Local Magnetic Field Distribution Research Articles

Experimental AC loss study on REBCO coil assemblies coupled with an iron cylinder

In high-temperature superconducting (HTS) power devices, the presence of iron cores changes the magnetic field profile around the HTS coil windings, potentially affecting their AC loss characteristics. AC loss measurements for HTS coil windings coupled with an iron core using the electrical method can lead to a significant error, owing to the indirect estimation of the iron core loss through using a copper test coil. To investigate the cause of the experimental error and the influence of an iron core on coil AC losses, transport AC losses of REBCO double pancake coil (DPC) assemblies coupled with an iron cylinder were measured. A 40-turn 1DPC and an 80-turn 2DPC assembly wound with 4 mm SuperPower wire were employed in the measurements. To ensure the same iron core loss using the HTS coil assembly and the copper coil, 2D finite element method simulations were conducted iteratively to design the iron core and the copper coil to get the same local magnetic field distributions in the designed iron core for the two cases. The main cause of the error is due to the difference in local magnetic flux densities in the iron core generated by the HTS coil assembly and the copper coil even when the ampere-turns of the coils are identical. We showed that the simulation-guided measurement method can assure accurate AC loss measurement in the HTS coil assemblies coupled with iron cores. Compared with the AC losses in the 1DPC and 2DPC coil assemblies without the iron cylinder, the presence of the iron cylinder significantly increases the coil losses. Frequency dependence is observed in the coil AC losses of the 1DPC and 2DPC assemblies when coupled with the iron cylinder. This is due to the eddy current induced in the iron cylinder generating a magnetic field, which influences the coil AC loss.

Intrinsic high frequency permeability of magnetic nanocomposites: uncertainty principle

The intrinsic high frequency permeability spectra of ferromagnetic conductive nanocomposites containing different volume fractions of nanoscale iron and cobalt have been simulated. A law is proposed to explain the simulated results by assuming that there are plenty of Landau–Lifshitz–Gilbert (LLG) type natural resonances contributing to the intrinsic permeability spectra. The results clearly show that the spectra strongly depend on the distribution of local effective magnetic field, the interaction between the magnetic particles, the inhomogeneous damping constant of LLG precession, and the initial equilibrium states. Especially, the effect of particles shape distribution in each sampling on the local effective magnetic field. In view of this fact: it is absolutely impossible to have the same effect from these factors when someone prepares several measurement samples, an uncertainty principle is believed to hold for measuring the intrinsic permeability of an electromagnetic (EM) composite. Therefore, this law tells us that it should be cautious when comparing or evaluating the EM properties of composites (for instance, EM wave absorbing composites). Memory effect can be used to restore the intrinsic high frequency permeability for a specific defunct composite sample.

Probing the strongly correlated magnetic state of Co2C nanoparticles at low temperatures using μSR

Co2C nanoparticles (NPs) are amongst transition metal carbides whose magnetic properties have not been well explored. An earlier study (Roy et al 2021 J. Phys.: Condens. Matter 33 375804) showed that a pellet made from Co2C NPs exhibits exchange bias (EB) effect below a temperature, T EB = 50 K and a spin glass (SG) feature emerges below T SG = 5 K. In the current study we use magnetic, electrical transport, specific heat, and muon spin rotation (μSR) measurements to explore further the magnetic properties of a pellet made with 40 nm diameter pure Co2C NPs. We uncover the onset of Kondo localization at Kondo temperature T K (= 40.1 K), which is close to the onset temperature (T EB) of the EB effect. A crossover from the Kondo-screened scenario to the Ruderman–Kittel–Kasuya–Yosida interaction-dominated regime is also observed for T < T K. Temperature-dependent specific heat measurement further supports the Kondo localization scenario in the pellet and shows the heavy fermionic nature of the strongly correlated electronic state in Co2C. The zero field μSR asymmetry spectra in the low-temperature regime are characterized by two distinct fast and slow relaxation rates. The spectra show the absence of long-range magnetic order in the sample. However, our analysis suggests the NPs-pellet shows the presence of a dominant magnetically disordered fraction and a smaller fraction with short-range order. Muons in the disordered fraction exhibit a slower relaxation rate, while muons in the smaller fraction with short-range order exhibit a faster relaxation rate. We observe an increase in this fast relaxation rate between T EB and T SG. This increase below T EB ∼ 50 K suggests a slowing down of the fluctuating local magnetic environment around muons. Transverse field-μSR asymmetry spectra show the emergence of a stable, multi-peaked local magnetic field distribution in the pellet below T EB. Longitudinal field μSR spectra shows distinct changes in the dynamics of fluctuations suggesting the presence of a frozen glassy like state below 6 K. Based on our results, we suggest that below T EB, the pellet of Co2C NPs develops a magnetic interface that separates the two magnetic fractions; one is a disordered fraction, and the other is a fraction with short-range order. The exchange interaction that sets in below T EB at the interface couples the two fractions, leading to a suppression of the fluctuations. With the suppression of magnetic fluctuations below T EB, strong correlation effects in the electronic state of Co2C lead to Kondo localization.

A Novel Analytical Formulation of the Magnetic Field Generated by Halbach Permanent Magnet Arrays

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement.

Asymmetric excitations of toroidal dipole resonance and magnetic dipole quasi-bound state in the continuum in hybrid graphene-dielectric metasurface

We study asymmetric excitations of toroidal dipole resonance and magnetic dipole quasi-bound state in the continuum (BIC) in hybrid graphene-dielectric metasurface consisting of a nanoring and a Y-shaped nanobar. Through reducing or increasing inner radius of nanoring, the quasi-BIC dominated by magnetic dipole moment can be excited and effectively modulated via adjusting the Fermi energy and layer numbers of the graphene. The proposed metasurface can not only produce a symmetric localized magnetic field distribution but also create two asymmetric localized magnetic field distributions in near-infrared wavelength, providing a new way of indirectly manipulating the localized magnetic field enhancement. Our results can be of practical interest for a variety of applications including optical modulator, filter, switches and light trapping.

Holographic reconstruction of magnetic field distribution in a Josephson junction from diffraction-like Ic(H) patterns

A general problem of magnetic sensors is a trade-off between spatial resolution and magnetic field sensitivity. With decreasing sensor size its resolution is improved but the sensitivity is deteriorated. Obviation of such the trade-off requires development of super-resolution imaging technique, not limited by the sensor size. Here we present a proof of concept for a super-resolution method of magnetic imaging by a Josephson junction. It is based on a solution of an inverse problem - reconstruction of a local magnetic field distribution within a junction from the dependence of the critical current on an external magnetic field, Ic(H). The method resembles the Fourier-transform holography, with the diffraction-like Ic(H) pattern serving as a hologram. A simple inverse problem solution, valid for an arbitrary symmetric case, is derived. We verify the method numerically and show that the accuracy of reconstruction does not depend on the junction size and is only limited by the field range of the Ic(H) pattern. Finally, the method is tested experimentally using planar Nb Josephson junctions. Super-resolution reconstruction of stray magnetic fields from an Abrikosov vortex, trapped in the junction electrodes, is demonstrated. Thus, our method facilitate both the high field sensitivity and high spatial resolution, obviating the trade-off problem of magnetic sensors. We conclude that the holographic magnetic imaging by a planar Josephson junction can be used in scanning probe microscopy.

Muon-Spin Motion at the Crossover Regime between Gaussian and Lorentzian Distribution of Magnetic Fields

Abstract The muon spin relaxation method (μSR) is a powerful microscopic tool to probe electronic states of materials observing local magnetic field distributions on the muon. It often happens that a distribution of local magnetic fields shows intermediate state between Gaussian and Lorentzian shapes. In order to generally describe intermediate field distributions, we dealt the convolution of two isotropic distributions in the three dimension and derived exact muon-spin relaxation functions which can be applied to all crossover regimes between the Gaussian and Lorentzian.

NMR study of magnetic structure and hyperfine interactions in the binary helimagnet FeP

We report a detailed study of the ground state helical magnetic structure in monophosphide FeP by means of ${}^{31}$P NMR spectroscopy. We show that the zero-field NMR spectrum of the polycrystalline sample provides strong evidence of an anisotropic distribution of local magnetic fields at the P site with substantially lower anharmonicity than that found at the Fe site by M\"{o}ssbauer spectroscopy. From field-sweep ${}^{31}$P NMR spectra we conclude that a continuous spin-reorientation transition occurs in an external magnetic field range of 4 - 7 T, which is also confirmed by specific-heat measurements. We observe two pairs of magnetically inequivalent phosphorus positions resulting in a pronounced four-peak structure of the single crystal ${}^{31}$P NMR spectra characteristic of an incommensurate helimagnetic ground state. We revealed a spatial redistribution of local fields at the P sites caused by Fe spin-reorientation transition in high fields and developed an effective approach to account for it. We demonstrate that all observed ${}^{31}$P spectra can be treated within a model of an isotropic helix of Fe magnetic moments in the ($ab$)-plane with a phase shift of 36$^{\circ}$ and 176$^{\circ}$ between Fe1-Fe3 (Fe2-Fe4) and Fe1-Fe2 (Fe3-Fe4) sites, respectively, in accordance with the neutron scattering data.

Visualization of relativistic laser pulses in underdense plasma

We present experimental evidence of relativistic electron-cyclotron resonances (RECRs) in the vicinity of the relativistically intense pump laser of a laser wakefield accelerator (LWFA). The effects of the RECRs are visualized by imaging the driven plasma wave with a few-cycle, optical probe in transverse geometry. The probe experiences strong, spectrally dependent and relativistically modified birefringence in the vicinity of the pump that arises due to the plasma electrons' relativistic motion in the pump's electromagnetic fields. The spectral birefringence is strongly dependent on the local magnetic field distribution of the pump laser. Analysis and comparison to both 2D and 3D particle-in-cell simulations confirm the origin of the RECR effect and its appearance in experimental and simulated shadowgrams of the laser-plasma interaction. The RECR effect is relevant for any relativistic, magnetized plasma and in the case of LWFA could provide a nondestructive, in situ diagnostic for tracking the evolution of the pump's intensity distribution with propagation through tenuous plasma.

Magneto-optical imaging of stepwise magnetic domain disintegration at characteristic temperatures in EuB6

Prior to the onset of the ferromagnetic transition in semimetallic EuB_6, unusual magnetic and electric behavior have been reported. Using a highly sensitive magneto-optical imaging (MOI) technique, we visualize the behavior of magnetic domains in a EuB_6 single crystal.The transformation from a paramagnetic to a ferromagnetic state is shown to be non-Curie Weiss like and proceeds via multiple breaks in the curvature of the temperature-dependent local magnetization. From our experiments, we identify three characteristic boundaries, T^*(H),T^*_c1(H) and T_c2(H),in a field - temperature magnetic phase diagram.Using scaling and Modified Arrott plot analysis of isothermal bulk magnetization data, we determine the critical exponents $\beta$ = 0.22 $\pm$ 0.01, $\gamma$ = 0.88 $\pm$ 0.05 and $\delta$= 5.0 $\pm$ 0.1 and a critical transition temperature = 12.0 $\pm$ 0.2 K which is found to be equal to T_c2. The critical exponents are close to those associated with the universality class of tricritical mean field model. The absence of a model with which the exponents correspond with directly, suggests the presence of large critical fluctuations in this system. The critical fluctuations in this system are sensitive to the applied magnetic field, which leads to field dependence of boundaries in the magnetic phase diagram. With increasing T the magnetic domains disintegrate into finger-like patterns before fragmenting into disjoint magnetized puddles at T^*_c1 and ultimately disappearing at T*. At T^*_c1 we observe a significant increase in the spatial inhomogeneity of the local magnetic field distribution associated with the magnetic domain structure disintegrating into smaller magnetized structures. We explain our results via the formation of magnetic polaronic clusters and their coalescing into larger domains.

Design of Fluxgate Sensors for Different Applications from Geology to Medicine

In this study, we have shown that fluxgate sensors can be used for different application areas. Alternative sensor configurations have been developed for three different application areas. These are mainly rod- and ring-type fluxgate sensors. In the first study, a measurement system with the rod-type fluxgate sensor has been developed in order to monitor the local magnetic field distributions on a magnetic tape (e.g., credit card). With this system, the magnetic recording data on the credit card were measured and imaged successfully. The second and the third application areas, which are monitoring the influence of solar storms on the earth field and heartbeat analysis of mankind, were carried out by using a ring-core fluxgate sensor geometry.

Numerical and experimental study on vorticity measurement in liquid metal using local Lorentz force velocimetry

Local Lorentz force velocimetry (local LFV) is a contactless velocity measurement technique for liquid metals. Due to the relative movement between an electrically conductive fluid and a static applied magnetic field, eddy currents and a flow-braking Lorentz force are generated inside the metal melt. This force is proportional to the flow rate or to the local velocity, depending on the volume subset of the flow spanned by the magnetic field. By using small-size magnets, a localized magnetic field distribution is achieved allowing a local velocity assessment in the region adjacent to the wall. In the present study, we describe a numerical model of our experiments at a continuous caster model where the working fluid is GaInSn in eutectic composition. Our main goal is to demonstrate that this electromagnetic technique can be applied to measure vorticity distributions, i.e. to resolve velocity gradients as well. Our results show that by using a cross-shaped magnet system, the magnitude of the torque perpendicular to the surface of the mold significantly increases improving its measurement in a liquid metal flow. According to our numerical model, this torque correlates with the vorticity of the velocity in this direction. Before validating our numerical predictions, an electromagnetic dry calibration of the measurement system composed of a multicomponent force and torque sensor and a cross-shaped magnet was done using a rotating disk made of aluminum. The sensor is able to measure simultaneously all three components of force and torque, respectively. This calibration step cannot be avoided and it is used for an accurate definition of the center of the magnet with respect to the sensor’s coordinate system for torque measurements. Finally, we present the results of the experiments at the mini-LIMMCAST facility showing a good agreement with the numerical model.

Quantitative and high-resolution magnetic images obtained by STM-SQUID microscope with distance modulation technique

We have developed an STM-SQUID microscope, in which a scanning tunnelling microscope (STM) is combined with an rf-SQUID. The issue in our STM-SQUID microscope was that the obtained magnetic image was not the same as the sample’s ideal magnetic field distribution. This was because the magnetic image could be affected not only by the sample’s local magnetic field distribution, but also by the magnetic field distribution above the sample, namely “background field”. In this work, we applied the distance modulation technique to our microscope. In this technique, the change of the SQUID output signal was detected while the distance between the sample and the probe tip was modulated in a constant amplitude. As a result, the influence of the background field was cancelled out, and the magnetic information near the sample surface was largely extracted. We successfully obtained the quantitative magnetic images in ~100 nm spatial resolution by using the distance modulation technique.

Magnetic-field-induced vortex-lattice transition in HgBa2CuO4+δ

Measurements of the $^{17}$O nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in HgBa$_{2}$CuO$_{4+\delta}$ were performed over a range of magnetic fields from 6.4 to 30\,T in the superconducting state. Oxygen isotope exchanged single crystals were investigated with doping corresponding to superconducting transition temperatures from 74\,K underdoped, to 78\,K overdoped. The apical oxygen site was chosen since its NMR spectrum has narrow quadrupolar satellites that are well separated from any other resonance. Non-vortex contributions to the spectra can be deconvolved in the time domain to determine the local magnetic field distribution from the vortices. Numerical analysis using Brandt's Ginzburg-Landau theory was used to find structural parameters of the vortex lattice, penetration depth, and coherence length as a function of magnetic field in the vortex solid phase. From this analysis we report a vortex structural transition near 15\,T from an oblique lattice with an opening angle of $73^{\circ}$ at low magnetic fields to a triangular lattice with $60^{\circ}$ stabilized at high field. The temperature for onset of vortex dynamics has been identified with vortex lattice melting. This is independent of the magnetic field at sufficiently high magnetic field similar to that reported for YBa$_2$Cu$_3$O$_7$ and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and is correlated with mass anisotropy of the material. This behavior is accounted for theoretically only in the limit of very high anisotropy.

Investigations of CuFeS2 semiconductor mineral from ocean rift hydrothermal vent fields by Cu NMR in a local field

The results of investigating natural samples of chalcopyrite mineral CuFeS2 from massive oceanic sulfide ores of the Mid-Atlantic ridge by the 63Cu nuclear magnetic resonance (NMR 63Cu) in a local field at room temperature are presented. The significant width of the resonance lines found in the 63Cu NMR spectrum directly testifies to a wide distribution of local magnetic and electric fields in the investigated chalcopyrite samples. This distribution can be the consequence of an appreciable deviation of the structure of the investigated chalcopyrite samples from the stoichiometric one. The obtained results show that the pulsed 63Cu NMR can be an efficient method for studying the physical properties of deep-water polymetallic sulfides of the World Ocean.

μSR study of stoichiometric NbFe2

The magnetic ground state of nominally stoichiometric single crystalline NbFe2 is investigated by bulk magnetisation and muon spin relaxation techniques. Magnetic order clearly emerges below the critical temperature TN=10.3K and is dominated by randomly orientated quasi-static moments. The local field distribution observed by muons can be explained by the phenomenological Gaussian-broadened-Gaussian Kubo Toyabe relaxation function. The observed short range order could be used to describe a new magnetic ground state, but a helical spin density wave with an incommensurate amplitude modulation cannot be ruled out. The sensitivity of μSR to the local magnetic field distribution in the vicinity of the quantum critical point (QCP) in NbFe2 is clearly demonstrated via comparison with already published work. This suggests detailed measurements of the muon relaxation as the QCP is approached will reveal further details of the field distribution and fluctuations in Nb1−yFe2+y.

Metastable inhomogeneous vortex configuration with non-uniform filling fraction inside a blind hole array patterned in a BSCCO single crystal and concentrating magnetic flux inside it

Using magneto-optical imaging, we map the local magnetic field distribution inside a hexagonally ordered array of blind holes patterned in BSCCO single crystals. The nature of the spatial distribution of local magnetic field and shielding currents across the array reveals the presence of a non-uniform vortex configuration partially matched with the blind holes at sub-matching fields. We observe that the filling fraction is different in two different regions of the array. The mean vortex configuration within the array is described as a patchy vortex configuration with the patches having different mean filling fraction. The patchy nature of the vortex configuration is more pronounced at partial filling of the array at low fields while the configuration becomes more uniform with a unique filling fraction at higher fields. The metastable nature of this patchy vortex configuration is revealed by the application of magnetic field pulses of fixed height or individual pulses of varying height to the array. The metastability of the vortex configuration allows a relatively easy way of producing flux reorganization and flux focusing effects within the blind hole array. The effect of the magnetic field pulses modifies the vortex configuration within the array and produces a uniform enhancement in the shielding current around the patterned array edges. The enhanced shielding current concentrates magnetic flux within the array by driving vortices away from the edges and towards the center of the array. The enhanced shielding current also prevents the uninhibited entry of vortices into the array. We propose that the metastable patchy vortex configuration within the blind hole array is due to a non-uniform pinning landscape leading to non-uniform filling of individual blind holes.

Image patch analysis of sunspots and active regions

Separating active regions that are quiet from potentially eruptive ones is a key issue in Space Weather applications. Traditional classification schemes such as Mount Wilson and McIntosh have been effective in relating an active region large scale magnetic configuration to its ability to produce eruptive events. However, their qualitative nature prevents systematic studies of an active region's evolution for example. We introduce a new clustering of active regions that is based on the local geometry observed in Line of Sight magnetogram and continuum images. We use a reduced-dimension representation of an active region that is obtained by factoring the corresponding data matrix comprised of local image patches. Two factorizations can be compared via the definition of appropriate metrics on the resulting factors. The distances obtained from these metrics are then used to cluster the active regions. We find that these metrics result in natural clusterings of active regions. The clusterings are related to large scale descriptors of an active region such as its size, its local magnetic field distribution, and its complexity as measured by the Mount Wilson classification scheme. We also find that including data focused on the neutral line of an active region can result in an increased correspondence between our clustering results and other active region descriptors such as the Mount Wilson classifications and the $R$ value. We provide some recommendations for which metrics, matrix factorization techniques, and regions of interest to use to study active regions.

Electromagnetic resonance modes on a two-dimensional tandem grating and its application for broadband absorption in the visible spectrum.

In this work, we numerically investigate the electromagnetic resonances on two-dimensional tandem grating structures. The base of a tandem grating consists of an opaque Au substrate, a SiO(2) spacer, and a Au grating (concave type); that is, a well-known fishnet structure forming Au/SiO(2)/Au stack. A convex-type Au grating (i.e., topmost grating) is then attached on top of the base fishnet structure with or without additional SiO(2) spacer, resulting in two types of tandem grating structures. In order to calculate the spectral reflectance and local magnetic field distribution, the finite-difference time-domain method is employed. When the topmost Au grating is directly added onto the base fishnet structure, the surface plasmon and magnetic polariton in the base structure are branched out due to the geometric asymmetry with respect to the SiO(2) spacer. If additional SiO(2) spacer is added between the topmost Au grating and the base fishnet structure, new magnetic resonance modes appear due to coupling between two vertically aligned Au/SiO(2)/Au stacks. With the understanding of multiple electromagnetic resonance modes on the proposed tandem grating structures, we successfully design a broadband absorber made of Au and SiO(2) in the visible spectrum.

Excitation of magnetic dipole transitions at optical frequencies.

We use the magnetic field distribution of an azimuthally polarized focused laser beam to excite a magnetic dipole transition in Eu^{3+} ions embedded in a Y2O3 nanoparticle. The absence of the electric field at the focus of an azimuthally polarized beam allows us to unambiguously demonstrate that the nanoparticle is excited by the magnetic dipole transition near 527.5 nm. When the laser wavelength is resonant with the magnetic dipole transition, the nanoparticle maps the local magnetic field distribution, whereas when the laser wavelength is resonant with an electric dipole transition, the nanoparticle is sensitive to the local electric field. Hence, by tuning the excitation wavelength, we can selectively excite magnetic or electric dipole transitions through optical fields.