Magnetic Alignment Research Articles

Magnetic Field Alignment Relative to Multiple Tracers in the High-mass Star-forming Region RCW 36

We use polarization data from SOFIA HAWC+ to investigate the interplay between magnetic fields and stellar feedback in altering gas dynamics within the high-mass star-forming region RCW 36, located in Vela C. This region is of particular interest as it has a bipolar H ii region powered by a massive star cluster, which may be impacting the surrounding magnetic field. To determine if this is the case, we apply the histogram of relative orientations (HRO) method to quantify the relative alignment between the inferred magnetic field and elongated structures observed in several data sets such as dust emission, column density, temperature, and spectral line intensity maps. The HRO results indicate a bimodal alignment trend, where structures observed with dense gas tracers show a statistically significant preference for perpendicular alignment relative to the magnetic field, while structures probed by the photodissociation region (PDR) tracers tend to align preferentially parallel relative to the magnetic field. Moreover, the dense gas and PDR associated structures are found to be kinematically distinct such that a bimodal alignment trend is also observed as a function of line-of-sight velocity. This suggests that the magnetic field may have been dynamically important and set a preferred direction of gas flow at the time that RCW 36 formed, resulting in a dense ridge developing perpendicular to the magnetic field. However, on filament scales near the PDR region, feedback may be energetically dominating the magnetic field, warping its geometry and the associated flux-frozen gas structures, causing the observed preference for parallel relative alignment.

Pr-modified microstructure enhances coercivity in Sm2Co17-type magnets

Optimizing components of the cellular structure is a strategy to enhance the magnetic performance of Sm2Co17-type magnets. In this study, Pr is used to modify the cellular structure in Sm2Co17-type magnets, achieving synergistic optimization of coercivity from 32.12 kOe to 34.71 kOe and remanence from 11.23 kGs to 11.36 kGs. Analyses reveal that the increased remanence is attributed to the enhanced saturation magnetization and better grain alignment in the Pr-5 magnet. The incomplete cellular structures and Cu-lean region near grain boundaries are ameliorated in the Pr-5 magnets. Meanwhile, the Pr-modified and Cu-enriched cellular boundary phase, which has a lower magnetocrystalline anisotropy field, enhances the pinning strength of the domain-wall and contributes to the increase in coercivity. The substitution of Pr for Sm has a lower substitution energy in SmCo5 than in Sm2Co17, leading to the slight enrichment of Pr in the 1:5H phase. However, excessive Pr leads to increased amounts of oxides and deteriorates magnetic properties. This work provides valuable insights into developing high-performance Sm2Co17-type magnets by optimizing the microstructure and microchemical components.

Magnetoplasmonic Triblock Nanorods for Collective Linear Dichroism.

Polarized light detection is crucial for advancements in optical imaging, positioning, and obstacle avoidance systems. While optical nanomaterials sensitive to polarization are well-established, the ability to align these materials remains a significant challenge. Here, we introduce Au-Fe3O4-Au triblock nanorods as a novel solution. Synthesized via a space-confined seeded growth method, these magnetoplasmonic nanocomposites uniquely combine the strong polarization capabilities of Au nanorods with the magnetic alignment properties of Fe3O4 nanorods. This architecture results in exceptional collective linear dichroism, achieving a polarization ratio of approximately 14 at the device level. Our nanorods exhibit high detection sensitivity and laser damage resistance, positioning them as a promising platform for developing advanced optical devices.

An innovative 4D printing approach for fabrication of anisotropic collagen scaffolds

Collagen anisotropy is known to provide the essential topographical cues to guide tissue-specific cell function. Recent work has shown that extrusion-based printing using collagenous inks yield 3D scaffolds with high geometric precision and print fidelity. However, these scaffolds lack collagen anisotropy. In this study, extrusion-based 3D printing was combined with a magnetic alignment approach in an innovative 4D printing scheme to generate 3D collagen scaffolds with high degree of collagen anisotropy. Specifically, the 4D printing process parameters-collagen (Col):xanthan gum (XG) ratio (Col:XG; 1:1, 4:1, 9:1 v/v), streptavidin-coated magnetic particle concentration (SMP; 0, 0.2, 0.4 mg ml-1), and print flow speed (2, 3 mm s-1)-were modulated and the effects of these parameters on rheological properties, print fidelity, and collagen alignment were assessed. Further, the effects of collagen anisotropy on human mesenchymal stem cell (hMSC) morphology, orientation, metabolic activity, and ligamentous differentiation were investigated. Results showed that increasing the XG composition (Col:XG 1:1) enhanced ink viscosity and yielded scaffolds with good print fidelity but poor collagen alignment. On the other hand, use of inks with lower XG composition (Col:XG 4:1 and 9:1) together with 0.4 mg ml-1SMP concentration yielded scaffolds with high degree of collagen alignment albeit with suboptimal print fidelity. Modulating the print flow speed conditions (2 mm s-1) with 4:1 Col:XG inks and 0.4 mg ml-1SMP resulted in improved print fidelity of the collagen scaffolds while retaining high level of collagen anisotropy. Cell studies revealed hMSCs orient uniformly on aligned collagen scaffolds. More importantly, collagen anisotropy was found to trigger tendon or ligament-like differentiation of hMSCs. Together, these results suggest that 4D printing is a viable strategy to generate anisotropic collagen scaffolds with significant potential for use in tendon and ligament tissue engineering applications.

Modeling of planar germanium hole qubits in electric and magnetic fields

Hole-based spin qubits in strained planar germanium quantum wells have received considerable attention due to their favorable properties and remarkable experimental progress. The sizeable spin-orbit interaction in this structure allows for efficient qubit operations with electric fields. However, it also couples the qubit to electrical noise. In this work, we perform simulations of a heterostructure hosting these hole spin qubits. We solve the effective mass equations for a realistic heterostructure, provide a set of analytical basis wavefunctions, and compute the effective g-factor of the heavy-hole ground state. Our investigations reveal a strong impact of highly excited light-hole states located outside the quantum well on the g-factor. We find that sweet spots, points of operations that are least susceptible to charge noise, for out-of-plane magnetic fields are shifted to impractically large electric fields. However, for magnetic fields close to in-plane alignment, partial sweet spots at low electric fields are recovered. Furthermore, sweet spots with respect to multiple fluctuating charge traps can be found under certain circumstances for different magnetic field alignments. This work will be helpful in understanding and improving the coherence of germanium hole spin qubits.

Tri-axial magnetic alignment and magnetic anisotropies in misfit-layered calcium-based cobaltites doped with rare-earth ions

In this study, we introduce an original method for quantifying tri-axial magnetic anisotropy in [Ca2CoO3-δ]0.62CoO2, and its rare earth (RE)-doped variants, [(Ca1-xREx)2CoO3-δ]0.62CoO2, utilizing a modulated rotating magnetic field of 10 T. Our findings reveal a significant correlation between the magnetic anisotropy and local structure of RE ions, particularly bond lengths and coordination numbers, which influence the magnetization axes of these magnetically aligned powders. We introduce an analytical methodology employing linear equations to calculate the magnetic susceptibilities along distinct crystallographic axes, enabling the prediction of tri-axial magnetic anisotropies at elevated concentrations of Er ions. This research not only advances our understanding of magnetic anisotropy control but also paves the way for the successful fabrication of triaxially-aligned ceramics using magneto-science techniques.

Low magnetic field alignment of carbon fibers in a polymer matrix for high-performance thermal interface materials

Carbon-based materials like carbon nanotubes, graphene nanoplatelets, graphite, and carbon fibers (CF) are highly promising fillers for enhancing the thermal conductivity of thermal interface materials (TIMs) due to their high thermal conductivity and low thermal expansion. Aligning these fillers can further improve thermal conductivity, but current alignment methods using high magnetic fields are impractical for industrial use. In this study, we investigated the enhancement of the thermal conductivity of CF–polymer composites by aligning CF fillers with a low magnetic field. We observed up to 17 times enhancement of the thermal conductivity (from 3.1 to 52.8 W/mK) in a CF–graphene–polymer composite film by vertically aligning the CF fillers with a magnetic field of 0.75 T. The analysis of the structural properties of the films using X-ray diffraction and field-emission scanning electron microscopy imaging confirmed that the crystalline c-axis of the graphite plates in the CF was oriented perpendicular to the magnetic field direction. The large anisotropy in the diamagnetic susceptibility of the laminated graphene structure of the CF flakes is at the origin of the filler alignment. Furthermore, the thermal conductivity of the composites showed a strong correlation with the degree of filler alignment, which was dependent on the CF–graphene hybridization and the type of polymer matrix. This study provides a scalable and cost-effective method for enhancing the physical properties of carbon composites by controlling their microarchitecture using a low magnetic field.

Characterization of an Environmentally Responsive Organic-Inorganic Hybrid Fe3O4/SiO2/PPy-c Core-Shell Nanocomposite with Magneto-Chromatic Ability for Synergistic Electrical Properties.

The aim of this study was to analyze the properties of a composite that incorporates carbon black and polypyrrole within an Fe3O4/SiO2 core-shell structure, synthesized using the Stöber method under high ultrasonic irradiation conditions (120 W) for Fe3O4/SiO2 nanocomposite. The Fe3O4/SiO2 core-shell indicates magnetochromatic behavior characterized by temperature-dependent coloration and magnetic alignment. Incorporating carbon black and polypyrrole at moderate temperature (5-15 °C) enhanced the electrical conductivity. The electrical resistivity ρ was 7.30 × 106 Ω·cm for Fe3O4, 3.19 × 108 Ω·cm for Fe3O4/SiO2, and 242.56 Ω·cm for Fe3O4/SiO2/PPy-c at room temperature. When it was performed at moderate temperature (5-15 °C), the ρ of the prepared Fe3O4/SiO2 and Fe3O4/SiO2/PPy-c nanocomposite was 1.08 × 108 and 0.00799 Ω·cm, respectively. Current-voltage measurements revealed a linear relationship, with butterfly shaped curves in the forward-bias region for all samples. The Fe3O4/SiO2/PPy-c nanocomposite's tunable synergistic electrical properties at moderate temperatures make it useful for environmental applications, electrical wiring, and circuitry.

Magnetic field-assisted vertically aligned NiFe2O4 nanosheets in composite solid polymer electrolytes for advanced all solid-state lithium metal batteries

Two-dimensional materials (2D Ms) as fillers have been applied in polyethylene oxide (PEO)-based electrolyte to enhance the low ionic conductivity and poor interface compatibility. However, the randomly dispersed fillers in PEO matrix result in anisotropy of Li+ transportation and insufficent ionic conductivity. Herein, NiFe2O4 (NFO) nanosheets are firstly introduced in polymer matrix to form vertically aligned NFO-PEO (ANFO-PEO) composite solid-state electrolytes (CSEs) through magnetic field-assisted alignment strategy. The vertically aligned NFO/PEO interface in CSEs can construct oriented Li+ transport channels and maximize the utilization of high in-plane conductivity. Meanwhile, the NFO nanosheets with abundant oxygen vacancies could effectively anchor TFSI− to promote the dissociation of Li salts. Furthermore, the optimized Li+ transport flux in CSEs enables homogeneous Li deposition and effectively mitigates the growth of dendrites. Owing to the synergistic effects, the ANFO-PEO CSEs exhibit high ionic conductivity (9.16 × 10−4 S cm−1 at 60 °C) and stable potential window up to 5.0 V vs Li/Li+. Therefore, LiFePO4 in the full cell and pouch cell with ANFO-PEO CSEs could deliver excellent cycling performance (92.78 % capacity retention after 1000 cycles at 0.5C; 96.88 % capacity retention after 105 cycles at 0.1C).

Magnetic splitting induced ferromagnetism in chromium-doped HfSe2

Two-dimensional (2D) magnetic layered materials have gained significant interest in spintronic for memory storage devices. Herein, the electronic and magnetic properties of high-quality single crystals of chromium (Cr)-doped hafnium diselenide were studied. The electronic study indicated that the Cr-doped HfSe2 reveals the semiconducting nature with a proper bandgap as identified by angle-resolved photoemission spectroscopy and first-principle density functional theory (DFT) calculations. The magnetic results indicate that the HfSe₂ exhibited ferromagnetic characteristics with the substitution of Cr atoms in a perpendicular direction. The Cr-doped HfSe2 sample shows a ferromagnetic phase below ∼58 K, indicating the critical temperature (Tc) of magnetic order, while above this temperature, it shows a paramagnetic phase that can follow the Curie-Weiss Law. It can be seen that the magnetic moment is approximately 0.16 emu/g at 5 K, which further decreases with increasing temperature until 60 K and then transforms to a paramagnetic phase. The sample can clearly show a weak out-of-plane magnetic anisotropy with a coercivity of around 50.56 Oe and a saturation magnetization value of 0.029 emu/g. Convincingly, it was observed from the ARPES results that the valence band is split due to the spin-orbit interaction of Cr atoms, which can induce ferromagnetic order. At the same time, the temperature-dependent ARPES data shows that the splitting is higher below the Tc, while it is weaker above the Tc. The DFT results revealed that near the Fermi level, the spin-up and spin-down are spin-polarized with asymmetric trends. It can be observed that substituting Cr on the octahedral sites of Hf atoms influences the electron spin order created by Hf vacancies (as validated by the magnetic coupling measured by electron paramagnetic resonance spectroscopy experiments), which can change the magnetic alignment to induce the magnetism in HfSe2. This study highlights that doping transition metal in HfSe2 has promising potential for future applications, especially in memory devices and spintronic technologies.

Elucidating the impact of non-spherical morphology on kinetic behavior of graphite using single-particle microelectrode

The precise assessment of the kinetic properties of graphite is crucial for the design of the material and the development of electrochemical models for lithium-ion batteries. However, conventional evaluation methods using composite electrodes fall short in excluding the influence of its porous structure and evaluating the influence of particle shape on kinetic behavior. In this work, we elucidate the impact of non-spherical morphology on kinetic behavior of single artificial graphite particle, employing the single-particle microelectrode technique. Three single artificial graphite particles with different sizes are pre-cycled and exhibit outstanding rate capability, maintaining a maximum capacity retention of 78.1 % at 200 C. Further, exchange current density and diffusion coefficients are determined through Tafel plots and the potentiostatic intermittent titration technique (PITT), respectively. It is found that the particle with a higher exposure of edge planes present elevated exchange current density and diffusion coefficients. Considering that the graphite particles typically feature an ellipsoidal rather than spherical shape, we propose an approach based on an ellipsoidal diffusion model for extracting diffusion coefficients. This model takes into account the non-spherical morphology of graphite, addressing the limitations inherent in the geometric assumptions of previous methods. The average relative error between the diffusion coefficients derived from the ellipsoidal diffusion model and the previous method using spherical assumptions is 215 %, indicating that accurately depicting the shape of ellipsoidal graphite particles in the model is crucial for obtaining correct estimates of kinetic parameters. This study offers direct experimental evidence of superior kinetic behavior of edge planes over basal planes. To leverage this characteristic, it is recommended to employ an out-of-plane aligned architecture for composite electrodes using novel techniques, e.g., 3D printing or magnetic alignment techniques.

Short communication: The orientation of cubicles plays a role – greater deviation from the north–south direction, more technopathies in dairy cows

Magnetic alignment (MA) is a biological phenomenon denoting spontaneous orientation of an animal’s body at rest, when fleeing a threat, hunting, etc. in relation to the Earth’s magnetic field lines, often parallel to the field lines, i.e. in a north–south (NS) direction. MA has been demonstrated in several animal species, including grazing and resting domestic mammals. Based on the assumption that cows prefer to orientate their bodies in the NS direction when resting and sleeping, we hypothesised that MA could contribute to the incidence of technopathies in dairy cows, i.e. various disorders caused by the stable equipment that pose a serious animal welfare problem. It was hypothesised that the incidence of technopathies increases when the cubicles (resting places) orientation deviates from the NS position. The incidence of technopathies was recorded in 34 free-stall dairy farms. The type (hairless patch, scratch, swelling, wound), location and size of the lesions were recorded in almost 1 200 dairy cows. Based on the number of cubicles available and the number of cows, the cubicle-per-cow index (CC index) was calculated and divided into two groups: CC index ≥ 1 for stables with at least one cubicle per cow and CC index < 1 if the number of cows exceeded the number of cubicles available. The orientation of the cubicles was determined by the azimuth (the angle between north and the chosen clockwise direction). The farms were categorised into two groups according to azimuth: NS (azimuth deviating ± 15° from north or south, i.e. 345-15° and 165-195°) and non-NS (azimuth 15-165° and 195-345°). We found that the frequency of cows with technopathies was 30% lower in the NS-orientated cubicles and the number of technopathies per cow was 40% lower in the NS-orientated cubicles than in the non-NS-orientated cubicles. In addition, a higher number of technopathies per cow was observed when the CC index was ≥ 1, with a significant difference in the non-NS-aligned cubicles. According to our results, cubicle orientation has some influence on the incidence of technopathies. Although biological phenomena such as MA are seemingly unimportant and usually overlooked, they should be considered in livestock production when planning the positioning of stable equipment/ cubicle.

Magnetic Measurements and Alignment Results of LQXFA/B Cold Mass Assemblies at Fermilab

Magnetic Measurements and Alignment Results of LQXFA/B Cold Mass Assemblies at Fermilab

Nuclear magnetic resonance investigation of superconducting and normal state Nb3Sn

The superconductor Nb3Sn has important applications for construction of very high-field superconducting magnets. In this work we investigate its microscopic electronic structure with 93Nb nuclear magnetic resonance (NMR). The high-quality Nb3Sn powder sample was studied in both 3.2 T and 7 T magnetic fields in the temperature range from 4 K to 300 K. From measurement of the spectrum and its theoretical analysis, we find evidence for anisotropy despite its cubic crystal structure. Magnetic alignment of the powder grains in the superconducting state was also observed. The Knight shift and spin-lattice relaxation rate, T1−1 , were measured and the latter compared with BCS theory for the energy gap Δ(0)=2.7±0.3kBTc at 3.2 T and Δ(0)=2.33±0.07kBTc at 7 T, indicating suppression of the order parameter by magnetic field.

Electric field enhancement of the superconducting spin-valve effect via strain-transfer across a ferromagnetic/ferroelectric interface

In a ferromagnet/superconductor/ferromagnet (F/S/F) superconducting spin-valve (SSV), a change in the magnetization alignment of the two F layers modulates the critical temperature (Tc) of the S layer. The Tc-switching effect (the SSV effect) is based on the interplay between superconductivity and magnetism. The fast and large resistive switching associated with Tc-switching is suitable for nonvolatile cryogenic memory applications. However, the external magnetic field-based operation of SSVs is hindering their miniaturization, and therefore, electric field control of the SSV effect is desired. Here, we report epitaxial growth of a La0.67Ca0.33MnO3/YBa2Cu3O7/La0.67Ca0.33MnO3 SSV on a piezo-electric [Pb(Mg0.33Nb0.67)O3]0.7-[PbTiO3]0.3 (001) substrate and demonstrate electric field control of the SSV effect. Electric field-induced strain-transfer from the piezo-electric substrate increases the magnetization and Tc of the SSV and leads to an enhancement of the magnitude of Tc-switching. The results are promising for the development of magnetic-field-free superconducting spintronic devices, in which the S/F interaction is not only sensitive to the magnetization alignment but also to an applied electric field.

Design of magnetic elastomer composites with tunable magnetic responses from soft to hard magnetization

Magnetic elastomer composites with tunable magnetic responses from soft to hard magnetization have been synthesized. Co-Ti co-doped barium hexaferrite (BaCoxTixFe12–2xO19) nanopowders were used as the filling and polydimethylsiloxane (PDMS) as the matrix. The effects of magnetic field-induced alignment of BaM magnetic particles in the matrix on the properties of the prepared composites have been investigated. For anisotropic magnetic elastomers, the formed chain structure plays a positive role in the enhancement of the shear energy storage modulus of the elastomers. The enhanced energy storage modulus is increased by about 190 % compared with that of the isotropic magnetic elastomers. Due to the magnetic chain structure of the magnetic particles and its effect on the rubber molecular chain, the anisotropic magnetic elastomers can obtain higher magnetic deformation response capability in the direction of the parallel magnetic field. Their research lays a foundation for further designing tunable magnetic flexible sensors.

Unraveling the Molecular Weight Dependence of High Magnetic Field to Manipulate the Semiconducting Polymer Molecular Orientation.

The magnetic alignment of molecules, which exploits the anisotropy of diamagnetic susceptibility, provides a clean and versatile approach to the structural manipulation of semiconducting polymers. Here, the magnetic-alignment dynamics of two molecular-weight (MW) batches of a diketopyrrolopyrrole (DPP)-based copolymer (PDVT-8) were investigated. Microstructural characterizations revealed that the magnetically aligned, high-MW (Mn = 53.7 kDa) PDVT-8 film exhibited a higher degree of backbone chain alignment and film crystallinity compared with the low-MW (Mn = 17.6 kDa) PDVT-8 film grown via the same magnetic alignment method. We found that as the MW increases, the degree of preaggregation of the polymer molecules in solution significantly increases and the aggregation mode changes from H-aggregation to J-aggregation through a cooperative assembly mechanism. These events improved the responsiveness of high-MW polymer molecules to magnetic fields. Field-effect transistors based on the magnetic aligned high-MW PDVT-8 films exhibited a 6.8-fold increase in hole mobility compared to the spin-coated films, along with a mobility anisotropy ratio of 12.6. This work establishes a significant correlation among chain aggregation behavior in solution, polymer film microstructures, magnetic responsiveness, and carrier transport performance in donor-acceptor polymer systems.

Properties of a steel fiber reinforced cementitious composite stool with digitally distributed steel fibers

This study aims to maximize the reinforcement of steel fibers in cementitious composite structural members. A 3D-printing stool was chosen as a case study. The orientation of the steel fibers is designed to be parallel to the direction of the tensile stress, and the volume fraction of steel fibers everywhere meets the tensile requirements, which is defined as digitally distributed steel fiber reinforced cementitious composite (DD-SFRC) stool. The DD-SFRC stool was prepared using magnetic field aligning and 3D-printing, to control the volume fraction and orientation of steel fibers in the stool. The results show that digitally distributed steel fibers reinforce the mechanical properties of the stool more effectively, in terms of ultimate load, energy absorption capacity, joint ductility, and the width of the crack, compared with that of the stool with random and aligned steel fiber distribution. The methodology of design and approach of preparation of DD-stool are presented, which are valid and applicable to other structures in either laboratory or practice.

Mineral magnetism and palaeoenvironment recorded in loess in southern England

ABSTRACTExtensive research has focused on the loess deposits in southern England, aiming to unravel their stratigraphic and palaeoenvironmental significance. However, no systematic mineral magnetic study on these deposits has yet been undertaken. Here we address this by investigating the magnetic mineral composition and alignment of loess at two sites in southern England, Lowland Point (LP) on the Lizard Peninsula of Cornwall, and Pegwell Bay (PB) in eastern Kent on the Isle of Thanet. A set of rock magnetic analyses was conducted to understand mineral magnetism within the studied sections. In addition, the primary depositional origin of the magnetic fabrics as well as their overprinting caused by various possible post‐depositional processes were examined through anisotropy of magnetic susceptibility (AMS). The magnetic mineral composition is similar at both sites, derived from both sedimentary (aeolian) and post‐depositional processes. The AMS results show magnetic foliation that varies between the two sites, aligning with the bedding plane, indicating deposition from gravitational dust fall at the PB site, and a stronger wind transport energy at the LP site. Although the magnetic lineation of bulk AMS is relatively weak, there is a noticeable tendency towards alignment in most samples, with flow directions from the SE indicated at both sections if a strong wind is assumed at LP, although with a possible SW direction if a weaker wind is assumed. These observations may imply the preservation of palaeowind directions during dust transport, with a substantial southerly component, which contradicts previous assertions of dominant northerly or northeasterly winds. Indeed, a possible dominant southeasterly wind direction between 25 and 18 ka would suggest a limited influence of katabatic, westerly or polar northeasterly winds during dust transport, and rather may imply the effect of low‐pressure systems passing through the English Channel during that period.

Spin-resolved counting statistics as a sensitive probe of spin correlation in transport through a quantum dot spin valve

We investigate the noise in spin transport through a single quantum dot (QD) tunnel coupled to ferromagnetic (FM) electrodes with noncollinear magnetizations. Based on a spin-resolved quantum master equation, auto- and cross-correlations of spin-resolved currents are analyzed to reveal the underlying spin transport dynamics and characteristics for various polarizations. We find the currents of majority and minority spins could be strongly autocorrelated despite uncorrelated charge transfer. The interplay between tunnel coupling and the Coulomb interaction gives rise to an exchange magnetic field, leading to the precession of the accumulated spin in the QD. It strongly suppresses the bunching of spin tunneling events and results in a unique double-peak structure in the noise of the net spin current. The spin autocorrelation is found to be susceptible to magnetization alignments, which may serve as a sensitive tool to measure the magnetization directions between the FM electrodes.