Initialization-Free and Magnetic Field-Free Spin-Orbit p-Bits with Backhopping-like Magnetization Switching for Probabilistic Applications.

Probabilistic bits (p-bits) with thermal- and spin torque-induced nondeterministic magnetization switching are promising candidates for performing probabilistic computing. Previously reported spin torque p-bits include volatile low-energy barrier nanomagnets (LBNMs) with spontaneously fluctuating magnetizations and initialization-necessary nonvolatile magnets. However, initialization-free nonvolatile spin torque p-bits are still lacking. Here, we demonstrate moderately thermal stable spin-orbit torque (SOT) p-bits with non-consecutively deposited Pt//Pt/Co/Pt stacks. Backhopping-like (BH) magnetization switching with a wide range current-tunable probability of final up and down magnetization states from 0% to 100% was achieved, regardless of the initial magnetization state, which was attributed to the interplay of SOT and thermal contributions. Integer factorization using such BH-SOT p-bits in zero magnetic field was demonstrated at times that are significantly shorter than those of existing nonvolatile STT or volatile LBNMs p-bits. Our realization of initialization-free and magnetic field-free moderately thermally stable BH-SOT p-bits opens up a new perspective for probabilistic spintronic applications.

Spin-lock based fast whole-brain 3D macromolecular proton fraction mapping of relapsing-remitting multiple sclerosis.

A sensitive and efficient imaging technique is required to assess the subtle abnormalities occurring in the normal-appearing white matter (NAWM) and normal-appearing grey matter (NAGM) in patients with relapsing-remitting multiple sclerosis (RRMS). In this study, a fast 3D macromolecular proton fraction (MPF) quantification based on spin-lock (fast MPF-SL) sequence was proposed for brain MPF mapping. Thirty-four participants, including 17 healthy controls and 17 RRMS patients were prospectively recruited. We conducted group comparison and correlation between conventional MPF-SL, fast MPF-SL, and DWI, and compared differences in quantified parameters within MS lesions and the regional NAWM, NAGM, and normal-appearing deep grey matter (NADGN). MPF of MS lesions was significantly reduced (7.17% ± 1.15%, P < 0.01) compared to all corresponding normal-appearing regions. MS patients also showed significantly reduced mean MPF values compared with controls in NAGM (4.87% ± 0.38% vs 5.21% ± 0.32%, P = 0.01), NAWM (9.49% ± 0.69% vs 10.32% ± 0.59%, P < 0.01) and NADGM (thalamus 5.59% ± 0.67% vs 6.00% ± 0.41%, P = 0.04; caudate 5.10% ± 0.55% vs 5.53% ± 0.58%, P = 0.03). MPF and ADC showed abnormalities in otherwise normal appearing close to lesion areas (P < 0.01). In conclusion, time-efficient MPF mapping of the whole brain can be acquired efficiently (< 3 min) using fast MPF-SL. It offers a promising alternative way to detect white matter abnormalities in MS.

Towards assessing and improving the reliability of ultrashort echo time quantitative magnetization transfer (UTE-qMT) MRI of cortical bone: In silico and ex vivo study.

OBJECTIVE: To assess and improve the reliability of the ultrashort echo time quantitative magnetization transfer (UTE-qMT) modeling of the cortical bone. MATERIALS AND METHODS: Simulation-based digital phantoms were created that mimic the UTE-qMT properties of cortical bones. A wide range of SNR from 25 to 200 was simulated by adding different levels of noise to the synthesized MT-weighted images to assess the effect of SNR on UTE-qMT fitting results. Tensor-based denoising algorithm was applied to improve the fitting results. These results from digital phantom studies were validated via ex vivo rat leg bone scans. RESULTS: The selection of initial points for nonlinear fitting and the number of data points tested for qMT analysis have minimal effect on the fitting result. Magnetization exchange rate measurements are highly dependent on the SNR of raw images, which can be substantially improved with an appropriate denoising algorithm that gives similar fitting results from the raw images with an 8-fold higher SNR. DISCUSSION: The digital phantom approach enables the assessment of the reliability of bone UTE-qMT fitting by providing the known ground truth. These findings can be utilized for optimizing the data acquisition and analysis pipeline for UTE-qMT imaging of cortical bones.

Variable-density velocity-selective magnetization preparation for non-contrast-enhanced peripheral MR angiography.

Velocity-selective (VS) magnetization preparation has shown great promise for non-contrast-enhanced (NCE) magnetic resonance angiography (MRA) with the ability to generate positive angiographic contrast directly using a single 3D acquisition. However, existing VS-MRA methods have an issue of aliased saturation around a certain velocity, known as velocity field-of-view (vFOV), which can cause undesired signal loss in arteries. This study aimed to develop a new version of the VS preparation pulse sequence that overcomes the aliased saturation problem in conventional VS preparation. Utilizing the fact that an excitation profile is the Fourier transform of excitation k-space sampling, we sampled the k-space in a non-uniform fashion by scaling gradient pulses accordingly to have aliased excitation diffused over velocity. The variable density sampling function was numerically optimized to maximize the average of the velocity passband signal while minimizing its variance. The optimized variable density VS magnetization was validated through Bloch simulations and applied to peripheral NCE MRA in healthy subjects. The in-vivo experiments showed that the proposed variable density VS-MRA significantly lowered arterial signal loss observed in conventional VS-MRA, as evidenced by a higher arterial signal-to-noise ratio (58.50 ± 14.29 vs. 55.54 ± 12.32; p < 0.05) and improved artery-to-background contrast-to-noise ratio (22.75 ± 7.57 vs. 20.60 ± 6.51; p < 0.05).

Magnetic irreversibility and magnetization processes in Ni5Al3/NiO core/shell nanoparticle system.

This work brings out many interesting facets of magnetism in the Ni5Al3/NiO core/shell nanoparticle system. The weak and strong magnetic irreversibility lines (TWI(H) and TSI(H)) reproduce the previously reported H - T phase diagram at fields H ≤ 30 Oe, but strong departures occur for H > 30 Oe. Comparison with the theoretically predicted H - T phase diagram allows us to identify TWIwith TCG+SG, where the paramagnetic (PM)-chiral glass (CG) and PM-spin glass (SG) phase transitions occur simultaneously, and TSIwith TSG, the temperature at which transition to the replica symmetry breaking SG state takes place. The TSI(H) transition line abruptly ends at the point (H ≃ 30 Oe, T ≃ 90 K). As H exceeds 30 Oe, a new transition appears, which gets completely suppressed at fields H > 1 kOe, where the magnetic irreversibility ceases to exist. No intrinsic long-range ferromagnetic ordering exists, but fields as low as 3 kOe suffice to induce long-range ferromagnetic order. At fixed temperatures, the magnetocrystalline anisotropy fluctuations essentially govern the 'approach-to-saturation' in magnetization for fields in the range 3 - 70 kOe. The present nanocrystalline system behaves as an isotropic system with a random easy axis in which the magnetization reversal occurs through the coherent rotation of the magnetizations of weakly-interacting single-domain Ni5Al3particles. Saturation magnetization, like M(T) at H ≥ 2 kOe, exhibits an anomalous upturn at temperatures below ≈ 30 K. This upturn is associated with the anomalous softening of spin-wave modes, which results in the thermal excitation of a large number of non-equilibrium (finite lifetime) magnons. At sub-Kelvin temperatures, these magnons undergo Bose-Einstein condensation. .

Room-Temperature Highly Efficient Nonvolatile Magnetization Switching by Current in van der Waals Fe3GaTe2 Devices.

The ability to manipulate magnetic states by a low electric current represents a fundamental desire in spintronics. In recent years, two-dimensional van der Waals (vdW) magnetic materials have attracted an extensive amount of attention due to their appreciable spin-orbit torque effect. However, for most known vdW ferromagnets, their relatively low Curie temperatures (TC) limit their applications. Consequently, low-power vdW spintronic devices that can operate at room temperature are in great demand. In this research, we fabricate nanodevices based on a solitary thin flake of vdW ferromagnet Fe3GaTe2, in which we successfully achieve nonvolatile and highly efficient magnetization switching by small currents at room temperature. Notably, the switching current density and the switching power dissipation are as low as 1.7 × 105 A/cm2 and 1.6 × 1013 W/m3, respectively, with an external magnetic field of 80 Oe; both are much reduced compared to those of conventional magnet/heavy metal heterostructure devices and other vdW devices.

Chemical activation and magnetization of carbonaceous materials fabricated from waste plastics and their evaluation for methylene blue adsorption.

In this study, novel adsorbents were synthesized via the activation and magnetization of carbon spheres, graphene, and carbon nanotubes fabricated from plastics to improve their surface area and porosity and facilitate their separation from aqueous solutions. Fourier transform infrared spectroscopy "FTIR", X-ray diffraction "XRD", energy-dispersive X-ray spectroscopy "EDX", transmission electron microscope "TEM", and X-ray photoelectron spectroscopy "XPS" affirmed the successful activation and magnetization of the fabricated materials. Further, surface area analysis showed that the activation and magnetization enhanced the surface area. The weight loss ratio decreased from nearly 60% in the case of activated graphene to around 25% after magnetization, and the same trend was observed in the other materials confirming that magnetization improved the thermal stability of the fabricated materials. The prepared carbonaceous materials showed superparamagnetic properties according to the magnetic saturation values obtained from vibrating sample magnetometry analysis, where the magnetic saturation values were 33.77, 38.75, and 27.18 emu/g in the presence of magnetic activated carbon spheres, graphene, and carbon nanotubes, respectively. The adsorption efficiencies of methylene blue (MB) were 76.9%, 96.3%, and 74.8% in the presence of magnetic activated carbon spheres, graphene, and carbon nanotubes, respectively. This study proposes efficient adsorbents with low cost and high adsorption efficiency that can be applied on an industrial scale to remove emerging pollutants.

Rare-earth (Eu3+) substitution impact on the structural, morphological, magneto-dielectric, and electrochemical properties of Cd0.45Co0.55Fe2-yEuyO4spinel nanoferrites.

A series ofCd0.45Co0.55Fe2-yEuyO4(y= 0.0, 0.1, 0.2, 0.3) spinel nanoferrites (SNFs) were synthesized using a self-igniting process and employed as electrode materials for supercapacitor applications. The results demonstrated the formation of a single SNFs phase, as shown by the XRD data. The crystallite size lies between the range of 29.30-51.12 nm. The porosity percentage is within the range of 31.37%-32.99%. Rietveld refinement of XRD and Raman analysis revealed the pure spinel phase and no secondary phase was observed. The saturation magnetization and magnetic anisotropy were also decreased with the addition of Eu3+in Cd-Co SNFs. The high coercive field was enhanced for Eu3+doping as compared to pure Cd-Co SNFs. The dielectric constant was improved with the substitution of Eu3+in Cd-Co SNFs. The dielectric tangent loss was reduced with the doping of Eu3+. The electrochemical performance of the Eu3+doped Cd-Co SNFs achieved an impressive maximum specific capacitance at a lower scan rate. Based on these findings, the outstanding electrochemical performance of the Eu3+doped Cd-Co SNFs suggests their potential as promising materials for high-frequency, magnetic ferrofluid, and supercapacitor electrodes.

Nanoscale Visualization of Symmetry-Breaking Electronic Orders and Magnetic Anisotropy in a Kagome Magnet YMn6Sn6.

A kagome lattice hosts a plethora of quantum states arising from the interplay between nontrivial topology and electron correlations. The recently discovered kagome magnet RMn6Sn6 (R represents a rare-earth element) is believed to showcase a kagome band closely resembling textbook characteristics. Here, we report the characterization of local electronic states and their magnetization response in YMn6Sn6 via scanning tunneling microscopy measurements under vector magnetic fields. Our spectroscopic maps reveal a spontaneously trimerized kagome electronic order in YMn6Sn6, where the 6-fold rotational symmetry is disrupted while translational symmetry is maintained. Further application of an external magnetic field demonstrates a strong coupling of the YMn6Sn6 kagome band to the field, which exhibits an energy shift discrepancy under different field directions, implying the existence of magnetization-response anisotropy and anomalous g factors. Our findings establish YMn6Sn6 as an ideal platform for investigating kagome-derived orbital magnetic moment and correlated magnetic topological states.

Phase shift of coherent magnetization dynamics after ultrafast demagnetization in strongly quenched nickel thin films.

The remagnetization process after ultrafast demagnetization can be described by relaxation mechanisms between the spin, electron, and lattice reservoirs. Thereby, collective spin excitations in form of spin waves and their angular momentum transfer play an important role on the longer timescales. In this work, we address the question whether the magnitude of demagnetization-the so-called quenching-affects the coherency and the phase of the excited spin waves. We present a study of coherent magnetization dynamics in thin nickel films after ultrafast demagnetization using the all-optical, time-resolved magneto-optical Kerr-effect technique. The largest coherent precession amplitude was observed for strongly quenched systems, indicating a well-defined precession phase for all pump pulses at a demagnetization of up to 90% in this system. Moreover, the phase of the excited spin-waves in Ni increases with the pump fluence, indicating a delayed start of the precession during the remagnetization. We compare these findings to recent studies in Ni80Fe20(permalloy), to evaluate the influence of the magneto-elastic coupling and non-linear spin-wave dynamics on the magnetization dynamics.

Feasibility of interleaved multislice averaged magnetization inversion-recovery acquisitions of the spinal cord.

PURPOSE: To establish an interleaved multislice variant of the averaged magnetization inversion-recovery acquisitions (AMIRA) approach for 2D spinal cord imaging with increased acquisition efficiency compared with the conventional 2D single-slice approach(es), and to determine essential prerequisites for a working interleaved multislice AMIRA approach in practice. METHODS: The general AMIRA concept is based on an inversion recovery-prepared, segmented, and time-limited cine balanced SSFP sequence, generating images of different contrast. For AMIRA imaging of multiple, independent slices in a 2D interleaved fashion, a slice loop within the acquisition loops was programmed. The former non-selective inversions were replaced with slice-selective inversions with user-definable slice thickness. RESULTS: The thickness of the slice-selective inversion in 2D interleaved multislice AMIRA should be doubled compared with the manufacturer's standard setting to avoid an increased sensitivity to flow and pulsation effects particularly in the CSF. However, this solution also limits its practical applicability, as slices located at directly adjacent vertebrae cannot be imaged together. Successful interleaved two-slice AMIRA imaging for a "reference" in vivo protocol with 0.50 × 0.50 mm2 in-plane resolution and 8-mm slice thickness is demonstrated, therefore halving its acquisition time per slice from 3 min down to 1.5 min. CONCLUSION: The investigated 2D interleaved two-slice AMIRA variant facilitates spinal cord imaging that maintains similar contrast and the same resolution as the conventional 2D single-slice AMIRA approach, but does so with a halved acquisition time.

Ultra-low-field magnetization transfer imaging at 0.055T with low specific absorption rate.

PURPOSE: To demonstrate magnetization transfer (MT) effects with low specific absorption rate (SAR) on ultra-low-field (ULF) MRI. METHODS: MT imaging was implemented by using sinc-modulated RF pulse train (SPT) modules to provide bilateral off-resonance irradiation. They were incorporated into 3D gradient echo (GRE) and fast spin echo (FSE) protocols on a shielding-free 0.055T head scanner. MT effects were first verified using phantoms. Brain MT imaging was conducted in both healthy subjects and patients. RESULTS: MT effects were clearly observed in phantoms using six SPT modules with total flip angle 3600° at central primary saturation bands of approximate offset ±786 Hz, even in the presence of large relative B0 inhomogeneity. For brain, strong MT effects were observed in gray matter, white matter, and muscle in 3D GRE and FSE imaging using six and sixteen SPT modules with total flip angle 3600° and 9600°, respectively. Fat, cerebrospinal fluid, and blood exhibited relatively weak MT effects. MT preparation enhanced tissue contrasts in T2-weighted and FLAIR-like images, and improved brain lesion delineation. The estimated MT SAR was 0.0024 and 0.0008 W/kg for two protocols, respectively, which is far below the US Food and Drug Administration (FDA) limit of 3.0 W/kg. CONCLUSION: Robust MT effects can be readily obtained at ULF with extremely low SAR, despite poor relative B0 homogeneity in ppm. This unique advantage enables flexible MT pulse design and implementation on low-cost ULF MRI platforms to achieve strong MT effects in brain and beyond, potentially augmenting their clinical utility in the future.

Magnetic Hardening: Unveiling Magnetization Dynamics in Soft Magnetic Fe-Ni-B-Nb Thin Films at Cryogenic Temperatures.

Recent advancements in amorphous materials have opened new avenues for exploring unusual magnetic phenomena at the sub-nanometer scale. We investigate the phenomenon of low-temperature "magnetic hardening" in heterogeneous amorphous Fe-Ni-B-Nb thin films, revealing a complex interplay between microstructure and magnetism. Magnetization hysteresis measurements at cryogenic temperatures show a significant increase in coercivity (HC) below 25 K, challenging the conventional Random Anisotropy Model (RAM) in predicting magnetic responses at cryogenic temperatures. Heterogeneous films demonstrate a distinct behavior in field-cooled and zero-field-cooled temperature-dependent magnetizations at low temperatures, characterized by strong irreversibility. This suggests spin-glass-like features at low temperatures, which are attributed to exchange frustration in disordered interfacial regions. These regions hinder direct exchange coupling between magnetic entities, leading to magnetic hardening. This study enhances the understanding of how microstructural intricacies impact magnetic dynamics in heterogeneous amorphous thin films at cryogenic temperatures.

Colossal Orbital Current Induced by Gradient Oxidation for High-Efficiency Magnetization Switching.

Orbital angular momentum flow can be used to develop a low-dissipation electronic information device by manipulating the orbital current. However, efficiently generating and fully harnessing orbital currents is a formidable challenge. In this study, an approach is presented that induces a colossal orbital current by gradient oxidation in Pt/Ta to enhance spin-orbit torque (SOT) and achieve high-efficiency magnetization switching. The maximum efficiency of the SOT before and after the gradient oxidation of Ta is improved relative to that of Pt by ≈600 and 1200%, respectively. The large SOT originates from the colossal orbital current because of the orbital Rashba-Edelstein effect induced by the gradient oxidation of Ta. In addition, a large spin-to-charge conversion efficiency is observed in yttrium iron garnet/Pt/TaOx because of the inverse orbital Rashba-Edelstein effect. Harnessing the orbital current can help effectively minimize the critical current density of the current-induced magnetization switching to 2.26-1.08 × 106 A cm-2, marking a 12-fold reduction compared to that using Pt. This findings provide a new path for research on low-dissipation spin-orbit devices and improve the tunability of orbital current generation.

Magnetization dynamics in quasiperiodic magnonic crystals.

Quasiperiodic magnonic crystals, in contrast to their periodic counterparts, lack strict periodicity which gives rise to complex and localised spin wave spectra characterized by numerous band gaps and fractal features. Despite their intrinsic structural complexity, quasiperiodic nature of these magnonic crystals enables better tunability of spin wave spectra over their periodic counterparts and therefore holds promise for the applications in reprogrammable magnonic devices. In this article, we provide an overview of magnetization reversal and precessional magnetization dynamics studied so far in various quasiperiodic magnonic crystals, illustrating how their quasiperiodic nature gives rise to tailored band structure, enabling unparalleled control over spin waves. The review is concluded by highlighting the possible potential applications of these quasiperiodic magnonic crystals, exploring potential avenues for future exploration followed by a brief summary.

Voxel-Based Morphometry of Progressive Supranuclear Palsy Using a 3D Fast Low-angle Shot Localizer Image: A Comparison with Magnetization-Prepared Rapid Gradient Echo.

PURPOSE: Voxel-based morphometry (VBM) is widely used to investigate white matter (WM) atrophy in patients with progressive supranuclear palsy (PSP). In contrast to high-resolution 3D T1-weighted imaging such as magnetization-prepared rapid acquisition with gradient echo (MPRAGE) sequences, the utility of other 3D sequences has not been sufficiently evaluated. This study aimed to assess the feasibility of using a 3D fast low-angle shot sequence captured as a localizer image (L3DFLASH) for VBM analysis of WM atrophy patterns in patients with PSP. METHODS: This retrospective study included 12 patients with pathologically or clinically confirmed PSP, and 18 age- and sex-matched healthy controls scanned with both L3DFLASH and MPRAGE sequences. Image processing was conducted with the Computational Anatomy Toolbox 12 in statistical parametric mapping 12. In addition to the atrophic WM pattern of PSP on VBM, we assessed the WM volume agreement between the two sequences using simple linear regression and Bland-Altman plots. RESULTS: Despite the slightly larger clusters on MPRAGE, VBM using both sequences showed similar characteristics of PSP-related WM atrophy, including in the midbrain, pons, thalamus, and precentral gyrus. In contrast, VBM showed gray matter (GM) atrophy of the precuneus and right superior parietal lobule exclusively on L3DFLASH. Unlike the measured values of total intracranial volume, GM, and cerebrospinal fluid on MPRAGE, the value of WM was larger on L3DFLASH. In contrast to the total intracranial volume, brainstem, and frontal and occipital lobes, the correlation with WM volume in other regions was relatively low. However, the Bland-Altman plots demonstrated strong agreement, with over 90% of the values falling within the agreement limits. CONCLUSION: Both MPRAGE and L3DFLASH are useful for detecting PSP-related WM atrophy using VBM.

Modelling nanomagnet vertex dynamics through Coulomb charges.

We investigate the magnetization dynamics in nanomagnet vertices often found in artificial spin ices. Our analysis involves creating a simplified model that depicts edge magnetization using magnetic charges. We utilize the model to explore the energy landscape, its associated curvatures, and the fundamental modes. Our study uncovers specific magnonic regimes and transitions between magnetization states, marked by zero-modes, which can be understood within the framework of Landau theory. To verify our model, we compare it with micromagnetic simulations, demonstrating a noteworthy agreement.

A simple physical model for simulation and design magneto-plethysmograph in application non-invasive hemoglobin measurement.

The magneto-plethysmograph method is a combination of magnetic field and sensors used to detect changes in blood flow pulsation. However, to detect the magnetic properties of blood related to hemoglobin concentration, physical modeling and simulation are required. This approach involves designing simulations using magnetic field equations and magnetic susceptibility, where a permanent magnet is placed on the surface of blood vessels, and sensors based on giant magnetoresistance are placed at a distance r. The design originates from a simple approach involving the magnetization and detection of Fe atoms in hemoglobin. Parameters involved include the magnetic susceptibility of oxyhemoglobin and deoxyhemoglobin, with an external magnetic field exceeding 1 Tesla. From the physical modeling and simulation, graphs are obtained depicting the influence of hemoglobin concentration on the number of Fe atoms and its magnetization. This enables the design of non-invasive hemoglobin measurement sensor devices. The uniqueness of this simple physical model and simulation lies in its ability to produce specially designed device models for measuring hemoglobin concentration. This differs from other research focusing on blood flow pulse measurements; the results of this study provide new insights into the benefits of simple physics equations that can be developed for medical diagnostic research and device development.

Anisotropic longitudinal water proton relaxation in white matter investigated ex vivo in porcine spinal cord with sample rotation.

A variation of the longitudinal relaxation time T 1 in brain regions that differ in their main fiber direction has been occasionally reported, however, with inconsistent results. Goal of the present study was to clarify such inconsistencies, and the origin of potential T 1 orientation dependence, by applying direct sample rotation and comparing the results from different approaches to measure T 1 . A section of fixed porcine spinal cord white matter was investigated at 3 T with variation of the fiber-to-field angle θ FB . The experiments included one-dimensional inversion-recovery, MP2RAGE, and variable flip-angle T 1 measurements at 22 °C and 36 °C as well as magnetization-transfer (MT) and diffusion-weighted acquisitions. Depending on the technique, different degrees of T 1 anisotropy (between 2 and 10%) were observed as well as different dependencies on θ FB (monotonic variation or T 1 maximum at 30-40°). More pronounced anisotropy was obtained with techniques that are more sensitive to MT effects. Furthermore, strong correlations of θ FB -dependent MT saturation and T 1 were found. A comprehensive analysis based on the binary spin-bath model for MT revealed an interplay of several orientation-dependent parameters, including the transverse relaxation times of the macromolecular and the water pool as well as the longitudinal relaxation time of the macromolecular pool.

Residual Magnetic Field Testing System with Tunneling Magneto-Resistive Arrays for Crack Inspection in Ferromagnetic Pipes.

Ferromagnetic pipes are widely used in the oil and gas industry. They are subject to cracks due to corrosion, pressure, and fatigue. It is significant to detect cracks for the safety of pipes. A residual magnetic field testing (RMFT) system is developed for crack detection in ferromagnetic pipes. Based on this background, a detection probe based on an array of tunneling magneto-resistive (TMR) sensors and permanent magnets is exploited. The probe is able to partially magnetize the pipe wall and collect magnetic signals simultaneously. First, a theoretical analysis of RMFT is presented. The physics principle of RMFT is introduced, and a finite element model is built. In the finite element simulations, the effects of the crack length and depth on the RMFT signal are analyzed, and the signal characteristics are selected to represent the crack size. Next, the validated experiments are conducted to demonstrate the feasibility of the proposed RMFT method in this paper.