Micromagnetic Properties Research Articles

Pathways toward the Use of Non-Destructive Micromagnetic Analysis for Porosity Assessment and Process Parameter Optimization in Additive Manufacturing of 42CrMo4 (AISI 4140).

Laser-based powder bed fusion of metals (PBF-LB/M) is a widely applied additive manufacturing technique. Thus, PBF-LB/M represents a potential candidate for the processing of quenched and tempered (Q&T) steels such as 42CrMo4 (AISI 4140), as these steels are often considered as the material of choice for complex components, e.g., in the toolmaking industry. However, due to the presence of process-induced defects, achieving a high quality of the resulting parts remains challenging in PBF-LB/M. Therefore, an extensive quality inspection, e.g., using process monitoring systems or downstream by destructive or non-destructive testing (NDT) methods, is essential. Since conventionally used downstream methods, e.g., X-ray computed tomography, are time-consuming and cost-intensive, micromagnetic NDT measurements represent an alternative for ferromagnetic materials such as 42CrMo4. In this context, 42CrMo4 samples were manufactured by PBF-LB/M with different process parameters and analyzed using a widely established micromagnetic measurement system in order to investigate potential relations between micromagnetic properties and porosity. Using multiple regression modeling, relations between the PBF-LB/M process parameters and six selected micromagnetic variables and relations between the process parameters and the porosity were assessed. The results presented reveal first insights into the use of micromagnetic NDT measurements for porosity assessment and process parameter optimization in PBF-LB/M-processed components.

Modeling the effect of workpiece temperature on micromagnetic high-speed-3MA-testing in case of AISI 4140

The growing trend towards industry 4.0 requires in-process identification of the surface properties. The non-destructive highspeed-3MA-testing can be used to characterize surface layers of ferrous materials during turning processes. However, in-process measurements will result in higher workpiece temperatures and thus would interfere with the micromagnetic properties of the workpiece. In the presented study, workpiece surface temperatures will be experimentally determined when turning AISI 4140. Further on, workpieces will be heated up to the respective temperatures, which will then be measured with the 3MA-sensor as they rotate. The effect of temperature will be modelled and used for compensating the associated errors.

Micromagnetic and morphological characterization of heteropolymer human ferritin cores.

The physical properties of in vitro iron-reconstituted and genetically engineered human heteropolymer ferritins were investigated. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), electron energy-loss spectroscopy (EELS), and 57Fe Mössbauer spectroscopy were employed to ascertain (1) the microstructural, electronic, and micromagnetic properties of the nanosized iron cores, and (2) the effect of the H and L ferritin subunit ratios on these properties. Mössbauer spectroscopic signatures indicate that all iron within the core is in the high spin ferric state. Variable temperature Mössbauer spectroscopy for H-rich (H21/L3) and L-rich (H2/L22) ferritins reconstituted at 1000 57Fe/protein indicates superparamagnetic behavior with blocking temperatures of 19 K and 28 K, while HAADF-STEM measurements give average core diameters of (3.7 ± 0.6) nm and (5.9 ± 1.0) nm, respectively. Most significantly, H-rich proteins reveal elongated, dumbbell, and crescent-shaped cores, while L-rich proteins present spherical cores, pointing to a correlation between core shape and protein shell composition. Assuming an attempt time for spin reversal of τ 0 = 10-11 s, the Néel-Brown formula for spin-relaxation time predicts effective magnetic anisotropy energy densities of 6.83 × 104 J m-3 and 2.75 × 104 J m-3 for H-rich and L-rich proteins, respectively, due to differences in surface and shape contributions to magnetic anisotropy in the two heteropolymers. The observed differences in shape, size, and effective magnetic anisotropies of the derived biomineral cores are discussed in terms of the iron nucleation sites within the interior surface of the heteropolymer shells for H-rich and L-rich proteins. Overall, our results imply that site-directed nucleation and core growth within the protein cavity play a determinant role in the resulting core morphology. Our findings have relevance to iron biomineralization processes in nature and the growth of designer's magnetic nanoparticles within recombinant apoferritin nano-templates for nanotechnology.

A flow forming process model to predict workpiece properties in AISI 304L

The control of workpiece properties enables an application-oriented and time-efficient production of components. In reverse flow forming, e.g., the control of the microstructure profile, in contrast to the adjustment of the geometry, is not yet part of the state of the art. This is particularly challenging when forming seamless tubes made of metastable austenitic stainless AISI 304L steel. In this steel, a phase transformation from austenite to martensite can occur due to mechanically and/or thermally induced energy. The α’-martensite has different mechanical and micromagnetic properties, which can be advantageous depending on the application. For the purpose of local property control, the resulting α’-martensite content should be measured and controlled online during the forming process. In this paper, results from an empirical correlation model of process parameter combinations and resulting α’-martensite content as well as geometry will be presented. Based on this, the focus of the paper will be on process modeling by means of FEM in order to create the transition to a numerically supported process model. Furthermore, it will be specified how the numerical process model can be used in a predictive manner for an online closed-loop process control.

EFFECT OF THE DIRECTION OF AN EXTERNAL APPLIED MAGNETIC FIELD ON THE MICROMAGNETIC PROPERTIES OF Fe CUBOIDS

We present the results of the study of the micromagnetic properties and the magnetization dynamics of a system of Fe cuboids with a square base of length L = 120 nm and thickness, t = 9 nm, under free boundary conditions as a function of the angle of an in-plane applied external magnetic field, for which we have used the Ubermag micromagnetic program that uses the OOMMF package and the finite difference method with a cell size, c = 3 nm. Hysteresis loops show that the coercive field (Hc) decreases with increasing azimuthal angle, from one easy-magnetizing axis to the other; in turn, the remanent magnetization (Mr) remains constant and magnetization diagrams indicate the presence of magnetic domains and walls in the (x, y) plane, accompanied by a magnetization component that points, both, outward and inward of the plane. This behavior is associated with the type of anisotropy and the aspect ratio of the cuboid. Finally, energy graphs show how the competition between the dipole (Ed), the exchange (Eex), anisotropy (EK), and Zeeman (EZ) energies occurs along the hysteresis loops.

Micromagnetic Properties of Powder Metallurgically Produced Al Composites as a Fundamental Study for Additive Manufacturing

Resource-efficient manufacturing with a high degree of freedom in terms of component shape can be realised through additive manufacturing. The focus can lie not only on the manufacturing process in terms of geometrical correctness, stability, etc., but also on the targeted development of specific material properties. This study shows the development of hybrid material systems made of aluminium and the ferromagnetic particles iron, cobalt, and nickel. The aim is to use the ferromagnetic properties as sensor properties to enable the easy sensing of material properties such as the microstructure, fatigue, or occurring stresses. To easily adopt different compositions, hot isostatic pressing was selected for the characterisation of the material composites Al-Fe, Al-Ni, and Al-Co with regard to their magnetic properties. Subsequently, transfer to the additive manufacturing process of wire and arc additive manufacturing gas metal arc welding was carried out by mixing the powder separately into the weld pool. The study shows that it is possible to prevent a complete transformation of Ni and Co into intermetallic phases with Al by adjusting the influencing variables in the HIP process. Magnetic properties could be detected in the composites of Al-Co and Al-Fe. This work serves as a preliminary work to realise additive components made of hybrid material systems of Al-Fe, Al-Co, and Al-Ni with the GMA welding process.

Design of advanced micro-magnetic sensors for various applications

The state of the microstructures determines both the mechanical properties (hardness, yield strength, elongation, etc.) and micro-magnetic properties (magnetic Barkhausen noise (MBN), incremental permeability (IP), etc.). The non-destructive nature of the micro-magnetic testing technology facilitate it be a valuable tool for quality control in the manufacturing of ferromagnetic components. In the implementation of micro-magnetic testing, the functions and the geometry of the sensors need be customized for specific target properties and components. In this paper, four types of advanced or multifunctional sensors are presented and applied for micro-magnetic testing. First, a multifunctional sensor is developed for flat surface. Unique intermittent magnetizing method using superimposed magnetic fields of high and low frequencies enable the sensor to measure the magnetic Barkhausen noise, incremental permeability, eddy currents, tangential magnetic field and main flux. Second, to conduct magnetic Barkhausen noise testing at the inner corner of V-shape bending plate, a miniaturized sensor with U-shape roller magnetizer is designed to perfect contact with the corner region. Third, read head of a magnetic tape player is revised to act as high-lateral-resolution (up to 500μm) sensor for magnetic Barkhausen noise measurement in ferromagnetic film. Fourth, a slender probe is developed and embedded into an anti-bulking fixture that is clamped onto the flat specimen. With the slender probe together with the special fixture, the dependency of the magnetic Barkhausen noise on the compressive and tensile stress is first experimentally observed in a single flat specimen under continuous load.

Magnetic, structural, and fluorescence properties of Sr-hexaferrite nanoparticles embedded in a PV-OH film

The magnetic and fluorescence properties were studied for a polymer nanocomposite (PNC) based on strontium hexaferrite (Sr-M) nanoparticles embedded in a polyvinyl alcohol (PV–OH) matrix. This study reveals the effect of nanoparticles operating on the structural behavior and the functional properties of the polymer nanocomposite. The X-ray diffraction and the Rietveld method showed a change of the PV-OH semi crystallinity as the number of nanoparticles varies in the composite. This behavior has been related to the close interactions between the nanoparticles and the polymer which show to be capable of modifying the structural and functional properties of the matrix. Here, the nanoparticles promote a fluorescence quenching as the nanoparticles increase. Then, a close relationship between the polymer structure and its functional properties is discernible. Also, the number of nanoparticles and their arrangement in the PNCs promote the emergence of magnetic interactions which change the micromagnetic properties of the system.

Magnetic Barkhausen Noise Transient Analysis for Microstructure Evolution Characterization with Tensile Stress in Elastic and Plastic Status.

Stress affects the microstructure of the material to influence the durability and service life of the components. However, the previous work of stress measurement lacks quantification of the different variations in time and spatial features of micromagnetic properties affected by stress in elastic and plastic ranges, as well as the evolution of microstructure. In this paper, microstructure evolution under stress in elastic and plastic ranges is evaluated by magnetic Barkhausen noise (MBN) transient analysis. Based on a J-A model, the duration and the intensity are the eigenvalues for MBN transient analysis to quantify transient size and number of Barkhausen events under stress. With the observation of domain wall (DW) distribution and microstructure, the correlation between material microstructure and MBN transient eigenvalues is investigated to verify the ability of material status evaluation on the microscopic scale of the method. The results show that the duration and the intensity have different change trends in elastic and plastic ranges. The eigenvalue fusion of the duration and intensity distinguishes the change in microstructure under the stress in elastic and plastic deformation. The appearance of grain boundary (GB) migration and dislocation under the stress in the plastic range makes the duration and the intensity higher on the GB than those inside the grain. Besides, the reproducibility of the proposed method is investigated by evaluating microstructure evolution for silicon steel sheet and Q235 steel sheet. The proposed method investigates the correlation between the microstructure and transient micromagnetic properties, which has the potential for stress evaluation in elastic and plastic ranges for industrial materials.

Switchable magnetic frustration in buckyball nanoarchitectures

Recent progress in nanofabrication has led to the emergence of three-dimensional magnetic nanostructures as a vibrant field of research. This includes the study of three-dimensional arrays of interconnected magnetic nanowires with tunable artificial spin-ice properties. Prominent examples of such structures are magnetic buckyball nanoarchitectures, which consist of ferromagnetic nanowires connected at vertex positions corresponding to those of a C60 molecule. These structures can be regarded as prototypes for the study of the transition from two- to three-dimensional spin-ice lattices. In spite of their significance for three-dimensional nanomagnetism, little is known about the micromagnetic properties of buckyball nanostructures. By means of finite-element micromagnetic simulations, we investigate the magnetization structures and the hysteretic properties of several sub-micron-sized magnetic buckyballs. Similar to ordinary artificial spin-ice lattices, the array can be magnetized in a variety of zero-field states with vertices exhibiting different degrees of magnetic frustration. Remarkably, and unlike planar geometries, magnetically frustrated states can be reversibly created and dissolved by applying an external magnetic field. This easiness to insert and remove defect-like magnetic charges, made possible by the angle-selectivity of the field-induced switching of individual nanowires, demonstrates a potentially significant advantage of three-dimensional nanomagnetism compared to planar geometries. The control provided by the ability to switch between ice-rule obeying and magnetically frustrated structures could be an important feature of future applications, including magnonic devices exploiting differences in the fundamental frequencies of these configurations.

Target domains in nanometric Permalloy disks with columnar structure

We conducted a thorough experimental and numerical study of the micromagnetic properties of Permalloy (Ni80Fe20) microdisks exhibiting target domain structures at remanence. Vortex configurations are quite common in such microdisks and correspond to an in-plane (IP) flux closure configuration of cylindrical symmetry with an out-of-plane (OOP) magnetized core. In contrast, target domain configuration are observed in thicker microdisks and are characterized by a vortex configuration of the IP component of the magnetization superposed to an OOP component of magnetization which oscillates as a function of the distance to the microdisk center resulting in the formation of concentric domains. The ratio of the OOP oscillatory component of the magnetization to the IP vortex one increases with the thickness of the microdisk. Hysteresis loops were measured under IP and OOP field. The results at remanence and under magnetic field could be interpreted by micromagnetic simulations in which the microdisks were described as an assembly of partially coupled columns representing the granular nanostructure of the films from which the microdisks were patterned. Quite original magnetization processes take place in these microdisks exhibiting target domain remanent configuration. These include in particular entire flipping of the domain configuration and annihilation/creation of ring domains.

Bessel function descriptions of magneto-chiral interactions (DMI)-magnetic and spin flexoelectric skyrmions

In this work we present an exact Bessel function solution to the variation equations for a ground state of the chiral Hamiltonians in the continuum limit for cylindrical symmetry. The solution imposes no constraints on the magnetic spin moment magnitude. The formulation is consistent with the generalized view of U. K. Roessler et al. Nature 442, 797–801 (2006) that both the magnetic moment amplitude and magnetic stiffness ratio are micromagnetic properties and variations in amplitude may be allowed. With the exact solutions, we reveal that the added stabilization energy of the 2D skyrmion relative to the 1D solution is the result of the cylindrical symmetry rather than specifics of the chiral interactions. The methods can be employed to understand Bloch type magnetic spin textures observed in MnSi and FeGe and Néel type magnetization textures in antiferromagnetic dielectrics and ferrimagnetic thin sheets with the application of an electric field.

Effects of Laser Cutting on Microstructure and Magnetic Properties of Non-Orientation Electrical Steel Laminations

Non-oriented electrical steel (NOES) is commonly used as a core material in electric machines. These laminations are cut into the desired core shape that modifies the material properties near the cut edge, which consequently changes the magnetic performance of the core lamination. Magnetic property deterioration due to cutting has been reported in the literature but less attention has been given to the microstructural changes due to cutting and its relation to the magnetic properties. The present research focuses on the effects of laser cutting on microstructure and magnetic properties of NOES laminations. A number of lamination steel samples were laser-cut using an identical procedure to that expected on an industrial scale. Property measurements showed that the magnetic permeability of the samples decreased while the core losses increased. The core loss increase was significant, about 22% at 50 Hz and 1.5 T. This was attributed to the change in the micromagnetic characteristics of the sample due to cutting. The change in micromagnetics was investigated using magnetic domain imaging and distorted domain structure was observed near the laser-cut edge. Backscattered electron imaging and nanoindentation measurements were also used for further investigation of micromagnetic properties of the material.

Method of measuring the mechanical properties of ferromagnetic materials based on magnetostrictive EMAT characteristic parameters

The mechanical and micromagnetc properties of ferromagnetic materials are overall associated with their microstructure parameters. The magnetostriction refers to one of the micromagnetic properties. The magnetostrictive properties of ferromagnetic materials are characterized by the relationships between the intensity of the SH (Shear Horizontal) waves with magnetostrictive effect under the identical excitation and the static bias magnetic induction intensity. In this study, the characteristic parameters exhibiting sensitivity to the magnetostrictive properties of ferromagnetic materials in the relationships between the intensity of EMAT (electromagnetic acoustic transducer) signal and static magnetic field strength were extracted. Besides, with BP (back propagation) neural network, the mapping association between the magnetostrictive parameters and the mechanical properties of the materials was developed, and the mechanical properties of the materials were non-destructively determined. By verifying the testing samples of cold-rolled steel specimens synthesized by Bao-steel Inc., the method was found to be capable of achieving high prediction accuracy; the passing rate of relative error less than 10% can reach 90%.

Wide-Band Electromagnetic Wave Propagation and Resonance in Long Cobalt Nanoprisms

Electromagnetic wave interaction with confined metallic magnetic structures is complex due to the excitation of nonuniform electromagnetic fields and magnetic precession and spin-wave modes over length scales that are dependent on the geometric, electromagnetic, and micromagnetic properties of the magnetic structures. Here, we solve the coupled system of Maxwell's equations and the Landau-Lifshitz-Gilbert equation using a stable algorithm based on the finite-difference time-domain method to study the transient wide-band electromagnetic propagation and resonance in infinitely long cobalt nanoprisms with a square cross section of side lengths 50--1000 nm. In particular, we identify the resonance mechanisms through studying the local transient and spectral distributions of magnetization in the prisms. The nanoprisms are excited by an axially polarized plane wave at normal incidence with a 70 GHz Gaussian pulse profile. For this incident wave condition, the simulations confirm that resonance in the cobalt prisms is excited mainly by the current-induced magnetic fields and indicate a magnetization curling resonance mode for prism side lengths less than 100 nm. The eigenfrequencies for the curling mode are confirmed theoretically using a model for an equivalent long circular cylinder with radial spin-wave modes. For prism side lengths longer than 100 nm (but less than the nonmagnetic skin depth), the magnetic response is confined to thin regions along the prism edges due to resonance-induced skin effects. The simulations indicate predominately uniform magnetization precession in the confined edge regions with increased pinning in the corners. The uniform resonance mode in the central part of the edge regions increases in intensity with prism size, with frequency described using Kittel's ferromagnetic resonance frequency of a thin planar structure. A higher-frequency size-independent uniform resonance mode is observed in the corner regions with frequency determined by the local demagnetizing factors. Local and integrated power absorption spectra are calculated using the simulated transient magnetization and fields, and confirm the resonance modes and frequencies in the cobalt prisms and their size dependence. The profile of the local power absorption spectra is also used to estimate the thickness of the confined edge regions or magnetic skin depth in the cobalt prisms at the fundamental resonance mode and is found to be approximately 50 nm. The outcomes of this work would benefit the design and engineering of lightweight and compact materials and devices incorporating metallic magnetic nanostructures. This work also provides a foundation for further modeling and understanding of electromagnetic transmission and propagation in more complex metallic ferromagnetic structures and composites excited by different electromagnetic wave conditions.

Magnetic quantification of single-crystalline Fe and Co nanowires via off-axis electron holography.

Investigating the local micromagnetic structure of ferromagnetic nanowires (NWs) at the nanoscale is essential to study the structure-property relationships and can facilitate the design of nanostructures for technology applications. Herein, we synthesized high-quality iron and cobalt NWs and investigated the magnetic properties of these NWs using off-axis electron holography. The Fe NWs are about 100 nm in width and a few micrometers in length with a preferential growth direction of [100], while the Co NWs have a higher aspect-ratio with preferential crystal growth along the [110] direction. It is noted that compact passivation surface layers of oxides protect these NWs from further oxidation, even after nearly two years of exposure to ambient conditions; furthermore, these NWs display homogeneous ferromagnetism along their axial direction revealing the domination of shape anisotropy on magnetic behavior. Importantly, the average value of magnetic induction strengths of Fe NWs (2.07 {±} 0.10 T) and Co NWs (1.83 {±} 0.15 T) is measured to be very close to the respective theoretical value, and it shows that the surface oxide layers do not affect the magnetic moments in NWs. Our results provide a useful synthesis approach for the fabrication of single-crystalline, defect-free metal NWs and give insight into the micromagnetic properties in ferromagnetic NWs based on the transmission electron microscopy measurements.

Magnetic properties of SrFe12O19 covered with copper by electrodeposition and sputtering

This work reports the micromagnetic properties of the strontium hexaferrite (SrM) when its surface is covered with a copper layer. The copper was deposited on the hexaferrite using two different methods, one based on the electrochemical deposition and the other one, using the magnetron sputtering technique. For each fabrication method, two different deposition times were selected to vary the copper quantity over the hexaferrite surface. The structural and morphological properties were analyzed from the X-ray diffraction patterns and scanning electron micrographs, while the magnetic behavior was investigated using alternating gradient magnetometry measurements. The samples obtained from chemical electrodeposition exhibited inhomogeneous copper deposits, while the ones obtained from sputtering presented homogeneous and well-distributed copper deposits. The results showed marked differences in the magnetic properties of the hexaferrite with deposited copper regarding the SrM without copper. Also, an improvement in the magnetic properties was observed when a homogeneous copper layer was deposited using sputtering than when electrodeposition was used. When copper was homogeneously deposited, the coercivity (Hc) exhibited an improvement from 2.5 kOe to 3.56 kOe, whereas the remanence squareness (Mr/Ms) increased from 0.5 to 0.7, which is equivalent to 40% increment as a consequence of the copper presence. The changes observed in the hysteresis loops and the dM/dH, H curves indicate that copper exerts a strong interaction on the magnetic moments of hexaferrite. This interaction couples the copper atoms with the interstitial cations of the hexaferrite structure. This copper-iron interaction would occur through a Cu–O–Fe superexchange mechanism, varying the intrinsic properties of the hexaferrite and modifying its micromagnetic behavior.

Quasidegenerate ice manifold in a purely two-dimensional square array of nanomagnets

We investigate numerically the micromagnetic properties and the low-energy physics of an artificial square spin system in which the nanomagnets are physically connected at the lattice vertices. Micromagnetic simulations reveal that the energy stored at the vertex sites strongly depends on the type of magnetic domain wall formed by the four connected nanomagnets. As a consequence, the energy gap between the vertex types can be partially modified by varying the geometrical parameters of the nanomagnets, such as their width and thickness. Based on the energy levels given by the micromagnetic simulations, we compute the thermodynamic properties of the corresponding spin models using Monte Carlo simulations. We found two regimes, both being characterized by an extensive ground state manifold, in sharp contrast with similar lattices with disconnected nanomagnets. For narrow and thin nanomagnets, low-energy spin configurations consist of independent ferromagnetic straight lines crossing the whole lattice. The ground state manifold is thus highly degenerate, although this degeneracy is subdominant. In the limit of thick and wide nanomagnets, our findings suggest that the celebrated square ice model may be fabricated experimentally from a simple square lattice of connected elements. These results show that the micromagnetic nature of artificial spin systems involves another degree of freedom that can be finely tuned to explore strongly correlated disordered magnetic states of matter.

Possibility of Analysis and Prediction of Magnetic Properties of Nanoobjects by Means of Simulation Taking into Account an Implicit Dependence of the Functional of Their Free Energy on the Magnetization Distribution

A short review of the results of a computer simulation of ferromagnets of limited sizes (nanoplatelets, thin films, and rods of rectangular section) using the method of minimizing the functional of the free energy of a magnetic system has been carried out. The implicit dependence of the functional on the magnetization distribution has been taken into account via the potential of the intrinsic field, which made it possible to exclude the points of the labile equilibrium upon minimizing the functional. The efficiency and adequacy of this method for studying micromagnetic properties of nanoobjects have been established. The specific features of the formation of domain structures of nanoobjects, as well as new possibilities of employing them in the magnetic recording of information have been shown.

Phase transition of iron sulphide minerals under hydrothermal conditions and magnetic investigations

Iron sulphide minerals have been used in industrial applications for many years, and more recently there has been increasing interest in the use of iron sulphide nanomaterials because of their useful properties and low cost. Previous studies have mainly focused on the synthesis of iron sulphides, but their phase transition and micro-magnetic properties are still unclear. In this study, iron sulphide minerals were synthesized via a hydrothermal method, and their phase transition mechanisms and magnetic properties were investigated. Ex situ and in situ X-ray diffraction results of the iron–sulphur system under hydrothermal conditions suggested that the transformation sequence followed the order of mackinawite (FeS) → greigite (Fe3S4) → smythite (Fe9S11) → pyrrhotite (Fe9S10). Pure greigite and pyrrhotite were obtained during the synthesis processes, after 1 h at 120 and 160 °C, respectively. Greigite showed a granular morphology with particle diameters around 30 nm, and pyrrhotite comprised stacked hexagonal sheets with thousands of nanometers in width. Pyrrhotite showed anti-ferromagnetic behaviour; however, it did not saturate up to magnetic field of 7 T. Greigite was ferrimagnetic, with a high saturation magnetization of 62.7 Am2 kg−1 and coercive magnetic field of 27.6 mT. Magnetic force microscope measurements of greigite revealed that its magnetic structure belonged to a spin-canted single domain. Overall, this study provides new information on the phase transition mechanism, related reaction formulas, and magnetic properties of iron sulphides, and it emphasizes the important role played by temperature/time in phase transitions.