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Over the past four years, the magnetism of 2D magnets has been extensively studied by the full arsenal of probing techniques. 2D magnets can be incorporated to form heterostructures with clean and sharp interfaces, which gives rise to exotic phenomena as a result of the interfacial proximity effect. Here we report a detailed study of the spin (ms) and orbital (ml) moments of an epitaxial (CrSb/Fe3GeTe2)6 superlattice. The synchrotron-radiation based x-ray magnetic circular dichroism (XMCD) technique was performed to probe the microscopic magnetic properties of the superlattices in an elemental resolved manner. We unambiguously obtained a bulk-like moment of Fe3GeTe2 i.e., ms = 1.58 ± 0.2 μB/Fe and ml = 0.22 ± 0.02 μB/Fe. Future works to explore the tuning of the spin polarized band structure of 2D ferromagnetic superlattices will be of great interest and can have strong implications for both fundamental physics and the emerging spintronics technology.

We report the magnetovolume effect of quaternary Heusler alloy CoFeCrAl as a potential candidate of spin gapless semiconductor. The crystal structure of CoFeCrAl was confirmed as the single phase of the ordered LiMgPdSn-type structure. From magnetization measurements at ambient pressure, the Curie temperature TC and the spontaneous magnetization Ms were determined to be 575.2 K and 2.01 μ B/f.u., respectively. The TC is higher enough than room temperature and the Ms follows the Slater-Pauling rule. High-pressure magnetization measurements showed that the Ms is almost independent of applying pressures not only at 10 K but also up to 300 K, exhibiting that the electronic state of CoFeCrAl is fully spin polarized and it is preserved even at 300 K. The experimental results reveal that the quaternary Heusler alloy CoFeCrAl is an attractive material for functional electrode ferromagnets in spintronics devices.

We report the results of micromagnetic simulations of low-frequency resonances associated with gyrotropic motion of exchange-coupled magnetic vortices in a system of two overlapping ferromagnetic disks. The dependences of the resonance frequencies on the method of excitation, the mutual direction of the vortex cores and on the external magnetizing magnetic field are analyzed. The modeling demonstrates that the most effective influence on the change in the resonance frequency is realized when the system is magnetized in the sample plane in the direction perpendicular to the line connecting the disks centers, opposite to the direction of magnetization in the area of disks overlapping. It is shown that for the state with opposite core polarity there are two resonant modes in which the cores and consequently the in-plane dipole moments induced in vortex shells are rotated in the opposite directions. On the contrary, in the resonant mode of the state with the same core polarity, the cores are rotated in the same directions and induced dipole moments are rotated in phase. The possibilities of using the overlapping disks system for the synchronization of vortex nano-oscillators are discussed.

Three nanocrystalline samples of ZnO doped with MnO (with 20, 30, and 40 wt% of MnO in initial mixture) were synthesized by the wet chemical method. Previous X-ray diffraction study has found that they contained only hexagonal ZnO and cubic ZnMnO3 nanocrystals. DC magnetization study revealed a paramagnetic (PM) state above 50 K, the presence of mixed valence of Mn ions (Mn3+ and Mn4+) and an important role played by magnetic clusters influencing the behavior of the effective magnetic moment and effective interaction type. Low temperature results indicated a chain of magnetic transformation from PM to ferrimagnetic, to superparamagnetic and to blocked states. Electron spin resonance (ESR) provided additional information about magnetic relaxation of the spin clusters and possible location of separate Mn2+ and Mn4+ ions. Large magnetic inhomogeneity of our samples was evidenced, and it is the result of magnetic ions clustering, various valences of Mn ions, distribution of nanoparticle sizes, and competition of magnetic interactions.

In this study, the electronic structures and magnetic and elastic properties of Cr2FeZ (Z = Sb, As) Heusler alloys were investigated through density functional theory calculations, which uses the generalized gradient approximation for the exchange-correlation functional included in the CASTEP software package. The results revealed that the Cr2FeSb and Cr2FeAs alloys successfully formed stable Hg2CuTi-type structures at finite temperatures. The ground-state properties of the stable structures were calculated, including lattice parameters, magnetic moments, and bulk moduli. The Cr2FeSb and Cr2FeAs alloys exhibited nearly half-metallic properties and high spin-polarization levels and thus can be used as half-metal/ferromagnetic metal (HM-FM) materials.

In this article, electromagnet layouts are presented, which generate a magnetic field with a magnitude gradient that does not vary significantly in a horizontal plane but decreases monotonically with the vertical height above the magnet. Such a one-direction magnetic field gradient is a specific requirement for magnetic density separation (MDS), a novel recycling technology that combines a vertical magnetic field gradient with a ferrofluid to separate a mixture of non-magnetic materials based on their mass density. We are assembling the first superconducting magnet to be used for this application. In contrast to other separation technologies that use ferrofluid, multiple products can be separated in a single process step. First, the idealized current distribution is introduced that produces such a magnetic field with a magnitude that decays only in one direction. This ideal field can be approximated with practical coil configurations, which are evaluated with a Fourier analysis to derive an optimal cross-sectional layout based on flat racetrack coils. The analysis concludes with a discussion of the effect of winding pack thickness on the value of the magnetic field above the magnet system and the peak field inside the winding pack. The conclusions of this study are applicable not just for MDS but for any application that requires a magnetic field gradient that changes only in one direction.

In this article, we present a novel micromagnetic model for L10 ordered FePt grains based on their atomic structure. In this model, each monolayer of Fe atoms is represented by a magnetic moment vector and the entire grain consists of a stack of magnetic moments coupled by magnetostatic and nearest-neighbor exchange fields. The grain model enables simulation of incoherent magnetization switching, especially near the Curie temperature. The model is applied to simulate the heat-assisted recording process in granular L10 FePt thin-film media. One of the unique findings is that grains at transition centers could have a domain wall trapped within, provided sufficient grain height. The existence of these grains, whose magnetic moments could be fractional at transition centers, resulting in significant reduction of medium noise. The noise reduction is effectively equivalent to an increase of the number of grains across the read track width. Enhancing and controlling this mechanism by material engineering could lead to significant increase of area density capability, specifically, increase of track density, without decreasing grain size.

Strained oxygen-deficient perovskite SrFeO $_{3 - \delta }$ (SFO) films have been epitaxially grown by pulsed laser deposition (PLD) on SrTiO3 (STO) (001) substrates. Oxygen deficiency of the films in comparison with the stoichiometric perovskite SrFeO3 is manifested in the increased lattice parameter, $c = 3.97$ A, the decreased mass density, $\rho = 4.825$ gcm−3, and the presence of Fe3+ cations. The SFO perovskite structure is monoclinically distorted with an increase of the film thickness, resulting in the reduction of the total magnetic moment. A wasp-waisted hysteresis loop and a negative exchange bias are observed for the 69 nm thick film due to the possible magnetic sublayers arising from a proper monoclinically distorted surface layer and a substrate-locked core layer.

Magnetic dynamic damping is significantly important in determining the relaxation time of magnetic moments and the speed of magnetic memory devices. Here, magnetic dynamic behaviors of permalloy (Py) films capped with gadolinium (Gd) are studied, and the effects of the interface are investigated by the Cu insert layer. For Py/Gd bilayer films, both the saturation magnetization ( ${M}_{s}$ ) and the surface anisotropy constant ( ${K}_{{\bot }}$ ) are decreased with increasing Gd thickness, while the Gilbert damping ( $\alpha$ ) is enhanced. With the insert of Cu at Py/Gd interface, the above tendencies of ${M}_{s}$ , ${K}_{\bot }$ , and $\alpha $ are suppressed. We attribute these phenomena to the antiferromagnetic coupling between Gd and Py near the interface, which are caused by the magnetic proximity effect (MPE) instead of the spin relaxation in the rare earth Gd themselves.

This article is devoted to the experimental investigation of the occurrence of the so-called “low-temperature Belov point” $T_{B}$ predicted previously for the mixed rare earth-yttrium iron garnet compounds RE $_{x}Y_{\mathrm {3 - {}}x}$ Fe5O12 possessing or not a magnetic compensation point $T_{\mathrm {comp}}$ . Isothermal magnetizations $M_{T}(H)$ of two single crystals of Tb $_{x}Y_{3-x}$ Fe5O12 with rare-earth (RE) = Tb, and $x = 1.98$ , 0.37, were measured in the 4.2–300 K range, using dc magnetic field $H$ up to 100 kOe applied in one or more of the three main crystallographic directions. Anomalies are observed in the region of $T_{B}^{\mathrm {TbIG}} \approx 58$ K, the previous estimated value for TbIG ( $x = 3$ ), in the temperature dependences of the paraprocess susceptibility $\chi _{p}$ , the parameter $\vert b\vert $ of the bH 2 term of the quadratic expansion of $M_{T}(H)$ curves, and other pertinent magnetic characteristics. For $x = 1.98$ with $T_{\mathrm {comp}} = 137$ K and when $H$ is applied along $\langle 110\rangle $ , the $\chi _{p}$ - and $\vert b\vert $ -maxima take place close to $T_{B}^{\mathrm {TbIG}}$ . The anisotropy of the $\chi _{p}$ -data gives evidence for a spontaneous noncollinear structure around the easy axis of magnetization $\langle 111\rangle $ at 4.2 K. For $x = 0.37$ which has no $T_{\mathrm {comp}}$ point and when $H$ is applied along $\langle 100\rangle $ , the $\chi _{p}$ - and $\vert b\vert $ -maxima are clearly disturbed by the sign anomalies caused by the noncollinear structure instability mechanism due to the crossing of the Tb3+ levels at the critical point $T^{\ast } = 16$ K and by the lower continuous change from the easy axis to a low-symmetry angular phase $\langle $ uuw $\rangle $ due to the first spontaneous spin reorientation phase transition at $T_{\mathrm {SR1}} = 40$ K. When $x$ decreases from 3 to 0.37, it is found that despite different anisotropy effects of the Tb3+ ion, its magnetic moment $m_{\mathrm {Tb}}$ close to $T_{B}^{\mathrm {TbIG}}$ is practically constant (~4.99 in $\mu _{B}$ per Tb3+ ion).

We report here on sample length dependence measurements in a second-order gradiometer superconducting quantum interference device (SQUID) magnetometer of pure nickel (Ni) cylinders, having a diameter of 1 mm and a length of 1–7 mm. The measured magnetic moment per unit mass significantly decreases with the sample length of the Ni cylinder, when a magnetic field of 7 T was applied parallel to the long axis of the cylinder. As an example, the magnetic moment per unit mass for the 5 mm Ni cylinder is between 97% and 94% of that for the 1 mm Ni cylinder, the number depending on the specific type of magnetometer used. The magnitude of decrease also depends on the length of the second-order gradiometer superconducting coil which differs with different models of SQUID magnetometers.

A system of differential equations describing the stability of a spin–torque oscillator (STO) with two free layers is introduced. The system is derived from the Landau–Lifshitz–Gilbert (LLG) equation for two freely rotating magnetic moments interacting via spin–torque. In the case of two free magnetic layers, the magnetization of each layer can precess at its own frequency, which is directly proportional to the local effective field in the layer. The spin–torque depends on the relative angle between two layers. Therefore, if the magnetization in two magnetic layers rotates with different frequencies, the spin–torque will vary in time. This can lead to instabilities of the precession angle in both the layers. When two layers oscillate at equal frequencies, instabilities due to spin–torque variations are eliminated. The requirement for the synchronization leads to a system of three differential equations for three unknowns. The stable oscillation orbits for each layer are obtained by finding fixed point solutions of the system. The results were confirmed using finite-element method (FEM) micromagnetic simulations.

Intrinsic magnetic properties and uniaxial magnetic anisotropy ( $K_{u}$ ) of $\alpha ''$ -phase ordered Fe16N2– x B x and Fe16N2– x C x alloys have been investigated through first-principles calculations. Being in agreement with experimental results, the lattice parameters, magnetic moments, and $K_{u}$ of $\alpha ''$ -Fe16N2 have been determined. Small addition of B or C dopant atoms enhances tetragonal distortion and $K_{u}$ up to 0.75 MJ $\cdot \text{m}^{-3}$ for both Fe16N1.75B0.25 and Fe16N1.75C0.25 compounds, which is more than 20% larger compared with that (0.6 MJ $\cdot \text{m}^{-3}$ ) of $\alpha ''$ -Fe16N2. Furthermore, the presence of B and C reduces magnetic moments of its neighboring Fe atoms at the 4e and 8h sites, resulting in reduced magnetization, due to less electron transfer from Fe to B and C than N. The underlying mechanism for the enhancement in $K_{u}$ is discussed in connection with the Jahn–Teller lattice distortion, atom-decomposed magnetocrystalline anisotropy, and orbital magnetism.

In this article, magnetic and structural characteristics of CoFe2O4 nanopowders with mean diameter 17.8(4) and 63.7(2.4) nm [denoted as NM(18) and CP(60), respectively] were studied by applying X-ray diffraction method (XRD), transmission electron microscopy (TEM), and vibrating sample magnetometer (VSM). It was established that for NM(18), the nanoparticle size corresponds to one crystallite while CP(60) nanoparticle forms a multi-crystallite system which means certain kind of averaging of magnetic moments. Magnetic analysis was performed according to the ZFC-FC protocol in the temperature range of 10–380 K, and magnetization curves $M(H)$ were recorded at the magnetic field up to 7 T. It was shown that, independently on nanoparticle size distribution, the magnetic response of both nanopowders is mainly determined by superspin glass type interaction of magnetic moments corresponding to a single crystallite. In addition, basic magnetic characteristics such as anisotropy constant $K_{1} =$ (3.9–12.5) $\times 10^{5}$ J/ $\text{m}^{3}$ , anisotropy field $\mu _{0}H_{\mathrm {A}} = 1.80$ –5.80 T, or magnetic moment per formula unit $\mu =3.45$ (5) $\mu _{\mathrm {B}}$ [for CP(60)] and $\mu =3.50$ (5) $\mu _{\mathrm {B}}$ [for NM(18)] were also determined and discussed.

This paper analyzes the torque characteristics of a magnetic rack-and-pinion gear using an analytical method based on the spatial harmonic method. We obtain the magnetic field distribution due to the permanent magnets and derive the magnetic torque from the magnetic field using the Maxwell stress tensor. The analytical results are extensively validated by comparing with finite element analysis results. Finally, we obtain an accurate analytical solution to reduce the analysis time and experimentally verify this solution by applying it to a newly manufactured rack–pinion gear model.

We demonstrated crystal structures, magnetic, and optical properties of the B-site substituted double-perovskite Ba 2 Pr(Bi 1-x Sb x ) O 6 (x = 0, 0.1, 0.2, 0.25, 0.3, 0.4, 0.5, and 1.0). The single-phase polycrystalline samples with the light Sb substitution are formed in a monoclinic structure (C 2 /m). The heavily Sb-substituted samples crystallize in the rhombohedral system accompanied by B-site disorder. Magnetization measurements show that the effective magnetic moments are located around 3.2 μ B for the lightly Sb-substituted samples, indicating the valence mixing between Pr 3+ and Pr 4+ . The magnetic moments with the heavy Sb substitution are close to the valence of Pr 3+ . The magnitudes of bandgap energy for the two end-member samples were estimated from the optical measurements to be E g = 0.977 eV at x = 0 and 2.395 eV at x = 1.0. The effect of the bandgap opening due to Sb substitution is examined by using the density functional theory. The lightly and heavily Sb-doped compounds show typical absorption edges in indirect and direct semiconductors, respectively. These findings are qualitatively consistent with the calculated results.

Permanent magnets are one of the key parts in energy conversion devices to realize the utmost efficiency. DC motors up to the 100-kW class are used in some ‘‘strong’’ hybrid electric vehicles (HEV), in which the top-grade Nd-Dy-Fe-B-type permanent magnets are required. Such motors have inner permanent magnet (IPM) rotors with which the combination of magnet torque and reluctance torque is optimized. For such an optimized design, permanent magnets are shaped in thin plate-like blocks with a thickness of about 5 mm, inserted into slots in a laminated rotor core, and magnetized perpendicularly to the largest surfaces of the block. The weight of the magnets may amount to about 2 kg or less per vehicle. The reason why Nd-Dy-FeB permanent magnets are used is simply because the highest performance of this class of material in terms of residual flux density, Br, can be generated with them. These magnets have high intrinsic coercivity, HcJ, typically about 2.0–2.4 MA/m. Such high HcJ values are certainly not necessary at room temperature, but the magnet temperature can rise to about 200C at which HcJ is only about 0.6–0.8 MA/m, being marginally enough to withstand the armature magnetic fields generated by driving current. Dysprosium (Dy) or terbium (Tb) is used in the magnet in order just to obtain such high HcJ but have been indispensable in the permanent magnets. Since Dy and Tb can be mined industrially only in a southern province of China in a limited quantity, Dy and Tb are now typical critical elements, overreliance on these elements should be avoided. For this very reason, permanent magnets beyond Nd-Dy-Fe-B are now extensively sought. Development of permanent magnets beyond the Nd-Dy-Fe-B is a challenge because Nd2Fe14B, the main hard magnetic phase of the magnet, is the compound that has the largest magnetization at room temperature among all existing hard magnetic compounds, and that, in terms of elemental abundance, already consists mainly of Fe and Nd, both of which are the most abundant elements carrying magnetic moments in the 3d and 4f transition metal series, respectively. One of the approaches is to reduce the overall average Dy content over the entire commercial grades down to a sustainable level, which may be about 1–1.5 mass percent in the magnets, even if the crustal abundance ratio with Nd is considered. Another approach is to seek for an entirely new material with or without rare earth elements. In advanced economic blocks that have benefitted from functional critical elements, governments have taken strategic actions to promote developments in technologies that will lead to reduced society’s dependence upon those elements. In Japan, well

The 1-D nanoscale structures are studied with a potential relief containing magnetic barriers separated by nonmagnetic quantum wells in the absence of exchange interaction between the magnetic moments of adjacent barriers. The considered structure is the sequence of N barriers divided into two “ferromagnetic domains” of the length n and N - n-1, both having parallel internal fields. In contrast, the internal field of the nth barrier is not coplanar with respect to the internal fields of the left and/or right “domains.” The degree of spin polarization of an electron wave transmitted through this system is calculated with the assumption that the incident wave is unpolarized with the degree of its polarization equals zero. It is shown that the degree of polarization of the transmitted wave as a function of the impulse exhibits a sequence of sufficiently wide plateaus, which are close to unity. In particular, there are significant deviations from the known spintronics phenomena found earlier in this system such as the valve, filter, and giant magnetoresistance effects. This circumstance provides opportunities for managing the transport properties of the system by varying the noncoplanar degrees of freedom of the system.

The electronic structures and magnetic properties of the transition-metal (TM)-doped WS 2 monolayers are investigated by using the first-principles calculations within the density functional theory. The W atoms of the pristine WS 2 monolayer are partially replaced by the 3d TMs of Mn, Fe, Co, and Cu with the impurity concentration of about 4%. For the uniformly distributed doping, the ferromagnetic phases are found to be stabilized with the total spin magnetic moments of 1.00, 2.00, 3.00, and 1.00 μB for the Mn-, Fe-, Co-, and Cu-doping, respectively, where not only the spin moments of the TM dopants but also the induced spin moments of the W and S atoms contribute significantly depending on the dopant type as well as on the relaxation. All systems are found to be half-metallic with the spin gap of 0.10-0.53 eV. Among them, the biggest spin gap is found for the doping of Co which is the ingredient of the well-known half-metallic Heusler alloys. When the TM dopants were brought closer keeping the same impurity concentration, the preference of the substitutional doping site and the magnetic phase is changed sensitively depending on the type of doping and the interatomic distance between the TM dopants.

We report here on the reproducibility of measurements on a second-order gradiometer superconducting quantum interference device magnetometer of two different yttrium iron garnet spheres, both having a diameter of 1 mm: 1) the National Institute of Standards and Technology magnetic moment standard reference material (SRM) and 2) a commercial sample. It has been suggested that rotating the sample rod around its axis can move the sample center toward the center of the second-order gradiometer coil. The observed value of the magnetic moment will be theoretically a minimum when the radial offset is 0, and this value will increase in a “quadratic” manner with the radial offset. When the magnetic moment of the SRM was repeatedly measured as a function of rotation angle φ from 0° to 360°, we observed a sinusoidal variation in the measured values. The radial offset dependence of the observed magnetic moment was experimentally confirmed by the measurements of the commercial sphere placed in a hole in several cylindrical containers, wherein the distance between the center of the hole and the center of the container was r. The r-dependence of the minimum from each φ-dependent measurement series is qualitatively consistent with the theoretical curve. When the φ-dependent measurements for the SRM in a capsule were repeated 12× over 21 months, the relative standard deviation of the minimums improved up to 0.1%. Knowledge of these facts will be necessary for the accurate measurement of the magnetic moment of other sample forms (e.g., powders).

We report a systematic study of room temperature large positive and negative magnetoresistance (MR) in the reduced graphene oxide (RGO) thin-film devices grown by pulsed-laser deposition (PLD) at high and low applied magnetic fields, respectively. Raman spectroscopy, X-ray photoelectron spectroscopy, and electrical measurements on the RGO films help to explain the observed MR properties in the device. The temperature-dependent (5–400 K) electrical characterization of the thin films shows two distinct transport regimes: at low temperature, it follows 2-D Efros-Shoklovoski variable range hopping (VRH) transport mechanism and above 200 K, the device shows Arrhenius-like transport behavior. The crossover from VRH transport to Arrhenius transport is due to shortening in the characteristic lengths in the disordered 2-D system. We interpret the source of negative MR by vacancy and disorder-induced magnetic moments and the diffuse scattering at crystallite boundaries. At the high applied magnetic field, the lifting in degeneracy due to the Lorentz force explains the large positive MR effect. The highest value of the measured MR (160%) is surprisingly high for a non-magnetic material at room temperature, which can be attributed to the greater inhomogeneity in the PLD grown wafer-scale RGO thin films.

This paper presents a method for position measurement under uncertainty using magnetic sensing. The statistical transformation of magnetic field data in the presence of noise is first developed. An unscented Kalman filter is then formulated based on a stochastic dynamic model that would allow for position estimation from magnetic field sensing. Finally, applications of magnetic sensing-based positioning in robotics and vehicle guidance are provided to validate the algorithm. The methods presented in this paper extend filtering theory for extracting positioning information from magnetic fields.

Magnetic flux leakage (MFL) testing is a widely applied method for the ferromagnetic specimen defect detection. In this paper, we present a solenoid analytical model to MFL field based on the molecular current model of a magnetic medium. This model applies $B$ – $H$ characteristics of the material to confirm the homogeneous magnetization of the specimen and to obtain the magnetic moment of solenoids, and then it uses a semi-infinite solenoid as the source to simulate the leakage field. Furthermore, this model proves that the edge effect and defect geometry can be represented properly by setting ellipsoid defects at different positions in the specimen. The results of the proposed model are influenced not only by defect shape as that of the magnetic dipole model but also by the relationship between the magnetization and the normal direction of the defect surface, which leads to the more accurate reconstruction of defects. Based on these findings, the error from the assumption of homogeneous magnetic dipole distribution or magnetization can be explained by the solenoid interaction. This explanation provides a new way to eliminate the computation error, and the solenoid model shows higher computational efficiency compared with the numerical model.

In this paper, we present a strategy employing four coplanar magnetic sensors with a single sensitive direction to detect the position of a magnet in a 2-D plane parallel and above the sensors’ plane. By positioning the magnet in such a way that its magnetic moment vector lies on the direction orthogonal to the sensing elements’ sensitive direction, the signal on the sensor plane assumes a quadrupolar characteristic, which takes advantage of both the negative and positive sensing ranges of the magnetic sensors, maximizing signal variability in the sensing plane. To validate this strategy, a sensing device with a $3\times 3$ mm2 active area containing four magnetic tunnel junction arrays as magnetic sensors was fabricated. Since the combination of the measured signal in each sensor is correlated with the magnet position, these were fitted using predictive methods to map both the quantities to each other. The two best performing predictive methods, artificial neural network fitting and regression forest fitting, were verified against an independently acquired data set, yielding a position root mean square error of 178 and $96~\mu \text{m}$ , respectively.

Macroscopic hysteresis loops and microscopic magnetic moment distributions have been determined by 3-D model for Co nanowire with various easy axis deviations from applied field. It is found that both the coercivity and the remanence decrease monotonously with the increase of easy axis deviation as well as the maximum magnetic product, indicating the large impact of the easy axis orientation on the magnetic performance. Moreover, the calculated angular distributions and the evolution of magnetic moments have been shown to explain the magnetic reversal process. It is demonstrated that the large demagnetization field in the two ends of the nanowire makes the occurrence of reversal domain nucleation easier, hence the magnetic reversal. In addition, the magnetic reversal was illustrated in terms of the analysis of the energy evolution.

The realization of the magnetic moment of Mn atoms in ferromagnetic alloys is investigated theoretically. This paper is partly motivated by the recent discovery of high-magnetization Fe–Co–Mn thin films by Snow et al. , who reported moments of up to 3.25 $\mu _{\text {B}}$ per atom. Structural and strain effects are discussed with particular emphasis on the distinction between tetragonal martensitic lattice distortions and Bain transitions in body-centered cubic, CsCl, and Heusler alloys. It is outlined how these lattice distortions affect the electronic structure of the alloys, and ab initio calculations are used to determine the net moment of cubic Fe6Co63Mn31. The calculated moment, $2.90~\mu _{\text {B}}$ per atom, is reasonably close to the experimental value.

The effects of the partial substitution of Mn by Co/Fe on the structural, magnetostatic, and magnetodynamic properties of Ni–Mn–In Heusler alloy films were studied using X-ray diffraction, field-dependent magnetization, and ferromagnetic resonance studies. It was observed that the substitution of up to 3 at.% Co or Fe atoms in Mn sites does not alter the crystal structure much. However, an increase in grain size and surface roughness was noticed upon substitution of the fourth element. The magnetic moment of the films could be increased up to 120 kA/m by introducing Co/Fe in Mn sites. For the first time, low Gilbert damping constant ( $\alpha$ ) of 0.008 is observed in Co substituted Ni–Mn–In film together with high saturation magnetization, high perpendicular anisotropy, and an easy axis along film plane, which are the promising factors for application in high-density random-access memory devices.

Soft magnetic films have attracted considerable attentions for high frequency applications, such as on-chip power inductors, transformers and voltage regulaters. Loss control is the most critical tasks for these applications.[1] The high frequency loss of magnetic thin films typically includes hysteresis loss, eddy current loss, and ferromagnetic resonance (FMR) damping loss. Nanogranular FeCo-X-O (N) (X denotes Si, Hf, Zr, Ti, Zn etc.) have higher resistivity and saturation magnetization than those of permalloy or amorphous alloys. Meanwhile, the critical thickness can be 500 nm or above due to the suppressed growth of columnar structures by insulating layers.[2] All these make the nanogranular films very attractive for on-chip passive devices. So far, nanogranular films are mainly grown by sputtering. The in-plane uniaxial anisotropy $( H_{\mathrm {k}})$ required for hard-axis exited inductors and transformers can be induced through in-situ magnetic biasing field $( H_{\mathrm {bias}})$ during growth or oblique sputtering, both of which are widely adopted in the fabrication of CMOS compatible magnetic devices.[4] However, the research about high frequency magnetic loss related to these two processes is still scarce. We here report our efforts to reducing the effective damping factor of nanogranular FeCoTiO films. Fig. 1(a-c) show the imaginary part of the permeability spectra of FeCoTiO films deposited at different oblique angles (β) upon applying magnetic field along the easy axis (called low-field FMR). It can be seen that the FMR frequency $( f_{\mathrm {r}})$ increases from 3 GHz to 5 GHz upon increasing β from 17° to 32° at zero field. Therefore, the working frequency of nanogranular films can be simply tuned by adjusting β angle. Fig. 1(d) shows that full width at half maximum (Δf) of the imaginary permeability spectra. The lowest Δf about 0.76 GHz was obtained in the film with β of 17°, corresponding to a low $\alpha _{\mathrm {eff}}$ of 0.013. Further increasing β angle cause significant structural inhomogeneities and larger $\alpha _{{\mathrm {eff}}}$. Fig. 2(a-c) show the permeability spectra of FeCoTiO films deposited with in-situ $H_{\mathrm {bias}}$ of 15, 70 and 115 Oe, respectively. Regardless of the magnitude of $H_{\mathrm {bias}}$, it is found that $H_{\mathrm {k}}$ varies in a small range between 70 Oe and 80 Oe. Our results clearly reveal that the rearrangement of Fe-Fe(Co) atom pairs almost fully completed at an external field as small as 15 Oe during sputtering. According to the two magnon theory, the extrinsic $\alpha _{\mathrm {eff}}$ is generally related to the magnetic inhomogenieties.[4] The low field FMR results in Fig. 2 indicate that (i) further increasing biasing field cannot fully suppress magnetic inhomogenieties, which is true for even for $H_{\mathrm {bias}}$ up to 900 Oe (not shown); and (ii) Δf decreases with the increase of the external field and the minimal Δf is 0.55 at an external field of 200 Oe, as shown in Fig. 2 (d). Finally, we calculated the high frequency loss μ”/μ’ of FeCoTiO films. The two sets of data are from the film deposited under in-situ $H_{\mathrm {bias}}$ of 115 Oe and the film by oblique sputtering at β = 17°. The μ”/μ’ of oblique sputtered FeCoTiO film dominantly comes from FMR damping above 1.6 GHz, below which only hysteresis loss can be observed. However, for the FeCoTiO film deposited under $H_{\mathrm {bias}}$ of 115 Oe, the FMR damping can be observed down to 200 MHz due to a large $\alpha _{ {eff}}$ of 0.026. Furthermore, the overall high frequency loss of oblique sputtered FeCoTiO film is much smaller than that of the FeCoTiO film deposited under in-situ Hbias, although the coercivity along the hard axis $( H_{\mathrm {ch}})$ of the former (11 Oe) is much larger than the latter, 3 Oe. The large $H_{\mathrm {ch}}$ of oblique sputtered FeCoTiO films may come from the pinning effect of columnar structures. On the other hand, such columnar structure also brings the advantages of well aligned magnetic moments and reduced magnetic inhomogeneities in the FeCoTiO film.

On the basis of damping principle of vibration, the domain wall processes is investigated and modeled at low-to-medium frequencies in electrical steel sheets. Due to the energy dissipation chiefly descends from a micro-vortex current caused by domain wall motion, the coupled Landau-Lifshitz-Gilbert (LLG) and Maxwell electromagnetic diffusion equations are thus considered to describe the high-frequency characteristics. The overall core losses are eventually deduced in terms of separate contributions by domain wall processes and classical eddy current. Moreover, the calculation model can be extended to rotational excitation pattern. Hence, taking the typical electrical steel sheets as example, the novel core losses calculation model is analysed and compared with the total alternating core losses supplied by electrical steel sheets manufacturers and the 3-D rotating experimental core losses of sheets specimens which are carried out by using a 3-D magnetic properties testing system, and also achieve some beneficial conclusions. 1. Since the domain wall processes is essentially the magnetic moment rotation, then domain wall motion can be interpreted by solving LLG equation, that is [1], [2]:\begin{align*} \partial J/ \partial t \quad =- xJ \times [H_{eff}+(\alpha /J_{s}) J\times H_{eff}], (1)\\ \vert J \vert = \quad J_{s}(1) \end{align*}where, $J \quad = \mu _{0}M$ represents the magnetic polarization vector inside the domain, $M$ is the magnetization vector, $\mu _{0}$ is the permeability of vacuum, $ \chi =|e| / m_{e} \quad = 1.76 \times 10 ^{11} \mathrm {T}^{-1} \mathrm {s}^{-1}$ is the absolute value of the electron gyromagnetic ratio [3]; $H_{eff}$ represents the overall effective field, which affects on the magnetic moments; $\alpha = \eta J_{s}$ is the qualitative dimensionless damping constant (Landau-Lifshitz damping coefficient), $eta$ is the damping coefficient of domain wall motion, $J_{s}$ is the saturation polarization. The first term on the right side of Eq. (1) describes the magnetic moment precession around the effective field direction, while the second term is the damping motion towards the effective field. 2. As regard to the right sheet with the walls in Fig. 1, in effect of the high-frequency excitation field $H$, the wall moves to make on both sides of the domains contraction and expansion. Now, by applying Maxwell electromagnetic diffusion equation:\begin{equation*} \partial ^{2}H_{vor}/ \partial y^{2} \quad =\sigma \mu _{0}[ \partial (M+H_{vor}+H)/\partial t](2)\end{equation*}where, $\sigma $ is the electrical conductivity of magnetic materials and the vortex current field $H_{vor}$ is directed to $y -$axis. At this point, such a response can be described in general terms by the solution of the coupled LLG (Eq. (1)) and Maxwell electromagnetic diffusion (Eq. (2)) equations. 3. According to the above derivation, the overall core losses per unit mass of electrical steel sheets are eventually deduced in terms of separate contributions by classical eddy current and domain wall processes, as follows:\begin{equation*} P_{cl} \quad = P_{cel}+P_{mel}^{-} \quad = \left({ \sigma \pi ^{2}d^{2}/ 3 \rho }\right) f^{2}(B_{m})^{2}+\left({\sigma \pi ^{2}d^{2}/ 4 \rho }\right) f^{2}(B- \mathrm {m}) ^{2}=\left({ 7 \sigma \pi ^{2}d^{2}/ 12 \rho }\right) f^{2}(B_{m})^{2}[\mathrm {W} /kg](3)\end{equation*}where, $P_{cl}$ is the overall core losses per unit mass of electrical steel sheets; $P_{cel}$ is the classical eddy current loss per unit mass; $P_{mel}^{-}$ is the mean micro-vortex current losses per unit mass; $d$ is the thickness of the magnetic sheet; $ \rho$ is the mass density of magnetic materials; $f$ is the excitation frequency; $B_{m}$ is the peak flux density. 4. In order to validate the precision of the calculation model, the total alternating core losses supplied by electrical steel sheets manufacturers are used to compare with the calculation of Eq. (3), including cold-rolled GO electrical steel, NO electrical steel and hot-rolled electrical steel over wide range of excitation frequency [4], [5]. In addition, the model can be extended to rotational excitation pattern, so the 3-D rotational experimental core losses of typical electrical steel sheets carried out by using a 3-D magnetic properties testing system are also considered in the validity of the calculation model [6], [7]. The typical comparison result is shown in Fig. 2.

Mn ${_{1-x}}$ Zn x Fe2O4 ( $0.1\le x\le 0.8$ ) thin films with nanocrystalline grains were deposited on amorphous quartz substrate using pulsed laser ablation technique, at a substrate temperature of 650 °C. For $x\le 0.3$ , the room temperature spontaneous magnetization ( $4\pi M_{S}$ ) of thin films was observed to be lower than the bulk composition. For $x=0.7$ , the room temperature $4\pi M_{S}$ value (~6.1 kG) is 7.5 times the bulk value for same x. This value is only 1.4 times of the bulk at 10 K, signifying a large enhancement in the exchange constant for thin films. The exchange stiffness constant (D) values were evaluated by fitting the $4\pi M_{S}$ data to the Bloch equation. The D values of thin films were always higher than that of the bulk. This result can be explained on the basis of occupancy of nonmagnetic Zn2+ on both the tetrahedral (A) and octahedral (B) sites. This is unlike in the bulk, where all the Zn2+ ions occupy only A site.

Using density functional theory, the interface local magnetic moment and its variation are explored in SrRuO3|LaAlO3|vacuum (001) heterostructures with increasing number of LaAlO3 unit cells. The computed magnetic moment projected on interface planes is found to modulate nearly periodically as the number of LaAlO3 unit cells is increased in SrRuO3|LaAlO3|vacuum structure. The magnetic moment localized at the interface RuO2 plane shifts from a lower value of $\sim 0.7~\mu _{B}$ to a higher value of $\sim 1.35~\mu _{B}$ and changes by ~42% as LaAlO3 changes from non-stoichiometric to stoichiometric with increase in its thickness. However, the magnitude shifts from higher to lower value as LaAlO3 changes from stoichiometric to non-stoichiometric with further increase in thickness. The large variation and nearly periodic modulation of magnetic moment localized at the interface with increasing LaAlO3 thickness arise due to spin-dependent screening of effective total charge of LaAlO3 film by accumulated free carriers at the interface in heterostructure. The modulation of interface local magnetic moment using ultrathin LaAlO3 film at the oxide heterointerfaces can be exploited as an additional functionality, in conjunction with those reported recently such as control of band alignment and enhancement of the electric conductivity at the interface.

Nanocrystalline (NC) alloy may confront saturation problems with different high-frequency operation circumstances, which are summarized as two typical situations in this paper. One case is “dynamic saturation (DS)” where the alternating magnetic field contains the weak dc biasing field. Another situation is “static saturation (SS)” where the hybrid field comprises not only the weak time-varying field but also the strong dc biasing field. The external and internal factors that affect the saturation magnetization process for the NC alloys were analyzed, under two types of saturation magnetic fields. Two parameters including the saturation time and the rotational velocity of magnetic moment were employed. The external factors, which determine the working condition of the NC alloys, are the dc biasing field and the frequency of the alternating field. The effects of the above two factors are related to the type of saturated magnetic field. In the DS field, the promoting effect of frequency increase on the magnetization process is greater than that of the biasing field, while in the SS field, the opposite is true. The internal factor, which is the grain size, is essential to the soft magnetic properties of the NC alloys. The effects of this factor are independent of the type of saturation field. Increasing the grain size of the NC alloys will delay the magnetization process.

Ni1−xMgxFe2O4 (x = 0.2–0.8) nanoparticles are prepared by hydrothermal synthesis followed by microwave processing. The effect of microwave processing in reducing the required heat treatment is discussed. The samples are characterized by powder X-ray diffraction, field emission scanning electron microscopy, transmission electron microscopy, vibrating sample magnetometer, and LCR bridge. Microwave processing has enhanced the chemical reaction to form ferrites without any stray ferric oxide phases. Microscopic images have confirmed that the particles still retain nanoscale after microwave processing. An appreciably high magnetic moment is noticed. The experimental magnetic moment is used to estimate the cation distribution in tetrahedral and octahedral sites. Temperature and frequency dependence of initial permeability is discussed in the light of magnetic spin canting.

Dysprosium (Dy) is ranked among those rare earths which have relatively high magnetic moment and behaves as a ferromagnetic well below room temperature (RT) with low Curie temperature. RT ferromagnetism in Dy-based alloys presents itself as a highly efficient candidate for thermally induced magnetic switching applications. A minute content of Fe in specifically designed nanostructure could introduce RT magnetization in Dy-based alloyed nanostructure. In this context, here, we present underlying magnetic dynamics and laser-induced magnetic switching in the novel design of Dy–Fe nanostructures by atomic spin model simulations. Monte Carlo and Landau–Lifshitz–Gilbert–Heun simulation integrators in addition to a femtosecond pulsed laser for an abrupt thermal pulse applied to explore the unprecedented magnetic behavior of random alloy, bilayer, and core–shell novel nanostructural designs of 5 nm sizes with 5 at % Fe contents in Dy. The practicability of these nanostructures having various sizes and designs for ultrafast magnetic switching in magnetic recording media is demonstrated.

Magnetic force microscopy (MFM) has been used to probe the influence of an in situ applied in-plane elastic strains and/or magnetic field on the static magnetic configuration of a 530 nm magnetostrictive FeCuNbSiB thin film. The film shows a typical magnetic stripe domain configuration with 180 nm magnetic domain width presenting its magnetic moments oriented perpendicularly to the film plane. The in-plane strain was induced via the application of a voltage in a piezoelectric (PE) actuator on which the film/substrate system was glued. The FeCuNbSiB film was deposited onto a compliant polyimide substrate (Kapton) in order to avoid clamping effects that can lead to low transmission of strains from the actuator to the film/substrate system. The instrumental setup was modified with a custom-built electromagnet for performing in situ MFM experiments under the application of an in-plane magnetic field. We could compare the strain-mediated effect upon the magnetic domain configuration with the effect of an applied magnetic field. This paper clearly shows a better-defined electric field/strain control of the local domain magnetization (size and orientation). The efficient coupling between the magnetostrictive properties of the FeCuNbSiB film and the PE ones of the actuators allows a complete switching of the out-of-plane domain magnetization toward an in-plane homogeneous magnetic one. This magnetoelectric heterostructure can thus open the way for new devices allowing the electric control of the magnetic information at the nanoscale level.

We proposed track-etched membrane with a ferromagnetic coating, comparable in thickness to pore diameter, as a separating unit for high-gradient magnetic separation of magnetic nanoparticles (MNPs). A high-gradient magnetic field arisen on a membrane surface in pore vicinity can capture particles of the highest magnetic moment. Ferromagnetic track-etched membrane (FTEM) with pore diameter of $3 ~\mu \text{m}$ has been coated with a layer of Permalloy (Fe20Ni80) of 1 and $2~ \mu \text{m}$ replicating the membrane pore structure. MNPs were separated by their size and magnetic properties on the FTEM. Magnetite hydrosol of an average particle size of 50 nm was fractioned into eluate with an average particle diameter 30–35 nm and retentate with an average particle diameter 65 nm using the FTEM with the $3~\mu \text{m}$ pores. The advantages of thicker ferromagnetic layers for effective separation of sub-micrometer magnetic particles have been confirmed both theoretically and experimentally.

Understanding of magnetization behavior in magnetic nanostructures is a key issue for future magnetic/spintronic devices. Time-resolved X-ray magnetic circular dichroism (XMCD) is a powerful measurement technique with potential of nanometer spatial resolution, picosecond time resolution, and element selectivity. We have carried out time and spatially resolved XMCD microscopy measurement on a Co/Pt multilayer dot by detecting XMCD at the Pt $L_{3}$ edge at BL39XU of SPring-8 using hard X-ray. Transient magnetic response of Co/Pt multilayer dots with diameter of $2.6~\mu \text{m}$ was investigated against pulsed RF field with frequency around 2.5 GHz and the maximum amplitude of about 400 Oe. By synchronizing excitation RF field pulse with X-ray pulses, the growth of magnetization precession of the induced Pt magnetic moment in the dot was clearly observed with sub-100 ps time resolution and submicrometer spatial resolution. The developed measurement setup can be applicable for a wide range of studies for time-resolved hard X-ray experiments.

Cu2+ substituted manganese ferrite nanoparticles (Cu x Mn1– x Fe2O4, $x = 0$ , 0.3, 0.5) were prepared using the Coprecipitation method. The effects of Cu2+ doped on the structure and the magnetic properties of the products were characterized by X-ray diffraction (XRD), Fourier transform infrared, and vibrating sample magnetometer (VSM), respectively. The scanning electron microscopy and energy dispersive X-ray analysis were carried to the morphological assessment and the percentage of Cu/Mn values. The crystallite size of the samples is in the range of ~35–42 nm, and the lattice parameter is decreased from 8.50 to 8.394 °A with Cu2+ content. Cation distribution and structural parameters of the synthesized powder were determined by Rietveld analysis of the XRD data. Room temperature VSM measurements show that the products have a ferromagnetic behavior with the saturation magnetization ( $M_{s}$ ) values in the range of ~42–30 emu/g. The results showed that the decrease of $M_{s}$ with increasing the copper concentration can be attributed to the influence of the occupancy in the specific sites and the difference in the magnetic moment of Cu2+ and Fe3+.