AC Excitation Field Research Articles

Research on Spatial Localization Method of Magnetic Nanoparticle Samples Based on Second Harmonic Waves

Existing magnetic tracer detection systems primarily rely on fundamental wave signal acquisition using non-differential sensor configurations. These sensors are highly susceptible to external interference and lack tomographic localization capabilities, hindering their clinical application. To address these limitations, this paper presents a novel method for achieving the deep spatial localization of tracers. The method exploits second harmonic signal detection at non-zero field points. By considering the combined nonlinear characteristics of the coil’s axial spatial magnetic field distribution and the Langevin function, a correlation model linking the signal peak and bias field is established. This model enables the determination of the tracer’s precise spatial location. Building on this framework, a handheld device for localizing magnetic nanoparticle tracers was developed. The device harnesses the second harmonic response generated by coupling an AC excitation field with a DC bias field. Our findings demonstrate that under conditions of reduced coil turns and weak excitation fields, the DC bias field exhibits exclusive dependence on the axial distance of the detection point, independent of particle concentration. This implies that the saturated DC bias field corresponding to the second harmonic signal can be used to determine the magnetic nanoparticle sample detection depth. The experimental results validated the method’s high accuracy, with axial detection distance and concentration reduction errors of only 4.8% and 4.1%, respectively. This research paves the way for handheld probes capable of tomographic tracer detection, offering a novel approach for advancing magnetically sensitive biomedical detection technologies.

Calibration method for AC electromagnetic positioning systems distorted by eddy currents

Electromagnetic positioning technologies are frequently-used in surgical navigation systems to achieve precise position of surgical instruments in bodies. Still, in operating rooms with complex environments, they would be disturbed by eddy currents of metals. This paper explores a calibration method to mitigate eddy current interference. Initially, The study examined the generation mechanisms of eddy currents and established the expression of secondary magnetic fields they produced, which exhibited a 90-degree phase difference with the AC excitation field. Subsequently, an integral calibration method was proposed, leveraging fields’ distinct phases for separating. Through simulation, various metal materials were modeled to study their impact on magnetic fields. The effectiveness of the calibration method was evaluated by comparing positioning accuracy before and after calibration. Results demonstrated over 80 % average calibration efficiency, effectively mitigating errors induced by metals and enhancing the system’s reliability. This calibration method is crucial for the broader application of electromagnetic positioning systems.

Field-dependent Néel relaxation time of magnetic nanoparticles in AC excitation fields: Boundary field between Néel- and Brownian-dominant regions

We investigated the field-dependent Néel relaxation time of magnetic nanoparticles (MNPs) in an AC excitation field. Specifically, a fundamental component of the magnetization for immobilized MNPs was studied by numerical simulation while changing the frequency f and amplitude Hac of the field. From the simulation results, we clarified the Hac dependence of the effective Néel relaxation time τN,e and obtained an empirical expression for τN,e(Hac) for the first time. The expression was obtained for the cases when the angle of the easy axis of magnetization in MNPs is fixed and randomly distributed. Using the Hac dependencies of τN,e and the previously reported Brownian relaxation time τB,e, we showed that the behavior of suspended MNPs changes from Brownian-dominant to Néel-dominant when Hac increases, even when the MNP parameters are fixed, and we obtained an expression for the boundary field between them. Furthermore, we classified several types of responses for the suspended MNPs in the AC field using the magnitude relationship among τN,e(Hac), τB,e(Hac), and 1/(2πf). Finally, we experimentally verified the classification, and reasonable agreement was observed between the experiment and analysis. The results are useful for determining suitable MNP parameters and excitation conditions for various biomedical applications.

Measurement and calculation for high frequency magnetic losses of Terfenol-D alloy rod under coupled stress and DC bias fields

Compressive stress, a DC bias magnetic field, and an AC excitation field significantly affect hysteresis characteristics and magnetic energy losses of magnetostrictive materials. Therefore, studying high frequency magnetic losses of magnetostrictive materials under coupling of these three conditions is of great importance for improving the output performance of high power magnetostrictive transducers. In this paper, a magnetic property testing system for magnetostrictive materials has been constructed. It enables the magnetic property testing of Terfenol-D alloy rods under the simultaneous application of stress and DC bias at high frequency excitation (a maximum AC magnetic flux density of 0.5 T at an excitation frequency of 9 kHz). Based on Bertotti separation theory and experimental data, considering the coupling effect of stress and DC bias, a computational model for the high frequency magnetic losses of Terfenol-D materials is proposed. The model incorporates relevant parameters of stress and DC bias to modify loss coefficients, and the expressions for loss coefficients are identified using the symbolic regression method. A comparative analysis between experimental data and model calculation shows good agreement, with the maximum and average errors of 4.68% and 1.74%, respectively.

Sub-pT oscillatory magnetometric system using magnetoresistive sensor array for a low-field magnetic particle imaging

Implementing low ac excitation fields toward clinical magnetic particle imaging (MPI) system is critical to avoid magnetostimulation effects. However, low-field MPI scenario demands high sensitivity to probe the change in monotone magnetization response of magnetic nanoparticles. Here, we use an array of ultrasensitive MR sensors to detect sub-pT magnetic signal and obtain its spatial distribution. While each sensor is operated at 5 V, signal processing circuit rises its sensitivity to 20 mV pT−1 at 10 kHz with 0.25 pT noise level. In evaluating sensor performance, we initially measured a 10-kHz magnetic field from a 40-turns coil with 1 mm in diameter. MR sensor recognizes magnetic signal of mini coil to be linear with the coil input current. We then recorded the signals simultaneously from a 6 × 6 sensor channels to map the fields at 0.2 kHz. While placing mini coil 50 mm apart from the array, we obtained high-contrast field image showing coil position and its change in field polarity. For practical nanoparticle detection, we later used a 3 × 3 array configuration for the 10 kHz oscillatory magnetometry while compensating the MR sensor magnetically from the ac excitation field. Despite a 20-pT noise floor associated with the field compensation circuit, we were able to map stray fields of a 37-mgFe iron oxide nanoparticle sample distanced 100 mm from the array, under 12.4 µT/μ0 field amplitude. This result highlights usability of MR sensor array for low-field MPI system.

A Linear Slope Analyzing Strategy of GMR Sensor Transfer Curve for Static Detection of Magnetic Nanoparticles

For giant magnetoresistance (GMR) sensors, the in-plane DC detection mode is commonly applied because it offers higher tolerance to the misorientation of the excitation magnetic field as compared to vertical detection mode, and it does not suffer the undesired coupling due to induction by the AC excitation field. However, the quantification result was typically obtained by subtraction method whereby the concentration of the magnetic nanoparticles (MNPs) is determined from the difference between the sensor output voltage signals with and without DC excitation field respectively. While this method is simple, it leads to a high noise level, especially when the concentration of the MNPs is low and the sensor output signal is weak and spiky, resulting in unreliable quantification results. This work aimed at developing a new signal analyzing strategy to obtain quantification results with a higher signal-to-noise ratio (SNR). A linear slope analyzing strategy (slope method) was proposed. The slope of the linear region of the output transfer curve measured with a sweeping excitation field is compared before and after depositing MNPs resulting in $\Delta $ Slope, which indicates the quantity of the MNPs presented on the sensor surface. The slope being the trendline of a transfer curve is more stable and statistically less susceptible to random behavior. Experimental implementation was performed using an MNPs detection platform constructed with a commercial GMR sensor. Results showed that the $\Delta $ Slope increased linearly with the concentration of biotinylated superparamagnetic iron oxide nanoparticles (biotin-IONPs). In comparison with the traditional subtraction method, the SNR was improved from 17.3 dB to 25.3 dB.

AC Magnetization of Immobilized Magnetic Nanoparticles With Different Degrees of Parallel Alignment of Easy Axes

Magnetic nanoparticles (MNPs) are physically immobilized in some biomedical applications. In this case, dynamic ac magnetization that determines MNPs' performance has strong dependence on the relative direction between the magnetic easy axes of MNPs and the applied excitation field. To study this dependence, we prepared immobilized MNP samples with different degrees of easy axes' alignment. The degree of alignment was changed by setting the strength of a dc field that is applied during the immobilization process. The magnetic properties of these samples, such as ac magnetization, coercive field, amplitude of third-harmonic signal, and hysteresis loss, are compared with those of a randomly oriented easy axes' sample. It was shown that these values are significantly affected by the degree of easy axes' alignment when the strength of the ac excitation field, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , is relatively small. The alignment effect gradually becomes smaller when H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is increased. These findings are important for immobilized MNP applications in hyperthermia and magnetic particle imaging.

Compact susceptometer for studies under transverse field geometries at very low temperatures.

We present the design of a compact AC susceptometer for studies under arbitrarily oriented static magnetic fields, in particular magnetic fields oriented transverse to the AC excitation field. The small size of the susceptometer permits versatile use in conventional cryostats with superconducting magnet systems. The design of the susceptometer minimizes parasitic signal contributions while providing excellent thermal anchoring suitable for measurements in a wide range down to very low temperatures. The performance is illustrated by means of measurements of the transverse susceptibility at the magnetic field tuned quantum phase transition of the dipolar-coupled Ising ferromagnet LiHoF4.

Effect of viscosity on the AC magnetization of magnetic nanoparticles under different AC excitation fields

Abstract For in vivo applications of magnetic nanoparticles (MNPs), environment viscosity is one of the most important parameters that determines their AC magnetization. In this study, we investigate the effect of viscosity on the AC magnetization of MNPs under different AC excitation field conditions. We show that the AC M − H curve and harmonic magnetization spectrum strongly depend on the viscosity for a small excitation field intensity and low excitation frequency, while they are insensitive to the viscosity for a large excitation field intensity and high excitation frequency. We then show that the difference in the AC magnetization between these cases can be qualitatively explained by taking the field dependent Brownian fB(Hac) and Neel fN(Hac) frequencies into account. The frequencies are obtained from numerical simulations based on the Fokker-Planck equations. Finally, we show that an excitation field with a relatively large intensity and a frequency f that satisfies fB(Hac) ≪ f ≤ fN(Hac) is suitable for the magnetic fluid hyperthermia (MFH) application.

Temperature dependence in magnetic particle imaging

Experimental results are presented demonstrating how temperature can influence the dynamics of magnetic nanoparticles (MNPs) in liquid suspension, when exposed to alternating magnetic fields in the kilohertz frequency range. The measurements used to probe the nanoparticle systems are directly linked to both the emerging biomedical technique of magnetic particle imaging (MPI), and to the recently proposed concept of remote nanoscale thermometry using MNPs under AC field excitation. Here, we report measurements on three common types of MNPs, two of which are currently leading candidates for use as tracers in MPI. Using highly-sensitive magnetic particle spectroscopy (MPS), we demonstrate significant and divergent thermal dependences in several key measures used in the evaluation of MNP dynamics for use in MPI and other applications. The temperature range studied was between 296 and 318 Kelvin, making our findings of particular importance for MPI and other biomedical technologies. Furthermore, we report the detection of the same temperature dependences in measurements conducted using the detection coils within an operational preclinical MPI scanner. This clearly shows the importance of considering temperature during MPI development, and the potential for temperature-resolved MPI using this system. We propose possible physical explanations for the differences in the behaviors observed between the different particle types, and discuss our results in terms of the opportunities and concerns they raise for MPI and other MNP based technologies.

Highly Sensitive DC Magnetic Field Sensor Based on Nonlinear ME Effect

Under a high ac excitation field, the output voltage of magnetoelectric (ME) composite at the third harmonic is linearly proportional to dc magnetic field, which makes it an excellent dc magnetometer. We fabricated a PZT and metallic glass (MG) composite with a multi-pushpull mode configuration, which has large values of linear ME coefficient. We systematically investigated the nonlinear ME effect of the PZTMG composite at its electricmechanical resonance frequency of 30 kHz. The sensitivity to dc magnetic field is studied under different ac excitation field and dc bias field. We found that the highest sensitivity is 17.6VOe at zero bias field. The nonlinear ME magnetic sensor has been demonstrated with a limit of detection of $2\times 10^{{- 5}}$ Oe to dc magnetic field.

Effect of alignment of easy axes on dynamic magnetization of immobilized magnetic nanoparticles

In some biomedical applications of magnetic nanoparticles (MNPs), the particles are physically immobilized. In this study, we explore the effect of the alignment of the magnetic easy axes on the dynamic magnetization of immobilized MNPs under an AC excitation field. We prepared three immobilized MNP samples: (1) a sample in which easy axes are randomly oriented, (2) a parallel-aligned sample in which easy axes are parallel to the AC field, and (3) an orthogonally aligned sample in which easy axes are perpendicular to the AC field. First, we show that the parallel-aligned sample has the largest hysteresis in the magnetization curve and the largest harmonic magnetization spectra, followed by the randomly oriented and orthogonally aligned samples. For example, 1.6-fold increase was observed in the area of the hysteresis loop of the parallel-aligned sample compared to that of the randomly oriented sample. To quantitatively discuss the experimental results, we perform a numerical simulation based on a Fokker-Planck equation, in which probability distributions for the directions of the easy axes are taken into account in simulating the prepared MNP samples. We obtained quantitative agreement between experiment and simulation. These results indicate that the dynamic magnetization of immobilized MNPs is significantly affected by the alignment of the easy axes.

Evaluation of Complex Harmonic Signals From Magnetic Nanoparticles for Magnetic Particle Imaging

We evaluated the complex harmonic signals from magnetic nanoparticles (MNPs) for magnetic particle imaging (MPI). We measured the complex harmonic signals from Resovist MNPs, one of the candidates for an MPI tracer, when only an ac excitation field and both the ac and the dc excitation fields were applied. To evaluate the complex harmonic magnetization spectra, we performed a numerical simulation accounting for the distributions of magnetic moments, anisotropy energy barriers, and hydrodynamic sizes of MNPs in the sample. The simulation results agreed well with experimentally obtained amplitude of the harmonic signals. The simulation results of the phase lag, which was caused by the finite relaxation time, agreed with the experiments for low harmonic numbers. The phase lag deviation between them became significant for higher harmonic numbers. For quantitative evaluation of the phase lag for higher harmonic numbers, a more accurate estimation of the Neel relaxation time is required.

The effect of field-orientation on the magnetoelectric coupling in Terfenol-D/PZT/Terfenol-D laminated structure

The field-orientation dependent magnetoelectric coupling is experimentally studied for a rectangular Terfenol-D/PZT/Terfenol-D laminated structure. The considered magnetic field, namely the dc-bias magnetic field or the ac-excitation magnetic field, is allowed to be spatially re-orientated between two orthogonal geometric dimensions of the composite. In the study, the direction of the excitation can be fixed in the longitudinal (Scheme-I) or thickness (Scheme-II) directions, while considering the bias orientation. Alternatively, the bias field can be restricted to the longitudinal (Scheme-III) or thickness (Scheme-IV) directions, while the excitation orientation is considered. The variation in magnetoelectric coefficient as a function of the bias magnitude is studied with special attention paid to the field-orientation dependency. For the testing schemes of I and II, the direction of the dc-bias field can be re-oriented by forming an angle with the fixed direction of the ac-excitation field. As the angle changes from 0° to 90°, the magnetoelectric coupling evolves from L-T mode to S-T surface shear for Scheme-I, and from T-T mode to S-T thickness shear for Scheme-II. The bias-field-orientation dependence demonstrates a complex pattern due to the varying overall state of anisotropy in Terfenol-D. In Scheme-I with low bias magnitude, the orientation dependence can be represented by the measured effective longitudinal piezomagnetic coefficient. In addition, the optimal bias field for maximum magnetoelectric coefficient is observed to linearly increase with the bias orientation angle. Alternatively, the orientation dependence in Schemes III and IV is more predictable due to the barely changed overall state of anisotropy. In this case, Scheme-III shows that the magnetoelectric coefficient decreases monotonically with the orientation angle and Scheme-IV indicates that the maximum coefficient is attained at around 60°. The dependence of the magnetoelectric coupling on the excitation-filed orientation can be understood via analysis of the resultant magnetostriction in Terfenol-D with assumed effective magnetization, which may depart from the bias field due to the strong demagnetization effect. The analysis is supported by the computed field-orientation dependence of the magnetostriction in Terfenol-D.

Low frequency noise of anisotropic magnetoresistors in DC and AC-excited metal detectors

Magnetoresistors can replace induction sensors in applications like non-destructive testing and metal detection, where high spatial resolution or low frequency response is required. Using an AC excitation field the magnetic response of eddy currents is detected. Although giant magnetoresistive (GMR) sensors have higher measuring range and sensitivity compared to anisotropic magnetoresistors (AMR), they show also higher hysteresis and noise especially at low frequencies. Therefore AMR sensors are chosen to be evaluated in low noise measurements with combined processing of DC and AC excitation field with respect to the arrangement of processing electronics. Circuit with a commercial AMR sensor HMC1001 and AD8429 preamplifier using flipping technique exhibited 1-Hz noise as low as 125 pT/. Without flipping, the 1-Hz noise increased to 246 pT/.

Comment on "Al-in-Hornblende Thermobarometry and Sr-Nd-O-Pb Isotopic Compositions of the Early Miocene Alaçam Granite in NW Anatolia (Turkey)"

High harmonic response of high-Tc and Chevrel-phase polycrystalline superconductors are measured in the presence of small ac excitation field and dc magnetic field applied on it. The aim of this work is to study the Josephson weak link behavior and compare the two systems in order to understand the granular nature of polycrystalline superconductors. Critical state models are used to explain the nonlinear magnetic response in polycrystalline superconductors.

Low Field ac Susceptibility and High Harmonics Studies in PbMo6S8 Polycrystalline Superconductor

The ac susceptibility and high harmonic response of polycrystalline PbMo6S8 superconductor are measured in the presence of small ac excitation field and dc magnetic field applied on it. Our experimental results could be explained by the classical Bean critical state model, when the current does not depend on the field and even harmonics are not observed.

AMR gradiometer for mine detection

Anisotropic magnetoresistors (AMRs) are used to build an advanced mine detector. The sensing head involves a gradiometric pair of AMR sensors and a continuous-wave driven excitation coil, so the gradiometer is capable of detection of ferromagnetic materials as well as diamagnetic metals. The sensors are specially arranged to suppress the large AC-excitation field, so the mine detector senses both DC and AC field gradient responses of the object of interest. Being limited by the sensor and electronics noise of 268pT/√Hz at 1kHz, we were able to detect a 50mm×50mm×1.5mm aluminum test object in a 20cm depth using a 150μT, 1-kHz excitation field.

Flux avalanches triggered by AC magnetic fields in superconducting thin films

Flux avalanches are known to occur as a consequence of thermomagnetic instabilities. Some of their fingerprints are jumps in magnetization curves, or a paramagnetic reentrance in AC susceptibility measurements. In this work we have studied flux avalanches triggered by an AC field cycle by means of AC susceptibility and residual magnetization after an applied AC field measured as a function of an AC excitation field (h). These measurements allow comparing both results with magneto-optical imaging carried out in similar conditions. The results show a correspondence for the onset of the avalanche activity, as well as between the residual magnetic moment and the mean gray value calculated from the magneto-optical images in the remanent state.

Magneto-optical Kerr effect susceptometer for the analysis of magnetic domain wall dynamics

Domain wall dynamics in thin magnetic films with perpendicular and in-plane anisotropy is studied using a novel magneto-optical Kerr effect susceptometery method. The method allows for measurements of domain wall motion under ac field excitation and the analysis of dynamic modes as a function of driving frequency and magnetic field amplitude. Domain wall dynamics in the perpendicular anisotropy system, a Co/Pt multilayer, is characterized by thermally activated creep motion. For this dynamic mode, a polydispersivity exponent of β = 0.50 ± 0.03 is derived at small excitation energy, which is in excellent agreement with theoretical models. The dynamics of the other system, a Co wire with transverse uniaxial anisotropy, is dominated by viscous slide motion in a regular magnetic stripe pattern. Analytical expressions are derived for this magnetic configuration and by using these expressions, accurate values for the depinning field and the domain wall mobility are extracted from the susceptibility measurements.