control of VT was observed in epitaxial Fe3O4 thin films grown on PMN-PT (011) substrate [4], as shown in four-point geometry (Figure 10(a)). Through ferroelastic control of lattice strain, the TV shot up by 8 K, evidenced by large changes in resistivity once the sample is poled with a DC field of 10 kV/cm (inset Figure 10(a)). Thus, electrical modulation of in-plane epitaxial strain is a far more effective way to manipulate VT than a pure volume change argument. On the other hand, epitaxial Fe3O4 films incorporated into a gated device structure [51] (Figure 10(b)) demonstrate the ability to control the VT with static electric fields. The TV increases for both polarities of the electric field, indicating that the effect is not driven by changes in carrier concentration. The energetics of induced electric polarization and strain within the Fe3O4 film provides a possible explanation for this behaviour.Figure 10
Schematics of four-point resistance measurement for Fe3O4/PMN-PT structure and ferroelastic strain state dependence of resistivity as a function of temperature (a) [4]. Electrical gating of Fe3O4 where the dielectric layer consists of PMMA (900 nm)/Al2O3 (50 nm)/MgO (10 nm). Temperature dependence of resistance for applied electric fields of +1.8 MV/cm (blue), +0.9 MV/cm (orange), 0 MV/cm (black), −0.9 MV/cm (green), and −1.8 MV/cm (red). The arrows show TV for each electric field, which is summarized in the inset (b) [51].
(a)
(b)Another example of magnetoelectric coupling is the magnetic properties of Fe3O4/BaTiO3 heterostructures which observe remarkable changes (as shown in Figure 11) at various structural phase transitions of BaTiO3 substrate [70]. Upon tetragonal to orthorhombic transition (T to O), the lattice parameter of BaTiO3 dramatically decreases, which induces compressive strain in the Fe3O4 thin film. This increased strain anisotropy leads to an abrupt increase of in-plane magnetization, coercivity, and remanent magnetization of Fe3O4 (Figures 11(b) and 11(c)) [70]. While in transition from orthorhombic to rhombohedral (O to R), the lattice parameter of BaTiO3 now dramatically increases, resulting in a decrease of the compressive strain, which leads to an opposite effect on magnetic properties of Fe3O4 (Figures 11(b) and 11(c)). The Fe3O4 (001) film, which has a negative magnetostriction coefficient, is under compressive stress when it is in contact with BaTiO3. With the decrease of temperature, the lattice mismatch between Fe3O4 and BaTiO3 increases. These temperature-driven structural transformations of BaTiO3 induce various anisotropies that cause magnetic properties to change, in a way similar to the VT, however at elevated temperatures.Figure 11
In-planeM-H loops of Fe3O4/BaTiO3 (100) heterostructures [70] measured at different temperatures (a); a variation of the in-plane magnetization vs. T under a magnetic field of 0.1 T (b). The in-plane Mr/Ms vs. T obtained from the magnetization hysteresis loops (c).The quantitative understanding of converse magnetoelectric effects, i.e., the variation of the magnetization as a function of an applied electric field in extrinsic multiferroic hybrids, is a key prerequisite for the development of future spintronic devices. The strain-mediated converse magnetoelectric effect in Fe3O4/BaTiO3 heterostructures was also realized at room temperature [34]. This demonstrates that the electric-field-induced changes of the magnetic state in the Fe3O4 thin film can be well described by the presence of two different ferroelastic domains in the BaTiO3 substrate, resulting in two differently strained regions in the Fe3O4 film with different magnetic properties. The two-region model allows predicting the converse magnetoelectric effects in multiferroic hybrid structures consisting of ferromagnetic thin films on ferroelastic substrates.Digital memory comes with the ability to switch between distinct electronic and magnetic phases with a control voltage. Small changes in structure and charge density near a transition between competing phases can tip the balance among them, leading to large changes in electronic and magnetic properties. Devices based on this principle can be both fast and energy efficient [71], overcome some of the intrinsic limitations in conventional field-effect transistors [72], and also provide new functionalities [73–75]. While these properties point to a pathway for creating novel functionalities, reversible and nonvolatile switching between different phases using strain has been unexplored. In nonvolatile switching, the electronic/magnetic states that are realized remain in a stable remnant state after the control voltage has been switched off.


### 4.2. Spin Seebeck Effect

The spin Seebeck effect (SSE) refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimetres. Despite decades of research into thermoelectric materials and properties, the efficiency of thermoelectric devices has remained low due to the interdependence of the Seebeck voltage,S; the resistivity, q; and the thermal conductivity [76, 77]. One promising approach to overcome this problem and increase the versatility of thermoelectric devices involves exploiting the spin of the electron in addition to its charge and heat transport properties. In contrast to conventional thermoelectrics, this effect offers the possibility for another approach in all-solid-state energy conversion devices, since it involves properties of at least two different materials that can be optimized independently. The SSE for the laser-ablated Fe3O4 (thickness=50nm)//SrTiO3(001) (thickness=0.5mm) samples was measured using the so-called longitudinal configuration. In such geometry (as shown in Figure 12(a)), a temperature gradient (δT) is applied in the ±z-direction, generating a temperature difference (±δT) between the bottom and the top of the sample, with temperatures T±δT and T, respectively [5]. The voltage (Vy) is measured along they-direction, while a sweeping magnetic field is applied at an angle h concerning the x-direction.Figure 12
Schematic of the measurement setup (a) and estimated SSE coefficient (Szy) vs. T (b) for the Fe3O4//SrTiO3 (001) sample [5].
(a)
(b)The focus is to observe the SSE below the Verwey transition (T<TV) (Figure 12(b)), and an SSE coefficient (Szy) at 105 K was estimated to be 52 nV/K. There is a clear reduction in SSE compared to the value observed at 300 K that could be related to the changes induced by the VT on the thermal and magnetic properties of the film, which can affect the thermal spin pumping at the Fe3O4/Pt interface and therefore the observed SSE signal. Such thermoelectric effects result from the combination between charge and heat current in suitable materials having applications as electric cooling systems or thermal power generators.


### 4.3. Exchange Bias

An exchange bias (EB) phenomenon is a property of coupled antiferromagnetic- (AFM-) ferromagnetic (FM) systems that occur due to magnetic interface effects [78]. It manifests itself in a shifting (HEB) of M-H loop along the field axis and enhancement of coercivity (HC) when the system is cooled down in an external magnetic field through the magnetic ordering temperatures of the AFM (TN) and FM (TC) phases. It has been reported that the EB can be influenced by many factors in the FM/AFM system, such as the FM magnetization MFM, the thickness of FM layer tFM or AFM layer tAFM, and the anisotropy of AFM (KAFM) or FM (KFM) [79]. A rapid change in KFM is observed in the vicinity of TV=120K due to the structural transformation from cubic to a more anisotropic monoclinic phase. Therefore, this change in KFM will result in variation in HE. Liu et al. [6] verify this transition tunability by preparing an interface with thicknesses of Fe3O4 and CoO as 40 nm and 5 nm, respectively, in the FM/AFM bilayer system.The FC-ZFC magnetization curves of CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) AF/FM system in Figure 13(a) show a rapid change in magnetization at the VT. At the same temperature, HC observes a sharp enhancement in the AF/FM system compared to the bare Fe3O4 (40 nm)/MgO (001) layer (inset a), indicating exchange anisotropy that is coupled with magnetocrystalline anisotropy change due to structural transformation. Figure 13(b) shows notable HE change below VT. For Fe3O4, the low-temperature monoclinic magnetocrystalline anisotropy constants are considerably greater (about 10 times) than those of the high-temperature cubic structure. The correlation between HE2 and HC (inset b) indicates further that KFM has a sole responsibility for such enhancement at VT.Figure 13
FC-ZFC magnetization curves of CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) AF/FM system (a). Inset of (a): temperature dependence of coercivity field (HC) for CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) and Fe3O4(40 nm)/MgO (001) systems. The exchange bias field (HE) as a function of temperature at the cooling field of 10 kOe and 2 kOe (b). Inset of (b): HC vs. HE2 (right) [6].
(a)
(b)


### 4.4. Spin Accumulation

Spin-dependent transports (particularly spin injection, manipulation, and detection) are the integral parts of semiconductor spintronic devices and have attracted tremendous attention. Recent studies have demonstrated that spin-polarized carriers injected from a ferromagnetic material to a semiconductor lead to nonequilibrium spin accumulation and spin current over spin diffusion length [80, 81]. The magnitude of spin accumulation in any system depends on factors like type of the injector, the spin polarization of the ferromagnet/insulator combination, junction resistance, and the uniformity of film at the interface. Half-metallic Fe3O4 can be a potential choice for spin injector material compared to the ferromagnetic metals.Recently, Bhat and Kumar [7] investigated spin injection from Fe3O4 as a spin source into GaAs and Si (both n and p-type) semiconductors using with and without a tunnel barrier (MgO) via three-terminal electrical Hanle (3TH) measurement, as shown in Figure 14(a). Application of a constant current I through the Fe3O4 layer makes sure that sufficient spin-polarized carriers are pumped into the semiconductor where the decay of spin-polarized carriers will be measured. Once, the spins are injected into the semiconductor, these accumulated spin-polarized carriers at the junction of semiconductor get scattered or processed depending on the type of semiconductor. Thus, there is a gradient in the measured voltage ΔV between the device and the far end of semiconductor due to the spin-scattering process within these semiconductors which can be further controlled by applying a perpendicular magnetic field B. The ΔV can be expressed as ΔV=TSP×Δμ/2, where TSP is the tunnel spin polarization of the ferromagnet/insulator combination and Δμ=μ↑−μ↓ the difference in chemical potential for up-spins and down-spins, which is nothing but the spin accumulation at the injected material. Strikingly, the normalized spin accumulation voltage (ΔV/ΔVmax) (see Figure 14(b)) in the semiconductor is found to be associated with a drastic increment in Fe3O4-based devices below TV. Such an enhancement of ΔV is absent in the devices with Fe as a spin source. Further, the overall device resistance measured by 2 probes has no drastic difference at the TV (see Figure 14(c)). From this, it can be concluded that the TV of the Fe3O4 film has a direct influence on the magnitude of spin accumulation, and the resistance enhancement of Fe3O4 film itself has no vital role in the observed enhancement of spin accumulation. This result is consistent with the investigation of Wang et al. [82] and Ziese et al. [83] showing the maximum spin polarization of Fe3O4 observed at TV using MR measurements.Figure 14
Schematics of the electrical 3TH measurement and the spin relaxation in a semiconductor (a). The plot of normalized spin accumulation voltageΔV vs. T of Fe3O4/MgO/GaAs, Fe3O4/GaAs, Fe3O4/MgO/Si, and Fe/MgO/GaAs devices showing the Verwey transition (shaded region) coinciding exactly the region of enhancement in ΔV (b) while the normalized value of local 2-probe voltages as a function of T for this sample is plotted for comparison (c) [7].
(a)
(b)
(c)Thus, an anomalous increase inΔV can be attributed purely to the spin subband modification across TV but not to the increase in resistance. Since the VT is associated with a structural modification, the configuration of subbands of Fe3O4 along with the tunnel barrier might influence the total spin accumulation, as ΔV depends directly on the tunnel spin polarization of Fe3O4/MgO. But the similar magnitude of enhancement in spin accumulation is even present in the Schottky junction of Fe3O4 on GaAs, ruling out the role of MgO electronic band structure. Hence, the spin injection and detection into conventional semiconductors like GaAs and Si can be improved with the help of materials like Fe3O4 with higher spin polarization. This result also suggests that the theoretical prediction of room temperature half-metallicity of Fe3O4 above and below TV has to be reinvestigated.


### 4.5. Organic Spintronics

Π-conjugated organic semiconductors (OS) are extremely attractive materials for the transport of spin-polarized electrons to long distances [84, 85]. The major difference between inorganic and organic solids is that electrical transport is via band conduction in the former and carrier hopping in the latter. The conduction (carrier/spin injection and extraction) takes place through an abstract spin valve (SV) (shown in the inset of Figure 15(c)) that filters spin-polarized electrons by alignment of the energetic position of the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LUMO) of the OS relative to the Fermi level (EF) of the ferromagnetic (FM) electrode (Figure 15(a)). This concept is applied to make memory and sensor devices working on giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR). As discussed previously, Fe3O4 provides excellent spin injection at RT and supplementary spin accumulation at and below TV [6]. Convincingly, tuning of charge gap (0.15 eV) at EF across VT due to charge ordering on the octahedral iron sites of Fe3O4 is believed to result in a corresponding tuning of conduction mode and a unique crossover from GMR to TMR in Fe3O4/Alq3(C27H18N3O3Al)/Co interface as proposed by Dey et al. [86] with the energy band diagram given in Figure 15(a).Figure 15
Energy level diagram at the interfaces of Alq3 and Fe3O4/Co electrodes (a). Current-voltage (I-V) characteristics of Fe3O4/Alq3/Co/Au SV at T=100K (b). Inset in (b) shows I-V curves at T=200 and 300 K. Differential conductance vs. bias voltage at T=100K and 250 K (c). Inset in (c) shows a schematic view of transport measurement geometry [84].
(a)
(b)
(c)Interestingly, theI-V curves (Figure 15(b)) at higher temperatures T>TV exhibit clear signs of tunnelling which further confirms from parabolic differential dI/dV curves (Figure 15(c)). But, at T<TV, the curve is different and exhibits the beginning of the injection mode at a bias of 2 V (Figure 15(b)). The conduction observed at T<TV is described by “activated” carrier injection into the molecular orbitals of OSC at the electrode-OSC interface, followed by “activated” carrier hopping through the molecular orbitals towards the opposite electrode, where the extraction of carriers from OSC takes place. While the T>TV conduction is achieved through carrier tunnelling process, there is a drastic change in conductivity mode in SV from injection to tunnel mode as a function of “temperature,” signifies VT, as the origin of this effect. For T<TV, there is a formation of charge gap at EF; consequently, activated carrier transport with the device current governed by carrier injection and transport through molecular levels of Alq3 could be assigned as GMR. For T>TV, with the decrease or even closure of this energy gap, all the charge carriers take part in the conduction process. Activated carrier transport no more remains relevant in this scenario, and the device current should be governed by tunnelling conduction in this temperature regime. Both GMR and TMR have been observed in a single SV below/above the TV, and a drastic tuning in SV properties is triggered by VT of Fe3O4 electrode.


## 4.1. Multiferroic Properties

In addition to all its acclaimed fame, Fe3O4 is also probably one of the first multiferroics, which shows the ferroelectric effect (FE) in its insulating state below VT [39–48]. However, the microscopic nature of the FE in Fe3O4 is still a matter of debate. Probably, it is related to the coexistence of bond-centred and charge-centred charge ordering. In the proposed structural and charge pattern, besides the site-centred charge ordering, one also notices the alternation of the formal Fe2+ and Fe3+ valence states and strong modulation of the Fe-Fe distances (the bond lengths). In the structure shown in Figure 9(a) [49], one sees that, e.g., along the Fe chains running in the (110) direction (in cubic setting), i.e., in the xy chains, there is an alternation of Fe2+ and Fe3+ (open and filled circles), but simultaneously there is an alternation of short and long Fe-Fe bonds. This direction corresponds to the monoclinic b-direction, in which the polarization is observed. In this framework, each of such (110) mixed bond- and site-centred charge-ordering chains gives a nonzero contribution to the electrical polarization.Figure 9
Sketch of the possible origin of ferroelectricity in Fe3O4 and emphasis on the Fe chains running in the (110) direction of Fe3O4 []. In the xy chains, there is an alternation of Fe2+ and Fe3+ ions (open and filled circles). Concurrently, there is an alternation of short and long Fe-Fe bonds; shifts of Fe ions are shown by black arrows. The resulting polarization is indicated by the red arrows (a) [49]. Electric saturation polarization of the Fe3O4 films made by pulsed laser deposition and sputtering (b) [50].
(a)
(b)Firmly, the proof for the existence of FE order (as shown in Figure9(b)) in 150 nm thick Fe3O4 films synthesized by pulsed laser deposition and magnetron sputtering on Nb-doped SrTiO3 substrates has been investigated recently [50]. The appearance of ferroelectric order below 38 K was explained by the existence of spontaneous electric polarization in the noncentrosymmetric monoclinic Cc structure, which arises from an alternation of charge states and bond lengths [51, 52]. However, it is surprising that the electric polarization does not already develop at the VT. This is because in between 40 K and TV, the electric polarization is suppressed by relaxation processes due to electron tunnelling and electron hopping processes [53], glassy polar degrees of freedom [54], or thermally activated structural processes [55]. Since the easy-axis direction is generally stabilized by the film-substrate strain, it would be easier to observe a ferroelectric polarization in thin films than in bulk. Indeed, the polarization values measured in Fe3O4 films tend to be larger than in single crystals. This scenario explains the close relation between magnetoelectric effects and relaxation processes observed both in the electric and magnetic susceptibilities. In contrast to conventional relaxor ferroelectrics [56], the relaxor behaviour in Fe3O4 is not driven by chemical heterogeneity but by the dynamical structural disorder.Conventionally, the multiferroics are single-phase materials with the coexistence of ferromagnetism, ferroelectricity, or ferroelasticity, which can result in novel functionalities. Because of advancement of the thin-film growth techniques and computational capabilities, the coupling in multiferroics that was predicted in 1894 has developed rapidly [57, 58]. In the class of single-phase multiferroic materials, magnetism occurs independently from ferroelectricity. Some multiferroic heterostructures have been produced by compound ferromagnetics (Fe3O4) with ferroelectrics BaTiO3 [59], Pb(Mg1/3Nb2/3)O3-PbTiO3(PMN-PT) [60], PdZrxTi1-xO3 (PZT) [61], BiFeO3 [62], HoMnO3, and YMnO3 [63]. These multiferroic heterostructures show the strong interfacial magnetoelectric effects [64–69], which can be used in multifunctional spintronic, nanoelectronic, and optoelectronic devices.Electric-field-controlled magnetism and VT in highly correlated Fe3O4 materials have generated great interest recently both scientifically and technologically [51]. Ferroelastic strain control of VT was observed in epitaxial Fe3O4 thin films grown on PMN-PT (011) substrate [4], as shown in four-point geometry (Figure 10(a)). Through ferroelastic control of lattice strain, the TV shot up by 8 K, evidenced by large changes in resistivity once the sample is poled with a DC field of 10 kV/cm (inset Figure 10(a)). Thus, electrical modulation of in-plane epitaxial strain is a far more effective way to manipulate VT than a pure volume change argument. On the other hand, epitaxial Fe3O4 films incorporated into a gated device structure [51] (Figure 10(b)) demonstrate the ability to control the VT with static electric fields. The TV increases for both polarities of the electric field, indicating that the effect is not driven by changes in carrier concentration. The energetics of induced electric polarization and strain within the Fe3O4 film provides a possible explanation for this behaviour.Figure 10
Schematics of four-point resistance measurement for Fe3O4/PMN-PT structure and ferroelastic strain state dependence of resistivity as a function of temperature (a) [4]. Electrical gating of Fe3O4 where the dielectric layer consists of PMMA (900 nm)/Al2O3 (50 nm)/MgO (10 nm). Temperature dependence of resistance for applied electric fields of +1.8 MV/cm (blue), +0.9 MV/cm (orange), 0 MV/cm (black), −0.9 MV/cm (green), and −1.8 MV/cm (red). The arrows show TV for each electric field, which is summarized in the inset (b) [51].
(a)
(b)Another example of magnetoelectric coupling is the magnetic properties of Fe3O4/BaTiO3 heterostructures which observe remarkable changes (as shown in Figure 11) at various structural phase transitions of BaTiO3 substrate [70]. Upon tetragonal to orthorhombic transition (T to O), the lattice parameter of BaTiO3 dramatically decreases, which induces compressive strain in the Fe3O4 thin film. This increased strain anisotropy leads to an abrupt increase of in-plane magnetization, coercivity, and remanent magnetization of Fe3O4 (Figures 11(b) and 11(c)) [70]. While in transition from orthorhombic to rhombohedral (O to R), the lattice parameter of BaTiO3 now dramatically increases, resulting in a decrease of the compressive strain, which leads to an opposite effect on magnetic properties of Fe3O4 (Figures 11(b) and 11(c)). The Fe3O4 (001) film, which has a negative magnetostriction coefficient, is under compressive stress when it is in contact with BaTiO3. With the decrease of temperature, the lattice mismatch between Fe3O4 and BaTiO3 increases. These temperature-driven structural transformations of BaTiO3 induce various anisotropies that cause magnetic properties to change, in a way similar to the VT, however at elevated temperatures.Figure 11
In-planeM-H loops of Fe3O4/BaTiO3 (100) heterostructures [70] measured at different temperatures (a); a variation of the in-plane magnetization vs. T under a magnetic field of 0.1 T (b). The in-plane Mr/Ms vs. T obtained from the magnetization hysteresis loops (c).The quantitative understanding of converse magnetoelectric effects, i.e., the variation of the magnetization as a function of an applied electric field in extrinsic multiferroic hybrids, is a key prerequisite for the development of future spintronic devices. The strain-mediated converse magnetoelectric effect in Fe3O4/BaTiO3 heterostructures was also realized at room temperature [34]. This demonstrates that the electric-field-induced changes of the magnetic state in the Fe3O4 thin film can be well described by the presence of two different ferroelastic domains in the BaTiO3 substrate, resulting in two differently strained regions in the Fe3O4 film with different magnetic properties. The two-region model allows predicting the converse magnetoelectric effects in multiferroic hybrid structures consisting of ferromagnetic thin films on ferroelastic substrates.Digital memory comes with the ability to switch between distinct electronic and magnetic phases with a control voltage. Small changes in structure and charge density near a transition between competing phases can tip the balance among them, leading to large changes in electronic and magnetic properties. Devices based on this principle can be both fast and energy efficient [71], overcome some of the intrinsic limitations in conventional field-effect transistors [72], and also provide new functionalities [73–75]. While these properties point to a pathway for creating novel functionalities, reversible and nonvolatile switching between different phases using strain has been unexplored. In nonvolatile switching, the electronic/magnetic states that are realized remain in a stable remnant state after the control voltage has been switched off.


## 4.2. Spin Seebeck Effect

The spin Seebeck effect (SSE) refers to the generation of a spin voltage caused by a temperature gradient in a ferromagnet, which enables the thermal injection of spin currents from the ferromagnet into an attached nonmagnetic metal over a macroscopic scale of several millimetres. Despite decades of research into thermoelectric materials and properties, the efficiency of thermoelectric devices has remained low due to the interdependence of the Seebeck voltage,S; the resistivity, q; and the thermal conductivity [76, 77]. One promising approach to overcome this problem and increase the versatility of thermoelectric devices involves exploiting the spin of the electron in addition to its charge and heat transport properties. In contrast to conventional thermoelectrics, this effect offers the possibility for another approach in all-solid-state energy conversion devices, since it involves properties of at least two different materials that can be optimized independently. The SSE for the laser-ablated Fe3O4 (thickness=50nm)//SrTiO3(001) (thickness=0.5mm) samples was measured using the so-called longitudinal configuration. In such geometry (as shown in Figure 12(a)), a temperature gradient (δT) is applied in the ±z-direction, generating a temperature difference (±δT) between the bottom and the top of the sample, with temperatures T±δT and T, respectively [5]. The voltage (Vy) is measured along they-direction, while a sweeping magnetic field is applied at an angle h concerning the x-direction.Figure 12
Schematic of the measurement setup (a) and estimated SSE coefficient (Szy) vs. T (b) for the Fe3O4//SrTiO3 (001) sample [5].
(a)
(b)The focus is to observe the SSE below the Verwey transition (T<TV) (Figure 12(b)), and an SSE coefficient (Szy) at 105 K was estimated to be 52 nV/K. There is a clear reduction in SSE compared to the value observed at 300 K that could be related to the changes induced by the VT on the thermal and magnetic properties of the film, which can affect the thermal spin pumping at the Fe3O4/Pt interface and therefore the observed SSE signal. Such thermoelectric effects result from the combination between charge and heat current in suitable materials having applications as electric cooling systems or thermal power generators.


## 4.3. Exchange Bias

An exchange bias (EB) phenomenon is a property of coupled antiferromagnetic- (AFM-) ferromagnetic (FM) systems that occur due to magnetic interface effects [78]. It manifests itself in a shifting (HEB) of M-H loop along the field axis and enhancement of coercivity (HC) when the system is cooled down in an external magnetic field through the magnetic ordering temperatures of the AFM (TN) and FM (TC) phases. It has been reported that the EB can be influenced by many factors in the FM/AFM system, such as the FM magnetization MFM, the thickness of FM layer tFM or AFM layer tAFM, and the anisotropy of AFM (KAFM) or FM (KFM) [79]. A rapid change in KFM is observed in the vicinity of TV=120K due to the structural transformation from cubic to a more anisotropic monoclinic phase. Therefore, this change in KFM will result in variation in HE. Liu et al. [6] verify this transition tunability by preparing an interface with thicknesses of Fe3O4 and CoO as 40 nm and 5 nm, respectively, in the FM/AFM bilayer system.The FC-ZFC magnetization curves of CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) AF/FM system in Figure 13(a) show a rapid change in magnetization at the VT. At the same temperature, HC observes a sharp enhancement in the AF/FM system compared to the bare Fe3O4 (40 nm)/MgO (001) layer (inset a), indicating exchange anisotropy that is coupled with magnetocrystalline anisotropy change due to structural transformation. Figure 13(b) shows notable HE change below VT. For Fe3O4, the low-temperature monoclinic magnetocrystalline anisotropy constants are considerably greater (about 10 times) than those of the high-temperature cubic structure. The correlation between HE2 and HC (inset b) indicates further that KFM has a sole responsibility for such enhancement at VT.Figure 13
FC-ZFC magnetization curves of CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) AF/FM system (a). Inset of (a): temperature dependence of coercivity field (HC) for CoO (5 nm)/Fe3O4 (40 nm)/MgO (001) and Fe3O4(40 nm)/MgO (001) systems. The exchange bias field (HE) as a function of temperature at the cooling field of 10 kOe and 2 kOe (b). Inset of (b): HC vs. HE2 (right) [6].
(a)
(b)


## 4.4. Spin Accumulation

Spin-dependent transports (particularly spin injection, manipulation, and detection) are the integral parts of semiconductor spintronic devices and have attracted tremendous attention. Recent studies have demonstrated that spin-polarized carriers injected from a ferromagnetic material to a semiconductor lead to nonequilibrium spin accumulation and spin current over spin diffusion length [80, 81]. The magnitude of spin accumulation in any system depends on factors like type of the injector, the spin polarization of the ferromagnet/insulator combination, junction resistance, and the uniformity of film at the interface. Half-metallic Fe3O4 can be a potential choice for spin injector material compared to the ferromagnetic metals.Recently, Bhat and Kumar [7] investigated spin injection from Fe3O4 as a spin source into GaAs and Si (both n and p-type) semiconductors using with and without a tunnel barrier (MgO) via three-terminal electrical Hanle (3TH) measurement, as shown in Figure 14(a). Application of a constant current I through the Fe3O4 layer makes sure that sufficient spin-polarized carriers are pumped into the semiconductor where the decay of spin-polarized carriers will be measured. Once, the spins are injected into the semiconductor, these accumulated spin-polarized carriers at the junction of semiconductor get scattered or processed depending on the type of semiconductor. Thus, there is a gradient in the measured voltage ΔV between the device and the far end of semiconductor due to the spin-scattering process within these semiconductors which can be further controlled by applying a perpendicular magnetic field B. The ΔV can be expressed as ΔV=TSP×Δμ/2, where TSP is the tunnel spin polarization of the ferromagnet/insulator combination and Δμ=μ↑−μ↓ the difference in chemical potential for up-spins and down-spins, which is nothing but the spin accumulation at the injected material. Strikingly, the normalized spin accumulation voltage (ΔV/ΔVmax) (see Figure 14(b)) in the semiconductor is found to be associated with a drastic increment in Fe3O4-based devices below TV. Such an enhancement of ΔV is absent in the devices with Fe as a spin source. Further, the overall device resistance measured by 2 probes has no drastic difference at the TV (see Figure 14(c)). From this, it can be concluded that the TV of the Fe3O4 film has a direct influence on the magnitude of spin accumulation, and the resistance enhancement of Fe3O4 film itself has no vital role in the observed enhancement of spin accumulation. This result is consistent with the investigation of Wang et al. [82] and Ziese et al. [83] showing the maximum spin polarization of Fe3O4 observed at TV using MR measurements.Figure 14
Schematics of the electrical 3TH measurement and the spin relaxation in a semiconductor (a). The plot of normalized spin accumulation voltageΔV vs. T of Fe3O4/MgO/GaAs, Fe3O4/GaAs, Fe3O4/MgO/Si, and Fe/MgO/GaAs devices showing the Verwey transition (shaded region) coinciding exactly the region of enhancement in ΔV (b) while the normalized value of local 2-probe voltages as a function of T for this sample is plotted for comparison (c) [7].
(a)
(b)
(c)Thus, an anomalous increase inΔV can be attributed purely to the spin subband modification across TV but not to the increase in resistance. Since the VT is associated with a structural modification, the configuration of subbands of Fe3O4 along with the tunnel barrier might influence the total spin accumulation, as ΔV depends directly on the tunnel spin polarization of Fe3O4/MgO. But the similar magnitude of enhancement in spin accumulation is even present in the Schottky junction of Fe3O4 on GaAs, ruling out the role of MgO electronic band structure. Hence, the spin injection and detection into conventional semiconductors like GaAs and Si can be improved with the help of materials like Fe3O4 with higher spin polarization. This result also suggests that the theoretical prediction of room temperature half-metallicity of Fe3O4 above and below TV has to be reinvestigated.


## 4.5. Organic Spintronics

Π-conjugated organic semiconductors (OS) are extremely attractive materials for the transport of spin-polarized electrons to long distances [84, 85]. The major difference between inorganic and organic solids is that electrical transport is via band conduction in the former and carrier hopping in the latter. The conduction (carrier/spin injection and extraction) takes place through an abstract spin valve (SV) (shown in the inset of Figure 15(c)) that filters spin-polarized electrons by alignment of the energetic position of the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LUMO) of the OS relative to the Fermi level (EF) of the ferromagnetic (FM) electrode (Figure 15(a)). This concept is applied to make memory and sensor devices working on giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR). As discussed previously, Fe3O4 provides excellent spin injection at RT and supplementary spin accumulation at and below TV [6]. Convincingly, tuning of charge gap (0.15 eV) at EF across VT due to charge ordering on the octahedral iron sites of Fe3O4 is believed to result in a corresponding tuning of conduction mode and a unique crossover from GMR to TMR in Fe3O4/Alq3(C27H18N3O3Al)/Co interface as proposed by Dey et al. [86] with the energy band diagram given in Figure 15(a).Figure 15
Energy level diagram at the interfaces of Alq3 and Fe3O4/Co electrodes (a). Current-voltage (I-V) characteristics of Fe3O4/Alq3/Co/Au SV at T=100K (b). Inset in (b) shows I-V curves at T=200 and 300 K. Differential conductance vs. bias voltage at T=100K and 250 K (c). Inset in (c) shows a schematic view of transport measurement geometry [84].
(a)
(b)
(c)Interestingly, theI-V curves (Figure 15(b)) at higher temperatures T>TV exhibit clear signs of tunnelling which further confirms from parabolic differential dI/dV curves (Figure 15(c)). But, at T<TV, the curve is different and exhibits the beginning of the injection mode at a bias of 2 V (Figure 15(b)). The conduction observed at T<TV is described by “activated” carrier injection into the molecular orbitals of OSC at the electrode-OSC interface, followed by “activated” carrier hopping through the molecular orbitals towards the opposite electrode, where the extraction of carriers from OSC takes place. While the T>TV conduction is achieved through carrier tunnelling process, there is a drastic change in conductivity mode in SV from injection to tunnel mode as a function of “temperature,” signifies VT, as the origin of this effect. For T<TV, there is a formation of charge gap at EF; consequently, activated carrier transport with the device current governed by carrier injection and transport through molecular levels of Alq3 could be assigned as GMR. For T>TV, with the decrease or even closure of this energy gap, all the charge carriers take part in the conduction process. Activated carrier transport no more remains relevant in this scenario, and the device current should be governed by tunnelling conduction in this temperature regime. Both GMR and TMR have been observed in a single SV below/above the TV, and a drastic tuning in SV properties is triggered by VT of Fe3O4 electrode.


## 5. Conclusions

The aim of current day research is to innovate electromagnetic devices with advanced materials that can operate at lower power with higher speed, yet without compromising the aim of shrinking their size. For this goal, a comprehensive review of the growth of various nanostructured Fe3O4 geometries and its hallmark Verwey transition is in a time of need. It is very exciting to observe the ensemble of anomalies VT brought forth at the nanoscale. It is not full-size dependent, but shape morphology also plays a crucial role in determining the energetically stable surface of stoichiometric Fe3O4. In nanocrystalline thin films, the electronic transport properties behave differently compared to the magnetic properties, particularly the absence of VT and the presence of antiphase boundaries caused by defects, off-stoichiometric Fe2+/Fe3+ ratio, and micro-/nanostrains emanating from different growth conditions. Interestingly, the Verwey transition temperature TV can be tailored in epitaxial Fe3O4 thin films either by compressive strain using underneath special spinel substrates or integrated with a gated circuit using the electric field.The following are the possible applications of nanostructured Fe3O4 wherein VT can be exploited in the future:
(1)
Different Fe3O4-based multiferroic heterostructures can be developed by interfacial engineering (epitaxial strain, charge, oxygen vacancy, exchange, and spin-orbital coupling) for various novel applications like resistive switching, spin filters for data storage, and spatial light modulators for optical switching(2)
In contrast to conventional thermoelectrics, the spin Seebeck effect in Fe3O4 thin films offers new possibility in all-solid-state energy conversion devices such as electric cooling systems and thermal power generators while the observation of large magnetocaloric effect paves the way for cooler on-chip devices for nano-/microelectromechanical systems(3)
The concept of integration ofπ-conjugated organic semiconductors into spintronic devices owing to its robust spin coherence can be realized by using band alignment at the electrode Fe3O4/Alq3 interface, which gives GMR to TMR crossover in a single spin valve(4)
Currently, basic research is mainly focused on spin dynamics and transport in semiconductor environment (spin transistors, spin diodes, optospintronic devices, memories, etc.) for all-electrical spin control via spin-orbit interactions and fixed or mobile spin qubits for quantum computing(5)
Lastly, Fe3O4 can be convincingly used for manufacturing cheap and efficient spintronic devices because of properties like excellent spin accumulation that can be successfully controlled using the Verwey transition. It can be used in various biomedical sensors like molecular detection, e.g., protein detection, and as a potential biomarker due to its positive integration with an organic semiconductor. Microarrays of sensing devices can make use of these properties of Verwey transition in cryogenic units for electrical fault sensingConvincingly, VT proves to be an efficient needle to tailor the fabric of Fe3O4 into useful nanoscale devices, yet shifting VT towards the room temperature range still remains a major challenge and can be manipulated by having in-depth knowledge of complicated electron-electron and electron-phonon interactions that involve the interplay of interaction, exchange orbital, and spin degrees of freedom.



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*Source: 8457383-2019-03-25.xml*