Inductive Thermal Effect of Ferrite Magnetic Nanoparticles

Localized heat induction using magnetic nanoparticles under an alternating magnetic field is an emerging technology applied in areas including, cancer treatment, thermally activated drug release and remote activation of cell functions. To enhance the induction heating efficiency of magnetic nanoparticles, the intrinsic and extrinsic magnetic parameters influencing the heating efficiency of magnetic nanoparticles should be effectively engineered. This review covers the recent progress in the optimization of magnetic properties of spinel ferrite nanoparticles for efficient heat induction. The key materials factors for efficient magnetic heating including size, shape, composition, inter/intra particle interactions are systematically discussed, from the growth mechanism, process control to chemical and magnetic properties manipulation.


Introduction
Ferrite (MFe 2 O 4 , M = Mn, Fe, Co, Ni and Zn) magnetic nanoparticles (typically, of size 5-100 nm) have attracted profuse attention because they are at the interfaces of chemistry, physics and biology, due to their remarkable size and shape-dependent magnetic properties [1][2][3]. Scientists have developed methods to produce magnetic nanoparticles with fine control of the morphology [4][5][6]. Many new phenomena such as superparamagnetism, superferromagnetism, and superspin glass have been observed in these magnetic nanoparticles (MNPs) [7][8][9]. Moreover, in the nano-regime the magnetic properties such as coercivity (H C ), saturation magnetization (M S ) and susceptibility (χ) strongly vary with the size, shape, and composition of the magnetic nanoparticles [2,6,10]. These unique magnetic properties, small size and biocompatibility make them particularly promising in various biomedical applications, for instance contrast enhancement in magnetic resonance imaging (MRI), nano-sized carrier in drug delivery, mediators in converting electromagnetic energy to heat, and as magnetic-targeting and bio-sensing agents [11][12][13][14][15]. All these biomedical applications require the MNPs to have high magnetic moments with small sizes and a narrow particle-size distribution, so that the nanoparticles could have well-defined physical and chemical properties [11,[16][17][18]. A general picture in Figure 1 schematically illustrates the uses of MNPs in four important areas of cancer theranostics.
In general, when the magnetic nanoparticle suspension is subjected to an alternating current magnetic field (ACMF), it can demonstrate prominent heating effects related to energy losses during the magnetization reversal of the nanostructures. This heating ability depends on the properties of the nanostructures, such as mean size, magnetization and magnetic anisotropy, and the ACMF amplitude (H ac ) and frequency (f ) [19,20]. Therefore, to improve the inductive heating characteristics of magnetic nanostructures, many approaches have been taken to improve the magnetic properties of the nanostructures [21][22][23][24][25]. Over the past few years, substantial progress has been made to precisely control the size, composition, morphology and multifunctionalities of magnetic nanostructures [11,[26][27][28][29]. Based on the heat activation ability, these nanostructures have been utilized in cancer therapy, on-demand drug carrier and gene therapy applications [32,33]. The magnetic nanoparticles have also been as contrast agent in magnetic particle imaging (MPI) and magnetic resonance imaging (MRI).

Magnetism at Nanoscale
As first predicted by Frenkel and Dorfman, when the size of the ferromagnet or ferrimagnet decreases below a critical size, the amount of energy required to produce domain walls becomes greater than the reduction in the magnetostatic energy [34]. As a consequence, only single domain formation is favored. A single domain particle consists of large numbers of atomic spins and, thus, can be viewed as 'supermoment' that has a magnetic moment ~10 3 to 10 5 µB [35]. The single domain size can be estimated from the equation [34][35][36]: Figure 1. Based on the heat activation ability, these nanostructures have been utilized in cancer therapy, on-demand drug carrier and gene therapy applications [32,33]. The magnetic nanoparticles have also been as contrast agent in magnetic particle imaging (MPI) and magnetic resonance imaging (MRI).

Magnetism at Nanoscale
As first predicted by Frenkel and Dorfman, when the size of the ferromagnet or ferrimagnet decreases below a critical size, the amount of energy required to produce domain walls becomes greater than the reduction in the magnetostatic energy [34]. As a consequence, only single domain formation is favored. A single domain particle consists of large numbers of atomic spins and, thus, can be viewed as 'supermoment' that has a magnetic moment~10 3 to 10 5 µ B [35]. The single domain size can be estimated from the equation [34][35][36]: where µ 0 is the permeability of free space (4π × 10 −7 H/m), A is the exchange stiffness in J/m and K is the magnetocrystalline anisotropy in J/m 3 . For example, the typical value of single domain size is around 128 nm for Fe 3 O 4 , while for MnFe 2 O 4 it is 50 nm (due to a smaller K and a higher M S ) [37][38][39]. Further, at the particle size d = D SD , the single domain prefers to be uniformly magnetized along one of its anisotropic easy axes, which leads to a strong enhancement in coercivity. Below D SD , due to the decrease of the magnetic anisotropy energy (E a = KV, V is volume of the particle) the coercivity value decreases with decrease in the size (see Figure 2) [40]. On further reduction in size, the anisotropy energy value decreases further and becomes comparable to or even lower than the thermal energy (k B T, k B is Boltzmann constant). As a consequence, the energy barrier for magnetization reversal is dominated by thermal energy ( Figure 3A, orange line). Thus, the supermoment thermally fluctuate like spins in a paramagnetic material, which leads to a net magnetization of zero; this phenomenon is called superparamagnetism. Superparamagnetic materials have no coercivity at room temperature, whereas ferromagnetic materials have a high coercivity. On application of an external magnetic field, the superparamagnetic nanoparticles react like the paramagnets (i.e., supermoment rotation) with the one exception that their magnetic susceptibility 'χ' is much larger or even comparable to bulk value. However, in ultra-small sized MNPs, the χ value is always lower than the bulk value. This lower value is explained by the magnetically inactive surface atomic layer of the nanoparticles. Since a large fraction of atoms reside at the surface of MNPs, the surface spin disorder effect is dramatically pronounced with decrease of MNPs size. Thus, with a decrease of the size of MNPs, χ value decreases.
The alternative approach to modulate the magnetic properties (χ and H C ) at the nanoscale is to develop the anisotropy through other mechanisms such as the shape anisotropy and the exchange coupling. The effects of shape anisotropy and the exchange coupling on the magnetic properties of MNPs will be disscused in the Sections 3.3 and 3.4, respectively. where μ0 is the permeability of free space (4π × 10 −7 H/m), A is the exchange stiffness in J/m and K is the magnetocrystalline anisotropy in J/m 3 . For example, the typical value of single domain size is around 128 nm for Fe3O4, while for MnFe2O4 it is 50 nm (due to a smaller K and a higher MS) [37][38][39]. Further, at the particle size d = DSD, the single domain prefers to be uniformly magnetized along one of its anisotropic easy axes, which leads to a strong enhancement in coercivity. Below DSD, due to the decrease of the magnetic anisotropy energy (Ea = KV, V is volume of the particle) the coercivity value decreases with decrease in the size (see Figure 2) [40]. On further reduction in size, the anisotropy energy value decreases further and becomes comparable to or even lower than the thermal energy (kBT, kB is Boltzmann constant). As a consequence, the energy barrier for magnetization reversal is dominated by thermal energy ( Figure 3A, orange line). Thus, the supermoment thermally fluctuate like spins in a paramagnetic material, which leads to a net magnetization of zero; this phenomenon is called superparamagnetism. Superparamagnetic materials have no coercivity at room temperature, whereas ferromagnetic materials have a high coercivity. On application of an external magnetic field, the superparamagnetic nanoparticles react like the paramagnets (i.e. supermoment rotation) with the one exception that their magnetic susceptibility 'χ' is much larger or even comparable to bulk value. However, in ultra-small sized MNPs, the χ value is always lower than the bulk value. This lower value is explained by the magnetically inactive surface atomic layer of the nanoparticles. Since a large fraction of atoms reside at the surface of MNPs, the surface spin disorder effect is dramatically pronounced with decrease of MNPs size. Thus, with a decrease of the size of MNPs, χ value decreases. The alternative approach to modulate the magnetic properties (χ and HC) at the nanoscale is to develop the anisotropy through other mechanisms such as the shape anisotropy and the exchange coupling. The effects of shape anisotropy and the exchange coupling on the magnetic properties of MNPs will be disscused in the Sections 3.3 and 3.4, respectively. The top of (A) depicts the reversal of magnetization in ferromagnetic particles. The energy diagram below illustrates the difference in energy barrier for a large particle behaving as ferromagnet and a small particle behaving as superparamagnet. The bottom of (A) depicts the relaxation process in superparamagnetic particles. (B) A typical correlation between the Néel relaxation time and the MNPs diameters. MNPs with extremely high τN are promising for recording media applications.
The superparamagnetic relaxation time can be modeled by the Néel-Brown theory as shown below [41,42]: where Ea = KV is the anisotropy energy which determines the flipping angle of the nanoparticle, and τ0 is an attempt relaxation time factor that lies in the range of 10 -9 to 10 -13 s [43]. The relaxation time exponentially increases with the increase of MNPs size ( Figure 3B). When the relaxation time 'τN' is small or comparable to the time scale of the experimental technique (τN ≤ tm, tm is the measuring time), we measure an average value of the magnetization; however, if the τN ≥ tm, we measure the instantaneous value of the magnetization. The transition temperature at which τN = tm is known as superparamagnetic blocking temperature (TB) and can be expressed as From the above equation it is clear that the magnetocrystalline anisotropy and the volume of magnetic nanoparticles are the two key parameters on which the TB depends. The larger the size of the nanoparticles, the larger 'kBT' is required for superparamagnetic transition. Thus, TB increases with the increase in the size of the nanoparticles. However, in the case of nanoparticle assemblies and multicore nanoparticles, the interparticle interaction modifies the energy barrier and produces collective properties. The magnetic properties of interacting MNPs are well described by the Vogel-Fulcher model [44,45]  The top of (A) depicts the reversal of magnetization in ferromagnetic particles. The energy diagram below illustrates the difference in energy barrier for a large particle behaving as ferromagnet and a small particle behaving as superparamagnet. The bottom of (A) depicts the relaxation process in superparamagnetic particles. (B) A typical correlation between the Néel relaxation time and the MNPs diameters. MNPs with extremely high τ N are promising for recording media applications.
The superparamagnetic relaxation time can be modeled by the Néel-Brown theory as shown below [41,42]: where E a = KV is the anisotropy energy which determines the flipping angle of the nanoparticle, and τ 0 is an attempt relaxation time factor that lies in the range of 10 −9 to 10 −13 s [43]. The relaxation time exponentially increases with the increase of MNPs size ( Figure 3B). When the relaxation time 'τ N ' is small or comparable to the time scale of the experimental technique (τ N ≤ t m , t m is the measuring time), we measure an average value of the magnetization; however, if the τ N ≥ t m , we measure the instantaneous value of the magnetization. The transition temperature at which τ N = t m is known as superparamagnetic blocking temperature (T B ) and can be expressed as From the above equation it is clear that the magnetocrystalline anisotropy and the volume of magnetic nanoparticles are the two key parameters on which the T B depends. The larger the size of the nanoparticles, the larger 'k B T' is required for superparamagnetic transition. Thus, T B increases with the increase in the size of the nanoparticles. However, in the case of nanoparticle assemblies and multicore nanoparticles, the interparticle interaction modifies the energy barrier and produces collective properties. The magnetic properties of interacting MNPs are well described by the Vogel-Fulcher model [44,45] where T 0 is known as Vogel-Fulcher temperature, a measure of the interaction strength and E a /k B is the activation energy required to overcome the barrier of the reversal of the magnetization. With a further increase of nanoparticle interaction, a spin-glass like collective state can be formed (known as superspin glass) [35,46]. When the strength of the interparticle interactions is strong enough, a long-range ferromagnetic ordering can occur, and the state is known as superferromagnet [41,42].
Recently, the superspin glass and superferromagnetic ordering have been observed in Fe 3 O 4 and Co nanoparticle systems [47,48]. As discussed above the magnetic properties of MNPs can be controlled with exploitation of several parameters such as size, composition and morphology. In addition, the inter/intra particles interactions can be controlled to further optimize the magnetic properties, which will be discussed in the Section 3.4.

Effects of Magnetic Anisotropy and Magnetic Susceptibility
When colloids of magnetic nanoparticles are subjected to an ac magnetic field, they convert electromagnetic energy into heat due to losses from the reversal of magnetization [49][50][51]. The magnetization reversal mainly occurs through two different processes: Hysteresis loss (seen in ferromagnetic NPs) and susceptibility loss (seen in superparamagnetic NPs). Hysteresis loss strongly depends on the field amplitude (H ac ) as well as the magnetic coercive field (H K = 2K/µ 0 M S , however in experiment the coercivity will be much lower than the H K ) [52]. When the ACMF is applied to a ferromagnetic particle with moment (µ), the magnetization state becomes metastable, as shown in Figure 4A. Subsequently, µ reverses and, therefore, the Zeeman energy falls from µ 0 µH K to -µ 0 µH K and the corresponding energy difference dissipates as heat. In the magnetization reversal event, the work done in one cycle of the ACMF 'H ac sin (2πft)' is 0 for H ac << H K and 4µ 0 µH K for H ac ≥ H K . In the latter case, the heat dissipation from MNPs per unit weight during unit time, also known as specific loss power P H can be expressed as 4µ 0 µH K fϕ −1 (4µ 0 M S H K fρ −1 ), where ϕ and ρ are the weight and density of the MNPs, respectively. In short, the P H value increases from 0 to 4µ 0 µH K fϕ −1 with increase of H ac and flattens out if H ac is strengthened above H K . Thus, the guiding principle for maximizing P H is that H ac is adjusted to H K and the number of ACMF cycles is maximized. Unfortunately, because of the technical restrictions on the ACMF amplitude and physiological limitations, the hysteresis loss cannot be completely used. Figure 4C shows the schematic representation of a typical hyperthermia setup.
In smaller-sized magnetic nanoparticles (KV ≤ k B T), the magnetization reversal of 'µ' is caused by thermal fluctuation. The magnetization reversal in a zero-magnetic field is associated with Néel relaxation and Brownian rotation of the nanoparticles ( Figure 4B) [53]. The Néel (τ N ) and Brownian (τ B ) relaxation times are given by [54] The Néel relaxation is controlled by anisotropy energy (KV) of nanoparticles. Equation (6) for the Brownian rotation is directly related to hydrodynamic parameters such as the hydrodynamic volume (V H ) and the viscosity of the medium (η).
If Néel relaxation and Brownian rotation occur in parallel, the effective relaxation time τ is given by [54] 1 Hence, τ = M S 2γ 0 K 3/2 For superparamagnetic nanoparticles, τ is determined only by τ N because it decreases exponentially with decreasing the nanoparticles volume, while the decrease of τ B is directly proportional to V H . Further, for small H ac , a linear response of the thermodynamic equilibrium state of the superparamagnetic nanoparticles (i.e., ACMF driven reversals) can be considered. In this case, the average of out-of-phase component of AC susceptibility χ can be expressed as follows, Consequently, the susceptibility loss occurs, and the corresponding specific loss power P is expressed as [54].
Equation (10) indicates that P increases in proportion to f 2 in the low frequency range 2π f τ, whereas, it flattens out at πµ 2 0 µ 2 H 2 ac /3ρk B T even though f is increased further in the high frequency range 2π f τ. Thus, the guiding principle for maximizing the specific loss power in the superparamagnetic regime is that f can be fine-tuned to τ −1 and H ac can be maximized ( Figure 4D-F). Further, from the above equation 8 and 10, it is evident that the increased M S values lead to a higher P and hence metallic nanoparticles including Fe, Co and FeCo (M S in the range of 150-220 emu/g) are suitable heating mediators, but they have not been considered for their cytotoxicity and poor stability in physiological environment. The heating activity of MNPs also need fine-tuning of the magnetic anisotropy constant K, it shifts the critical MNPs size that corresponds to the maximum P to a lower value. However, smaller-sized MNPs possess the low moment and, hence they can exhibit poor heating activities. In short, an ideal material in the superparamagnetic regime would have a high M S and intermediate K value.

Effect of Curie Temperature (TC)
One of the most important restrictions of magnetic hyperthermia treatment is the risk of overheating in healthy tissues. A direct approach for overcoming this issue is to make the nanoparticles self-controlled, which can be realized by taking advantage of the MNPs' Curie temperature (TC) and adjusting the TC to the therapeutic temperature (42−45 °C). When the temperature increases above the TC, the MNPs lose their ferromagnetic properties and instead shows  [56,57]. (B) Susceptibility loss given by the out-of-phase component of AC susceptibility is associated to the nanoparticle's relaxation. As demonstrated in the schematic, in Néel relaxation, the magnetic moment shown by the black arrow reverses (the particle does not rotate), while in Brownian relaxation, the particle (the sphere) rotates as a whole. (C) Schematic view of a typical hyperthermia setup. The variation of SAR based on (D) susceptibility (χ) and (E) magnetic anisotropy (K). (F) Size dependent SAR resulting from the susceptibility loss and the hysteresis loss [55]. The amount of heat generated by MNPs is usually quantified in terms of the specific absorption rate (SAR), given by [21] SAR = C m dT dt (11) where C is the specific heat of the colloid (i.e., for water, this value is 4.18 J g −1 C −1 ), dT/dt is the initial slope of the temperature versus time graph, and m is mass of magnetic material (mg/ml) in the suspension. As such, both the susceptibility loss and the hysteresis loss are strongly dependent on the MNPs size, and the SAR can show two maxima as shown in Figure 4F [55]. The 1 st peak in the superparamagnetic regime is related to the resonance condition ( 2π f ∼ τ −1 ) and 2 nd peak in the ferromagnetic regime is attributed to the hysteresis loss. In addition, in both regimes a high M S is required to further optimize the SAR values, which will be discussed later in the Section 3.

Effect of Curie Temperature (T C )
One of the most important restrictions of magnetic hyperthermia treatment is the risk of overheating in healthy tissues. A direct approach for overcoming this issue is to make the nanoparticles self-controlled, which can be realized by taking advantage of the MNPs' Curie temperature (T C ) and adjusting the T C to the therapeutic temperature (42−45 • C). When the temperature increases above the T C , the MNPs lose their ferromagnetic properties and instead shows paramagnetic behavior. Thus, the induction heating is immediately suppressed above the T C . Recently, this phenomenon has been used to formulate ferrite-based self-controlled heating mediators, mainly the mixed ferrites such as Zn x Fe 3-x O 4 , MnZnFe 2 O 4 , MgFe 2 O 4 , etc. [58][59][60][61].
The Curie temperature of a magnetic spinel ferrite can be assessed by the strength of exchange interactions between magnetic moments in the octahedral (O h ) and the tetrahedral (T d ) sublattices. The exchange interactions in ferrites are mediated by intermediating oxygen p-orbitals, known as super-exchange interactions. Thus, the T C can be adjusted by controlling compositions (i.e., magnetic moments of cations in two sublattices) and the distance between cations ions. Table 1 lists several spinel ferrite nanoparticles in which T C is adjusted by alteration in chemical composition via doping suitable amount of magnetic or nonmagnetic elements. Despite having the T C in the therapeutic temperature range, a high M S and moderate K are required to obtain high SAR values. Thus, only a few of the ferrites (Zn x Fe 3-x O 4 , MnZnFe 2 O 4 , MgFe 2 O 4 ) have shown promising heating activities after adjusting their Curie temperature values to the required therapeutic limit.

Size Effects
In the past few years, significant attention has been devoted to synthesizing monodispersed magnetic nanoparticles with precise control over their size, composition and shape. While several synthetic strategies have been proposed to synthesize ferrite nanoparticles, the high-temperature solution phase methods appear to be the most interesting because it permits a good control over the size and the morphology of the nanoparticles [33,64]. In this approach, the high-temperature reaction of iron (III) acetylacetonate or iron oleate in the presence of oleic acid, and/or oleylamine leads to the formation of Fe 3 O 4 nanoparticles [65,66]. A brief pictorial detail of the synthesis procedure is shown in Figure 5. An exciting development in the synthesis of monodispersed iron oxide NPs was demonstrated by Park et al. [33]. In a typical reaction, Fe-oleate complex was prepared by reacting iron chloride with sodium oleate, which was thermally decomposed into monodispersed Fe 3 O 4 NPs in octadecene at 320 • C. With the help of the seed-mediated growth, Fe 3 O 4 NPs with 4 to 13 nm diameters were obtained [64]. Later, Xu et al. found that by changing the heating conditions, and ratios of oleylamine and oleic acid, the size of Fe 3 O 4 NPs can be tuned from 14 to 100 nm [67]. Recently, oleylamine was used as a multitasking agent, acting as a solvent, and reducing and surface functionalizing agents, to prepare monodispersed Fe 3 O 4 NPs with a reasonably large magnetization value [68][69][70][71]. The experiment confirms that the presence of excess amount of oleylamine offers an adequately strong reductive environment for the Fe-precursor and leads to the formation of Fe 3 O 4 NPs at a reasonably low temperature of 240 • C. Figure 6A shows the representative TEM micrographs of monodispersed Fe 3 O 4 nanoparticles of size ranging from 6 to 24 nm, prepared by thermolysis of Iron(III) acetylacetonate in oleic acid and oleylamine [71]. These synthesis methods were also extended to formulate MFe 2 O 4 (M = Co, Ni, and Mn) NPs.

Size Effects
In the past few years, significant attention has been devoted to synthesizing monodispersed magnetic nanoparticles with precise control over their size, composition and shape. While several synthetic strategies have been proposed to synthesize ferrite nanoparticles, the high-temperature solution phase methods appear to be the most interesting because it permits a good control over the size and the morphology of the nanoparticles. [33,64] In this approach, the high-temperature reaction of iron (III) acetylacetonate or iron oleate in the presence of oleic acid, and/or oleylamine leads to the formation of Fe3O4 nanoparticles [65,66]. A brief pictorial detail of the synthesis procedure is shown in Figure 5. An exciting development in the synthesis of monodispersed iron oxide NPs was demonstrated by Park et.al [33]. In a typical reaction, Fe-oleate complex was prepared by reacting iron chloride with sodium oleate, which was thermally decomposed into monodispersed Fe3O4 NPs in octadecene at 320 °C. With the help of the seed-mediated growth, Fe3O4 NPs with 4 to 13 nm diameters were obtained [64]. Later, Xu et al. found that by changing the heating conditions, and ratios of oleylamine and oleic acid, the size of Fe3O4 NPs can be tuned from 14 to 100 nm [67]. Recently, oleylamine was used as a multitasking agent, acting as a solvent, and reducing and surface functionalizing agents, to prepare monodispersed Fe3O4 NPs with a reasonably large magnetization value [68][69][70][71]. The experiment confirms that the presence of excess amount of oleylamine offers an adequately strong reductive environment for the Fe-precursor and leads to the formation of Fe3O4 NPs at a reasonably low temperature of 240 °C. Figure 6A shows the representative TEM micrographs of monodispersed Fe3O4 nanoparticles of size ranging from 6 to 24 nm, prepared by thermolysis of Iron(III) acetylacetonate in oleic acid and oleylamine. [71] These synthesis methods were also extended to formulate MFe2O4 (M = Co, Ni, and Mn) NPs. The size-dependent characteristics of MNPs are magnetization and blocking temperature, and their values increase with the increase of NPs size ( Figure 6). An inherent characteristic of superparamagnetic nanoparticles is that they possess a magnetically disordered spin structure at the The size-dependent characteristics of MNPs are magnetization and blocking temperature, and their values increase with the increase of NPs size ( Figure 6). An inherent characteristic of superparamagnetic nanoparticles is that they possess a magnetically disordered spin structure at the surface, because of the reduced exchange coupling between spins at the surface (due to the cations vacancy, ligands and high surface energy). Thus, magnetic nanoparticles are considered to be core-shell structures that are composed of a magnetically ordered core and a disordered shell that is known as spin canting/spin disorder [72,73]. The magnetization as a function of nanoparticles size 'd' and disordered surface layer thickness 't' is described as [74]. The size effect on the M S value has been observed in both ferrimagnetic and ferromagnetic nanoparticles. Figure 6B shows sharp increases of M S value with increase in the size of Fe 3 O 4 nanoparticles prepared via thermal decomposition of Fe-precursor. The calculated spin disorder layer thickness is around 0.2 to 0.5 nm. However, the surface spin disorder effect increases with decreasing the particle size due to the higher surface-to-volume ratio. Therefore, the M s value approaches to the bulk value (92 emu g −1 ) with the increase of Fe 3 O 4 NPs size [75]. and disordered surface layer thickness 't' is described as = [1 − (6 ⁄ )] [74]. The size effect on the MS value has been observed in both ferrimagnetic and ferromagnetic nanoparticles. Figure 6B shows sharp increases of MS value with increase in the size of Fe3O4 nanoparticles prepared via thermal decomposition of Fe-precursor. The calculated spin disorder layer thickness is around 0.2 to 0.5 nm. However, the surface spin disorder effect increases with decreasing the particle size due to the higher surface-to-volume ratio. Therefore, the Ms value approaches to the bulk value (92 emu g −1 ) with the increase of Fe3O4 NPs size [75]. The blocking behavior in MNPs is observed when the thermal energy (kBT) exceeds the anisotropy energy [Ea = KeffVsin 2 θ, where Keff is the sum of several terms such as magnetocrystalline anisotropy, shape anisotropy, surface anisotropy, and inter-particle coupling between nanoparticles]. Since anisotropy energy is directly proportional to the volume of the nanoparticles, the blocking temperature (TB) increases with the increase in the size of nanoparticles. The zero-field-cooled magnetization (MZFC) curves (at applied field 100 Oe) for the Fe3O4 nanoparticles are shown in Figure  6C. The obtained TB values for different sized Fe3O4 nanoparticles indicates a linear increasing trend of TB with the size of MNPs as shown in Figure 6D. The effective anisotropy constant can be calculated using the Neél law (TB = KeffV/25kB). The obtained Keff (1.1 × 10 6 to 1.5 × 10 4 J m −3 ) values are much larger than that The blocking behavior in MNPs is observed when the thermal energy (k B T) exceeds the anisotropy energy [E a = K eff Vsin 2 θ, where K eff is the sum of several terms such as magnetocrystalline anisotropy, shape anisotropy, surface anisotropy, and inter-particle coupling between nanoparticles]. Since anisotropy energy is directly proportional to the volume of the nanoparticles, the blocking temperature (T B ) increases with the increase in the size of nanoparticles. The zero-field-cooled magnetization (M ZFC ) curves (at applied field 100 Oe) for the Fe 3 O 4 nanoparticles are shown in Figure 6C. The obtained T B values for different sized Fe 3 O 4 nanoparticles indicates a linear increasing trend of T B with the size of MNPs as shown in Figure 6D. The effective anisotropy constant can be calculated using the Neél law (T B = K eff V/25k B ). The obtained K eff (1.1 × 10 6 to 1.5 × 10 4 J m −3 ) values are much larger than that for bulk magnetite (1.35 × 10 4 J m −3 ) [40]. The high K eff value is due to the surface anisotropy contribution from the disordered surface spins layer of the nanoparticles and interparticle interactions between neighbouring nanoparticles. The ZFC magnetization for the 20 and 24 nm sized Fe 3 O 4 NPs showed a sharp drop at 120 K. This is a characteristic transition of pristine magnetite phase, known as the Verwey transition. Below the Verwey transition temperature, the magnetic easy axis switches from the 111 to the 100 direction, which leads to the reduction of M ZFC . More importantly, the Verwey transition is extremely sensitive to oxidation, in fact it disappears when off-stoichiometry parameter δ, defined as Fe 3(1-δ) O 4 , is larger than 1% [79].
The Néel relaxation time and the Brownian relaxation time can be calculated using effective magnetic anisotropy constant (K eff ) and the hydrodynamic diameter, respectively. The obtained Brownian, Néel and effective relaxation times for MNPs are plotted as a function of size in Figure 6E. Note that the τ N value depends more strongly on the MNP size than the τ B value. Moreover, the τ N value can be further tuned by controlling the composition of MNPs. Above the superparamagnetic critical size limit, the Brownian relaxation dominates. As the τ B value is proportional to the V H of the particles, it can be increased by coating the MNPs with a long-chain surfactant molecule. The scaling relationship between magnetic properties and MNPs size is schematically illustrated in Figure 7. Since the hyperthermia heating efficiency is dependent on the M S and K eff of the MNPs, the size control synthesis of MNPs will result in enhanced hyperthermia effects for an optimum size.
contribution from the disordered surface spins layer of the nanoparticles and interparticle interactions between neighbouring nanoparticles. The ZFC magnetization for the 20 and 24 nm sized Fe3O4 NPs showed a sharp drop at 120 K. This is a characteristic transition of pristine magnetite phase, known as the Verwey transition. Below the Verwey transition temperature, the magnetic easy axis switches from the〈111〉to the〈100〉direction, which leads to the reduction of MZFC. More importantly, the Verwey transition is extremely sensitive to oxidation, in fact it disappears when off-stoichiometry parameter δ, defined as Fe3(1-δ)O4, is larger than 1% [79].
The Néel relaxation time and the Brownian relaxation time can be calculated using effective magnetic anisotropy constant (Keff) and the hydrodynamic diameter, respectively. The obtained Brownian, Néel and effective relaxation times for MNPs are plotted as a function of size in Figure 6E. Note that the τN value depends more strongly on the MNP size than the τB value. Moreover, the τN value can be further tuned by controlling the composition of MNPs. Above the superparamagnetic critical size limit, the Brownian relaxation dominates. As the τB value is proportional to the VH of the particles, it can be increased by coating the MNPs with a long-chain surfactant molecule. The scaling relationship between magnetic properties and MNPs size is schematically illustrated in Figure 7. Since the hyperthermia heating efficiency is dependent on the MS and Keff of the MNPs, the size control synthesis of MNPs will result in enhanced hyperthermia effects for an optimum size. It is known that according to linear response theory (LRT, Equation (10)), the SAR of superparamagnetic particles is proportional to the applied ACMF amplitude and frequency. Furthermore, the maximum absorption of magnetic energy occurs when the effective relaxation time of MNPs is close to the frequency of the applied ACMF (ωτ ≈ 1). This indicates that for a given ACMF frequency (ω = 2πf) there is an optimal size that resonates well with the applied ACMF. Figure 8A illustrates the size dependency of loss power for different MNPs [80]. As can be seen, the maximum value for heating efficiency occurs at the resonance condition when ωτ ≈ 1. Further, the relaxation time τ is inversely related to the effective magnetic anisotropy and is determined by the MNPs' structure. Thus, the critical size corresponding to the maximum loss power is smaller for high magnetic anisotropy materials such as FePt (206 kJ/m 3 ), Co (412 kJ/m 3 ), and Fe (48 kJ/m 3 ) compared to Fe3O4 (9 kJ/m 3 ). In the superparamagnetic regime, Vreeland et al. observed that for an ACMF of Hac = 36.5 kA/m and f = 341 kHz, the optimum size corresponding to maximum SAR is around 22 nm, which matches the theoretical prediction of the LRT ( Figure 8B) [81]. Moreover, the heating activity in superparamagnetic regime is mainly ascribed to the Néel relaxation and thus the optimum SAR is achieved at the resonance condition (ωτN ≈ 1). Most experimental studies on the size dependency of It is known that according to linear response theory (LRT, Equation (10)), the SAR of superparamagnetic particles is proportional to the applied ACMF amplitude and frequency. Furthermore, the maximum absorption of magnetic energy occurs when the effective relaxation time of MNPs is close to the frequency of the applied ACMF (ωτ ≈ 1). This indicates that for a given ACMF frequency (ω = 2πf ) there is an optimal size that resonates well with the applied ACMF. Figure 8A illustrates the size dependency of loss power for different MNPs [80]. As can be seen, the maximum value for heating efficiency occurs at the resonance condition when ωτ ≈ 1. Further, the relaxation time τ is inversely related to the effective magnetic anisotropy and is determined by the MNPs' structure. Thus, the critical size corresponding to the maximum loss power is smaller for high magnetic anisotropy materials such as FePt (206 kJ/m 3 ), Co (412 kJ/m 3 ), and Fe (48 kJ/m 3 ) compared to Fe 3 O 4 (9 kJ/m 3 ). In the superparamagnetic regime, Vreeland et al. observed that for an ACMF of H ac = 36.5 kA/m and f = 341 kHz, the optimum size corresponding to maximum SAR is around 22 nm, which matches the theoretical prediction of the LRT ( Figure 8B) [81]. Moreover, the heating activity in superparamagnetic regime is mainly ascribed to the Néel relaxation and thus the optimum SAR is achieved at the resonance condition (ωτ N ≈ 1). Most experimental studies on the size dependency of heating efficiency in the superparamagnetic regime reported that the maximum SAR can be achieved with iron oxide NPs of size ∼15 to 22 nm, depending on the ACMF amplitude and frequency [82][83][84][85][86]. heating efficiency in the superparamagnetic regime reported that the maximum SAR can be achieved with iron oxide NPs of size ∼15 to 22 nm, depending on the ACMF amplitude and frequency [82][83][84][85][86]. Nevertheless, the recent results are contradictory with the LRT model showing that some of the highest SAR values were observed in MNPs with particle size > 20 nm. Tong et.al have shown that both in the superparamagnetic and ferromagnetic regime the SAR values increased monotonically with nanocrystal size and the most dramatic increases by 50-fold occurred between 11 and 33 nm sized Fe3O4 nanoparticles [76]. In fact, the maximum SAR values attended are 1026 and 2560 W/g of Fe at 9.35 and 20.7 kA/m field strength, respectively for 40 nm Fe3O4 nanoparticles. A similar size  [71]. Figure 8C shows the relative heating performance of Fe 3 O 4 nanoparticles in the 3-32 nm size range measured under applied ACMF amplitudes of 184, 324, 491 and 625 Oe at a fixed frequency of 265 kHz. It can be seen from the figure that the SAR increases with the increase of nanoparticle size and attains a maximum value at a particle size of 28 nm, then the value decreases with further increase of the particles size. Remarkably, the increasing trend of the SAR has two different scenarios with respect to the MNPs size. The SAR value increases from 27-298 W/g of Fe 3 O 4 (with H ac = 625 Oe) with the increases of MNPs size from 3-16 nm and with further increase of the MNPs size it increases rapidly. The comparison between the LRT model prediction and the experimental SAR values ( Figure 8B) indicates that the LRT model is applicable only for MNPs size ≤ 16 nm (i.e., the superparamagnetic regime). In theory, increasing the MNPs size above 16 nm can suppress the susceptibility loss due to the particle moment blocking, and consequently the SAR should reduce. Instead, the SAR value increases sharply with the increase of MNPs size from 16-28 nm. The fast increase of the SAR (above 16 nm) values is due to the combined effect of susceptibility loss and hysteresis loss. In the ferromagnetic regime, the amount of dissipated heat as a result of hysteresis loss is proportional to the area under the hysteresis loop, which increases with the increase of MNPs size [87][88][89]. According to the dynamic hysteresis model, the quasi-static hysteresis loops change with the field strength and the frequency of the ACMF. In particular, the hysteresis loop enlarges with the frequency, the magnetic field ( Figure 8D) and MNPs size. The improvement of the hysteresis loop area results in the enhanced hysteresis loss in the larger sized MNPs.
To illustrate the potential applications of ferromagnetic MNPs in cancer treatment, Tong et al., tested 6, 19 and 40 nm MNPs on the mouse xenograft tumor model for glioblastoma multiforme (GBM) [76]. GBM is an aggressive and invasive brain cancer, thus surgical resection will be complicated. An alternative treatment strategy is local hyperthermia treatment. T 2 -weighted magnetic resonance (MR) images acquired before and after injection of MNPs (50 µg of Fe) display the sharp contrast of the tumor region (see Figure 8E). A more accurate dosimetry of the spatial temperature profiles during heating treatment are obtained by in vivo quantitative MR imaging of MNPs. Following imaging, the mice are exposed to an ACMF (9.35 kA/m, 325 kHz) for 1 h. The tumors injected with the 6 nm MNPs did not show a temperature increase compared to the control, whereas the 19 and 40 nm MNPs showed a temperature increase of 2.5 and 10.1 • C, respectively ( Figure 8F). The 40 nm MNPs are able to reach 43.4 ± 1.5 • C during the course of the treatment, which could be sufficient for many cancer thermal therapies. NPs, respectively [92]. Interestingly, the ZnFe 2 O 4 nanoparticles have saturation magnetization of 40 emu/g which indicates random magnetic ordering at the nanoscale (6 nm), which would otherwise be antiferromagnetic in the bulk regime [93]. Further, the M S values increase rapidly towards the bulk value as the nanoparticle size is increased. For example, the 2 nm MnFe 2 O 4 nanoparticles have an M S value of 39 emu/g, which increases to 86 emu/g (close to the magnetization value of 89 emu/g of bulk MnFe 2 O 4 ) [94,95] as the size is increased to 16 nm. This increasing trend in magnetization value is attributed to the decay in surface spin disorder effects with the increase of the particle size.

Composition Effects
The blocking behavior of MFe 2 O 4 NPs is also strongly related to the composition as the magnetocrystalline anisotropy varies with the spin-orbit coupling strength of M 2+ cations. Figure 9B shows the size dependence blocking behavior of MFe 2 O 4 NPs. The exchange coupled CoFe [92].  Figure 9C) [99,100]. The M S value of Fe 3 O 4 nanoparticles is 86 emu/g, and it is decreased to 82, 78 and 77 emu/g, respectively with the increase of Co 2+ ion concentration due to the smaller magnetic moment of Co 2+ (3µ B ) as compared to Fe 2+ (4µ B ) [91]. Figure 9D shows the typical variation of M S value with modulation of the Co and Zn content in Fe 3 O 4 nanoparticles. Interestingly, with the increasing Zn content in Zn x Fe 3-x O 4 (x from 0 to 0.6) nanoparticles, the M S value increases (from 84.5 to 91.9 emu/g) and a further increase of Zn content, the M S value sharply decreases. The initial increase in M S with increasing Zn content is believed to be due to the cation distribution among T d and O h -sites in the spinel structure. When the nonmagnetic Zn 2+ ion replaces the magnetic Fe 3+ ions in T d -site the net magnetic moment between O h and T d sites increases up to x = 0.6 [101]. A further increase of Zn content above 0.6 can partially replace the Fe 2+ ions and also impair the superexchange interaction between the magnetic ions at O h and T d sites, which causes a rapid decrease in the net magnetic moment.
Like the magnetic properties, the heating efficiency of MNPs is strongly related to the composition. In order to demonstrate the effect of composition on hyperthermia properties, we take Co x Fe 3−x O 4 nanoparticles as an example, since Co strongly alter the magnetic anisotropy. Figure 10A shows the variation of SAR values for Co x Fe 3−x O 4 nanoparticles of size 12 nm. The obtained SAR value of pure Fe 3 O 4 nanoparticles is 132 W/g at 265 kHz with an ACMF amplitude of 491 Oe and after being doped with Co 2+ ions, the heating efficiency is greatly improved to 534 W/g. Besides, with the increase of the ACMF amplitude from 184 to 491 Oe, the SAR values of Fe 3 O 4 and Co 0.5 Fe 2.5 O 4 nanoparticles increase from 81 to 132 W/g and 220 to 534 W/g, respectively. As discussed above, the substitution of Co ions leads to an increase in H C at the cost of lower saturation magnetization. However, as nanoparticles with high H C and moderate M S are found to be the best heating agents, the modification of the composition proved to be effective in maximizing the SAR. As can be seen in Figure 10B-D, the SAR values are related to the hysteresis loop area. When the applied field keeps increasing, the H C and hysteresis loop area rapidly increase and strongly enhance the SAR value. It is important to note that, the Co-doped Fe 3 O 4 NPs exhibit better heating activity compared to the pristine Fe 3 O 4 and CoFe 2 O 4 NPs prepared by a similar approach [97]. The effect of composition on the hyperthermia heating properties will be further discussed in the Section 3.4. Like the magnetic properties, the heating efficiency of MNPs is strongly related to the composition. In order to demonstrate the effect of composition on hyperthermia properties, we take CoxFe3−xO4 nanoparticles as an example, since Co strongly alter the magnetic anisotropy. Figure 10A shows the variation of SAR values for CoxFe3−xO4 nanoparticles of size 12 nm. The obtained SAR value of pure Fe3O4 nanoparticles is 132 W/g at 265 kHz with an ACMF amplitude of 491 Oe and after being doped with Co 2+ ions, the heating efficiency is greatly improved to 534 W/g. Besides, with the increase of the ACMF amplitude from 184 to 491 Oe, the SAR values of Fe3O4 and Co0.5Fe2.5O4 nanoparticles increase from 81 to 132 W/g and 220 to 534 W/g, respectively. As discussed above, the substitution of Co ions leads to an increase in HC at the cost of lower saturation magnetization. However, as nanoparticles with high HC and moderate MS are found to be the best heating agents, the modification of the composition proved to be effective in maximizing the SAR. As can be seen in Figure 10B-D, the SAR values are related to the hysteresis loop area. When the applied field keeps increasing, the HC and hysteresis loop area rapidly increase and strongly enhance the SAR value. It is important to note that, the Co-doped Fe3O4 NPs exhibit better heating activity compared to the pristine Fe3O4 and CoFe2O4 NPs prepared by a similar approach [97]. The effect of composition on the hyperthermia heating properties will be further discussed in the Section 3.4.

Shape Effects
Shape anisotropy is an extrinsic energy that comes from an induced demagnetizing field (Hd = -NdMS, where Nd is the demagnetizing factor determined by the shape) of a magnetized body. In the case of spherical morphology, the surface poles are distributed over the surface such that there are none at the equator and most are at the poles. Hence the demagnetizing field is Hd = -1/3MS and Nd = 1/3 (for sphere). While, in the case of anisotropic morphology, the distribution of surface poles

Shape Effects
Shape anisotropy is an extrinsic energy that comes from an induced demagnetizing field (H d = -N d M S , where N d is the demagnetizing factor determined by the shape) of a magnetized body. In the case of spherical morphology, the surface poles are distributed over the surface such that there are none at the equator and most are at the poles. Hence the demagnetizing field is H d = -1/3M S and N d = 1/3 (for sphere). While, in the case of anisotropic morphology, the distribution of surface poles depends on the direction of magnetization. For example, in a prolate ellipsoid that is magnetized parallel to the major axis c, the free poles are farther apart, hence, N c < 1/3 (as H d α 1/r 2 ). Similarly, if it is magnetized along axis a, the free poles are close to each other, hence, N a > 1/3. The general expression of shape anisotropy constant (K sh ) is K sh = M S 2 (N a -N c )/2 [35,103]. A predominant effect of shape anisotropy on stoichiometry, coercivity and M S values has been observed in different anisotropic magnetic nanostructures [104][105][106][107][108][109][110]. Recently, Fe 3 O 4 nanowires were synthesized via high-temperature reduction of α-FeOOH NWs in a fluidized bed reactor [111]. The removal of water molecules and the shearing of the oxide ion planes from AB to ABC stacking during phase transformation from the FeOOH to Fe 3 O 4 make these Fe 3 O 4 NWs porous ( Figure 11A,B) [112]. The magnetization curves for Fe 3 O 4 parallel to aligned NWs exhibited a M R of 0.51M S and H C of 583 Oe, respectively. When the samples were measured perpendicular to the alignment direction, remanence of M R = 0.30 M S was obtained, which indicates the influence of shape anisotropy [113,114]. A prominent effect of the MNPs shape on the surface anisotropy has also been observed in anisotropic-shaped nanoparticles. For example, the Verwey transition in Fe 3 O 4 is a structural phase transition that is observed in the smallest octahedral NPs (6 nm) but does not even occur in the bigger size spherical NPs (13 nm) ( Figure 12B,C) [68]. While the spherical-shape NPs shows the predictable superparamagnetic blocking behavior, which indicates the role of shape anisotropy on the stoichiometry. It is found that the facets of octahedral particles are consist of the most energetically stable [111] planes and the facets are protected against surface oxidation due to oleylamine coating. Thus, the surface anisotropy is significantly reduced, since the flat surface of the octahedron has fewer broken bonds and oxygen vacancies. A lower concentration of defects and almost no oxidized layer at the surface afford a better stoichiometry to the octahedral shape NPs and make the appearance of Verwey transition. In contrast, spherical NPs have highly disordered spins distributed across its outer surface which contribute to poor stoichiometry. As the Verwey transition is highly sensitive to stoichiometry, it is suppressed by the superparamagnetic blocking behavior.
The effect of shape anisotropy on ordering of surface atomic spins has also been well demonstrated by Cheon et al. [2]. Among a cube and a sphere with the same material volume and number of cations of Zn 0.4 Fe 2.6 O 4 nanoparticles, the cube has greater M S (165 emu/g (Fe+Zn) ) compared to that of the sphere (145 emu/g (Fe+Zn) ) ( Figure 12D). The cube has lower energy surface facets of family (100); in contrast, the surface of a spherical nanoparticle is constructed of different facets, which results in a larger surface spin disorder, hence higher surface anisotropy. A simulated result shows that the density of the disordered spins is higher in the sphere than in the cube ( Figure 12E,F). The images are color-mapped according to the angle of the spin deviation versus the external magnetic field, red indicates ordered spins and blue indicates highly disordered spins. The disordered spins in blue are dominant at the corners of the cube, while they are broadly distributed at the surface of the sphere. The shape effect has also been noticed in Fe 3 O 4 nanostructures of different shapes. The change in magnetization value with respect to shape and size of these nanostructures is summarized in Figure 12G. Among all these magnetic nanostructures, cube and octahedron exhibit enhanced M S values. The enhanced M S values are assumed to be due to anisotropic shape which lowers the surface spin disordered effect as explained in Zn 0.4 Fe 2.6 O 4 nanocubes case [2,68]. The M S value of the rods is 50-65 emu/g. The low M S value is attributed to the surface spin canting or surface organic defective layer of the nanorods. particles are consist of the most energetically stable [111] planes and the facets are protected against surface oxidation due to oleylamine coating. Thus, the surface anisotropy is significantly reduced, since the flat surface of the octahedron has fewer broken bonds and oxygen vacancies. A lower concentration of defects and almost no oxidized layer at the surface afford a better stoichiometry to the octahedral shape NPs and make the appearance of Verwey transition. In contrast, spherical NPs have highly disordered spins distributed across its outer surface which contribute to poor stoichiometry. As the Verwey transition is highly sensitive to stoichiometry, it is suppressed by the superparamagnetic blocking behavior. The effect of shape anisotropy on ordering of surface atomic spins has also been well demonstrated by Cheon et. al [2]. Among a cube and a sphere with the same material volume and number of cations of Zn0.4Fe2.6O4 nanoparticles, the cube has greater MS (165 emu/g(Fe+Zn)) compared to that of the sphere (145 emu/g(Fe+Zn)) ( Figure 12D). The cube has lower energy surface facets of family (100); in contrast, the surface of a spherical nanoparticle is constructed of different facets, which results in a larger surface spin disorder, hence higher surface anisotropy. A simulated result shows that the density of the disordered spins is higher in the sphere than in the cube ( Figure 12E and 12F). The images are color-mapped according to the angle of the spin deviation versus the external magnetic field, red indicates ordered spins and blue indicates highly disordered spins. The disordered spins in blue are dominant at the corners of the cube, while they are broadly distributed at the surface of the sphere. The shape effect has also been noticed in Fe3O4 nanostructures of different shapes. The change in magnetization value with respect to shape and size of these nanostructures is summarized in Figure 12G. Among all these magnetic nanostructures, cube and octahedron exhibit enhanced MS values. The enhanced MS values are assumed to be due to anisotropic shape which lowers the surface spin disordered effect as explained in Zn0.4Fe2.6O4 nanocubes case [2,68]. The MS value of the rods is 50-65 emu/g. The low MS value is attributed to the surface spin canting or surface organic defective layer of the nanorods.  [115], octahedrons (10 nm) [68], octopods [116] and rods [69] are obtained through thermolysis of iron salt. FC and ZFC magnetization curves of (B) spherical and (C) octahedral Fe3O4 nanoparticles at the applied field of 200 Oe [68]. (D) Room temperature M-H curves of cube and sphere-shaped Fe3O4 nanoparticles [2]. Simulated magnetic spin structures of (E) cube and (F) sphere. The color map indicates the degree of spin disorder in an external magnetic field, where red indicates ordered spins and blue indicates disorder spins. The right corners of parts E and F show their local surface spin arrangements [2]. (G) The variation of MS of different anisotropic Fe3O4 with increase of size [68,69,117].
From the above discussion, we have seen that magnetic properties, particularly the MS and magnetic anisotropy strongly varied with the shape of the MNPs. Based on the superior magnetic properties, these anisotropic nanoparticles have also been shown to be a better heating candidate compared to the spherical counterpart. Recently, a large improvement in SAR has been reported for cubes, octopods, octahedrons, plates and rods, as a result of their improved magnetic anisotropy. Taking into account the proven advantages of high-aspect-ratio Fe3O4 nanowires/nanorods over their spherical and cubic counterparts, such as larger surface area, enhanced blood circulation time, and prolonged retention in tumors, Das et. al demonstrated higher heating activity in Fe3O4 nanorods of  [115], octahedrons (10 nm) [68], octopods [116] and rods [69] are obtained through thermolysis of iron salt. FC and ZFC magnetization curves of (B) spherical and (C) octahedral From the above discussion, we have seen that magnetic properties, particularly the M S and magnetic anisotropy strongly varied with the shape of the MNPs. Based on the superior magnetic properties, these anisotropic nanoparticles have also been shown to be a better heating candidate compared to the spherical counterpart. Recently, a large improvement in SAR has been reported for cubes, octopods, octahedrons, plates and rods, as a result of their improved magnetic anisotropy. Taking into account the proven advantages of high-aspect-ratio Fe 3 O 4 nanowires/nanorods over their spherical and cubic counterparts, such as larger surface area, enhanced blood circulation time, and prolonged retention in tumors, Das et al. demonstrated higher heating activity in Fe 3 O 4 nanorods of aspect ratio from 6 to 11 [89]. Figure 13A shows a comparison between spherical and cubic NPs and compared their SAR values with those of the Fe 3 O 4 nanorods. Interestingly, the nanorods have higher SAR values than those obtained for the sphere and cube-shaped NPs, particularly in the high field region (>600 Oe). At 800 Oe the SAR value is 862 W/g for the nanorod, while it is only about 140 and 314 W/g for the spheres and cubes, respectively. The nanorods exhibit superior heating efficiency because of their larger K eff values, related with their shape anisotropy. Further, increasing the aspect ratio of the nanorods from 6 to 11 improves the SAR by 1.5 times.  From the above discussion we have already seen a higher heating activity for cubes than the spheres. For further understanding, Nemati et. al demonstrated a comparison between sphere and cube-shaped nanoparticles in a wide range of sizes, ∼10-100 nm ( Figure 13B) [118]. The spheres show negligible SAR for sizes less than 13 nm, but then sharply increases beginning near 26 nm until it reaches a broad maximum of ~650 W/g at 800 Oe around 52 nm. The very low SAR values observed by the small-sized nanospheres is related to their broader size distribution. However, for the cubeshaped NPs, the heating efficiency shows a very different trend; the size evolution of the SAR surprisingly increases at 30 nm up to ∼800 W/g at 800 Oe and then decays immediately with increasing size, reaching a minimum for the 42 nm cubes.

Effect of Interparticle Interactions
It is known that in concentrated particle systems the magnetic behavior of the particles is significantly influenced by interparticle interactions. The magnetic properties of such MNP systems are studied using a frozen state of ferrofluid where MNPs are dispersed in solvent or by embedding the MNPs in a solid matrix [43,[119][120][121]. Multiple studies report that the anisotropic-energy barrier in interacting nanoparticle systems increases with the increase of interparticle interaction, i.e. by decreasing the separation distance among the MNPs. Thus, the blocking temperature of strongly interacting MNP systems is higher than that in the corresponding isolated MNP system [122][123][124]. From the above discussion we have already seen a higher heating activity for cubes than the spheres. For further understanding, Nemati et al. demonstrated a comparison between sphere and cube-shaped nanoparticles in a wide range of sizes, ∼10-100 nm ( Figure 13B) [118]. The spheres show negligible SAR for sizes less than 13 nm, but then sharply increases beginning near 26 nm until it reaches a broad maximum of~650 W/g at 800 Oe around 52 nm. The very low SAR values observed by the small-sized nanospheres is related to their broader size distribution. However, for the cube-shaped NPs, the heating efficiency shows a very different trend; the size evolution of the SAR surprisingly increases at 30 nm up to ∼800 W/g at 800 Oe and then decays immediately with increasing size, reaching a minimum for the 42 nm cubes.

Effect of Interparticle Interactions
It is known that in concentrated particle systems the magnetic behavior of the particles is significantly influenced by interparticle interactions. The magnetic properties of such MNP systems are studied using a frozen state of ferrofluid where MNPs are dispersed in solvent or by embedding the MNPs in a solid matrix [43,[119][120][121]. Multiple studies report that the anisotropic-energy barrier in interacting nanoparticle systems increases with the increase of interparticle interaction, i.e., by decreasing the separation distance among the MNPs. Thus, the blocking temperature of strongly interacting MNP systems is higher than that in the corresponding isolated MNP system [122][123][124]. For example, Fe 3 O 4 /SiO 2 core-shell nanoparticles with different shell thicknesses ( Figure 14A-C) are prepared to understand the effect of interparticle interactions on the magnetic properties [125][126][127]. As the shell thickness decreases, the influence of interparticle dipolar interaction becomes apparent and quasi-magnetostatic states like superspin-glass (SSG) and super-ferromagnetic are observed. Figure 14D shows the temperature-dependent magnetization of Fe 3 O 4 /SiO 2 core-shell nanoparticles. With increasing the SiO 2 -shell thickness on the MNPs, the T B is lowered and the field-cooled magnetization (M FC ) at low temperature becomes pronounced. These features are particularly observed in conventional superparamagnetic NPs systems in which the interparticle interaction is negligible. In the most concentrated sample, L12, the M FC at low-temperature displays no increase but rather a slight decrease, which is a superspin-glass like behavior. The flat nature of M FC curves can be more prominent in dense nanoparticle assemblies. This cooperative magnetic behavior can also be described from the field dependence of M ZFC and M FC measurements. When the applied magnetic field increases, the superspin glass transition peak is prominent and changes to a plateau like shape as observed in 4 nm Fe 3 O 4 nanoparticle assemblies ( Figure 14E). Further, the temperature at which the irreversibility between M ZFC and M FC curves appears shifts towards lower values with the increases in magnetic field (5-500 Oe), a characteristic of spin-glass systems. observed in conventional superparamagnetic NPs systems in which the interparticle interaction is negligible. In the most concentrated sample, L12, the MFC at low-temperature displays no increase but rather a slight decrease, which is a superspin-glass like behavior. The flat nature of MFC curves can be more prominent in dense nanoparticle assemblies. This cooperative magnetic behavior can also be described from the field dependence of MZFC and MFC measurements. When the applied magnetic field increases, the superspin glass transition peak is prominent and changes to a plateau like shape as observed in 4 nm Fe3O4 nanoparticle assemblies ( Figure 14E). Further, the temperature at which the irreversibility between MZFC and MFC curves appears shifts towards lower values with the increases in magnetic field (5-500 Oe), a characteristic of spin-glass systems. The inter-particle interaction can become more pronounced in the case of nanoparticle assemblies, superlattices or aggregates. In fact, these secondary nanostructures (magnetic nanoparticle nano-assemblies, noted MNPAs), the dipolar coupling and exchange-coupling ( Figure  15A) between the neighboring nanocrystals can be comparable to the magnetic anisotropy energy. The inter-particle interaction can become more pronounced in the case of nanoparticle assemblies, superlattices or aggregates. In fact, these secondary nanostructures (magnetic nanoparticle nano-assemblies, noted MNPAs), the dipolar coupling and exchange-coupling ( Figure 15A) between the neighboring nanocrystals can be comparable to the magnetic anisotropy energy. Therefore, the energy barrier of individual nanoparticles is strongly impacted by exchange and dipolar interactions [70]. The increase in the energy of the barrier shifts the superparamagnetic blocking temperature of MNPAs to a higher temperature than that of the isolated nanoparticles. Moreover, the MNPAs also exhibits a phase transition, from a superparamagnetic state to a collective magnetic behavior at low temperature. The quasi-magnetostatics state is caused by the frustration of interparticle interactions that are induced due to randomness in nanoparticle positions and anisotropy-axes orientations. The collective behavior is called superspin-glass and has been recently observed in Fe 3 O 4 , γ-Fe 2 O 3 and CoFe 2 O 4 nanoparticle nano-assemblies [7,8,128]. For example, Lartigue et al. synthesized different sized nanoparticle assemblies (19.7, 22.2, 24.0, and 28.8 nm) of γ-Fe 2 O 3 nanoparticles (10 nm) using a single-step high-temperature hydrolysis approach ( Figure 15B,C) [24,25]. These MNPAs present a bulk-like M S value (80 emu/g for maghemite), while the 10 nm nanoparticles show a 30% reduction of M S value with respect to the bulk value ( Figure 15E). The susceptibility of the MNPAs is higher than that of the 10 nm nanoparticles and increases with the increase in the sizes of the MNPAs. The higher M S values in the case of the MNPAs is believed to be due to the existence of exchange interactions between the surface atoms of neighboring nanoparticles. The exchange-coupling between closely packed nanoparticles with different orientations of easy axes can certainly result in a rotation of the spin structure to an aligned ordered structure at the interface as shown in Figure 15A. The collective behavior of spins at the interface lowers the surface anisotropy and also results in high magnetic susceptibility ( Figure 15D). Further, in comparison to nanoparticles, a large increase in the blocking temperature by 150 K is observed for MNPAs ( Figure 15D). In addition, as expected the FC curve flattens out below T B . The M FC remains flat below T B , indicating the presence of a spin-glass-like state due to magnetic interactions among the nanoparticles within the assembled structure [8].  Figure 15B and 15C) [24,25]. These MNPAs present a bulk-like MS value (80 emu/g for maghemite), while the 10 nm nanoparticles show a 30% reduction of MS value with respect to the bulk value ( Figure 15E). The susceptibility of the MNPAs is higher than that of the 10 nm nanoparticles and increases with the increase in the sizes of the MNPAs. The higher MS values in the case of the MNPAs is believed to be due to the existence of exchange interactions between the surface atoms of neighboring nanoparticles. The exchange-coupling between closely packed nanoparticles with different orientations of easy axes can certainly result in a rotation of the spin structure to an aligned ordered structure at the interface as shown in Figure 15A. The collective behavior of spins at the interface lowers the surface anisotropy and also results in high magnetic susceptibility ( Figure 15D). Further, in comparison to nanoparticles, a large increase in the blocking temperature by 150 K is observed for MNPAs ( Figure 15D). In addition, as expected the FC curve flattens out below TB. The MFC remains flat below TB, indicating the presence of a spin-glass-like state due to magnetic interactions among the nanoparticles within the assembled structure [8]. Recently, the MNPAs, also named nanoflowers, nanocluster, and nanocrystal assemblies have shown good heating efficiency due to cooperative magnetism among nanocrystals within the multidomain nanostructure. Lartigue et. al demonstrated a comparison of heating performance of MNPAs (multi-core nanostructures) with the single-core nanoparticles [25]. Under field conditions of 29 kA/m Figure 15. (A) Schematic illustration of the supermoment structure and the intra-particle as well as inter-particle interactions in a nanoparticle assembly. Outermost light green color: Surfactant polymeric layer [70]. (B) TEM and (C) HR-TEM micrographs and Fourier transformation of flowerlike nanoparticles [24]. (D) Magnetization curves of 11 nm-sized nanoparticles synthesized via coprecipitation (green dotted line), 6 nm nanoparticles synthesized in diethylene glycol (black solid line) and 11 nm nanoparticle assemblies synthesized in a mixture of diethylene glycol and N-methyl diethanolamine (red dashed line). (E) ZFC-FC magnetization curves taken with an applied field of 50 Oe: 24 nm (cyan), 29 nm (blue)-sized nanoparticles assembly and 10 nm (red)-sized nanoparticles [25].
Recently, the MNPAs, also named nanoflowers, nanocluster, and nanocrystal assemblies have shown good heating efficiency due to cooperative magnetism among nanocrystals within the multi-domain nanostructure. Lartigue et al. demonstrated a comparison of heating performance of MNPAs (multi-core nanostructures) with the single-core nanoparticles [25]. Under field conditions of 29 kA/m and 520 kHz, the temperature increased at a rate of 1.04 • C/s for MNPAs, while that for single-core nanoparticles showed only 0.15 • C/s ( Figure 16A). Compared to the rest of the size-sorted multi-core nanostructures, the largest sized sample showed the highest SAR ( Figure 16B). More importantly, the SAR of the multi-core nanoparticles is much higher than that reported for single-core nanoparticles. In fact, they are among the best heating materials reported so far for iron oxide nanoparticles. A similar trend is also observed in  Figure 16C). The results from the magnetic characterization verify the enhancement of M S value with the increase of MNPAs size and the presence of collective magnetic dynamics, i.e., the collective Néel relaxation of nanocrystals within the assembly. Thus, the increase of SAR with MNPAs size is ascribed to the cooperative Néel relaxation and the high particle magnetic moment. An important composition effect has also been noticed in MFe 2 O 4 MNPAs. In contrast to CoFe 2 O 4 (high K eff ) and MnFe 2 O 4 (high M S ), the Fe 3 O 4 MNPAs have an exclusively high SAR value in all the size ranges ( Figure 16D). From the Section 2, we know that high K eff leads to a shift in the critical particle size associated with the maximum heating to a lower particle size value (as critical radius 'R 0 ' corresponding to maximum heating R 0 ∝ 1/K eff ). In this case, the calculated critical nanocrystal size corresponding to maximum SAR are 6, 15 and 27 nm for CoFe 2 Figure 16C). The results from the magnetic characterization verify the enhancement of MS value with the increase of MNPAs size and the presence of collective magnetic dynamics, i.e. the collective Néel relaxation of nanocrystals within the assembly. Thus, the increase of SAR with MNPAs size is ascribed to the cooperative Néel relaxation and the high particle magnetic moment. An important composition effect has also been noticed in MFe2O4 MNPAs. In contrast to CoFe2O4 (high Keff) and MnFe2O4 (high MS), the Fe3O4 MNPAs have an exclusively high SAR value in all the size ranges ( Figure 16D). From the Section 2, we know that high Keff leads to a shift in the critical particle size associated with the maximum heating to a lower particle size value (as critical radius 'R0' corresponding to maximum heating R0 ∝ 1/Keff  In order to demonstrate the efficacy of magnetic nanoparticles solution for cancer treatment, the hyperthermia heating properties of magnetic nanoparticles are measured in the cellular environment. The study demonstrated that irrespective of size, shape, and compositions of the magnetic nanoparticles, the heating activity rapidly dropped following the internalization [129]. More importantly, the SAR values in the cellular environments are half than those obtained in the solution. The low SAR values are related to the cellular confinement effect, which completely inhibited the  [25]. (B) SAR values as a function of the ACMF amplitude at frequency f = 520 kHz for multi-core 24 nm (cyan), multi-core 29 nm (blue), multi-core 22 nm (green), multi-core 20 nm (orange), and single-core 10 nm (red) [25]. (C) The SAR as a function of nanoassembly size of MFe 2 O 4 (M = Mn, Fe and Co) with nanocrystal size 4 nm [70]. (D) The SAR as a function of nanoassembly size of MFe 2 O 4 with variation of nanocrystal size from 6 to 21 nm [70].
In order to demonstrate the efficacy of magnetic nanoparticles solution for cancer treatment, the hyperthermia heating properties of magnetic nanoparticles are measured in the cellular environment. The study demonstrated that irrespective of size, shape, and compositions of the magnetic nanoparticles, the heating activity rapidly dropped following the internalization [129]. More importantly, the SAR values in the cellular environments are half than those obtained in the solution. The low SAR values are related to the cellular confinement effect, which completely inhibited the Brownian relaxation. In contrast to the superparamagnetic nanoparticles, the heating properties of ferromagnetic nanoparticles are significantly impacted after contact with cells. Despite the above issues, several research works have demonstrated that the nanoparticles morphology, magnetic and chemical property modification can address the above challenges [130][131][132][133].

Effects of Intraparticle Interactions
Exchange coupled core-shell nanoparticles with soft core (low anisotropy, high magnetization) and hard shell (high anisotropy) or vice versa is a prominent example of an intraparticle interacting system. The core-shell nanoparticles exhibit improved magnetic properties, but more importantly they produce an intermediate magnetic anisotropy and saturation magnetization compared to both the constituents ( Figure 17A) [124][125][126][127][128][129][130][131][132][133][134][135][136][137][138]. In the nanocomposite system, the magnetization of the soft magnetic phase is able to rotate coherently with that of the hard-magnetic phase, thus allowing us to utilize the advantages of soft and hard magnetic phases. From the above discussion we have noticed that the magnetic anisotropy, which plays a critical role in hyperthermia heating can be tuned by controlling the core-shell dimensions. Theoretical analysis discussed in the Section 2.2 confirmed that the SAR of superparamagnetic NPs could be optimized when the Keff will be in the range from 0.5 × 10 4 to 4.0 × 10 4 J/m 3 (i. e. the case of 2~ ), but the Ms factor must also be considered in attempting to maximize the SAR. To attain the right Keff Recently, the exchange-coupled core-shell nanoparticles have been explored to modulate magnetic properties of the spinel ferrite and have shown substantial importance in biomedical applications [139,140]. By picking cobalt ferrites and/or other soft magnetic ferrites as starting materials, a core-shell structure with distinctly controllable uniformity and size dimensions can be acquired. In a typical synthesis of CoFe 2 O 4 /MnFe 2 O 4 core-shell nanoparticles, the CoFe 2 O 4 NPs dispersed in hexane were injected into the mixture of MnCl 2 , Fe(acac) 3 , oleic acid and oleylamine [134]. The reaction was then refluxed at 365 • C for 1 h and MnFe 2 O 4 was overgrown onto the surface of the CoFe 2 O 4 seeds to form a core-shell structure. The same approach can be extended to synthesize other core-shell nanoparticles such as CoFe 2 O 4 /Fe 3 O 4 , CoFe 2 O 4 /ZnFe 2 O 4 and MnFe 2 O 4 /ZnFe 2 O 4 . The core-shell structures can be confirmed from the high-resolution TEM and electron energy-loss spectrum (EELS) mapping analysis as shown in Figure 17B-D. Figure 17D shows superimposed EELS mapped images of CoFe 2 O 4 /MnFe 2 O 4 nanoparticles. In this figure Co, Fe, and Mn are color-coded in green, red and blue respectively. While Co is present only in the core region of each nanoparticle, Fe is distributed throughout the nanoparticle, and Mn only on the shell. The exchange-coupled magnetism is confirmed from the enhanced coercivity and magnetic anisotropy values. At  core-shell NPs with a core diameter of 6 nm, and the shell thickness can be precisely controlled from 0.5 to 3 nm [139]. The relationship of the shell thickness with the blocking temperature and the coercivity of MnFe 2 O 4 /CoFe 2 O 4 core-shell nanoparticles with changing the shell thickness from 0.5 to 3 nm are shown in Figure 17E,F. The blocking temperature and coercivity in the core-shell nanoparticles increase as the shell thickness increases.
From the above discussion we have noticed that the magnetic anisotropy, which plays a critical role in hyperthermia heating can be tuned by controlling the core-shell dimensions. Theoretical analysis discussed in the Section 2.2 confirmed that the SAR of superparamagnetic NPs could be optimized when the K eff will be in the range from 0.5 × 10 4 to 4.0 × 10 4 J/m 3 ( i.e., the case of 2π f ∼ τ −1 ), but the M s factor must also be considered in attempting to maximize the SAR. To attain the right K eff and M S combination, the exchange-coupled core-shell nanoparticles of hard/soft magnetic ferrites are important. A typical example is the core/shell nanoparticles composed of magnetically hard CoFe 2 O 4 (K = 2 × 10 5 J/m 3 ) core and magnetically soft MnFe 2 O 4 shell (K = 3 × 10 3 J/m 3 ) [31]. The exchange coupled CoFe 2 O 4 /MnFe 2 O 4 nanoparticles (~15 nm in size) preserved the superparamagnetism at room temperature and showed a K eff of 1.5 × 10 4 J/m 3 , which is in the best possible K eff range. As a result, the core/shell nanoparticles exhibited 5 times higher SAR value of 2280 W/g of magnetic elements compared to single component NPs (443 W/g for the CoFe 2 O 4 NPs and 411 W/g for the MnFe 2 O 4 NPs) in an ACMF of H ac = 37.3 kA/m and f = 500 kHz ( Figure 18A). In addition, the SAR values can be tuned by varying the combination of the core and shell components as shown in Figure 18B,C. The magnetic coupling of core and shell components provides K eff values of ∼1.5 × 10 4 to 2.0 × 10 4 J/m 3 , which fits in the optimal K eff range. Interestingly, the Zn 0.4 Co 0.6 Fe 2 O 4 /Zn 0.4 Mn 0.6 Fe 2 O 4 NPs show an extremely high M S of 150 emu/g of magnetic elements and when used for hyperthermia heating it shows SAR around 3886 W/g of magnetic elements. This is 1.7 times greater than that for CoFe 2 O 4 /MnFe 2 O 4 and 34 times larger than that for Feridex, the commercial iron-oxide magnetic nanoparticle (115 W/g). While the SAR values of core-shell nanoparticles are comparable to those of ferromagnetic and anisotropic nanoparticles, the advantage of core-shell nanoparticles over the latter's is that they exhibit superparamagnetism at room temperature, an important property for the clinical applications.
The in vivo hyperthermia treatment is performed by injecting 75 µg of the CoFe 2 O 4 /MnFe 2 O 4 core/shell nanoparticles into the U87MG human brain cancer cells in mice and then applying the ACMF for 10 min. The tumor volume continuously shrinks with time, which is noticed for the core/shell NPs ( Figure 18D). In fact, the tumor is eliminated after an 18 days hyperthermia treatment with the formulated core/shell NPs solution. While, the tumors volume did not shrink by using Feridex (commercial ferrofluid), or chemotherapeutic doxorubicin cancer drug under the similar treatments, but displayed growth behavior like the untreated control ( Figure 18E). In short, these core-shell ferrites can be an effective new nanoscale tool beneficial for a variety of systems that rely on heat induction, including hyperthermia therapy and other advanced nanobiotechnology applications such as on-demand drug release and thermal activation of metabolic pathways within a single cell.
The in vivo hyperthermia treatment is performed by injecting 75 μg of the CoFe2O4/MnFe2O4 core/shell nanoparticles into the U87MG human brain cancer cells in mice and then applying the ACMF for 10 min. The tumor volume continuously shrinks with time, which is noticed for the core/shell NPs ( Figure 18D). In fact, the tumor is eliminated after an 18 days hyperthermia treatment with the formulated core/shell NPs solution. While, the tumors volume did not shrink by using Feridex (commercial ferrofluid), or chemotherapeutic doxorubicin cancer drug under the similar treatments, but displayed growth behavior like the untreated control ( Figure 18E). In short, these core-shell ferrites can be an effective new nanoscale tool beneficial for a variety of systems that rely on heat induction, including hyperthermia therapy and other advanced nanobiotechnology applications such as on-demand drug release and thermal activation of metabolic pathways within a single cell.

Conclusions
In this review, the close correlations are discussed between the ferrite nanoparticles properties (magnetic and morphological) and the hyperthermia performance. The size, composition, shape, inter-particle interaction and inter-phase exchange coupling are utilized to tune the magnetic properties and consequently the heating performance of MNPs. The control over size from a nanometer to a submicron length scale and incorporation of different transition metal ions lead to the improvement of magnetic properties (M S and K eff ). The size dependence of magnetic and inductive heating properties reveals that the large size Fe 3 O 4 nanoparticles (>16 nm) are in ferromagnetic regime which gives extremely high SAR value above 800 W/g. Alternatively, the M S and H C are improved by introducing the shape anisotropy. Particularly, the iron oxide nanorods and nanocubes exhibit unprecedented heating ability compared to spherical nanoparticles of equivalent material volume. Besides, the collective magnetic response is achieved by modifying interaction strength between the nanoparticles. The nanostructures composed of number of magnetic domains such as, superlattice, nanoflowers and nanocrystal assemblies have also demonstrated efficient heating effect due to the cooperative magnetism among nanocrystals. Hard and soft ferrite core-shell architecture with strong exchange coupling optimizes K eff to an intermediate value of the soft and hard ferrites. The intermediate K eff value makes the nanoparticles relax with a frequency of ACMF, which enhances the SAR value to a surprisingly high value of 3886 W/g of magnetic elements. The prominently high SAR values obtained via optimization of magnetic performance demonstrate the promising future of iron oxide nanoparticles for biomedical applications. Nevertheless, a long-term stability, toxicological impact, site-specific internalization and metabolism of the magnetic nanoparticles are still open questions and more extensive research is needed. Finally, new types of smart magnetic nanoparticles with multifunctional properties are still needed for cancer theranostics. A reproducible and large-scale synthesis approach of magnetic nanoparticles also needs to be established for the industry perspective. Although the described magnetic nanoparticles are functionalized with a suitable surfactant for the hyperthermia application, but it can also be further functionalized or decorated with various functional materials such as targeting molecules, biomarker/quantum dots, radioisotopes and drugs. The multifunctional magnetic nanoparticles will facilitate early diagnosis with multimodal imaging and simultaneous therapy.