Current Bias Field Research Articles

Current induced hidden states in Josephson junctions

Josephson junctions enable dissipation-less electrical current through metals and insulators below a critical current. Despite being central to quantum technology based on superconducting quantum bits and fundamental research into self-conjugate quasiparticles, the spatial distribution of super current flow at the junction and its predicted evolution with current bias and external magnetic field remain experimentally elusive. Revealing the hidden current flow, featureless in electrical resistance, helps understanding unconventional phenomena such as the nonreciprocal critical current, i.e., Josephson diode effect. Here we introduce a platform to visualize super current flow at the nanoscale. Utilizing a scanning magnetometer based on nitrogen vacancy centers in diamond, we uncover competing ground states electrically switchable within the zero-resistance regime. The competition results from the superconducting phase re-configuration induced by the Josephson current and kinetic inductance of thin-film superconductors. We further identify a new mechanism for the Josephson diode effect involving the Josephson current-induced phase. The nanoscale super current flow emerges as a new experimental observable for elucidating unconventional superconductivity, and optimizing quantum computation and energy-efficient devices.

Deep learning based correction of RF field induced inhomogeneities for T2w prostate imaging at 7 T.

At ultrahigh field strengths images of the body are hampered by B1 -field inhomogeneities. These present themselves as inhomogeneous signal intensity and contrast, which is regarded as a "bias field" to the ideal image. Current bias field correction methods, such as the N4 algorithm, assume a low frequency bias field, which is not sufficiently valid for T2w images at 7 T. In this work we propose a deep learning based bias field correction method to address this issue for T2w prostate images at 7 T. By combining simulated B1 -field distributions of a multi-transmit setup at 7 T with T2w prostate images at 1.5 T, we generated artificial 7 T images for which the homogeneous counterpart was available. Using these paired data, we trained a neural network to correct the bias field. We predicted either a homogeneous image (t-Image neural network) or the bias field (t-Biasf neural network). In addition, we experimented with the single-channel images of the receive array and the corresponding sum of magnitudes of this array as the input image. Testing was carried out on four datasets: the test split of the synthetic training dataset, volunteer and patient images at 7 T, and patient images at 3 T. For the test split, the performance was evaluated using the structural similarity index measure, Wasserstein distance, and root mean squared error. For all other test data, the features Homogeneity and Energy derived from the gray level co-occurrence matrix (GLCM) were used to quantify the improvement. For each test dataset, the proposed method was compared with the current gold standard: the N4 algorithm. Additionally, a questionnaire was filled out by two clinical experts to assess the homogeneity and contrast preservation of the 7 T datasets. All four proposed neural networks were able to substantially reduce the B1 -field induced inhomogeneities in T2w 7 T prostate images. By visual inspection, the images clearly look more homogeneous, which is confirmed by the increase in Homogeneity and Energy in the GLCM, and the questionnaire scores from two clinical experts. Occasionally, changes in contrast within the prostate were observed, although much less for the t-Biasf network than for the t-Image network. Further, results on the 3 T dataset demonstrate that the proposed learning based approach is on par with the N4 algorithm. The results demonstrate that the trained networks were capable of reducing the B1 -field induced inhomogeneities for prostate imaging at 7 T. The quantitative evaluation showed that all proposed learning based correction techniques outperformed the N4 algorithm. Of the investigated methods, the single-channel t-Biasf neural network proves most reliable for bias field correction.

Preparation of X5R type Ni-MLCCs and capacitance response to combined out-field variations

With the continuous development of electronic devices, miniaturization and high capacitance have become important factors in the fabrication of multilayer ceramic capacitors (MLCCs) with a Ni internal electrode (Ni-MLCCs). The typical thickness of the dielectric layer of commercial MLCCs is less than 1 μm, which implies a higher capacitance compared to MLCCs with a thicker dielectric layer. In this study, 1210-type Ni-MLCCs were prepared via a tape casting method using a BaTiO3 powder chemically coated with Dy and Ho additives. The high capacitance (390 nF) Ni-MLCC sintered at 1220 °C exhibited a low dielectric loss (tan δ < 2%), high insulation resistance (>9000 MΩ), and temperature stability comparable to that of the EIA X5R standard (capacitance-temperature coefficient (TCC) = ΔC/C25 °C ≤ ±15%, between -55–85 °C). Relaxation behavior was observed between 1 Hz and 10 kHz, following the modified Curie–Weiss law and the Vogel–Fulcher relationship. The capacitive temperature stability of Ni-MLCC is closely related to the applied direct current (DC) bias field. The EIA X7R stability (TCC ≤ ±15%, between -55–125 °C) of the Ni-MLCCs at 1220 °C was gained under dc-bias field 3 and 5 V/μm. The capacitance varied as alternating current (AC) electric fields were applied. The grain shell was sensitive to both the DC bias and AC fields, but the grain core was more sensitive to the DC bias electrical field than the AC field. Furthermore, the ferroelectric response in MLCC decreases with rising temperature.

A working-point perturbation method for the magnetoelectric sensor to measure DC to ultralow-frequency-AC weak magnetic fields simultaneously

Magnetoelectric (ME) sensors for the weak magnetic field measurement have attracted a lot of attention because of their high sensitivity and easy integration. However, the ME sensor performs well only at its working-point under a direct current (DC) bias field (Hbias) and mechanical resonance frequency (fres). The measurement of DC to ultralow frequency (0–100 Hz) weak magnetic fields has increasing demands, such as in geomagnetic anomaly fields, geological and mineral exploration, magnetocardiography, and magnetoencephalography. Unfortunately, fres of ME sensors is on the order of several tens of kilohertz, which is far higher than the ultralow frequency desired. Moreover, if the operation frequency deviates from fres, the sensitivity will deteriorate rapidly. In this study, a working-point perturbation method was used to measure the weak magnetic fields at 0–100 Hz with a high magnetic field resolution. (1) The perturbation of fres using an ultralow frequency (fac) magnetic field results in two modulation peaks with frequencies of fres ± fac. The frequency and resolution of the measured alternating current magnetic field can be obtained by varying fac and the modulation depth. A resolution around 1 nT for fac &amp;gt; 10 Hz and a lowest operation frequency of 0.1 Hz were achieved using our measurement system. (2) A high field resolution of 3 nT (better than the frequency perturbation method with a resolution of 16 nT at 0.1 Hz) can be achieved by the perturbation of Hbias at fres because the ME sensor is still working at the quasi-working-point and helped by lock-in amplifier technology.

Electric field dependent polarization switching of tetramethylammonium bromotrichloroferrate(III) ferroelectric plastic crystals

Tetramethylammonium bromotrichloroferrate(III) ([N(CH3)4][FeBrCl3]) is a plastic crystal ferroelectric with small dielectric constant &amp;lt;20 and piezoelectric coefficient as high as 110 pC/N. Here, super-coercive hysteresis and dielectric properties under direct current (DC) bias fields up to 260 and 120 kV/cm, respectively, were studied to shed light on the polarization switching [N(CH3)4][FeBrCl3] and the related family of plastic crystal and supramolecular ferroelectrics. [N(CH3)4][FeBrCl3] exhibited peak-to-peak strains of 0.1% and saturated ferroelastic switching at fields of 170 kV/cm. Above 170 kV/cm, rates of field increase were too fast for domain switching, resulting in reduced strain rates during the switching cycle. Leakage currents had larger contributions at higher field amplitudes. This was also reflected in the switching behavior at higher frequencies, 100 Hz, in which hysteresis was asymmetric and switching incomplete. The dielectric constant and loss exhibited a butterfly-like shape during application of DC bias electric fields indicative of domain switching, but showed a small dielectric tunability of 0.038 and no signs of dielectric stiffening, with the relative permittivity from 16.9 to 17.3 at fields from 0 to 120 kV/cm. The present findings provide insight into the domain switching kinetics and dielectric properties of [N(CH3)4][FeBrCl3] that will assist with further development of plastic crystal ferroelectrics.

Preparation and Magnetoelectric Behavior of Ni/BaTiO3 Heterostructures with 0‐3 Connectivity

Magnetoelectric 0‐3 composites consisting of small ferromagnetic Ni particles in the micrometer range embedded in a ferroelectric BaTiO3 matrix are synthesized by reductive sintering in flowing nitrogen with carbon as the oxygen getter. Phase purity of the samples Nix/(BaTiO3)1 − x (x = 0.1–0.7) is verified by powder X‐ray diffraction in combination with scanning electron microscopy/energy‐dispersive X‐ray spectroscopy analyses and magnetization investigations. The magnetoelectric coefficient (αME) is studied for parallel and perpendicular orientations of polarization and magnetic field. For the latter orientation, a reverse sign and a much weaker signal are found. The dependence of αME on the magnetic direct current bias field shows a linear behavior between ≈±2 kOe and a drop to almost zero above ≈4 kOe. Largest values are obtained for x = 0.4. With increasing frequency of the alternating current driving field, αME becomes larger. At low temperatures, two step‐like decreases in the magnetoelectric coefficient occur, reflecting the phase transitions of BaTiO3 (tetragonal→orthorhombic and orthorhombic→rhombohedral). While this finding corroborates the interpretation of αME being a product property of magnetostriction and piezoelectricity, distinct deviations between the field dependence of the integrated ME signal and the magnetostriction of nickel are found.

Influence of tetragonality (c/a) on dielectric nonlinearity and direct current (dc) bias characteristics of (1-x)BaTiO3-xBi0.5Na0.5TiO3 ceramics

The incorporation of Bi0.5Na0.5TiO3 (BNT) into BaTiO3 (BT) in a (1-x)BT-xBNT system, with 0 ≤ x ≤ 0.3, creates an increase in the Curie temperature and the tetragonality (c/a) of the system. This causes (1) a decrease in the dielectric constants in the entire alternating current driving field range up to ∼4.5 V/μm; (2) an increase in the threshold field beyond which the dielectric constants begin to increase; and (3) a steep decrease in the dielectric constants when a direct current (dc) bias field is applied. The Preisach analysis shows that the enhancement of c/a, and its supposed increase in the lattice incompatibility during the domain wall motion, reduces the reversible domain wall contribution to polarization. This enhancement also reduces the mobility of the irreversible domain walls, thus requiring a higher driving field to trigger motion. The steep decrease in the dielectric constants under a dc bias field caused by the enhanced c/a can be associated with an increase in the anisotropy of the dielectric constants, which results in their reduction in the crystallographic c-axis direction. These results demonstrate that a high c/a is not desirable for capacitor applications, although it is the origin of ferroelectricity in perovskite materials.

Magnetic Properties of Nanocrystalline Powder Cores Fabricated by Mechanically Crushed Powders

Fe73.5Cu1Nb3Si15.5B7 nanocrystalline powder cores with different particle sizes ranging from 10 to 125 μm were fabricated by cold-pressing techniques. The cores exhibited increased core loss Pcv and decreased initial permeability μi with addition of fine powders below 50 μm in size, and the content should be less than 40 mass%. It was thought to be closely related to the high coercive force Hc due to the stresses generated during the crushing process and high demagnetization fields of small powders. Furthermore, modifying the alloy compositions by adding defined amount of Ni could improve the soft magnetic properties, including superior characteristics of permeability under high direct current (DC) bias field and comparable low core loss at high frequency.

Parametric controls on giant magnetoimpedance (GMI) behaviour of CoFeSiBCr amorphous wires for prospective sensor applications

Investigation is focused on the effect of different parametric controls like driving frequency, amplitude of the alternating current (ac), direct current (dc) bias field and anisotropy field (Hk) on the Giant Magneto-Impedance (GMI) properties of rapidly quenched soft magnetic Co66Fe2Si13B15Cr4 amorphous wires developed by in-water quenching technique. Optimal controls of these parameters like driving frequency and amplitude of the ac were found to display a sensitive change in GMI properties at optimal frequency of 5MHz and 5mA driving current. The influence of these controls on the output factors like maximum GMI ratio (GMImax), transition from single peak (SP) to double peak (DP), field sensitivity of GMI (η) and anisotropy field (Hk) throw light on the application of the developed wires for sensors. In addition to high Hk, driving frequency of 5MHz also delivered a combination of desirable sensor properties like high level of sensitivity and its enhanced span of stability. Joule heating further improved the GMI response of the material through current annealing at a current density of 5A/mm2.

Characterization of the electrocaloric effect and hysteresis loss in relaxor ferroelectric thin films under alternating current bias fields

We report characterization and analysis of the frequency-dependent temperature responses in thin films exhibiting the electrocaloric (EC) effect under AC bias fields using a high-precision lock-in technique. The temperature response detected by an embedded thin-film resistance thermometer is analyzed using the steady-periodic solutions of a 3D heat conduction model to extract the equivalent volumetric heat sources/sinks, which represent the combined effects of electrocaloric cooling/heating and hysteresis loss. The dependence of the measured heat source strengths on the bias field frequency and amplitude is consistent with our model prediction and independently measured dielectric properties. The volumetric heating rate due to hysteresis loss is estimated to be as much as 15% of the EC heating/cooling rates for solution-cast relaxor ferroelectric polymer films studied here. Our experimental approach enables a systematic study of the electrocaloric performance of thin films and deleterious impact of hysteresis loss.

Synthesis, structure, luminescence, and magnetic properties of a single-ion magnet "mer"-[tris(N-[(imidazol-4-yl)-methylidene]-DL-phenylalaninato)terbium(III) and related "fac"-DL-alaninato derivative.

Two Tb(III) complexes with the same N6O3 donor atoms but different coordination geometries, "fac"-[Tb(III)(HL(DL-ala))3]·7H2O (1) and "mer"-[Tb(III)(HL(DL-phe))3]·7H2O (2), were synthesized, where H2L(DL-ala) and H2L(DL-phe) are N-[(imidazol-4-yl)methylidene]-DL-alanine and -DL-phenylalanine, respectively. Each Tb(III) ion is coordinated by three electronically mononegative NNO tridentate ligands to form a coordination geometry of a tricapped trigonal prism. Compound 1 consists of enantiomers "fac"-[Tb(III)(HL(D-ala))3] and "fac"-[Tb(III)(HL(L-ala))3], while 2 consists of "mer"-[Tb(III)(HL(D-phe))2(HL(L-phe))] and "mer"-[Tb(III)(HL(D-phe))(HL(L-phe))2]. Magnetic data were analyzed by a spin Hamiltonian including the crystal field effect on the Tb(III) ion (4f(8), J = 6, S = 3, L = 3, gJ = 3/2, (7)F6). The Stark splitting of the ground state (7)F6 was evaluated from magnetic analysis, and the energy diagram pattern indicated easy-plane and easy-axis (Ising type) magnetic anisotropies for 1 and 2, respectively. Highly efficient luminescences with Φ = 0.50 and 0.61 for 1 and 2, respectively, were observed, and the luminescence fine structure due to the (5)D4 → (7)F6 transition is in good accordance with the energy diagram determined from magnetic analysis. The energy diagram of 1 shows an approximate single-well potential curve, whereas that of 2 shows a double- or quadruple-well potential within the (7)F6 multiplets. Complex 2 displayed an onset of the out-of-phase signal in alternating current (ac) susceptibility at a direct current bias field of 1000 Oe on cooling down to 1.9 K. A slight frequency dependence was recorded around 2 K. On the other hand, 1 did not show any meaningful out-of-phase ac susceptibility. Pulsed-field magnetizations of 1 and 2 were measured below 1.6 K, and only 2 exhibited magnetic hysteresis. This finding agrees well with the energy diagram pattern from crystal field calculation on 1 and 2. DFT calculation allowed us to estimate the negative charge distribution around the Tb(III) ion, giving a rationale to the different magnetic anisotropies of 1 and 2.

Synthesis, Structure, Luminescent, and Magnetic Properties of Carbonato-Bridged ZnII2LnIII2 Complexes [(μ4-CO3)2{ZnIILnLnIII(NO3)}2] (LnIII = GdIII, TbIII, DyIII; L1 = N,N′-Bis(3-methoxy-2-oxybenzylidene)-1,3-propanediaminato, L2 = N,N′-Bis(3-ethoxy-2-oxybenzylidene)-1,3-propanediaminato)

Carbonato-bridged Zn(II)2Ln(III)2 complexes [(μ4-CO3)2{Zn(II)L(n)Ln(III)(NO3)}2]·solvent were synthesized through atmospheric CO2 fixation reaction of [Zn(II)L(n)(H2O)2]·xH2O, Ln(III)(NO3)3·6H2O, and triethylamine, where Ln(III) = Gd(III), Tb(III), Dy(III); L(1) = N,N'-bis(3-methoxy-2-oxybenzylidene)-1,3-propanediaminato, L(2) = N,N'-bis(3-ethoxy-2-oxybenzylidene)-1,3-propanediaminato. Each Zn(II)2Ln(III)2 structure possessing an inversion center can be described as two di-μ-phenoxo-bridged {Zn(II)L(n)Ln(III)(NO3)} binuclear units bridged by two carbonato CO3(2-) ions. The Zn(II) ion has square pyramidal coordination geometry with N2O2 donor atoms of L(n) and one oxygen atom of a bridging carbonato ion at the axial site. Ln(III) ion is coordinated by nine oxygen atoms consisting of four from the deprotonated Schiff-base L(n), two from a chelating nitrate, and three from two carbonate groups. The temperature-dependent magnetic susceptibilities in the range 1.9-300 K, field-dependent magnetization from 0 to 5 T at 1.9 K, and alternating current magnetic susceptibilities under the direct current bias fields of 0 and 1000 Oe were measured. The magnetic properties of the Zn(II)2Ln(III)2 complexes are analyzed on the basis of the dicarbonato-bridged binuclear Ln(III)-Ln(III) structure, as the Zn(II) ion with d(10) electronic configuration is diamagnetic. ZnGd1 (L(1)) and ZnGd2 (L(2)) show a ferromagnetic Gd(III)-Gd(III) interaction with J(Gd-Gd) = +0.042 and +0.028 cm(-1), respectively, on the basis of the Hamiltonian H = -2J(Gd-Gd)ŜGd1·ŜGd2. The magnetic data of the Zn(II)2Ln(III)2 complexes (Ln(III) = Tb(III), Dy(III)) were analyzed by a spin Hamiltonian including the crystal field effect on the Ln(III) ions and the Ln(III)-Ln(III) magnetic interaction. The Stark splitting of the ground state was so evaluated, and the energy pattern indicates a strong easy axis (Ising type) anisotropy. Luminescence spectra of Zn(II)2Tb(III)2 complexes were observed, while those of Zn(II)2Dy(III)2 were not detected. The fine structure assignable to the (5)D4 → (7)F6 transition of ZnTb1 and ZnTb2 is in good accord with the energy pattern from the magnetic analysis. The Zn(II)2Ln(III)2 complexes (Ln(III) = Tb(III), Dy(III)) showed an out-of-phase signal with frequency-dependence in alternating current susceptibility, indicative of single molecule magnet. Under a dc bias field of 1000 Oe, the signals become significantly more intense and the energy barrier, Δ/kB, for the magnetic relaxation was estimated from the Arrhenius plot to be 39(1) and 42(8) K for ZnTb1 and ZnTb2, and 52(2) and 67(2) K for ZnDy1 and ZnDy2, respectively.

Pyroelectric response mechanism of barium strontium titanate ceramics in dielectric bolometer mode: The underlying essence of the enhancing effect of direct current bias field

Pyroelectric response mechanism of Ba0.70Sr0.30TiO3 ceramics under dielectric bolometer (DB) mode was investigated by dielectric and pyroelectric properties measurement. The variations of total, intrinsic, and induced pyroelectric coefficients (ptot, pint, pind) with temperatures and bias fields were analyzed. pint plays the dominant role to ptot through most of the temperature range and pind will be slightly higher than pint above T0. The essence of the enhancing effect of DC bias field on pyroelectric coefficient can be attributed to the high value of pint. This mechanism is useful for the pyroelectric materials (DB mode) applications.

Dielectric and enhanced pyroelectric properties of (Pb0.325Sr0.675)TiO3 ceramics under direct current bias field

(Pb0.325Sr0.675)TiO3 (PST) ceramics were prepared by a traditional solid-state reaction technique. The dielectric and enhanced pyroelectric properties of PST ceramics were investigated under a DC bias field. The dielectric permittivity and dielectric loss of PST ceramics at Curie temperature were 2.97 × 10−4 and 0.006 without DC bias field, respectively. With a DC electric field of 0–500 V/mm, the maximum pyroelectric coefficient and the largest figure of merit (Fd) of PST ceramics were obtained, about 60 × 10−8 C cm−2 K−1 and 26 × 10−5 Pa−1/2, respectively. PST ceramics with such superior electric field enhanced pyroelectric properties have the potential for uncooled focal plane array detectors application.

The SushiBar: An automated system for paleomagnetic investigations

We present a new, automated system based on a three‐axis superconducting magnetometer and a custom‐made coil designed to experiment on cylindrical specimens used in typical paleomagnetic investigations. The system, which resembles a sushi bar, facilitates stepwise alternating field demagnetization of up to 99 samples per loaded track. It also enables researchers to explore magnetic properties using an anhysteretic remanent magnetization (ARM) in any coercivity window up to peak alternating fields of 95 mT with direct current bias fields up to 0.17 mT. For example, partial ARM (pARM) spectra characterize magnetic grain size distributions in rocks, yet rarely are pARM spectra measured because the complete curve for one sample takes at least two hours to acquire manually. The SushiBar achieves 99 such curves in slightly less than 100 hours. Using the SushiBar, we measured the pARM sprectra, as well as the viscosity and anisotropy of ARM in three discrete switching field windows, of continental sediments from the Xishuigou section (western China). The average grain size remains constant along the 2200 m‐thick section, yet magnetic viscosity varies systematically from bottom to top of the section; samples with high magnetic viscosities also have higher proportions of non‐viscous material on average. Principal anisotropy axis directions from the lowest switching fields correlate well with principal axis directions from anisotropy of magnetic susceptibility. Principal axis directions defined at higher switching fields systematically deviate from those at lower switching fields, perhaps defining the fabric of the remanence‐carrying grains.

Dielectric properties and electrical behaviors of tunable Bi1.5MgNb1.5O7 thin films

The Bi1.5MgNb1.5O7 (BMN) thin films were prepared on Au-coated Si substrates by rf magnetron sputtering. We systematically investigated the structure, dielectric properties and voltage tunable property of the films with different annealing temperatures. The relationships of leakage current and breakdown bias field with annealing temperature were firstly studied and a possible explanation was proposed. The deposited BMN thin films had a cubic pyrochlore phase when annealed at 550°C or higher. With the increasing of annealing temperature, the dielectric constant and tunability also went up. BMN thin films annealed at 750°C exhibited moderate dielectric constant of 106 and low dielectric loss of 0.003–0.007 between 10kHz and 10MHz. The maximum tunability of 50% was achieved at a bias field of 2MV/cm. However, thin films annealed at 750°C had lower breakdown bias field and higher leakage current density than films annealed below 750°C. The excellent physical and electrical properties make BMN thin films promising for potential tunable capacitor applications.

High pyroelectric properties of (Pb0.87La0.02Ba0.1)(Zr0.75Sn0.25–xTix)O3 ceramics near AFE/RFE phase boundary under DC bias field

Abstract

ON THE CHAOTIC FLUX DYNAMICS IN A LONG JOSEPHSON JUNCTION

Flux dynamics in an annular long Josephson junction is studied. Three main topics are covered. The first is chaotic flux dynamics and its prediction via Melnikov integrals. It turns out that DC current bias cannot induce chaotic flux dynamics, while AC current bias can. The existence of a common root to the Melnikov integrals is a necessary condition for the existence of chaotic flux dynamics. The second topic is on the components of the global attractor and the bifurcation in the perturbation parameter measuring the strength of loss, bias and irregularity of the junction. The global attractor can contain coexisting local attractors, e.g. a local chaotic attractor and a local regular attractor. In the infinite dimensional phase space setting, the bifurcation is very complicated. Chaotic attractors can appear and disappear in a random fashion. Three types of attractors (chaos, breather, spatially uniform and temporally periodic attractor) are identified. The third topic is ratchet effect. Ratchet effect can be achieved by a current bias field which corresponds to an asymmetric potential, in which case the flux dynamics is ever lasting chaotic. When the current bias field corresponds to a symmetric potentially, the flux dynamics is often transiently chaotic, in which case the ratchet effect disappears after sufficiently long time.

Influences of axial field upon circular magnetization and eddy‐current anomaly factor in Fe‐based nanocrystalline wire

AbstractFe‐based soft magnetic wire with transverse magnetic anisotropy was obtained by stress current annealing. Its circular permeability, µ = µ′ – jµ″, has been determined from the measurements of impedance, Z = R + jωL, as a function of frequency (f = 10 – 105 Hz), AC current amplitude (I = 0.1 – 100 mA) and DC bias field (H = 0 – 5.4 kA/m). An experimental study of the influence of H upon the circular magnetization and the f‐dependent µ = µ′ – jµ″ has been performed. It is concluded that the axial field, H, evolution of the circular permeability, µ = µ′ – jµ″, the relaxation frequency, fτ, and the eddy‐current anomaly factor, η, can be explained in terms of the modification of domain structure by the applied axial field H.

Influence of in-plane fields on the three kinds of hard domains

The influence of in-plane field on three kinds of hard domains was studied experimentally by means of direct current bias fields reconstruction. The experiment verifies that VBLs in those three kinds of hard domains collapse gradually under the in-plane field. And the conclusion we obtained that these hard domains have the same range of the critical in-plane field ［H1ip,H2ip］ corrects the previous view that (H1ip)IIDH1ip)IDH1ip)OHB. By revealing that the breakdown of VBLs affected by in-plane field is independent of the rigidity of the hard domains, this paper provides an important clue for interpreting the mechanism of the VBLs' vanishing and a new scheme for exactly measuring the critical in-plane field under which VBLs begin to disappear.