Magnetic Moment Distribution Research Articles

Efficient equivalent-layer technique for processing irregularly spaced magnetic data on uneven surfaces

We present a new rapid and robust equivalent layer method for processing large magnetic data sets that can deal with irregularly spaced data points on undulating surfaces. Our method estimates an equivalent layer by numerically solving the upward continuation integral for a given set of magnetic data. While this estimated layer allows performing specific spatial transformations such as interpolation and continuations of any potential-field data, it cannot be used to perform conventional phase transformations on magnetic data, such as the reduction to the pole, because it requires a magnetic moment distribution over the equivalent layer of dipoles. To overcome this drawback, we transform the estimated equivalent layer into a planar equivalent layer of dipoles that equally reproduces the observed magnetic data. To carry out this transformation, we first use the fact that the estimated layer obtained by solving the upward continuation integral is a scaled version of the magnetic data on the layer plane, i.e., it can be considered a harmonic function. Then we use the upward continuation integral to continue the estimated layer into a planar and regular grid, which results in a second equivalent layer. Finally, we apply a fast 2D discrete convolution to transform this second layer into a planar equivalent layer of dipoles that also fits the observed magnetic data. Applications to synthetic and real data show that our methodology is able to efficiently process magnetic data, combining the robustness of accommodating irregularly spaced data with the ability to perform phase transformations.

Finite Nuclear Size Effect on the Relativistic Hyperfine Splittings of 2s and 2p Excited States of Hydrogen-like Atoms

Hyperfine splittings play an important role in quantum information and spintronics applications. They allow for the readout of the spin qubits, while at the same time providing the dominant mechanism for the detrimental spin decoherence. Their exact knowledge is thus of prior relevance. In this work, we analytically investigate the relativistic effects on the hyperfine splittings of hydrogen-like atoms, including finite-size effects of the nucleis’ structure. We start from exact solutions of Dirac’s equation using different nuclear models, where the nucleus is approximated by (i) a point charge (Coulomb potential), (ii) a homogeneously charged full sphere, and (iii) a homogeneously charged spherical shell. Equivalent modelling has been done for the distribution of the nuclear magnetic moment. For the 1s ground state and 2s excited state of the one-electron systems H1, H2, H3, and He+3, the calculated finite-size related hyperfine shifts are quite similar for the different structure models and in excellent agreement with those estimated by comparing QED and experiment. This holds also in a simplified approach where relativistic wave functions from a Coulomb potential combined with spherical-shell distributed nuclear magnetic moments promises an improved treatment without the need for an explicit solution of Dirac’s equation within the nuclear core. Larger differences between different nuclear structure models are found in the case of the anisotropic 2p3/2 orbitals of hydrogen, rendering these excited states as promising reference systems for exploring the proton structure.

Sperimagnetic states in amorphous Gd x (FeCo)1-x (0.2 ≤ x ≤ 0.3) alloys: insights from stochastic magnetic anisotropy analysis

Materials crucial for the advancement of magnetic recording technologies stand as pivotal elements in the development of a new generation of recording devices. Recent advancements in the manipulation of magnetization through laser pulses have underscored the significance of magnetic materials exhibiting robust magneto-optical properties. This study explores the manifestation of a sperimagnetic state in ferrimagnetic amorphous Gd x (FeCo)1−x alloys utilizing a stochastic magnetic anisotropy approach. Phase diagrams ‘magnetic field’-‘temperature’ and temperature dependencies of magnetization and compensation point were calculated using the mean-field approximation for temperature range from 50 to 700 K and different stoichiometry of the alloy, namely 0.2 ≤ x ≤ 0.3. Accounting for the stochastic anisotropy intrinsic to rare earth ions, a distribution of magnetic moments within the amorphous solid is discerned. Notably, this distribution predominantly manifests at the fringes of a canted phase, constituting the sperimagnetic structure. We demonstrate a direct correlation between an increased variance in normally distributed anisotropy constants of rare earth ions and a corresponding augmentation in the standard deviation of magnetization within the sperimagnetic structure. These findings not only contribute to a deeper understanding of the interplay between material composition and magnetic properties but also provide valuable insights for the advancement of magnetic recording technologies.

Entanglement between Micro-Magnetism, electromagnetism and the Tensor Magnetic Phase Theory (TMPT) – Symmetry, conservation and invariance laws analysis at low frequency

Ferromagnetic materials show magnetic structures with domains and walls. Thanks to decades of research regarding the origin and behaviour of magnetic domains, we now possess a general foundation which has been verified experimentally in single crystals and powders. The governing equations at the microscopic scale were built in the 1960 s when Brown published calculations of the magnetic moments distribution inside domain walls. This micromagnetic theory uses the so called LLG ‘Landau-Lifshitz-Gilbert’ equation and can include the damping effects. The LLG equation requires a coupling to the field derived from energy contributions: exchange, anisotropy, magnetostriction, stray-field … and the anti-eddy field. At the macroscopic scale, such behaviours are lumped in a homogenized magnetization law for the electromagnetic field equations inside larger polycrystals. Therefore, the inhomogeneous magnetic material nature is always ignored. The Tensor Magnetic Phase Theory (TMPT) describes the magnetic structure and the magnetization thanks to a tensor variable at a mesoscopic scale. The material structuring is then explained thanks to an energy balance which will be discussed.This paper presents the results of investigations on entangled relationships between the micromagnetic theory, the electromagnetic theory and what is called the Tensor Magnetic Phase Theory (TMPT), which statistically describes the magnetic structures of soft ferromagnetic materials. It examines a connection between the TMPT and the LLG by deriving the main energy terms. Then, the TMPT must stay compatible and coupled to the Maxwell equations at low frequencies with volume and surface connections. Additionally, this paper investigates the way to derive the domains structuring and magnetization laws through the Lagrange principle and the corresponding conservation laws with invariants linked to the Nœther theorem. Finally, the TMPT must be discussed while checking its coherence and formulation when changing the reference frame.

Nanoscale dynamics of hydrogen in VO2 studied by μSR

Hydrogen dynamics in the nanoscale region of VO2 was investigated by muon spin rotation/relaxation (μSR) technique. Positively charged muon acts as a light radioisotope of protons and can be used as a probe to explore the inside of materials from an atomic perspective. By analyzing the muon hopping rate and the spatial distribution of the V51 nuclear magnetic moments, we have identified two types of diffusion paths in VO2 (via oxygen-muon bonds or defects) and the potential of a high diffusion coefficient in the 10−10cm2/s range at ambient temperature. Our results provide valuable information for developing hydrogen-driven VO2-related electronic devices. Published by the American Physical Society 2024

Magnetodielectric Effect in a Triangular Dysprosium Single-Molecule Toroics.

Single-molecule toroics are molecular magnets with vortex distribution of magnetic moments. The coupling between magnetic and electric properties such as the magnetodielectric effect will provide potential applications for them. Herein, the observation of significant magnetodielectric effect in a triangular Dy3 crystal with toroidal magnetic moment and multiple magnetic relaxations is reported. The analysis of magnetic and electric properties implies that the magnetodielectric effect is closely related to the strong spin-lattice coupling, magnetic interactions of Dy3+ ions, as well as molecular packing models.

Swimming polarity inversion in uncultured magnetotactic cocci.

Magnetotactic bacteria are microorganisms that produce intracellular magnetic nanoparticles organized in chains, conferring a magnetic moment to the bacterial body that allows it to swim following the geomagnetic field lines. Magnetotactic bacteria usually display two swimming polarities in environmental samples: the South-seeking (SS) polarity and the North-seeking (NS) polarity, characterized by the bacteria swimming antiparallel or parallel to the magnetic field lines, respectively. It has been observed that in the presence of inhomogeneous magnetic fields, NS magnetotactic bacteria can change their swimming polarity to SS or vice versa. The present study analyzes populations of NS cocci obtained from SS cocci isolated in the presence of a magnet. The aim was to study differences in the swimming characteristics and magnetic moment among both populations of cocci. For that, trajectories were recorded and the velocity and angle among the velocity and the applied magnetic field were calculated. In addition, micrographs from both SS and NS cocci were obtained and their magnetosomes were measured to analyze their length, width, aspect ratio and magnetic moment, to finally obtain the magnetic moment for each coccus. The results showed the following properties of NS relative to SS cocci: higher velocities, narrow bacterial magnetic moment distribution, higher dispersion in the distribution of angles among the velocity and the applied magnetic field and lower magnetic field sensibility. Those differences cannot be explained by the simple change in magnetic polarity of the magnetosome chain and can be related to the existence of an active magnetoreceptive process in magnetotactic bacteria.

Influence of the Spatial Distribution of Molecular Magnetic Moments on the Radiation Characteristics of Rotating Permanent Magnet Antennas

Influence of the Spatial Distribution of Molecular Magnetic Moments on the Radiation Characteristics of Rotating Permanent Magnet Antennas

Research on the microphysical mechanism of metal magnetic memory testing through 45 # steel under compressive stress

To explore the microphysical mechanism of metal magnetic memory testing (MMMT) technique, the effect of compressive stress on the domain structure in 45# steel specimen and the pinning effect of stress-induced defects on domain walls (DWs) were investigated by in-situ Lorentz Transmission Electron Microscopy (LTEM). The changes in domain structure and defects are observed simultaneously. And the deformation and magnetic moment distribution of the specimen under compressive stress were measured and analyzed. The results show that, the rotation of magnetic moment corresponding to the deformation of the specimen can greatly reduce the magnetoelastic energy according to the calculation of magnetoelastic energy. When stress is removed, the domain structures do not restore, and DWs’ pinning effect of defects could be clearly observed. The results provide a vigorous support for the memory effect of ferromagnetic material on historical stress.

Modelling the magnetization data of Fe3O4 nanoparticles above blocking temperature

Nanoparticles of Fe3O4 are prepared by simple co-precipitation method. The sample is characterized using an x-ray diffractometer, transmission electron microscope, and vibrating sample magnetometer. The x-ray diffraction pattern of the sample clearly shows that it is a single-phase magnetite. The transmission electron micrograph shows that the sample has a narrow distribution in particle size with average particle size of 9.9 nm. The SAED pattern only shows the diffraction planes correspond to magnetite and no other phase impurity is detected. The calculated thickness of the magnetic disordered shell due to the reduction in particle size is found to be 1.7 nm. The magnetization of the sample is measured as a function of temperature and applied magnetic field. The zero-field cooled and field cooled curves of the sample are measured in the presence of 250 Oe applied magnetic field and both the curves bifurcate at 170 K. The peak in the zero-field curve indicates that the sample has a blocking temperature of around 100 K. The magnetization as a function of applied magnetic field data at 200, 225, 250, 275 and 300 K are measured (up to ±20 kOe). These magnetization data are used for the fitting to analyze the magnetic behavior of Fe3O4 nanoparticles. . The magnetization of nanoparticles systems is influenced by several factors such as particle size distribution, disordered surface, magnetocrystalline anisotropy, magnetic moment distribution and magnetic interactions. The ignorance of such factors while analyzing the magnetization data leads to discrepancies in the results. The surface effects are sensitive to the reduction in particle size leading to the spin frustrations on the surface suggesting a magnetic disordered layer which affect the magnetic behavior of nanoparticles. This work presents the analysis of the magnetization data in an appropriate magnetization expression which takes into consideration the effect of magnetic moment distribution. This distribution in the magnetic moment is found to be significantly influenced the magnetization analysis and affected by the magnetic disordered surface which accounts for the presence of magnetic anisotropy and magnetic interactions on the particles surface. The results and observations are discussed in detail.

Extremely High Ferromagnetic Resonance Frequency Induced by Triclinic Lattice Distortion in Epitaxial FeCo/MgAl2O4 (001) Films

Theoretically, tetragonal lattice distortion of FeCo epitaxial films can result in a very large in‐plane magnetic anisotropy field, leading to an extremely high ferromagnetic resonance (FMR) frequency. Herein, thin films are epitaxially grown on (001) MgAl2O4 single‐crystal substrates. A triclinic lattice distortion with , instead of a tetragonal one, is found in the FeCo films. The cubic symmetry breaking leads to a deviation of easy axes from the directions, forming a distribution of magnetic moments with a strong perpendicular magnetic anisotropy (PMA) along the out‐of‐plane [001] directions and a deviation of the in‐plane components from the ([10 100]) directions. The effective field of the former is as high as 1.5–2.5 T, enough to overcome the thin film shape anisotropy, while that of the latter stays at a low value of around 0.05 T. The strain‐induced PMA gradually relaxes to in‐plane for thicker films with a strained sublayer remaining. As a result, an extremely high out‐of‐plane FMR frequency over 40 GHz is achieved, accompanied by a lower in‐plane FMR frequency around 8 GHz. This study provides a possible approach to prepare self‐biased soft magnetic films with extremely high‐resonance frequency for applications in microwave‐integrated circuits.

Generalized chiral kinetic equations

We derive the generalized chiral kinetic equations which are applicable to the fermions with arbitrary mass. We show how the dynamical magnetic-moment distribution function could lead to spin polarization and electric charge separation. We also show how the electric/magnetic moment distribution and pseudoscalar distribution could be induced by vorticity and electromagnetic field in global equilibrium.

Anomalous and inverse spin Hall effects in Pt1-xBix/(YLuBiCa)3(FeGa)5O12 heterojunction

A garnet film with spatial magnetic moment distribution has been grown on gadolinium gallium garnet wafer (111) crystal plane, by regulating liquid phase epitaxial growth parameters and sub-lattice ions substitution, then 10 nm Pt1-xBix (x = 2% – 8%) alloy film was deposited on the surface of the garnet films. A new spin heterojunction Pt1-xBix/(YLuBiCa)3(FeGa)5O12 with both inverse spin Hall effect (ISHE) and anomalous spin Hall effect (ASHE) was designed and fabricated. The spatial magnetic moment distribution of the heterojunction has been found, which lays the foundation of the spin heterojunction for multiple spin injection with both spin electron reverse injection and anomalous injection. Because Bi ions doping and substitution increases the spin–orbit torque and the mixed conductance of the heterojunction, an oblique ASHE voltage curve and an enhanced ISHE voltage curve with double resonance peak were observed. It was confirmed that the injection of spinning electron into the heterojunction can be enhanced with both the ISHE and ASHE effect by adjusting the spatial magnetic moment distribution, which is a foundation for the future application of spin wave 3D antenna and other devices.

Magnetic domain-dependent ultrafast optical demagnetization in stripe domain films

We investigated femto- and picosecond-time magnetization dynamics in a ferromagnetic Ni80Fe20 film with varying thicknesses (wedge-shaped film). We observed that the thickness gradient strongly affects the magnetic moment distribution, causing a magnetization reorientation from in-plane to out-of-plane, and formatting a stripe domain (SD) at the thicker end of the wedge. The magnetization dynamics measurements reveal that the part of the film displaying SDs follows a substantially faster demagnetization and magnetization recovery and smaller magnetization quenching compared to the in-plane domain film. The experiments and micromagnetic simulations support that the decrease in relaxation time is caused by a magnetic anisotropy of the films introduced by SD formation. Our results point out that the micromagnetic structure plays an important role in the magnetization dynamics in ferromagnetic films after optically triggered demagnetization.

Rise and fall of Mott insulating gaps in YNiO3 paramagnets as a reflection of symmetry breaking and remaking

The ${\mathrm{YNiO}}_{3}$ nickelate is a paradigm $d$-electron oxide that manifests the intriguing temperature-mediated sequence of three phases transitions from (i) magnetically ordered insulator to (ii) paramagnetic (PM) insulator and then to (iii) PM metal. Such phenomena raised the question of the nature of the association of magnetism and structural symmetry breaking with the appearance in (i) and (ii) and disappearance in (iii) of insulating band gaps. It is demonstrated here that first-principles mean-field--like density-functional theory (DFT), driven by molecular dynamics temperature evolution, can describe not only the origin of the magnetically long-range ordered insulating phase (i), but also the creation of an insulating paramagnet (ii) that lacks spin- long-range order, and of a metallic paramagnet (iii) as temperature rises. This approach provides the patterns of structural and magnetic symmetry breaking at different temperatures, in parallel with band gaps obtained when the evolving geometries are used as input to DFT electronic band-structure calculations. This disentangles the complex interplay among spin, charge, and orbital degrees of freedom. Analysis shows that the success in describing the rise and fall of the insulating band gaps along the phase transition sequence is enabled by allowing sufficient flexibility in describing diverse local structural and magnetic motifs as input to DFT. This entails the use of sufficiently large supercells that allow expressing structural disproportionation of octahedra, as well as a description of PM phases as a distribution of local magnetic moments (rather than using a single averaged moment). It appears that the historic dismissal of mean-field--like DFT as being unable to describe such Mott-like transitions was premature, as it was based on consideration of averaged crystallographic unit cells, a description that washes out local symmetry-breaking motifs. The magnetically ordered insulating ${\mathrm{YNiO}}_{3}$ phase (i) and the PM insulating phase (ii) result in DFT from allowing symmetry breaking, evident already by considering the athermal internal energy. In contrast, the PM metallic phase (iii) is formed thermally by smearing out thus weakening symmetry breaking. Analysis of snapshots of the different forms of structural vs magnetic symmetry breaking shows that only the loss of the polymorphous distribution of magnetic moments existing in (ii) causes the fall of the band gap, resulting in the metallic state in (iii). The interesting conclusion is that such a description of the rise [in phases (i) and (ii)] and fall [in phase (iii)] of the insulating gap does not rely on the traditional Mott-like strong correlation understanding, but on breaking and remaking of magnetic and structural symmetries reflected in energy lowering.

The effect of spin-polarization, atomic ordering and charge transfer on the stability of CoCrNi medium entropy alloy

The aim of this paper is to determine the effects of spin-polarization and atomic ordering on the phase stability of the medium entropy alloy CoCrNi by employing density functional theory calculations. We have found that high Cr ordering causes stabilisation of both the fcc and hcp structures compared to fully disordered alloy, while high Ni ordering leads to destabilisation of the hcp structure but has no effect on the fcc structure. The differences in the mutual stability of fcc and hcp structures for alloys with different levels of ordering are accompanied by differences in the distribution of local magnetic moments. However, their analysis revealed a generally increasing trend in the magnitude of the magnetic moment with the increasing number of Cr atoms in the 1st nearest neighbours (NN) shell for all Co, Cr, and Ni elements. Moreover, the charge analysis revealed a charge transfer from Cr to the other two elements in the alloy and also its dependence on the number of Cr atoms in the 1st NN shell. Thus, we have described the clear indirect dependence of the magnetic moment of all elements in this alloy on the ongoing charge transfer. This also points to the possibility that the charge transfer has the more important effect on stabilisation of particular atomic ordering rather than the spin-polarization as the same behaviour of charge transfer was observed also for results obtained without spin-polarization.

Pressure-induced insulator-to-metal transition in the van der Waals compound CoPS3

We have studied the insulator-to-metal transition and crystal structure evolution under high pressure in the van der Waals compound ${\mathrm{CoPS}}_{3}$ through in situ electrical resistance, Hall resistance, magnetoresistance, x-ray diffraction, and Raman scattering measurements. ${\mathrm{CoPS}}_{3}$ exhibits a $C2/m\ensuremath{\rightarrow}P\overline{3}$ structural transformation at 7 GPa accompanied by a $2.9%$ reduction in the volume per formula unit. Concomitantly, the electrical resistance decreases significantly and ${\mathrm{CoPS}}_{3}$ becomes metallic. This metallic ${\mathrm{CoPS}}_{3}$ is a hole-dominant conductor with multiple conduction bands. The linear magnetoresistance and the small volume collapse at the metallization suggest the incomplete high-spin $\ensuremath{\rightarrow}$ low-spin transition in the metallic phase. Thus, the metallic ${\mathrm{CoPS}}_{3}$ possibly possesses an inhomogeneous magnetic moment distribution and short-range magnetic ordering. This paper summarizes the comprehensive phase diagram of $M{\mathrm{PS}}_{3}$ ($M\phantom{\rule{4pt}{0ex}}=\phantom{\rule{4pt}{0ex}}\mathrm{V}$, Mn, Fe, Co, Ni, and Cd) that metalize under pressures.

Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics.

The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic ^{133}Cs. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Simultaneous estimation of magnetic moment and Brownian relaxation time distributions of magnetic nanoparticles based on magnetic particle spectroscopy for biosensing application.

Magnetic nanoparticles (MNPs) exhibit unique physicochemical characteristics owing to their comparable dimensions with important biological substances, high surface-to-volume ratios, size-dependent magnetic properties, and temperature sensitivity. In this study, we present a novel method for simultaneously estimating the magnetic moment and Brownian relaxation time distribution of MNPs based on AC magnetization harmonics. We provide a detailed description of the theoretical framework and experimental procedures. The dynamics of MNP magnetization are described using the Fokker-Planck equation, and a matrix equation is established to connect the magnetic moment, Brownian relaxation time, and magnetization harmonics. By employing a non-negative linear least squares algorithm with constraints, the magnetic moment and Brownian relaxation time distributions are inversed, which are then converted into the distributions of core sizes and hydrodynamic sizes. Finally, the estimated core size distribution reconstructed from M-H curves is consistent with the hydrodynamic size distribution measured by dynamic light scattering. This method is particularly useful for facilitating quantitative magnetic immunoassays.

A reverse Monte Carlo algorithm to simulate two-dimensional small-angle scattering intensities.

Small-angle scattering (SAS) experiments are a powerful method for studying self-assembly phenomena in nanoscopic materials because of the sensitivity of the technique to structures formed by interactions on the nanoscale. Numerous out-of-the-box options exist for analysing structures measured by SAS but many of these are underpinned by assumptions about the underlying interactions that are not always relevant for a given system. Here, a numerical algorithm based on reverse Monte Carlo simulations is described to model the intensity observed on a SAS detector as a function of the scattering vector. The model simulates a two-dimensional detector image, accounting for magnetic scattering, instrument resolution, particle polydispersity and particle collisions, while making no further assumptions about the underlying particle interactions. By simulating a two-dimensional image that can be potentially anisotropic, the algorithm is particularly useful for studying systems driven by anisotropic interactions. The final output of the algorithm is a relative particle distribution, allowing visualization of particle structures that form over long-range length scales (i.e. several hundred nanometres), along with an orientational distribution of magnetic moments. The effectiveness of the algorithm is shown by modelling a SAS experimental data set studying finite-length chains consisting of magnetic nanoparticles, which assembled in the presence of a strong magnetic field due to dipole interactions.