Magnetic Pulse Research Articles

Magnetoresistance and Magnetic Relaxation of La-Sr-Mn-O Films Grown on Si/SiO2 Substrate by Pulsed Injection MOCVD

The results of magnetoresistance (MR) and resistance relaxation of nanostructured La1−xSrxMnyO3 (LSMO) films with different film thicknesses (60–480 nm) grown on Si/SiO2 substrate by the pulsed-injection MOCVD technique are presented and compared with the reference manganite LSMO/Al2O3 films of the same thickness. The MR was investigated in permanent (up to 0.7 T) and pulsed (up to 10 T) magnetic fields in the temperature range of 80–300 K, and the resistance-relaxation processes were studied after the switch-off of the magnetic pulse with an amplitude of 10 T and a duration of 200 μs. It was found that the high-field MR values were comparable for all investigated films (~−40% at 10 T), whereas the memory effects differed depending on the film thickness and substrate used for the deposition. It was demonstrated that resistance relaxation to the initial state after removal of the magnetic field occurred in two time scales: fast’ (~300 μs) and slow (longer than 10 ms). The observed fast relaxation process was analyzed using the Kolmogorov–Avrami–Fatuzzo model, taking into account the reorientation of magnetic domains into their equilibrium state. The smallest remnant resistivity values were found for the LSMO films grown on SiO2/Si substrate in comparison to the LSMO/Al2O3 films. The testing of the LSMO/SiO2/Si-based magnetic sensors in an alternating magnetic field with a half-period of 22 μs demonstrated that these films could be used for the development of fast magnetic sensors operating at room temperature. For operation at cryogenic temperature, the LSMO/SiO2/Si films could be employed only for single-pulse measurements due to magnetic-memory effects.

Efficient scheme for time-dependent thermal pure quantum state: Application to the Kitaev model with armchair edges

We consider the time-dependent thermal pure quantum state method and introduce the efficient scheme to evaluate the change in physical quantities induced by the time-dependent perturbations, which has been proposed in our previous paper [H. Taguchi et al., Phys. Rev. B 105, 125137 (2022)]. Here, we treat the Kitaev model to consider the Majorana-mediated spin transport, as an example. We demonstrate how efficient our scheme is to evaluate spin oscillations induced by the magnetic field pulse.

MAGNETIC-PULSED TREATMENT TO IMPROVE THE STRENGTH PROPERTIES OF DEFECTIVE SECTIONS OF OIL AND GAS PIPELINES

Link for citation: Schipachev A.M., Mohammed Aljadly. Magnetic-pulse treatment to improve the strength properties of defective sections of oil and gas pipelines. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 5, рр.7-16.In Rus. The relevance. During the operation of oil and gas pipelines, continuity defects (including point and linear defects such as delamination, cracks of various nature, etc.) occur in their structure. The peculiarity of material continuity defects is caused by the fact that in the process of loading the defects cause stress concentration near their tops, which leads to a rapid increase in their number and geometric dimensions, followed by the merging of the latter and the formation of large discontinuities, and as a consequence, the strength properties of pipelines decrease. Consequently, early detection of metal continuity defects and their elimination before they reach a critical size are urgent tasks. The solution of which will significantly improve the operational and strength properties of the working elements of pipelines and extend their lifespan. The main aim of the research is to study the effectiveness of magnetic-pulse treatment to improve the strength properties of used oil and gas pipelines by reducing the defects size. Objects: defective sections of main oil and gas pipelines. Methods: magnetic pulse treatment of samples on a magnetic-pulse unit MPU-10-SSAU 10, determination of temperature changes caused by magnetic-pulse treatment, testing samples for impact strength on a pendulum-testing machine, comparison of the obtained results for treated and untreated samples, determination of the effect of magnetic-pulse treatment on the strength properties of gas pipeline metal, study of the fracture surface of samples after impact tests. Results. It was established experimentally that the impact strength of the treated samples increased by 14 % compared to the untreated samples. Snapshots of the temperature distribution during the magnetic-pulse treatment showed a significant increase in temperature near the crack tips. It was found that destruction of the metal subjected to magnetic-pulse action acquired more viscous character.

Pulsed field magnetization of a rectangular Y–Ba–Cu–O bulk, single grain superconductor assembly

The practical magnetization of arrays of multiple single grain, bulk high temperature superconductors is essential for practical applications, such as trapped flux rotating machines, magnetic resonance imaging and nuclear magnetic resonance. We report a systematic investigation of the pulsed field magnetization (PFM) of a bulk assembly consisting of two rectangular Y–Ba–Cu–O bulk single grains, in close proximity, at various temperatures. The measurements of the dynamic variation of the magnetic flux density, supported by numerical analysis, reveal that the induced screening currents during the rise of a pulsed field may greatly enhance the flux density in the region of the junction leading to uneven flux penetration and to an increased likelihood of flux jumps in this region. Such coupling between field and current promotes magnetic flux penetration and improves the peak trapped field from 3.01 T for a bulk single grain to 3.11 T for the bulk assembly at 30 K, improving the magnetization efficiency from 80% to 90%. The peak trapped field was further enhanced to 3.39 T and 3.31 T for the single bulk single grain and the bulk assembly, respectively, by employing a two-step multi-pulse PFM process.

Monophasic-quadri-burst stimulation robustly activates bilateral swallowing motor cortices.

A stable, reliable, non-invasive, quantitative assessment of swallowing function remains to be established. Transcranial magnetic stimulation (TMS) is commonly used to aid in the diagnosis of dysphagia. Most diagnostic applications involve single-pulse TMS and motor evoked potential (MEP) recordings, the use of which is not clinically suitable in patients with severe dysphagia given the large variability in MEPs measured from the muscles involved in swallowing. Previously, we developed a TMS device that can deliver quadripulse theta-burst stimulation in 16 monophasic magnetic pulses through a single coil, enabling the measurement of MEPs related to hand function. We applied a system for MEP conditioning that relies on a 5 ms interval-monophasic quadripulse magnetic stimulation (QPS5) paradigm to produce 5 ms interval-four sets of four burst trains; quadri-burst stimulation (QBS5), which is expected to induce long-term potentiation (LTP) in the stroke patient motor cortex. Our analysis indicated that QBS5 conditioned left motor cortex induced robust facilitation in the bilateral mylohyoid MEPs. Swallowing dysfunction scores after intracerebral hemorrhage were significantly correlated with QBS5 conditioned-MEP parameters, including resting motor threshold and amplitude. The degree of bilateral mylohyoid MEP facilitation after left side motor cortical QBS5 conditioning and the grade of severity of swallowing dysfunction exhibited a significant linear correlation (r = -0.48/-0.46 and 0.83/0.83; R2 = 0.23/0.21 and 0.68/0.68, P < 0.001; Rt./Lt. side MEP-RMT and amplitudes, respectively). The present results indicate that RMT and amplitude of bilateral mylohyoid-MEPs after left motor cortical QBS5 conditioning as surrogate quantitative biomarkers for swallowing dysfunction after ICH. Thus, the safety and limitations of QBS5 conditioned-MEPs in this population should be further explored.

Fatigue behavior of Al-CFRP spot-welded joints prepared by electromagnetic pulse welding

In this study, the fatigue performance of magnetic pulse welding (MPW) joints of AA5052 aluminum alloy and T300 carbon fiber reinforced polymer (CFRP) with sandwich structure was systematically investigated. Mechanical property tests and microscopic observations were used to evaluate joint performance and damage to the CFRP. The results showed that satisfactory tensile strength (up to 92.24% of the tensile strength of the base material) was obtained by optimization of discharge energy. However, the samples in the fatigue test exhibited more sensitive properties to the fatigue environment. The higher fatigue cycle life was demonstrated only when the stress amplitude Sa ≤ 20.41 MPa. The fatigue test data were analyzed by Weibull distribution to fit the S-N curves under different reliability levels, which can be used for reliability assessment and life prediction in practical applications. The CFRP surfaces in different states were studied by scanning electron microscope (SEM). It was found that MPW would not damage the surfaces, while delamination and cracking would gradually occur during the fatigue process.

Study on magnetic pulse crimping process for joining large-diameter aluminum alloy tube/magnesium alloy shaft

A structure for joining 6061T6 aluminum alloy tube and AZ31B magnesium alloy shaft via the magnetic pulse crimping process was proposed. The forming process, mechanical properties, failure modes, and corrosion behaviors of the joint were studied. The results showed that the enormous Lorentz force drove the wall of aluminum alloy tube to move towards the groove of magnesium alloy shaft at high velocity, thus realized mechanical locking and formed joint. Through torsion tests, it was found that the mechanical properties of the joint with different process parameters varied. There were two failure modes for joint: torsional separation and torsional crack. Specifically, discharge time, groove angle, and discharge energy for torsional crack were, respectively, 1, 90°, and 28 kJ and 3, 90°, and 25 kJ. The maximum torque was up to 961.99 N·m under discharged twice, 90° groove angle, and 25-kJ discharge energy. Through neutral salt spray corrosion tests, it was found that the maximum torque only decreased by 28.03% after corrosion for 192 h. It indicated that the corrosion resistance of joint was good relatively.

O-vacancies induced in co-doped ZnO:(Cu,Fe) synthesized via hydrothermal method by pulsed magnetic field

Parent ZnO nanoparticles dually doped (Cu, Fe) were synthesized by the hydrothermal method in the presence of variant pulse magnetic field (PMF) at (0, 4T). X-Ray diffraction (XRD) was used to find crystal structure, Scanning Electron Microscope (SEM) revealed that the transformation of elongated spheres into spheres with increasing magnetic pulse (4T), Raman scattering peaks appeared at 437.70 and 436.63 cm−1 belonged to ZFCO-0T and ZFCO-4T indicated defects and inclusion of dopant elements in parent sample, XPS analysis showed that the decline in compressive strain enhances the contents of vacancies of oxygen (VO) for ZFCO-4T sample, and Bound Magnetic Polarons (BMPs) explained the RTFM order i.e.the sample ZFCO-4T has a higher number of polarons and they overlap excellently.

An analytical approach of design for recycling of laminate structures by the use of magnetic pulse disassembling

Composite materials in association with metal sheets or ceramic coatings have found a variety of applications, especially as load-bearing components in composite structures. Their disassembly for recycling or maintenance has therefore become more complex. The magnetic pulse technique, usually dedicated to dynamic forming and welding processes, can be used to separate composite materials of a laminate structure of their recyclable adjacent materials. This technology profits from Lorentz forces appearing in electrically conductive materials placed in the vicinity of conductors in which high-intensity electrical discharges are performed. These body forces act locally during the fast energy discharge, from which a stress wave propagates in the structure. The propagation of this stress wave can be used to generate interfacial tensile stress in laminate structures or assemblies. Especially, this technique can be used for evaluating the dynamic bond strength of an interface. This works aims at determining the required conditions for disassembling a laminate structure using a magnetic pulse imposed on one side of the assembly, without significantly damaging the debonded layers. Ideally, the generated interfacial tensile stress should be greater than the interfacial bond strength. In this paper, a one-dimensional analytical analysis is performed in linear elastodynamics on a tri-layered laminate structure, infinite in transverse directions, based on the method of characteristics. An optimisation problem is defined, maximising the interfacial stress between the first two layers, whose solution requires to study various configurations of the assembly involving different sets of characteristics in the laminate, associated with different areas of the domain of feasibility spanned by the unknown vector. Some assumptions and introduced simplifications of the optimisation problem allows to follow a simple two-stage solution procedure, first with respect to the thickness of the first layer for a given stress pulse, then with respect to material impedances of all layers. Several configurations of the assembly are shown to create a sufficiently large interfacial tensile stress to reach the crack initiation and propagation, and a maximum tensile interface stress of twice the maximum applied pressure is obtained in the asymptotic limit.

Simultaneous measurement of specific heat and thermal conductivity in pulsed magnetic fields

We report an experimental setup for simultaneously measuring specific heat and thermal conductivity in feedback-controlled pulsed magnetic fields of 50ms duration at cryogenic temperatures. A stabilized magnetic field pulse obtained by the feedback control, which dramatically improves the thermal stability of the setup and sample, is used in combination with the flash method to obtain absolute values of thermal properties up to 37.2T in the 22-16K temperature range. We describe the experimental setup and demonstrate the performance of the present method with measurements on single-crystal samples of the geometrically frustrated quantum spin-dimer system SrCu2(BO3)2. Our proof-of-principle results show excellent agreement with data taken using a standard steady-state method, confirming the validity and convenience of the present approach.

The Transcallosal Highway: The ipsilateral silent period as a neural biomarker for impaired corpus callosum communication in multiple sclerosis

Multiple sclerosis is a neurodegenerative disease that damages myelin sheath within the central nervous system. This axonal demyelination impacts communication between the brain's hemispheres in persons with multiple sclerosis (PwMS). Changes in transcallosal communication impairs the coordination of movements requiring precise temporal and spatial components such as lower extremity function during gait. These bilateral movements require constant communication across the corpus callosum to excite and inhibit specific muscle groups. The ipsilateral silent period (iSP) is an indirect marker of the magnitude for transcallosal inhibition. We hypothesize that the iSP may also serve as a neural biomarker for transcallosal impairments originating from the more affected hemisphere and highlight underlying mechanisms for gait asymmetries in PwMS. Our ongoing study utilizes transcranial magnetic stimulation to assess the inhibitory capacity between the brain's hemispheres (i.e., iSPs). A focal magnetic pulse is delivered to the first dorsal interosseous resulting in a suppression of muscle activity, thus reflecting inhibitory transcallosal communication. There is a lack of research analyzing directionality data between the more and less affected hemisphere in PwMS. Therefore, we evaluate outcome metrics dependent upon the individual's more affected hemisphere. Twenty-three PwMS completed the ongoing protocol and inhibitory metrics such as depth iSP% average, duration, depth iSP% max, transcallosal conduction time, and onset latency were collected. No statistically significant differences have been found between the two hemispheres in PwMS. However, beyond directionality data, our study is investigating gait coordination with overall inhibitory capacity. Walking coordination is quantified using a metric called phase coordination index (PCI). A greater PCI value reflects poorer gait coordination. We hypothesize those who demonstrate better gait coordination (lower PCI values), will have a greater iSP. These findings will determine the potential of iSPs as a neural biomarker to address gait asymmetries and stratify participants into individualized mobility rehabilitation protocols. Multiple sclerosis is a neurodegenerative disease that damages myelin sheath within the central nervous system. This axonal demyelination impacts communication between the brain's hemispheres in persons with multiple sclerosis (PwMS). Changes in transcallosal communication impairs the coordination of movements requiring precise temporal and spatial components such as lower extremity function during gait. These bilateral movements require constant communication across the corpus callosum to excite and inhibit specific muscle groups. The ipsilateral silent period (iSP) is an indirect marker of the magnitude for transcallosal inhibition. We hypothesize that the iSP may also serve as a neural biomarker for transcallosal impairments originating from the more affected hemisphere and highlight underlying mechanisms for gait asymmetries in PwMS. Our ongoing study utilizes transcranial magnetic stimulation to assess the inhibitory capacity between the brain's hemispheres (i.e., iSPs). A focal magnetic pulse is delivered to the first dorsal interosseous resulting in a suppression of muscle activity, thus reflecting inhibitory transcallosal communication. There is a lack of research analyzing directionality data between the more and less affected hemisphere in PwMS. Therefore, we evaluate outcome metrics dependent upon the individual's more affected hemisphere. Twenty-three PwMS completed the ongoing protocol and inhibitory metrics such as depth iSP% average, duration, depth iSP% max, transcallosal conduction time, and onset latency were collected. No statistically significant differences have been found between the two hemispheres in PwMS. However, beyond directionality data, our study is investigating gait coordination with overall inhibitory capacity. Walking coordination is quantified using a metric called phase coordination index (PCI). A greater PCI value reflects poorer gait coordination. We hypothesize those who demonstrate better gait coordination (lower PCI values), will have a greater iSP. These findings will determine the potential of iSPs as a neural biomarker to address gait asymmetries and stratify participants into individualized mobility rehabilitation protocols.

Diffusion within pores fully revealed by magnetic resonance.

The diffusion propagator fully characterizes the diffusion process, which is highly sensitive to the confining boundaries and the structure within enclosed pores. While magnetic resonance has extensively been used to observe various features of the diffusion process, its full characterization has been elusive. Here, we address this challenge by employing a special sequence of magnetic field gradient pulses for measuring the diffusion propagator, which allows for "listening to the drum," mapping structural dispersity, and determining not only the pore's shape but also diffusive dynamics within it.

Energy characteristics for nanosecond current interrupter of semiconductor-magnetic pulse generator’s terminal stage

Introduction. A semiconductor diode based on reverse current interruption is used to increase a pulse amplitude and peak power delivered on the process load. Usually, a current interrupter is located in the last stage of semiconductor-magnetic pulse generator (SMPG) and is connected in parallel to the load. Problem. Most of publications on this topic mostly concern with analysis of physical processes in the diode structure itself within its oscillating circuit, which is separated from previous SMPG’s pulse compression stages under condition of unidirectional energy transfer from the generator to the load. In this sense, the efficiency of conversion should be determined by the joint of electromagnetic interaction between non-linear compression stages, current interrupter and process load. Goal. Develop a mathematical model of nanosecond current interrupter to determine its electrical and energy characteristics as part of a high-voltage parallel circuit with magnetic pulse compression, depending on the duration and moment of current interruption, the equivalent circuit for load resistance, and to set the most optimal modes of its operation. Methodology. In this work, it is proposed to use a comprehensive approach aimed at the study of electromagnetic processes in the SMPG circuit with a nanosecond current interrupter, which takes into account the topology of circuit, the design parameters of switching reactor, the magnetization curve, the equivalent load resistance, as well as the time parameters of power switches. Results. Analytical expressions describing the electrical and energy characteristics of the interrupter when it operating on the active load are obtained. A numerical simulation of interrupter in the SMPG’s double-loop pumping circuit is carried out, taking into account a nonlinearity of SR’s magnetization curve. Three operation modes of interrupter is described, depending on the initial moment of reverse conduction current interruption. The analysis of interrupter operation on the load with an active-capacitive component is carried out. Practical meaning. The results of the research can be applied in the development of high-voltage SMPG scheme with improved energy-dynamic parameters.

Fatigue Strength Assessment of Laser Beam Welded Joints Made of AA7075 and Magnetic Pulse Welded Joints Made of AA7075 and 3D‐Printed AlSi10Mg

The use of 7000 aluminum alloys has an important role in future lightweight structures in the field of mobility due to the low density and high strength. However, these alloys can only be fusion welded to a limited extent because welding defects can rarely be prevented. For this reason, investigations are carried out to identify the most suitable welding parameters for two processes: laser beam and magnetic pulse welding. Herein, laser beam welding is successfully used to manufacture a roll‐formed and longitudinally welded pipe made of AA7075 and joined by magnetic pulse welding with a 3D‐printed lug‐tube made of AlSi10Mg. The fatigue strength of these pipe joints and of laser beam welded butt joint specimens is determined using load‐controlled fatigue tests. For the characterization of the specimens, cross sections are prepared and examined metallographically, which reflect the local weld seam geometry in the joining area. A fatigue assessment is made using linear‐elastic approaches. The reference radius concept is applied to map the influence of geometric notches on the fatigue strength, assuming linear‐elastic stress–strain behavior. It is shown that the recommended notch stress fatigue class FAT 178 (von Mises stress) can be applied for a safe and reliable fatigue assessment.

FEATURES OF DEFORMING OF COMPOSITE INDUCTORS DURING ELECTROMAGNETIC PROCESSING OF MATERIALS

Introduction. The development of many branches of mechanical engineering at the current stage requires the development and application of new technologies that are characterized by high energy efficiency and a small amount of waste. Such technologies include those that use electromagnetic field energy. The energy of the electromagnetic field can be used to change the shape of workpieces, to connect individual structural elements (for example, by welding), to control the physical properties of the material (for example, by induction heating), etc. Carrying out calculation studies at the stage of designing and proving the appropriate technological equipment allows determining the rational values of key parameters, which ensures the achievement of the goals of the technological operation and the operability of the equipment. Purpose. When the energy of the electromagnetic field is used to exert a force on the processed workpiece, the technological equipment is equally subject to force. The purpose of the article is to create effective methods of calculating the strength of technological equipment together with the workpiece, and conducting the corresponding calculation analysis is an urgent task in the scientific and practical sense. Results. The article proposes an effective method of analyzing the elastic-plastic deformation of composite structures under the influence of an electromagnetic field. The general mathematical formulation of the coupled problem of the deformation of conductive bodies in the presence of an electromagnetic field is considered. To construct a numerical solution method, the initial problem is reduced to finding the minimum of the total energy of the system. The finite element method is used as a numerical solution method. The proposed method is applied to the analysis of the deformation of the "inductor-workpiece" system of the technological operation of magnetic pulse processing of metals. Conclusions. Some results are presented that allow making certain recommendations regarding the design and application of technological operations of a similar class.

Studying the Thermoelastic Waves Induced by Pulsed Lasers Due to the Interaction between Electrons and Holes on Semiconductor Materials under the Hall Current Effect

In the present work, the interaction between electrons and holes in semiconductor materials is investigated. According to the excitation process, the optical-elastic-thermal-diffusion (OETD) process is considered when the medium is exposed to a strong magnetic field and laser pulses. Photo-elastic and photo-electronics deformations are taken into account when the Hall current impact appears due to the magnetic field pressure on the semiconductor medium. Due to the complexity of the model, the governing equations that describe the system in one dimension (1D) are studied. Mathematical transformations (Laplace transform) were used to simplify the equations to obtain the physical quantities under study which were affected by laser pulses. To obtain complete solutions, some conditions were obtained from the free surface as well as from a mechanical ramp type and pulse heat flux, and then numerical transformations were applied using the inverse Laplace transform. Under the influence of several variables in this question, the results were explained graphically for silicon (Si) material and the results were analyzed in terms of their physical significance.

The CHIMERA facility development programme

The CHIMERA fusion technology facility will enable testing of large in-vessel component modules under reactor-like conditions of combined in-vacuum thermal power density and magnetic field. With an integral large superconducting magnet and a PWR-like water loop, CHIMERA is also ideally placed for experiments on liquid metal breeding blanket prototypes. Facility construction is underway at the UKAEA site in South Yorkshire. The superconducting magnet is fully wound and terminated, and the bespoke pulsed magnet power supply has been delivered. Even before construction and commissioning is complete, a parallel and supporting research and development programme is in progress and is reported here. A bespoke infrared heating system has been developed, capable of applying 0.5 MW/m2 to component surfaces up to the size of the ITER test blanket module first wall. The modules of this heater are highly specialised and designed to endure the high magnetic forces from the CHIMERA static and pulsed magnets. CHIMERA will feature a range of diagnostics, including load cells to measure static and pulsed magnetic forces, and induced current sensors, all of which have been tested to confirm acceptable operation in the pulsed magnetic field. Manufacture of the test mock-up to be used for facility commissioning is underway. Testing will be enhanced with simulation ‘digital twin’ capability, and a development project is now producing first virtual test results, informing commissioning of the CHIMERA device.

Magnetization reversal of the longitudinally magnetized film with cubic anisotropy by magnetic pulses

Magnetization reversal diagrams are constructed for a longitudinally magnetized film with the parameters of yttrium iron garnet doped with cobalt. The film is excited by nanosecond magnetic field pulses with an amplitude of up to 1000 Oe. It is shown that at a magnetizing field smaller than the anisotropy field, under the action of the pulse field, transitions between stable states, characterized by energy minima, occur.

Magnetization Reversal of a Longitudinally Magnetized Film with Cubic Anisotropy by Magnetic Pulses

Magnetization Reversal of a Longitudinally Magnetized Film with Cubic Anisotropy by Magnetic Pulses

Correlated gyrotropic motion of skyrmion clusters in ultrathin ferromagnetic nanodisks

We report the correlated gyrotropic motion of two-dimensional skyrmion clusters in ferromagnetic nanodisks. Based on the massless Thiele equation, we calculate the gyrotropic eigenmodes for the multi-skyrmion system. Micromagnetic simulations are performed to verify theoretical predictions with a good agreement. By applying an in-plane magnetic field pulse on four-skyrmion system, four gyrotropic modes have been excited. One of them has all skyrmions moving in-phase; two modes have the face-to-face skyrmions pair moving out-of-phase; the rest one has a pair of face-to-face skyrmions moving in-phase with side skyrmions rotating out-of-phase. Meanwhile, we identify a reversal of phase and rotation direction originating from the complex interaction between skyrmions for five-skyrmion system. By applying an out-of-plane magnetic field pulse, we observe the correlated breathing modes for four-skyrmion system with the face-to-face skyrmions breathing in-phase or out-of-phase, and all skyrmions breathing consistently in-phase. In particular, for the five-skyrmion system, a hybridization mode has been clarified with side skyrmions breathing and central skyrmion rotation. Our results provide useful insights for controlling the dynamic behavior of multiple skyrmions that are indispensable in the future skyrmion-based spintronic devices.