MnFe2O4 bulk,nanoparticles and film: A comparative study of structural and magnetic properties

MnFe₂O₄ bulk sample was synthesized by conventional solid state reaction method, at 1350 °C. Nanoparticles with mean size of 〈D〉_TEM=10.4(±1.1) nm were prepared by thermal decomposition of metal nitrates, at 350 °C. And a film sample was prepared by pulsed laser deposition of bulk ferrite on MgO(100) at substrate temperature of 600 °C. Then a comparative study of the structural and magnetic properties of the samples has been carried out using different measurements. X-ray diffraction pattern of bulk and nanoparticles samples confirmed formation of spinel phase. The film sample showed an epitaxial growth on MgO in (400) direction. Saturation magnetization of nanoparticles at 300 K, M_S=33 emu/g, was comparable with film sample, M_S=38 emu/g, both being ∼2.5 times smaller than that of bulk sample (M_S=82 emu/g). The results showed the importance of surface effects in the film sample and nanoparticles. The obtained zero coercivity of bulk sample at 300 K and the low value of 8 Oe at 5 K is attributed to soft magnetic behavior of the MnFe₂O₄. On the other hand, nanoparticles showed superparamagnetic behavior at 300 K; and blocked state with a large coercivity of 730 Oe at 5 K. The film sample showed non-zero corecivity at both 5 and 300 K which reveals higher magnetic anisotropy of film compared to the bulk ferrite.     

Magnetic and morphological characterization of Bi2Fe4O9 nanoparticles synthesized via a new reverse chemical co-precipitation method

Nano-sized Bi₂Fe₄O₉ (BFO) was successfully synthesized using a new reverse chemical co-precipitation method at different pH values of 8–12. These powders were examined by x-ray diffractometery (XRD), thermogravimetrical differential thermal analysis (TG-DTA), field emission scanning electron microscopy (FESEM) and vibrating sample magnetometery (VSM). The XRD analysis showed the formation of pure phase Bi₂Fe₄O₉ at calcination temperature over 700 ℃. The TG-DTA curves indicated the crystallization temperature of 617 ℃ for the Bi₂Fe₄O₉ sample. The FESEM micrographs revealed a precipitates agglomeration, which is related to the nature of the chemical co-precipitation method and free surface energy of nanoparticles. Furthermore, the particle size of the powder samples increased from 43 to 131 nm as the pH value increased from 8 to 12, respectively. Also, the morphological change from nearly cubic to rod-like shape in the nanoparticles was observed by increasing the pH value. The M-H curves of the as-prepared powders confirmed the antiferromagnetic behavior in all samples. Uncompensated spins from the surface led to the appearance of saturation magnetization in the Bi₂Fe₄O₉ nanoparticles. Besides, a decrease in the particles size resulted in more uncompensated spins, thereby improving the saturation and remnant magnetization from M_s = 0.35 emu/g and M_r = 0.010 emu/g for pH = 12 to M_s = 1.15 emu/g and M_r = 0.042 emu/g for pH = 8. Furthermore, as the pH values increase the coercive fields firstly rise up to 196 Oe for pH = 9 and then decrease to 151 for pH = 12.     

Structure and magnetic properties of Co3O4/SiO2 nanocomposite synthesized using combustion assisted sol-gel method

This paper reports on novel cobalt oxide nanoparticles (NPs) embedded in an amorphous silica (SiO₂) matrix, synthesized using a modified sol-gel method. SEM and TEM images show as-synthesized particles to aggregate in the shape of spheres and less than 5 nm in size, while XRD and SAED analysis both point to well crystallized cubic spinel cobalt oxide phase with an average crystallite size of about 4.6 nm. Raman analysis confirms the formation of cobalt (III) oxide (Co₃O₄) NPs. As-synthesized Co₃O₄ single-nanocrystallite has magnetic properties that correlate with finite size effects and uncompensated surface spins. Temperature dependence of ZFC-FC magnetization curves reveals a sharp peak around 10 K which corresponds to the blocking temperature. A Curie-Weiss behavior of magnetization above 25 K shows lower Néel temperature of the sample compared with its bulk counterpart T_N=40 K (possibly due to crystal defects and nano-dimensionality of the particles). The magnetic measurements exhibit high magnetization at low temperatures (M_S=54.3 emu/g) which can be associated with random canting of the particles’ surface spins and uncompensated spins in the core which tends to interact ferromagnetically at low temperatures. The initial magnetization curve falls out from the hysteresis loop at 5 K, which could be also the effect of surface spins.     

Sonochemical synthesis of CoFe2O4 nanoparticles and their application in magnetic polystyrene nanocomposites

CoFe₂O₄ (CoFe) nanoparticles were synthesized via a facile surfactant-free sonochemical reaction. For preparation of magnetic polymeric films, CoFe₂O₄ nanoparticles were added to polystyrene (PS). Nanoparticles were characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Magnetic properties of the samples were investigated using an alternating gradient force magnetometer (AGFM). CoFe₂O₄ nanoparticles exhibit a ferromagnetic behaviour with a saturation magnetization of 62 emu/g and a coercivity of 640 Oe at room temperature. By preparing magnetic films the coercivity is increased. The coercivity of PS/CoFe₂O₄ (10%) nanocomposites is higher than that obtained for PS/CoFe₂O₄ (30%).     

Synthesis and characterization of an iron oxide poly(styrene-co-carboxybutylmaleimide) ferrimagnetic composite

In situ precipitation of iron oxide nanoparticles within the cross-linked styrene-(N-4-carboxybutylmaleimide) copolymer was carried out by an ion-exchange method. The resulting composite was studied by X-ray photoelectron (XPS) and Fourier transform infrared (FTIR) spectroscopies. FTIR analysis showed the evolution of iron oxide deposition and the formation of sodium carboxylate due to the deposition treatment. In addition, XPS analysis indicated the complete oxidation of iron(II) to iron(III) by the presence of the representative peaks of iron oxide and iron oxyhydroxide. X-ray diffraction analysis was used to identify the inorganic phases. The results showed the formation of maghemite (γ-Fe₂O₃), and after several deposition cycles, goethite (α-FeOOH). The morphology and spatial distribution of iron oxide particles within the copolymer matrix were determined by transmission electron microscopy. The mean particle size of the iron oxide was of 14 nm as determined from wide-angle X-ray diffraction using the Scherrer equation. The evolution of magnetic properties with the number of deposition cycles was investigated by magnetometry at room temperature. The poly(styrene-co-N-4-carboxybutylmaleimide)/γ-Fe₂O₃/α-FeOOH/composite showed a soft ferrimagnetic behavior and, after the third deposition cycle, showed a saturation magnetization of 8.04 emu/g at 12 kOe and coercivity field of 51 Oe.     

Hollow polyaniline/Fe3O4 microsphere composites: Preparation,characterization, and applications in microwave absorption

Hollow polyaniline/Fe₃O₄ microsphere composites with electromagnetic properties were successfully prepared by decorating the surface of hollow polyaniline/sulfonated polystyrene microspheres with various amounts of Fe₃O₄ magnetic nanoparticles using sulfonated polystyrene (SPS) as hard templates and then removing the templates with tetrahydrofuran (THF). The synthesized hollow microsphere composites were characterized by FT-IR, UV/Vis spectrophotometry, SEM, XRD, elemental analysis, TGA, and measurement of their magnetic parameters. Experimental results indicated that the microspheres were well-defined in size (1.50–1.80 μm) and shape, and that they were superparamagnetic with maximum saturation magnetization values of 3.88 emu/g with a 12.37 wt% content of Fe₃O₄ magnetic nanoparticles. Measurements of the electromagnetic parameters of the samples showed that the maximum bandwidth was 8.0 GHz over ?10 dB of reflection loss in the 2–18 GHz range when the Fe₃O₄ content in the hollow polyaniline/Fe₃O₄ microsphere composites was 7.33 wt%.     

A sonochemical method for synthesis of Fe3O4 nanoparticles and thermal stable PVA-based magnetic nanocomposite

Fe₃O₄ nanoparticles were synthesized via a simple surfactant-free sonochemical reaction. Room temperature synthesis without using inert atmosphere is the novelty of this work. The effect of different parameters on the morphology of the products was investigated. The magnetic properties of the samples were also investigated using an alternating gradient force magnetometer. Fe₃O₄ nanoparticles exhibit a ferromagnetic behavior with a saturation magnetization of 66 emu/g and a coercivity of 39 Oe at room temperature. For preparation magnetic nanocomposite, Fe₃O₄ nanoparticles were added to the polyvinyl alcohol (PVA). Nanoparticles can enhance the thermal stability and flame retardant property of the PVA matrix.     

Effects of hydrothermal process parameters on the physical,magnetic and thermal properties of Zn0.3Fe2.7O4 nanoparticles for magnetic hyperthermia applications

Effects of hydrothermal temperature and time on physical, magnetic and thermal properties of Zn-substituted magnetite nanoparticles (Zn_0.3Fe_2.7O₄) were assessed. The magnetic nanoparticles were synthesized via citric acid-assisted hydrothermal reduction route at temperatures of 150, 175 and 200 °C for duration of 10, 15 and 20 h. The nanoparticles were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), vibrating sample magnetometer (VSM) and specific loss power (SLP) measurements. The results showed that temperature and time of the hydrothermal process both had significant effects on nanoparticles composition and properties. It was observed that at 150 °C, heat generation was insufficient to produce activation energy required for nucleation of Zn_0.3Fe_2.7O₄ spinel nanoparticles, even after a long time. At 175 °C, although temperature was low, but the suitable condition for nucleation of nanoparticles was made and spinel nanoparticles with the size of about 13 nm were formed after 15 h. Nonetheless, since crystallinity and SLP of the nanoparticles was low, they showed weak performance for magnetic hyperthermia. At 200 °C, the required activation energy was provided for nanoparticles nucleation; however, the spinel was oxidized to hematite, resulting in a decrease in thermal and magnetic properties. In overall, the nanoparticles synthesized at 200 °C for 15 h possessed the best characteristics of reasonable purity, saturation magnetization of about 35.9 emu/g and SLP of 18.7 W/g.     

Investigation of structural,optical, dielectric and magnetic studies of Mn substituted BiFeO3 multiferroics

A series of Mn doped BiFeO₃ with composition BiMn_xFe_1−xO₃ (x = 0.0, 0.025, 0.05, 0.075, 0.1) was synthesized via a citrate precursor method. Structural, morphological, optical, electrical and magnetic properties were investigated by using various measurement techniques. XRD patterns confirmed that the materials possess distorted rhombohedral structure with space group R3c. Average crystallite size was found to be in the range 18–36 nm. A decrease in the value of lattice parameters has been observed due to contraction of unit cell volume with Mn doping. Higher tensile strain for the prepared nanoparticles was observed in Hall-Williamson Plot. Field Emission Scanning Microscopy (FESEM) showed the spherical, uniform, dense nanoparticles in the range 80–200 nm. Reduction in grain size was observed which may be due to suppression of grain growth with Mn doping. FTIR studies reported two strong peaks at 552 cm⁻¹ and 449 cm^-1 which confirmed the pervoskite structure. Dielectric properties were studied by measuring the dielectric constant and loss in the frequency range 1 kHz to 1 MHz. Magnetic hysteresis loop showed the retentivity (M_r) increasing from 0.0514 emu/g of BFO to 0.0931 emu/g of 10% Mn doping. Coercivity was found to increase upto 0.0582 T for 5% Mn doping and then reduced to 0.0344 T for 7.5% Mn doping. Saturation magnetization was observed to increase from 0.6791 emu/g for BFO to 0.8025 emu/g for 7.5% and then reduced to 0.6725 emu/g for 10% Mn doping in BFO. Improvement in dielectric and magnetic properties makes this material as a promising candidate for multifunctional device applications.     

Processing and characterization of nano-magnetic Co0.5Ni0.5Fe2O4 system

Various techniques such as X-ray diffraction (XRD), infrared (IR) spectroscopy, scanning electron micrographs (SEM), energy dispersive X-ray (EDX) and a vibrating sample magnetometer (VSM) were used to investigate the structural, morphological, and magnetic properties of spinel Co_0.5Ni_0.5Fe₂O₄ system. XRD and IR analyses enabled us to determine the functional group and structural parameters of Co_0.5Ni_0.5Fe₂O₄. EDX measurements showed the concentrations of O, Ni, Fe, and Co species involved in Co_0.5Ni_0.5Fe₂O₄ specimen from the uppermost surface to the bulk layers. The magnetization and coercivity of the as synthesized composite were 77 emu/g and 128 Oe, respectively.     

New LiNi0.5PrxFe2−xO4 nanocrystallites: Synthesis via low cost route for fabrication of smart advanced technological devices

Praseodymium substituted nano-crystalline Li-Ni spinel ferrites with different Pr³⁺ contents were synthesized by micro-emulsion method. X-ray diffraction (XRD), scanning electron spectroscopy (SEM) and vibrating sample magnetometery (VSM) techniques were employed to study the impact of substitution of the Pr³⁺ on the structure, surface morphology and magnetic parameters. XRD confirmed the formation of the single phase spinel ferrites of all compositions of LiNi_0.5Pr_xFe_2−xO₄ nanocrystallites. The crystallite size determined from XRD data by Scherrer formula was calculated in range from 40 nm to 70 nm. However the nanoparticles size estimated by SEM was found 35–115 nm. The room temperature VSM measurements were carried out in the applied field range from “−10,000 Oe” to “10000” Oe. Saturation magnetization (M_S) (41 emu/g) and coercivity (H_C) values (156.9 Oe) of LiNi_0.5Fe₂O₄ were improved by the addition of rare earth Pr³⁺ cations. The value of Hc is low, which is a strong indication of soft ferrites. The synthesized LiNi_0.5Pr_xFe_2−xO₄ ferrites may be utilized for low core losses on transformers.     

Synthesis and magnetic properties of La3+-Co2+ substituted strontium ferrite particles using modified spray pyrolysis–calcination method

The purpose of the research was to improve the intrinsic magnetic properties of strontium ferrite by substituting lanthanum and cobalt for strontium and iron. The salt-assisted ultrasonic spray pyrolysis (SA-USP) following calcination process were used to from La-Co substituted strontium ferrite particles (La_xSr_1-xFe_12-yCo_yO₁₉), and their compositional dependent magnetic properties systemically investigated. All the samples were calcined at 1050 °C for 1 h in an air atmosphere to yield single-phased hexagonal particles several hundred nanometers to microns in size. A saturation magnetization of 70.76 emu/g and a coercivity 7265 Oe were obtained at a composition of La_0.25Sr_0.75Fe_11.75Co_0.25O₁₉. The amount of Co was reduced to obtain an optimized saturation magnetization of 71.40 emu/g and a coercivity of 7572 Oe at a composition of La_0.25Sr_0.75Fe_11.8Co_0.2O₁₉.     

Desulfurization and bio-regeneration of adsorbents with Magnetic P. delafieldii R-8 Cells

Superparamagnetic Fe₃O₄ nanoparticles are prepared with coprecipitation method followed by modification with ammonia oleate. Magnetic P. delafieldii R-8 cells can be prepared by mixing the cells with magnetite nanoparticles. Saturated magnetization of magnetic cells is about 7.41 emu/g. The pH value of magnetic suspension has significant influence on the desulfurization activity of magnetic cells. Desulfurization of the magnetic cells prepared with pH 7.0 magnetic suspension has similar activity with free cells. When the magnetic cells were used in the bioregeneration of desulfurization adsorbents Ag-Y, the concentration of dibenzothiophene (DBT) and 2-hydroxybiphenyl (2-HBP) with free cells is a little higher that that with magnetic cells. Adsorption capacity of the regenerated adsorbent is 93% that of the fresh one after being desorbed with magnetic P. delafieldii R-8, dried at 100 °C for 24 h and calcined in the air at 500 °C for 4 h.     

PVA assisted coprecipitation synthesis and characterization of MgFe2O4 nanoparticles

Single phase magnesium ferrite (MgFe₂O₄) nanoparticles were prepared by the coprecipitation method followed by calcination at 700 °C for 1 h. The effects of polyvinyl alcohol (PVA) agent on the structural, microstructure, magnetic properties and AC magnetically induced heating characteristics of MgFe₂O₄ nanoparticles were investigated. The structure and cation distributions investigated by X-ray diffraction method showed single phase MgFe₂O₄ powders had partially inverse spinel structure in which the inversion coefficient increased by adding more PVA. The small particle size and narrow size distribution of the coprecipitated MgFe₂O₄ powders characterized by scanning electron microscopy were achieved using PVA agent. Magnetic properties of MgFe₂O₄ nanoparticles studied by vibrating sample magnetometry showed ferrimagnetic characteristics with the highest saturation magnetization and coercivity of 24.6 emu/g and 17 Oe, respectively. The coprecipitated MgFe₂O₄ nanoparticles assisted by PVA exhibited the lower AC heating temperature of 5.6 °C and specific loss power of 2.4 W/g in comparison with 6.1 °C and 2.7 W/g for the powders coprecipitated without using PVA.     

Physical and magnetic properties of Mn–Zr doped La–Sr ferrite prepared by the auto-combustion route

This is the first report ever on (Mn²⁺–Zr⁴⁺) doped M-type lanthanum strontium hexaferrite with general formula, Sr_0.85La_0.15(MnZr)_xFe_12−2xO₁₉ where x=0.0, 0.25, 0.50, 0.75, and 1.0, prepared by citrate auto-combustion method. These ferrites were characterized by X-ray diffraction (XRD), Scanning electron microscope (SEM), Energy dispersive X-ray spectroscopy (EDX) and Vibrating sample magnetometer (VSM). X-ray diffraction patterns show the formation of high purity hexaferrite phase without other secondary phases for all the synthesized samples. It was observed from magnetic hysteresis data that the coercive force is reduced from 5692.5 Oe to 1669.2 Oe with increase in doping contents but the net magnetization of the samples varies slightly from 60.6 to 55.2 emu/gm. High saturation magnetization (M_s), low coercivity (H_c) and remanence magnetization (M_r) values of these materials make them particularly suitable for data recording.     

Preparation of ZnFe2O4–chitosan-doxorubicin hydrochloride nanoparticles and investigation of their hyperthermic heat-generating characteristics

In this study, the structural morphology and magnetic effects of magnetic ZnFe₂O₄ nanoparticles loaded with the cancer-fighting drug doxorubicin hydrochloride (DOX-HCl) were investigated. These nanoparticles have been found to have potential biomedical applications in targeted drug-delivery systems. The zinc ferrite nanoparticles were prepared by a chemical coprecipitation method and coated with chitosan. The nanoparticles were loaded with DOX-HCl and their surfaces improved by folic acid, which can be activated to target specific cancer cells. The specific absorption rate (SAR) values of the ZnFe₂O₄–chitosan–DOX-HCl nanoparticles were investigated at a frequency of 200 kHz and 1.5 kA/m amplitude in order to obtain Brownian relaxation time parameters. X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), vibrating sample magnetometry (VSM), and ultraviolet–visible spectrophotometry (UV–vis) were used to characterize the bulk properties of these nanoparticles. In addition, the impact of the nanoparticles under an alternating current (AC) magnetic field and their heat-generation ability were investigated using an experimental setup. The average nanoparticle size was found to be 8.5 nm. Magnetic hysteresis loops confirmed the superparamagnetism of the nanoparticles. The saturation magnetization was 6 emu/g. UV–vis was used to measure the amount of drug loaded onto the nanoparticles. The amount of drug absorption was significantly higher after 12 h, totaling 75%. The specific absorption rate parameter was 80.66 W/g, and the Brownian relaxation time was 188×10⁻⁹ s.     

Superparamagnetic zinc ferrite spinel–graphene nanostructures for fast wastewater purification

Superparamagnetic ZnFe₂O₄/reduced graphene oxide (rGO) composites containing ZnFe₂O₄ nanoparticles (with ∼5–20 nm sizes) attached onto rGO sheets (with ∼1 μm lateral dimensions) were synthesized by hydrothermal reaction method. By increasing the graphene content of the composite from 0 to 40 wt%, the size as well as the number of the ZnFe₂O₄ nanoparticles decreased and the saturated magnetization of the composites reduced from 10.2 to 1.8 emu/g, resulting in lower responses to external magnetic fields. Concerning this, the time needed for 90% separation of ZnFe₂O₄/rGO (40 wt%) composite from its solution (2 mg/mL in ethanol) was found 60 min in the presence of an external magnetic field (∼1 Tesla), while using ZnFe₂O₄/rGO (15 wt%), only 2 min was required (comparable to the separation time of pure ZnFe₂O₄ nanoparticles). Correspondingly, the magnetic separation time of 10 μM methyl orange and rhodamine B from aqueous solutions containing 2 mg/mL ZnFe₂O₄/rGO (15 wt%) was found <6 min, while using the ZnFe₂O₄/rGO (40 wt%) only 15–20% of the dyes could be separated after 16 min. Although the pure ZnFe₂O₄ nanoparticles could magnetically separate nearly whole of the dyes from the solutions, the separation time was too longer (>16 min).     

Development of novel magnetic-dielectric ceramics for enhancement of reflection loss in X band

The purpose of this research was to develop BaFe_9.5Al_1.5CrO₁₉-xCaCu₃Ti₄O₁₂ nanocomposites (x=10%, 20%, 30%, 40%, 50%) and investigate their structural and magnetic features. The substituted barium hexaferrite (BaFe_9.5Al_1.5CrO₁₉) nanoparticles and calcium copper titanate (CaCu₃Ti₄O₁₂) particles were synthesized by the auto-combustion sol-gel method. The structural, chemical composition and morphology of CaCu₃Ti₄O₁₂ (CCTO) and the nanocomposites were investigated by X-ray diffraction, Fourier transform infrared spectroscopy and scanning electron microscopy, respectively. The magnetic and microwave properties of nanocomposites were also investigated by vibrating sample magnetometer and vector network analyzer, respectively. The results confirmed that 1100 °C is the optimum synthesis temperature for CCTO, the mean particles size of the CCTO particles changing from 220 nm (at 850 °C) to 2.18 µm (1250 °C). The SEM micrograph revealed that in all of the BaM-xCCTO nanocomposites (x=10%, 20%, 30%, 40%, 50%), the CCTO dielectric particles were attached to the substituted barium hexaferrite nanoparticles, indicating the effectiveness of the adopted synthesis method. Due to the presence of a dielectric phase in the nanocomposites the saturation magnetization decreases from 22 emu/g to 12 emu/g. The coercive field was a slightly larger than substituted barium hexaferrite and increased from 5.558 kOe for substituted barium hexaferrite to 5.813 kOe for BaM-50CCTO due to hindered motion of the domain walls by the dielectric phase and also to the collective behavior of agglomerated barium ferrite nanoparticles. The BaM-30CCTO nanocomposite shows the highest value of reflection loss compared to other nanocomposites. The reflection dip frequency of BaM-30CCTO nanocomposite was −48.85 dB at 10.93 GHz.     

The effect of reaction temperature on the structural and magnetic properties of nano CoFe2O4

Nano cobalt ferrites (CoFe₂O₄) were co-precipitated at various reaction temperatures (60, 70 and 80 °C) for 1 h. The reaction temperature greatly influenced the crystallite size and the magnetic behaviours of the nano CoFe₂O₄. The mean crystallite size ranged from 9 to 15 nm with the increase in the reaction temperature and the intensity of metal oxide vibrations at 568–550 cm⁻¹ were also inclined. The synthesized samples were in the stoichiometric ratio of 1:2 (Co:Fe) with roughly spherical morphology. The synthesized cobalt nanoferrites exhibited ferromagnetism at room temperature and 5 K, and the saturation magnetization increased from 6.4 to 20 emu/g with the crystallite size.     

Enhancement of multiferroic properties of Aurivillius Bi5Ti3FeO15 ceramics by Co doping

Multiferroic Bi₅Ti₃Fe_1−xCo_xO₁₅ (BFCT-x, where x = 0, 0.1, 0.3, 0.5, 0.7) ceramics were synthesized via a conventional solid-state reaction process and their microstructural, ferroelectric, magnetic and magnetoelectric coupling properties were investigated in detail. All samples show layered perovskite Aurivillius phase with an orthorhombic structure. The highest remanent polarization (2P_r) (35 μC/cm²) has been observed in BFCT-0 ceramic while the BFCT-0.3 ceramic shows the highest remanent magnetization (M_r) (0.13 emu/g) and magnetoelectric coefficient (11.47 mV cm⁻¹ Oe⁻¹). The enhancement of magnetic properties and the magnetoelectric coupling of these ceramics are attributed to the structural distortion caused by Co substitution which subsequently led to ferromagnetic interactions via the Dzyaloshinskii-Moriya interaction.