Observation of magnetic vortex configuration in non-stoichiometric Fe3O4 nanospheres

Observation of magnetic vortex configuration in non-stoichiometric Fe 3 O 4 nanospheres† Gopal Niraula, ab Denilson Toneto, c Gerardo F. Goya, d Giorgio Zoppellaro, e Jose A. H. Coaquira, b Diego Muraca, f Juliano C. Denardin,* g Trevor P. Almeida, h Marcelo Knobel, f Ahmad I. Ayesh * i and Surender K. Sharma * ja Theoretical and micromagnetic simulation studies of magnetic nanospheres with vortex configurations suggest that such nanostructured materials have technological advantages over conventional nanosystems for applications based on high-power-rate absorption and subsequent emission. However, full experimental evidence of magnetic vortex configurations in spheres of submicrometer size is still lacking. Here, we report the microwave irradiation fabrication of Fe 3 O 4 nanospheres and establish their magnetic vortex configuration based on experimental results, theoretical analysis, and micromagnetic simulations. Detailed magnetic and electrical measurements, together with Mössbauer spectroscopy data, provide evidence of a loss of stoichiometry in vortex nanospheres owing to the presence of a surface oxide layer, defects, and a higher concentration of cation vacancies. The results indicate that the magnetic vortex spin configuration can be established in bulk spherical magnetite materials. This study provides crucial information that can aid the synthesis of magnetic nanospheres with magnetically tailored properties; consequently, they may be promising candidates for future technological applications based on three-dimensional magnetic vortex structures. 1. Introduction The existence of a magnetic vortex state, consisting of noncollinear spin conguration and in-plane curling, enables negligible remanent magnetization at low elds with high magnetization at high elds in magnetic nanoparticles (MNPs). The intrinsic stability, topology-driven dynamics, and more interestingly the switching eld-dependent electrical and magnetic properties (widely known as “on/off”switching property) offer a great opportunity to practice in industrial technology, from quantum computing to biomedical applications. 1–11 Many studies have reported the dimensionbased vortex nanostructures in magnetic-oxide MNPs with controlled shape and size, in a variety of morphologies such as ellipsoids, 12 cubes, 13,14 disks/dots, 5,6,8,15,16 and rings. 17,18 The three-dimensional (3D) vortex structure in MNPs with sizes of several hundred nanometers (i.e., above the single-domain size limit of most materials) allows manipulation of unusual noncollinear spin-textures, their electrical, magnetic, mechanical, and thermal properties comprising the crucial physical properties such as topology, geometry, vorticity and chirality. Interestingly, the 3D magnetic nano-/microstructure nds use in several areas from digital nanotechnology to cellular mechanobiology such as in sensing, giant data storage, magnetic random access memory technology, and actuation in the presence of magnetic eld. 5,19–29 Thus, an in-depth understanding of those physical properties is very important in the 3D structural arrangement at the sub-nanoscale level. Therefore, the 3D magnetic structure may serve as a great tool to respond/tackle the many unanswered questions and explore new research directions in an unprecedented way. Recently, theoretical and simulation studies were reported for 3D magnetic nanospheres where the vortex magnetic structure of a Department of Physics, Federal University of Maranhao, Sao Luis, 65080-805, Brazil. E-mail: [email protected] b Laboratory of Magnetic Materials, NFA, Institute of Physics, University of Brasilia, Brasilia 70910-900, Brazil c Universidad Central de Chile, 8330601 Santiago, Chile d Instituto de Nanociencia y Materiales de Arag´ on (INMA), Universidad de Zaragoza, 50018, Zaragoza, Spain e Regional Centre of Advanced Technologies and Materials, Palacky University in Olomouc, Slechtitelu 27, 77900 Olomouc, Czech Republic f Institute of Physics “Gleb Wataghin”(IFGW), University of Campinas (Unicamp), Campinas, SP, Brazil g Universidad de Santiago de Chile (USACH), CEDENNA and Departamento de F´ ısica, Santiago 9170124, Chile. E-mail: [email protected] h SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK i Physics Program, Department of Math., Stat. and Physics, College of Arts and Sciences, Qatar University, P. O. Box 2713, Doha, Qatar j Department of Physics, Central University of Punjab, Bathinda, 151401, India †Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3na00433c Cite this: Nanoscale Adv.,2023,5,5015 Received 20th June 2023 Accepted 14th August 2023 DOI: 10.1039/d3na00433c rsc.li/nanoscale-advances © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Adv.,2023,5,5015–5028 | 5015 Nanoscale Advances PAPER Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online View Journal | View Issue thecoreexhibitedauniqueprecessionmotionnearbythe direction of an externally applied static eld. 30–32 This unique vortex-core reversal behavior and its dependence on the frequency of the applied AC magnetic eld allowed large power absorption values, 30–32 making them appealing for potential application in bio-diagnostics and magnetic hyperthermia, 33 for example. While these studies have provided robust analytical and computational information on vortex nanospheres, there are not yet extensive reports on the successful production of ironoxide vortex nanospheres, which is the obvious step to validate experimentally the theoretical models and hence the signicant relevance of achieving the successful synthesis of such nanospheres with magnetic vortex conguration. The magnetic vortex state in materials with diverse sizes and shapes studied so far appeared in stoichiometric magnetite (bulk). 34–37 It is essential to obtain the materials properties in bulk to achieve effective performance in practical applications. Oen, the nanoparticles exhibit a bulk property if they preserve their stoichiometry, which depends on several factors like shape, size, surface defects, charge ordering, cation vacancies, etc. 6,38,39 Indeed, in magnetite, stoichiometry is strongly associated with a Verwey transition, which is essential for its potential applications in spintronics, sensors, energy conversion devices, and biomedical purposes. 40 The Verwey transition (T V )near120K, also called the metal-to-insulator transition, arises as a result of the charge order–disorder of Fe 2+ and Fe 3+ that leads to sharp changes in the electric, magnetic, and structural properties. 41,42 Particularly, the change in the unit cell structure from inversecubic-spinel to monoclinic, increase in resistance and sharp fall of magnetization below T V directly affect the efficacy of nanoparticles and limit prospective applications. 40 The absence of the Verwey transition directly leads to the loss of stoichiometry inuenced by several external factors, such as size, shape, growth during synthesis, defects, thermal treatment, etc. 43,44 It is well known that the Verwey transition is size-/shape-dependent, usually appears in larger nanoparticles in the range of blocked single domain/ferromagnetic particles and gets suppressed in the superparamagnetic range (precisely for particles smaller than 20 nm) and completely disappears for particle sizes below 6nm. 39,40,45 Despite the great experimental effort, however, the existence of ionic-charge ordering below the Verwey transition, surface defects, cation vacancies, and contribution of size/shape to the loss of stoichiometry in large-scale sphere magnetite still remains mysterious and under debate. 46,47 This paper reports for the rst time the microwave-assisted hydrothermal (MAH) synthesis route for Fe 3 O 4 nanospheres and examines their magnetic vortex-spin conguration by means of experiments, theoretical analysis, and micromagnetic simulation. Later, the role of surface defects and cation vacancies in the loss of stoichiometry (non-stoichiometric) in as-prepared magnetic vortex nanospheres is presented and discussed. 2. Materials/methods 2.1 Synthesis procedure The a-Fe 2 O 3 long ellipsoidal rods (LERs), short ellipsoidal rods (SERs) and nanospheres (NSs) were prepared by a microwaveassisted hydrothermal reaction of iron chloride (FeCl 3 )withthe addition of sodium phosphate (NaH 2 PO 4 ) and sodium sulfate (Na 2 SO 4 ) as additives to control the shape and morphology. Briey, 0.06 mol L −1 (∼370 mg) of FeCl 3 and 35 mL of distilled water were stirred for 15-20 minutes. The additives NaH 2 PO 4 and Na 2 SO 4 were mixed with 3 mL of distilled water separately and nally mixed with FeCl 3 solution to make a mixture of a nal volume of 38 mL; the concentrations of NaH 2 PO 4 solution were 2.7 ×10 −4 mol L −1 ,5.4×10 −4 mol L −1 ,molL −1 and 4.32 × 10 −3 mol L −1 , and that of Na 2 SO 4 $10H 2 O solution was 1.65 × 10 −3 mol L −1 .Aer vigorous stirring for 10 minutes, the mixture was transferred into a reaction vessel in a Synth's microwave reactor, with an output power of 1000 W. The working cycle of the microwave reactor was set as (i) 20 °C minutes −1 rapid heating until 200 °C from room temperature, and (ii) 60 minutes at 220 ° C. The system was then allowed to cool down to room temperature, and the nal material was centrifuged and washed with excess distilled water and absolute ethanol and dried ina vacuum oven at 50 °C. In this way, we have obtained ∼300 mg of a-Fe 2 O 3 nanoparticles. Fe 3 O 4 nanoparticles were obtained via a reduction process from the prepared a-Fe 2 O 3 .Thedrieda-Fe 2 O 3 powders were annealed in a tube furnace at 550 °C for 6 hours under a continuous hydrogen/argon gas ow [H 2 /(H 2 + Ar)), 4/100]. The furnace was then cooled down to room temperature while kept under a continuous H 2 gas ow. As compared with the starting materials of a-Fe 2 O 3 , the size, shape and morphology of Fe 3 O 4 nanostructures were well preserved aer the reduction process. The controlled conversion of a-Fe 2 O 3 to Fe 3 O 4 is not an easy task because it depends on several physio-chemical factors such as concentration of Fe 3+ , annealing temperatures, time, gas- ow rate, concentration of H 2 gas, and amount of phosphate anions. Usually, thermal reductions are performed using a mixture of trioctylamine (TOA) and oleic acid (OA) in order to avoid the coalescence of bare NPs as reported elsewhere. 8 However, in the present work, the size, phase and morphology without any addition of surfactants during the thermal reduction process. 2.2 Spectroscopic and magnetic characterization 2.2.1. X-ray powder diffraction. X-ray powder diffraction (XRPD) of the as-prepared materials was performed on a Bruker diffractometer (Bruker D8 Advance) using CuK a1 radiation (l= 1.5406 Å) and a LynxEye linear detector. Data were obtained in the 15° #2q#85° range with 0.02° step size. The XRD patterns were rened using the Rietveld renement method through TOPAS [Bruker AXS (2008): TOPAS V4: General prole and structure analysis soware for powder diffraction data.–User's Manual, Bruker AXS, Karlsruhe, Germany] soware. 2.2.2. Electron microscopy. The morphology of the samples was investigated by using a JEOL 7100FT eld emission scanning electron microscope (FESEM, 1.2 nm resolution, operated at 10–30 kV). The high-resolution transmission electron microscopy (HRTEM) was performed on a JEOL 2100F instrument using an accelerating voltage of 200 kV. The Lorentz microscopy was performed on a Thermo Fisher Tecnai T20 under eld-free conditions. A focal series of Fresnel contrast 5016 |Nanoscale Adv.,2023,5,5015–5028 © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Advances Paper Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online images were recorded at −1.5 mm underfocus, at focus and at +1.5 mm overfocus (Fig. S6†). A digital micrograph (DM) script was used to reconstruct the phase using the transport of intensity equation (TIE). The magnetic contribution to the phase was isolated by physically ipping the sample outside the microscope and image alignment/rotation was performed to calculate the differences in phase (ESI S6†). 2.2.3. Fourier transform infrared spectroscopy. A Fourier transform infrared (FT-IR) spectrometer (Bruker, model Tensor 27), equipped with an attenuated total reectance (ATR) accessory, was used to identify functional groups present in the nanoparticles. 2.2.4. Mössbauer spectroscopy. Room temperature 57 Fe Mössbauer spectra were taken in transmission geometry using a constant acceleration-type spectrometer with a 57 Co in Rh source also kept at room temperature. Calibration of the spectra was performed by using iron foil. The spectra were tted using the NORMOS soware. 2.2.5. Magnetometry. Magnetization measurements were carried out on a vibrating sample magnetometer superconducting quantum interference device (VSM-SQUID) (MPMS Quantum Design) under magnetic elds up to ±70 kOe, at temperatures from 5 K to 300 K. Zero-eld-cooled (ZFC)/eldcooled (FC) curves were obtained in the temperature range 5 K to 350 K. Both ZFC and FC data were collected while heating the samples, under a cooling eld H FC =50 Oe. M vs. H (hysteresis) data were obtained at different temperatures 5 K # T#300 K, in applied elds up to 70 kOe. 2.2.6. Electrical resistivity measurement. The pellets of iron oxide NPs were prepared and placed in an oxygen environment at a temperature of 60 °C for 24 hours inside the furnace. Once the sample was removed from the furnace, a copper wire was used to make contact between NPs and the insulator attached to the sample holder as shown in ESI S9.†In this four-probe method, the two contacts were made to pass the current across the NPs and the other two contacts were made to measure the voltage drop across them. The sample was xed in the cryostat; the cryostat was joined to a rotary pump to achieve a pressure of 10 −6 mbar and to a sensor of the digital thermometer (resistance to temperature detection RTD) near the sample position. A current was applied to the sample by a current source D.C power supply type (Keithley model 6220 precision current source); the voltage drop was measured by using a Keithley model 2182A nanovoltmeter. In addition, the temperature was recorded by using a temperature controller (LakeShore DRC-91CA). Further, the voltmeter and ammeter were connected to the cryostat through several connection boxes where the instruments were controlled through a LabView program. 2.2.7. Micromagnetic simulations. The micromagnetic simulations were performed using the Mumax 3.9 package. The MuMax3 is an open-source GPU-accelerated micromagnetic simulation program which solves the timeand spacedependent magnetization evolution in nano-to micro-scale magnets using a nite-difference discretization. Its high performance and low memory requirements allow for largescale simulations to be performed in a limited time and on inexpensive hardware. 48 In this package, the time evolution of magnetization distribution is obtained by solving the well known Landau–Lifshitz–Gilbert–Langevin equation. 49 The magnetic parameters of Fe 3 O 4 used in the micromagnetic simulation were as follows: saturation magnetization M S =480 emu cc −1 , exchange stiffness constant A=1.2 ×10 −6 erg cm −1 , magneto crystalline anisotropy constant K 1 =−1.35 ×10 5 erg cc −1 ,K 2 =−0.44 ×10 5 erg cc −1 . The cell size was assumed to be 5 nm and the Gilbert damping coefficient was set to a=0.5. 50,51 2.2.7.1 Construction of the phase diagram. We started investigating the lower energy congurations in the case of NSs of diameter ‘D’. The system was relaxed to a local energy minimum and the nal spin conguration and the lower energy states in NSs were studied. Thereaer, we compared the energy of each nal conguration, and the one with a lower energy value was selected as the ground state. This process was repeated for several diameters and the phase diagrams as a function of energy ‘E tot ’and diameter ‘d’were constructed. In this case, two idealized characteristic congurations have been evaluated: (i) a single domain state and (ii) a vortex state. 2.2.8. Theoretical approach to calculate the total energy in spherical particles. The topological magnetic vortex state in materials exists only when the particle size is greater than the exchange length, L ex . The total energy (E tot ) is dominated by exchange energy, i.e., the magnetostatic energy is almost assumed to be zero. The exchange energy of the vortex area/ region of spherical particles is Ev A¼ Js2ls 2R2ln b Rv 2mO (1) The anisotropy energy of the vortex area in the case of uniaxial anisotropy in the (x,y) plane Ev A¼ K1Vv(1þð34ln2Þb Rv2) 2(2) where V v =2pR v2 Ris the volume of the vortex region in NSs since the vortex evolves in the cylindrical form. Further, the stray eld energy of the vortex area can be written for the case R>l s Ev s¼ 2pJs2b3(0:083 ln 2 1 22b R) mO (3) Here, R v is the radius of the vortex region and b=R v /2 is the radius of the vortex core obtained by minimizing the total energy of the vortex region for somagnetic materials. 52 b¼0:68lsR ls0:33 (4) The energy of the curling region (volume V curl ) is composed of exchange energy (E Ac ) and magnetocrystalline energy (E Kc ) and is given as © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Adv.,2023,5,5015–5028 | 5017 Paper Nanoscale Advances Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online Ec A¼4pAR ln 2R Rv Ec K¼KVc 2(5) where Vc¼4 3pR32pRv2Ris the volume of the curling region. 3. Results and discussion Based on both recent reports and our own studies, 17,53 we used phosphate anions for the shape-controlled synthesis of nanospheres (NSs). The complete synthesis process of dened aFe 2 O 3 MNPs and their controlled conversion into Fe 3 O 4 are provided above in Section 2.1 as well as in the ESI S1–S3.†The morphological changes of the as-prepared nanoparticles, from long ellipsoidal rods (LERs), short ellipsoidal rods (SERs) to nanospheres (NSs) with the decrease in the ratio of iron(III)to phosphate anions are shown schematically in Fig. 1a and their corresponding FESEM Fig. 1b–d. It is observed that when the ratio of iron(III) to phosphate anions is reduced by one half; LERs shortened their length, resulting in SERs which are further converted into NSs because of the reduced ratio of iron(III) to phosphate anions by 20 times. The size distribution of the obtained NSs (ESI S2†) could be tted with a Gaussian distribution yielding an average diameter <d>=700 ±122 nm. The HRTEM images of the NSs (Fig. 1e) revealed lattice spacing of 0.251 nm and 0.210 nm, respectively, which corresponds to the lattice spacing of (311) and (400) planes of inverse spinel Fe 3 O 4 . 54 The fast Fourier transform (FFT) pattern reects the polycrystalline nature of NSs. Fig. 1f shows the XRD pattern of the Fe 3 O 4 LERs, SERs, and NS reaction products along with their Rietveld analysis. It is found that both LERs and SERs contain the mixed phase of Fe 3 O 4 and metallic iron (Fe 0 ) whereas NSs are pure Fe 3 O 4 . All the diffraction peaks are indexed readily according to a cubic spinel phase (space group: Fd 3mwith JCPDS No. 19-0629, a=b=c=8.37 Å) and the XRD Rietveld tted data are given in the ESI (Table 1).† The characteristic FTIR peaks between 600 cm −1 and 400 cm −1 observed in LERs, SERs and NS samples (ESI S3†) correspond to the a-Fe 2 O 3 and Fe 3 O 4 phases, with the absorption band at 545 cm −1 assigned to vibrational modes of Fe 3 O 4 .A second characteristic peak detected at 976 cm −1 is consistent with phosphate (PO 43− ) anions with typical wavenumbers within the 950–1200 cm −1 range. 55 A very sharp peak emerges in the NS sample suggesting that a high concentration of phosphate groups are trapped on the nanoparticle surfaces. Fig. 2a shows a schematic of the vortex structure simulated for NSs with a cross-section drawing (Fig. 2c) showing the internal vortex orientation, as inferred from the simulations of Fig. 1 (a) Schematic of the formation process of nanospheres (NS) through reduction in PO 43− concentration compared to the LERs and SERs; (b–d) FESEM image of reduced LERs, SERs, and NSs, respectively; (e) HRTEM images of NSs, and (f) XRD patterns with their Rietveld analysis. 5018 |Nanoscale Adv.,2023,5,5015–5028 © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Advances Paper Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online the spin congurations as shown in Fig. 2b. The size of the NSs is ∼700 nm in diameter, which is above the single-domain region, i.e., one can predict that it belongs to a vortex region that avoids the singularity point of the exchange energy. Based on Fig. 2b and c, we assumed that the NSs consist of two-region curling-in-plane (x–yplane) and vortex-out-of-plane (z-axis). It is interesting to note in Fig. 2c, and its corresponding simulated spin-conguration highlighted by red and yellow colors, that the vortex region is formed in the shape of solid rods/cylindrical disks of radius R v and height. Note that in the case of spheres, the simulations did not provide a vortex conguration in the whole particle volume, because of the aspect ratio (diameter/ height) being close to 1. Rather, it creates a vortex-core region (R v ) within a limited cylindrical volume having the sphere diameter's height but a smaller internal cylinder radius and thus the vortex evolved as a cylindrical/rod shape (Fig. 2b and ESI S5†). This vortex region stabilizes the core of radius b, which exhibited the out-of-plane magnetization under the application of a magnetic eld, i.e., magnetization has a non-zero component perpendicular to the plane of the vortex region (i.e., cylindrical disks). Within the vortex, core spins are aligned along the z-direction perpendicular to the in-plane circulating magnetizations (ESI S5†). Furthermore, in principle, the spin conguration within the vortex region should exhibit out-ofplane magnetization; from the simulated spin conguration (Fig. 2c); however, the region in between R v and bcan be considered as a transition domain from out-of-plane to inplane. This transition region is important in terms of change-inenergy (energy transition) from vortex to single-domain, which destroys the vortex state in NSs to the SD state. Overall, Fig. 2 indicates that the NS magnetic structure is described by a vortex-spin conguration with an unusual hysteresis loop, which needs to be investigated experimentally. The vortex conguration in submicrometric ferromagnetic nanoparticles can be experimentally visualized by imaging techniques such as electron holography/tomography and magnetic force microscopy (MFM) techniques. 13,56–61 Additionally, the transport of intensity equation (TIE)-based phase reconstruction through the Fresnel-contrast imaging technique in Lorentz transmission electron microscopy (LTEM) has been extensively used to examine the vortex behavior in magnetic NPs. 62–64 We used the TIE phase reconstruction method to examine the vortex conguration in NSs, by considering its advantages compared to off-axis electron holography since it doesn't require the region of interest to be near vacuum. Moreover, such an approach preserves the original magnetic properties of the system under analysis and allows a larger eld of view than typically found in off-axis electron holography. 63,65,66 The experimental setup for studying magnetic Fig. 2 Schematic representation of the micromagnetic simulations for the spin configuration in NSs (a and b) and the corresponding crosssectioned hemisphere (c) showing the curling vortex internal state. © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Adv.,2023,5,5015–5028 | 5019 Paper Nanoscale Advances Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online vortex behavior requires an optimized sample preparation method to obtain well dispersed and homogeneous NP distribution to analyze a single, isolated particle. Observation of isolated NSs is required to avoid any inuence of dipolar interactions among magnetic vortexes that could inuence the spin arrangement. 61 The Lorentz transmission electron microscopy results presented in Fig. 3 provide information on the size, morphology and magnetic properties of the NSs. The bright-eld TEM images of Fig. 3a and d display NSs with ∼700 nm in diameter. The TIE was used to reconstruct phase images of each NS from a through-focus series (ESI S6†)of Fresnel contrast TEM images that were acquired in eld-free Fig. 3 Evidence of magnetic vortex configuration in NSs: theoretical, experimental and simulation. (a and d) Bright-field TEM images of the NSs. (b and e) Associated TIE reconstruction of the magnetic contribution to the phase shift that allows construction of (c and f) magnetic induction maps corresponding to the amplified cosine of the experimental phase image to include phase contours. The direction of magnetization is indicated by the color wheels (inset). (g) Energy-diameter phase diagram of NSs, (h) experimental and simulated hysteresis of NSs, and (h(I–V)) field-dependent spin-configuration in NSs; the upper row represents the z-axis (perpendicular to the XY plane) view of NS spin configuration whereas the lower row represents the upper(eye) view of the hemisphere that shows clearly the vortex core in NSs. 5020 |Nanoscale Adv.,2023,5,5015–5028 © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Advances Paper Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online Lorentz mode. The magnetic contributions to the phase shi (Fig. 3b and e) were isolated by physically ipping the sample 180° outside the TEM and image alignment/rotation was performed to calculate the differences in phase (ESI S6†). The cosine of the phase was amplied to provide visualization of magnetic contours and the phase gradient provided directional information, using the color wheel shown in Fig. 3c and f, (inset). The result (Fig. 3c and f) clearly shows that both NSs are constituted by a spin vortex domain structure. The energy-diameter phase diagram obtained from micromagnetic simulations (Fig. 3g) shows the dependence of the nal spin state on the diameter of the NSs. Specically, the transition from a single-domain (SD) state to a vortex conguration occurs at the boundary line. This observation is fully consistent with both the theoretical model and micromagnetic simulation. It can be observed that the phase diagram is composed of three regions for increasing NS radius: a) single domain (in-plane); b) a transition (single-domain to a vortex) region; and c) a pure vortex region. The vortex state is the ground state for critical sizes above the single domain (z90–95 nm for Fe 3 O 4 ). 67 The single-domain state is the most favorable conguration for particles below the critical size, and the full energies of the distinctive magnetization patterns decrease with increasing diameter D. It is likely that all size-/shape-dependent phase transitions (SPM to SD to vortex) are rst-order temperaturedependent phase transitions from monoclinic to cubic, and in magnetite are associated with Verwey temperature, the so-called Verwey transition. The constructed energy-diameter phase diagram from the theoretical model agreed with the micromagnetic simulation. In any case, the small error at the boundary line is expected due to the impact of the cubic cell discretization within the micromagnetic recreation that contributes to the extra roughness energy and thus the full ground state energy of the framework that results in the discrepancy in overall theoretical and simulated energy proles. 9,51,68 The discreteness of the method and the utilization of a cubic mesh are the sources of systematic errors in nonrectangular systems, hence raising the imprecision of micromagnetic simulations reasoned by discretization. 68 This is more applicable to NSs since the circular boundary is assessed by a staircase of straight-line segments. Such impacts are not observed in the theoretical phase diagram. The vortex (ux-closure spin conguration) can occur in magnetic nanoparticles as a result of minimization of the total energy that includes magneto-crystalline anisotropy, exchange as well as magnetostatic energies. Although the formation of a vortex state is a consequence of energy competition between exchange and magnetostatic energy, the total energy of the curling-vortex state is mainly dominated by the exchange energy; thus, this interaction plays a key role in the formation of vortex states. The total energy, E tot , of NSs as a function of diameter (Fig. 3g) shows that E tot decreases with increasing diameter within the vortex region (R v ). The larger the particle diameter, the larger the vortex region which consequently increases the vortex core diameter, denoted by ‘b’in Fig. 2c. This statement implies that NSs with larger diameter try to get relaxed/stabilized at lower energy state as their vortex/ground state. For diameter values above the single-to multi-domain limit (z90–95 nm for Fe 3 O 4 ), the NSs become the more energetically favorable state (lower energy state). Increasing the diameter of NSs, longer becomes the vortex core displacement of the vortex core, lowering the exchange energy and providing better stability of the vortex state by decreasing the remanent magnetization. 69 While the total energy is the sum of several energies such as exchange, magneto-static (or demagnetizing energy), anisotropic energy etc. and magneto-static energy is dominated by the exchange interaction (ESI S8†), the singledomain state is dominated by the demagnetization energy at the surface. 68,70 For large structures, the vortex state reduces the system energy by reducing stray elds and hence lowering the magnetostatic energy. The central vortex core in NSs contributes to the out-of-plane magnetization (i.e.,m z s0) at the origin, which is stabilized by the exchange interactions and therefore the dynamic magnetization has noteworthy values outside of the vortex core, i.e., in-plane magnetization. 71 Such out-of-plane magnetization leads to the observed magnetic remanence at H=0, with the actual remanence values depending on the sizes of both NSs and the vortex core. In addition to the imaging techniques, we further examined the vortex conguration in NSs through the magnetometry technique which allows us to visualize an unusual irreversible hysteresis loop in ferromagnetic vortex nanoparticles with negligible remanence and coercive eld due to the switching behavior of the loop. 17,18,72 Fig. 3h shows the experimental and simulated hysteresis loops for NSs. The NSs are observed to exhibit a perfect irreversible magnetic behavior, as evidenced by the vortex conguration having magnetic remanence and coercive eld of approximately 10 emu g −1 and 21 Oe, respectively. The small magnetic remanence (10 emu g −1 ) is expected from the vortex core of the NSs that induces an out-of-plane magnetization. Micromagnetic simulations consisting of moderate hysteresis loops with zero remanence and a coercive eld of 21 Oe support these experimental results. The clear result of a vortex core in the center of NSs at H=0 and its gyrotropic shiduring the application of an external eld, H>0, evidences a vortex conguration in NSs. In such a domain structure of magnetic vortex, the hysteresis loop consists of a two-step magnetization reversal process which includes an S state in the present case to the vortex transition and vice versa. 73,74 At a high external magnetic eld Hvalue, NSs fall into a saturation state or a single domain state because all spins are aligned parallel to the external eld direction. To examine whether the simulated hysteresis ts the experimental data, we additionally calculated several hysteresis loops (ESI S4 and S5†) in two ways: (i) by varying the size; (ii) upon increasing the number of spheres with a diameter of 700 nm. We observed that the simulated hysteresis loops obtained by increasing the number of spheres tend to show results closer to the experimental ones. The simulated hysteresis loops evolve in a way more vertical, suggesting that the effect is gated by the number of spheres involved, and also periodic boundary conditions in the direction of the applied eld (x-axis in the present case). The complete hysteresis loop phenomena (saturated/single-domain state, S-state and C-state in the hemisphere, and the vortex © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Adv.,2023,5,5015–5028 | 5021 Paper Nanoscale Advances Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online state) with respect to the magnetic eld are presented in Fig. 3h and their magnetic state in Fig. 2b. Although the experimental coercive eld values agree with simulated ones, the complete irreversible hysteresis loop appears quite different. The origin of such discrepancies is the different energy proles as shown in the energy-diameter phase diagram (Fig. 3g) discussed above. In addition, the defect-/cation vacancy-free NPs require more accurate modeling data as compared to experimental ones. 61 Overall, the simulated hysteresis loop for NSs is more convincing than previously reported data, which still shows a small loop with narrow nucleation and expulsion eld (magnied inset in Fig. 3h); it is rare to nd a clear nucleation and expulsion eld (switching eld) in 3D spherical particles because of their isotropic nature, and because their aspect ratio (h/d) is 1, unlike the switching eld found in highly anisotropic particles such as 2D disk, 6 rings, 72 tubes and rods, 12 which encode aspect ratio <1. Taking all together the theoretical analysis, experimental, and micromagnetic simulation, our ndings conrm the existence of a vortex conguration in NSs. Fig. 4a and b show zero eld cooling and eld cooling (ZFCFC) magnetization versus temperature in the absence or presence of an external magnetic eld. The data clearly indicate a prominent Verwey transition (T v ) for the two samples i.e., LERs and SERs, which is typically met in stoichiometric Fe 3 O 4 , whereas no such transition is found in NSs. The Verwey transition for bulk Fe 3 O 4 occurs at a temperature T V =119 K, above which fast electron hopping among Fe 2+ and Fe 3+ ions occurs among the octahedral sites. 40 For our samples, the Verwey transition was observed at T V z122 K and z125 K for LERs and SERs, respectively. As mentioned, no jump of magnetization at the T V was observed for NSs, suggesting the absence of this transition from the monoclinic to cubic phase structure. 75,76 The M ZFC/FC versus T curves in the whole temperature range suggest that the blocking temperature of all the samples (LERs, SERs and NSs) exceeds our experimental temperature limits of 5 #T #350 K. We believe that LERs will exhibit the highest magnetic moment at the end of the process, likewise the highest magnetization obtained through the hysteresis curve (ESI S7†). In Fe 3 O 4 MNPs, the sharp transition is related to the high crystallinity of nanoparticles and electron hopping between Fe 2+ and Fe 3+ . 77,78 The slightly sharper transition in LERs as compared to SERs is attributed to the higher percentage of stoichiometric Fe 3 O 4 (i.e., 55% in LERs > 50% in SERs). This induces the comparatively effective ‘electron hopping’between the Fe 3+ and Fe 2+ cations in the B-site of LERs at temperatures T >T V . In addition, the sharper transition in LERs is supported by eqn (2) and (3); signicant cation vacancies were observed in SERs as compared to LERs and this fact should have hampered the regular Verwey transition. However, such a transition phenomenon does not appear in NSs, indicating that a longrange order for both Fe 2+ and Fe 3+ at the octahedral sites has been for T<T V . Fig. 4c shows the temperature-dependent resistance that exhibits a metal-to-insulator transition, i.e., the Verwey transition, which increases exponentially with decreasing temperature below 120 K in LERs and SERs and is indicative of stoichiometric Fe 3 O 4 . Here, the temperature-dependent resistance curves are acquired as a function of increasing temperature, with the temperature stabilized for 20 minutes before a measurement is taken. This electrical transport measurement for all the samples was performed in a temperature range of 90– 300 K. In the case of LERs and SERs, below 122 K and 125 K, Fig. 4 (a and b) ZFC-FC curves and their derivative from 5 K to 350 K; (c) measurements of resistance as a function of temperature; and (d) Mott's variable range hopping law (log R vs. T −1/4 ) for LERs, SERs and NSs. 5022 |Nanoscale Adv.,2023,5,5015–5028 © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Advances Paper Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online a very sharp increase in resistance is observed, whereas no change in resistance is detected for NSs that almost remains constant until 100 K. Such an increase of resistance with decreasing temperature below 120 K in LERs and SERs is a signature of stoichiometric Fe 3 O 4 . Also, we have tested Mott's variable range hopping law. 79 Fig. 4d shows the logarithmic resistance as a function of T −1/4 in which LERs and SERs exhibit a small kink around 122 K (shaded region) which is clear evidence of the Verwey transition. However, no such kink is found in the case of NSs. Thus, both M ZFC-FC versus temperature and electrical measurements provide clear evidence of surface defects and oxygen vacancies in NSs that suppress the Verwey transition, turning the material into non-stoichiometric Fe 3 O 4 . The Mössbauer spectroscopy can provide further insights upon disclosing the contributions of iron ions located either at A (tetrahedral) or B (octahedral) sites as well as surface defects and oxygen vacancy concentration. We have performed Mössbauer spectroscopy at 300 K as shown in Fig. 5a–c, as well as the hyperne tting parameters are shown in Table 3 of ESI.†The spectra of all samples were well tted considering sextet patterns (magnetic sub-spectra). The spectrum for LERs and SERs (Fig. 5a and b) is well resolved by four sextets (three sextets for Fe 3 O 4 and one for Fe 0 ) and exhibits almost similar behavior in light of compositions of Fe cation distributions. The calculated values of hyperne parameters for all the samples are consistent with the two crystallographic sites for iron ions in the cubic spinel (Fd 3m) structure of Fe 3 O 4 . 54 Nevertheless, the ratio of spectral area at Aand B-sites was found to be different as compared with bulk magnetite (i.e., 1 : 2 for free-defect crystals); such a ratio of composition indicates that the samples have not perfectly preserved their stoichiometry. We observed that much more Fe 3+ cations are present in the A-site than in the bulk reference. Therefore, further deep analysis of Mössbauer tting revealed that only ∼55% of Fe 3 O 4 preserved its bulk behavior i.e., stoichiometry in LERs; 18.86% of Fe 3+ in A-sites and 35.74% of Fe 3+ in B-sites and ∼50% of Fe 3 O 4 preserved its bulk behavior i.e., stoichiometry in SERs; 16.43% of Fe 3+ in A-sites and 33.64% of Fe 3+ in B-sites. The tted sextet drawn in navy color represents A-sites (represented by S A ) containing ∼26% and ∼41% of Fe 3+ cations somewhere in the samples LERs and SERs, respectively. When electron hopping occurs in B-sites of LERs and SERs, the valences of Fe 2+ and Fe 3+ ions are averaged to Fe 2.5+ , and the distribution of charge for the stoichiometric magnetite can be estimated as (Fe 3+ ) A [Fe 22.5+ ] B O 4 (6) As previously mentioned above, the ratio-metric Fe cation population in Aand B-sites must be X B /X A =2, where X B and X A are the area/population contained by Fe cations in each site, to claim the stoichiometric magnetite. However, according to the observed data shown in Table 3 (ESI†), the overall ratio X B /X A is about 0.78 and 0.59 for the samples LERs and SERs, respectively. This could be explained either by the presence of cation vacancies or/and by the surface effects. For the cation vacancy case (,) in B-sites, the LERs and SERs would correspond to the non-stoichiometric magnetite with the chemical formula for LERs (Fe 3+ ) A [Fe 0.782.5+ , 1.22 ] B O 4 (7) and, for SERs, (Fe 3+ ) A [Fe 0.592.5+ , 1.41 ] B O 4 (8) The cation vacancies are in increasing order which can be seen in eqn (2) and (3) as a result of a signicant reduction of charge ordering between Fe 3+ and Fe 2+ at temperatures T<T V Fig. 5 (a–c) Mössbauer spectra recorded at T=300 K for LERs, SERs, and NSs. © 2023 The Author(s). Published by the Royal Society of Chemistry Nanoscale Adv.,2023,5,5015–5028 | 5023 Paper Nanoscale Advances Open Access Article. Published on 31 August 2023. Downloaded on 1/29/2024 10:48:55 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online