Dynamic Dipole-Dipole Magnetic Interaction and Damped Nonlinear Oscillations

Static dipole-dipole magnetic interaction is a classic topic discussed in electricity and magnetism text books. Its dynamic version, however, has not been reported in scientific literature. In this article, the author presents a comprehensive analysis of the latter. We consider two identical permanent cylindrical magnets. In a practical setting, we place one of the magnets at the bottom of a vertical glass tube and then drop the second magnet in the tube. For a pair of suitable permanent magnets characterized with their mass and magnetic moment we seek oscillations of the mobile magnet resulting from the unbalanced forces of the anti-parallel magnetic dipole orientation of the pair. To quantify the observed oscillations we form an equation describing the motion of the bouncing magnet. The strength of the magnet-magnet interaction is in proportion to the inverse fourth order separation distance of the magnets. Consequently, the corresponding equation of motion is a highly nonlinear differential equation. We deploy Mathematica and solve the equation numerically resulting in a family of kinematic information. We show our theoretical model with great success matches the measured data.

Magnetic Interactions with Strain Gradient in Ultrathin Pr_(0.67)Sr_(0.33)MnO_(3) Films

Strain gradient is a normal phenomenon around a heterostructural interface in ultrathin film,and it is important to determine its effect on magnetic interactions to understand interfacial coupling.In this work,ultrathin Pr_(0.67)Sr_(0.33)MnO_(3)(PSMO)films on different substrates are studied.For PSMO film under different in-plane strain conditions,the saturated magnetization and Curie temperature can be qualitatively explained by double-exchange interaction and the Jahn-Teller distortion.However,the difference in the saturated magnetization with zero field cooling and 5 T field cooling is proportional to the strain gradient.Strain-gradient-induced structural disorder is proposed to enhance phonon-electron antiferromagnetic interactions and the corresponding antiferromagnetic-to-ferromagnetic phase transition via a strong magnetic field during the field cooling process.A non-monotonous structural transition of the MnO_(6) octahedral rotation can enlarge the strain gradient in PSMO film on a SrTiO_(3) substrate.This work demonstrates the existence of the flexomagnetic effect in ultrathin manganite film,which should be applicable to other complex oxide systems.

Model of self-generated magnetic field generation from relativistic laser interaction with solid targets

Generation of self-generated annular magnetic fields at the rear side of a solid target driven by relativistic laser pulse is investigated by using theoretical analysis and particle-in-cell simulations.The spatial strength distribution of magnetic fields can be accurately predicted by calculating the net flow caused by the superposition of source flow and return flow of hot electrons.The theoretical model established shows good agreement with the simulation results,indicating that the magnetic-field strength scales positively to the temperature of hot electrons.This provides us a way to improve the magnetic-field generation by using a micro-structured plasma grating in front of the solid target.Compared with that for a common flat target,hot electrons can be effectively heated with the well-designed grating size,leading to a stronger magnetic field.The spatial distribution of magnetic fields can be modulated by optimizing the grating period and height as well as the incident angle of the laser pulse.

Numerical Experiment for Dipole-Dipole Interaction in Electro-Magnetism with Help of a Regular Tetrahedron

Aim of this work is to try to explain, on a Rational basis, some equations of Electro-Magnetism, which are based on Experimental data. Any Electric Field can produce a Field of many small Electric Dipoles, continuously distributed in space. In a region, where the Electric Field is constant, in direction and magnitude, all the small Dipoles are parallel to the Electric Field, and are represented by a single, long, parallel to them, fixed in space, Electric Dipole, which is here called Compass. An Alternating current, in a straight Conductor, is studied, by a simple, short computer program, for step-by-step nonlinear dynamic analysis. It is found that, only an Alternating current, not a direct current, can produce an Electric Dipole, in a straight Conductor. The two above Dipoles (Compass-Conductor) are assumed with equal lengths ℓ, lying on two skew lines, perpendicular to each other, at a distance ℓ√2, thus forming, by their four ends, a Regular Tetrahedron, with side length ℓ. Repulsion, between Like Charges, obeys the simple Coulomb Electro-Static law. Whereas Interaction (Attraction or Repulsion), between Unlike Charges, obeys a more accurate Lennard-Jones law. The analysis of Dipole-Dipole (Compass-Conductor) Interaction is performed by hand calculator. The only out-of-balance forces, in the regular Tetrahedron, acting on the Rigid Conductor, are the so-called magnetic forces. Their direction is found, in a simple Rational way, with help of Regular Tetrahedron, without recoursing to a “right-hand-rule”. The proposed model is applied to 1) The force acting on an Electric Charge moving in a magnetic field. 2) The force acting on a Current carrying straight Conductor, due to a magnetic field. 3) The magnetic fields created around a Current carrying straight Conductor. In these applications, proposed model gives reasonable results. Particularly, in third application, results, obtained by proposed model, are found in satisfactory approximation with corresponding ones, obtained by an empirical formula, based on relevant Experimental observations of H.-C. Oersted and A.-M. Ampère. So, the reliability of proposed model is checked. Position and direction of magnetic field vector coincide with those of a corresponding fixed Compass of a constant Electric Field. Main point of present work is that, without introducing the concept of a magnetic field vector, by combining field of dipoles, produced by an electric field, with dipole of an alternating current carrying conductor, the magnetic forces can be determined.

Dzyaloshinskii–Moriya interaction and field-free sub-10 nm topological magnetism in Fe/bismuth oxychalcogenides heterostructures

Topological magnetism with strong robustness,nanoscale dimensions and ultralow driving current density(106 A/m^(2))is promising for applications in information sensing,storage,and processing,and thus sparking widespread research interest.Exploring candidate material systems with nanoscale size and easily tunable properties is a key for realizing practical topological magnetism-based spintronic devices.Here,we propose a class of ultrathin heterostructures,Fe/Bi_(2)O_(2)X(X=S,Se,Te)by deposing metal Fe on quasi-two-dimensional(2D)bismuth oxychalcogenides Bi_(2)O_(2)X(X=S,Se,Te)with excellent ferroelectric/ferroelastic properties.Large Dzyaloshinskii–Moriya interaction(DMI)and topological magnetism can be realized.Our atomistic spin dynamics simulations demonstrate that field-free vortex–antivortex loops and sub-10 nm skyrmions exist in Fe/Bi_(2)O_(2)S and Fe/Bi_(2)O_(2)Se interfaces,respectively.These results provide a possible strategy to tailor topological magnetism in ultrathin magnets/2D materials interfaces,which is extremely vital for spintronics applications.

Interactions of Sn and S and their effects on the magnetic properties of non-oriented silicon steel sheets

The interactions of Sn and S and their effects on the magnetic properties of non-oriented silicon steel sheets were discussed in reference to industrial production. Results show that minor amounts of Sn can improve magnetic induction sharply but have little effect on core loss when the S content is below 10 × 10 ^-4%. The precipitation of AlN can be restrained effectively by Sn. Sn, as the nucleus, can remove some of the inclusions with a size of 0.5μm or larger, but has little effect on inclusions smaller than 0.5 μm,which is the key factor affecting core loss. Sn improves the magnetic induction of finished steel sheets mainly through the change of the steel texture. The relationship between the magnetic induction and Sn and S content can be regressed as B50 = 1.69 -4.37 ws ＋0.30 Ws,. From the regression formulation,the magnetic induction can be improved by 0.03 T when 0.01% Sn is added under relatively low S content conditions.

Magnetic Array Assisted Triboelectric Nanogenerator Sensor for Real‑Time Gesture Interaction

In human-machine interaction,robotic hands are useful in many scenarios.To operate robotic hands via gestures instead of handles will greatly improve the convenience and intuition of human-machine interaction.Here,we present a magnetic array assisted sliding triboelectric sensor for achieving a real-time gesture interaction between a human hand and robotic hand.With a finger’s traction movement of flexion or extension,the sensor can induce positive/negative pulse signals.Through counting the pulses in unit time,the degree,speed,and direction of finger motion can be judged in realtime.The magnetic array plays an important role in generating the quantifiable pulses.The designed two parts of magnetic array can transform sliding motion into contact-separation and constrain the sliding pathway,respectively,thus improve the durability,low speed signal amplitude,and stability of the system.This direct quantization approach and optimization of wearable gesture sensor provide a new strategy for achieving a natural,intuitive,and real-time human-robotic interaction.

The influences of dipole-dipole interaction and detuning on the sudden death of entanglement between two atoms in the Tavis-Cummings model

The influences of dipole-dipole interaction and detuning on the entanglement between two atoms with different initial tripartite entangled W-like states in the Tavis Cummings model have been investigated by means of Wootters＇ concurrence, respectively. The results show that the entanglement between the two atoms can be enhanced via appropriately tuning the strength of dipole-dipole interaction of two atoms or the detunings between atom and cavity, and the so-called sudden death effect can he weakened simultaneously.

Pairwise thermal entanglement in a three-qubit Heisenberg XX model with a nonuniform magnetic field and Dzyaloshinski-Moriya interaction

Pairwise thermal entanglement in a three-qubit Heisenberg XX model is investigated when a nonuniform mag- netic field and the Dzyaloshinski-Moriya interaction are included. We find that the nonuniform magnetic field and Dzyaloshinski-Moriya interaction are the more efficient control parameters for the increase of entanglement and critical temperature. For both the nearest neighbour sites and the next nearest neighbour sites, the magnetic field can induce entanglement to a certain extent and the Dzyaloshinski-Moriya interaction can enhance the entanglement to a stable value. The steady value of the nearest neighbour site entanglement C12 is larger than the next nearest neighbour site entanglement C13. An interesting phenomenon is that the entanglement curve of C12 appears a peak value when the Dzyaloshinski-Moriya interaction is considered in a nonuniform magnetic field.

Position-dependent property of resonant dipole-dipole interaction mediated by localized surface plasmon of an Ag nanosphere

We use the photon Green-function method to study the quantum resonant dipole-dipole interaction（RDDI） induced by an Ag nanosphere（ANP）.As the distance between the two dipoles increases,the RDDI becomes weaker,which is accompanied by the influence of the higher-order mode of the ANP on RDDI declining more quickly than that of the dipole mode.Across a broad frequency range（above 0.05 eV）,the transfer rate of the RDDI is nearly constant since the two dipoles are fixed at the proper position.In addition,this phenomenon still exists for slightly different radius of the ANPs.We find that the frequency corresponding to the maximum transfer rate of RDDI exhibits a monotonic decrease by moving away one dipole as the other dipole and the ANP are kept fixed.In addition,the radius of ANP has little effect on this.When the two dipoles are far from the ANP,the maximum transfer rate of the RDDI takes place at the frequency of the dipole mode.In contrast,when the two dipoles are close to the ANP,the higher-order modes come into effect and they will play a leading role in the RDDI if they match the transition frequency of the dipole.Our results may be used in a biological detector and have a certain guiding significance for further application.

Effects of exchange interaction and spin-fluctuation on the magnetic and magneto-optic properties of NdF_3

The exchange interaction between the electrons in the different magnetic ions and the spin-fluctuation of the magnetic ions exist in the paramagnetic media NdF3. The exchange interaction between the electrons in the different magnetic ions may be equivalent to an effective field Hin that is in direct proportion to the magnetization M. The spin-fluctuation of the magnetic ions leads the coefficient of the effective field to vary with temperature. The effective field is given as Hin = -（0.75 ＋ 0.22T） × 10^-5M in NdF3. When the secondary crystal field effect is taken into account, the magnetic susceptibility and Verdet constant are calculated for NdF3 by means of the effective field Hin and the applied field He. The calculated results are in agreement with the measured ones.

Interaction of magnetic spheres in magnetic fields from the view of magnetic energy density:A 3D finite element analysis(FEA)

Magnetic interaction between magnetic particles is of great significance in the fields of magnetic separation and functional materials.A good understanding of interaction mechanism of magnetic particles would further boost its promising industrial applications.We hereby present our work which visualizes the movement behavior of magnetic spheres in magnetic fields employing high-speed imaging and simulates the dynamic behavior of spheres using an Arbitrary Lagrangian-Eulerian(ALE)based on finite element method.In this paper,we investigated the stress tensor,magnetic force,and dynamic behavior of magnetic spheres in magnetic fields,especially magnetic energy density in different domains.Results show that there are four relatively independent regions of magnetic energy density distribution in external spatial domains of a single sphere system.Attractive force will generate when the energy density in the spatial region between two spheres is relatively high,while a repulsive force will generate when the energy density in the spatial region between two spheres is relatively low.Every magnetic sphere spontaneously moves towards the region with high energy density and stays away from the region with low energy density.The total magnetic energy in magnetic spheres’domains(V_(1))and external spatial domains(V_(2))increases,but the magnetic energy in the external spatial domain decreases over time during the aggregation process.The magnetic spheres ultimately arrange in chain-like structures oriented along magnetic field direction.We hereby proposed a novel and efficient approach to predict the movement trends and final state of magnetic particle swarm from the view of energy density.

Effects of dipole-dipole interaction on entanglement transfer

A system consisting of two different atoms interacting with a two-mode vacuum, where each atom is resonant only with one cavity mode, is considered. The effects of dipole-dipole （dd） interaction between two atoms on the atom-atom entanglement and mode--mode entanglement are investigated. For a weak dd interaction, when the atoms are initially separable, the entanglement between them can be induced by the dd interaction, and the entanglement transfer between the atoms and the modes occurs efficiently; when the atoms are initially entangled, the entanglement transfer is almost not influenced by the dd interaction. However, for a strong dd interaction, it is difficult to transfer the entanglement from the atoms to the modes, but the atom-atom entanglement can be maintained when the atoms are initially entangled.

Effects of dipolar interactions on the magnetic hyperthermia of Zn_(0.3)Fe_(2.7)O_(4) nanoparticles with different sizes

Tumor-targeted magnetic hyperthermia has recently attracted much attention.Magnetic nanoparticles(NPs) are heat mediator nanoprobes in magnetic hyperthermia for cancer treatment.In this paper,single cubic spinel structural Zn_(0.3)Fe_(2.7)O_(4) magnetic NPs with sizes of 14 nm-20 nm were synthesized,followed by coating with SiO_(2) shell.The SLP value of Zn_(0.3)Fe_(2.7)O_(4)/SiO_(2) NPs below 20 nm changes non-monotonically with the concentration of solution under the alternating current(AC) magnetic field of 430 kHz and 27 kA/m.SLP values of all Zn_(0.3)Fe_(2.7)O_(4)/SiO_(2) NPs appear a peak value with change of solution concentration.The solution concentrations with optimal SLP value decrease with increasing magnetic core size.This work can give guidance to the better prediction and control of the magnetic hyperthermia performance of materials in clinical applications.

MSSBAUER EFFECT STUDY OF MAGNETIC INTERACTIONS IN Eu(Fe_(0.8)M_(0.2))O_3 (M=Sc, Cr, Mn, Co)

The solid state solutions of europium transition element oxides Eu (Fe0.8M0.2)O3 (M=Sc, Cr, Mn, Co) are synthesized. The X-ray diffraction of the compound shows that all the compounds possess the perovskite structures. Both the 151Eu Mossbauer spectra and the Fe Mossbauer spectra are measured. The hyperfine magnetic field and non-axisymmetric electric field gradient are observed in the Eu Mossbauer spectrum. The 57Fe Mossbauer spectrum shows that there are four components of hyperfine fields corresponding to four kinds of different neighbours of the Fe ion.

Exchange interactions and magnetic properties of intermetallic compounds

The temperature dependence of lattice parameters a and c of intermetallic compounds RMn 2Ge 2(R=La, Sm and Gd)were measured in the temperature range of 10800 K by using the X-ray diffractometer . It is found that the high temperature magnetic transitions of Mn-subsystem in light rare earth compounds from paramagnetic to antiferromagnetic state accompany the negative magnetoelastic anomalies of lattice parameters c, where a does not change. This indicates that the antiferromagnetic component of intralayer Mn-Mn exchange coupling is correlated with lattice constant c. The low temperature first order ferromagnetism→antiferromagnetism transitions(or antiferromagnetism→ferromagnetism transition) of Mn-subsystem in SmMn 2Ge 2 and GdMn 2Ge 2 accompany the abruptly decrease(or increase) of lattice parameter a, and Δa/a≈0.15%. This demonstrates that the interlayer Mn-Mn exchange interaction is very sensitive to the intralayer Mn-Mn distance. The critical value of lattice constant a k, at which the interlayer Mn-Mn coupling changes its sign, is 4.044 5×10 -10 m. Based on the molecular field model of exchange interaction the magnetic curves of GdMn 2Ge 2 single crystal at different temperatures were calculated and a good agreement with experimental data had gotten. The Gd-Gd, Gd-Mn, intralayer Mn-Mn and interlayer Mn-Mn exchange coupling parameters were estimated.

Computer Simulation of Effect of Intergrain Exchange Interaction on Magnetic Properties of Nanocomposite Magnets

Effects of the intergrain exchange interaction on magnetic properties of nanocomposite magnets were investigated by using the computer simulation based on the micromagnetic theory. The simulation was carried out under the assumptions that the strength of the intergrain exchange interaction is weaker than that of the intragrain exchange interaction, that inhomogeneous nanostructures result in the distribution of the strength of the intergrain exchange interaction, and that there exists nonmagnetic intergranular phase (NMIP) between grain boundaries. The distribution of the strength of the intergrain exchange interaction was simulated by the lognormal distribution with the standard deviation of σ.The calculations for Nd 2Fe 14B/α-Fe nanocomposite magnets reveal that a suitably weak intergrain exchange interaction and small grain size enable us to improve magnetic properties. It is also found that a Nd 2Fe 14B/α-Fe nanocomposite magnet has a potential of a (BH) max value exceeding 300 kJ·m -3. On the other hand, the calculations for Nd 2Fe 14B/Fe 3B nanocomposite magnets reveal that the distribution of the strength of the intergrain exchange interaction deteriorates magnetic properties significantly. Particularly, this tendency is remarkable, when the grain size L is larger than its optimum value, 11 nm. The existence of nonmagnetic boundary layers accelerats this tendency. At σ=0.2, the calculated demagnetization curve for the model magnet composed of Nd 2Fe 14B(36%)/Fe 3B(54%)/NMIP(10%) (Valume fraction) grains (L=15 nm) agrees with that obtained experimentally for a Nd 2Fe 14B/Fe 3B nanocomposite magnet. These results suggest importance of refinement of grain size, suppression of a nonmagnetic intergranular phase, and preparation of homogeneous nanostructure for superior magnetic properties.

Characterizing the Exchange Interaction of Sm-Co/Co(and Fe_(65)Co_(35))Magnetic Films

Exchange interaction plays an important role on magnetic properties of nanocomposite magnets consisting of hard- and soft-magnetic phases. Here the exchange interaction in the Sm-Co/Co （and Fe65Co35） magnetic films was characterized by measuring static （mr（H）） and demagnetized （md（H）） remanence curves. According to conventional method： δm（H）=md（H） - [1 - 2mr（H）], the exchange interaction was evaluated. The switching fields H′p and Hp, at which static （mr（H）） and demagnetized （md（H）） remanence show the fastest change, were identified. The relative ratio η=Hp-H′p/Hp of switching fields H′p and Hp has a linear relationship with the maximum value δmmax of δm（H） curves, proposing an alternative way to characterize the exchange interaction.

Grain Size Dependence of Exchange-Coupling Interaction between Magnetically Soft-Hard Grains and Effective Anisotropy

Taking α-Fe and Nd_2Fe_(14)B grains as example, the grain size dependence of the exchange-coupling interaction and effective anisotropy and also their variations depending on the ratio of magnetically soft and hard grain sizes, D_s∶D_h, were investigated. When grain size D>L_(ex), the grain’s anisotropy is the statistic value of the coupled and uncoupled part. The anisotropy constant of uncoupled part is the common value K_1 and that of coupled part varies with the distance to the grain surface. The effective anisotropy constant between magnetically soft and hard grains, K_(eff), can be expressed as the sum of the products of volume fractions for soft and hard grains, respectively, and the corresponding mean anisotropy constants. The calculation results indicate that the exchange-coupling interaction is enhanced with the reduction of grain size, and the effective anisotropy decreases with reducing grain size and increasing ratio of D_s∶D_h. In order to get high effective anisotropy constant, K_(eff), in composite magnetically soft-hard grains, the hard grain size should be larger than 30 nm and the soft grain size should be about 10 nm.

Relation between stabilization energy, crystal field coefficient and the magnetic exchange interaction for Tb^(3+) ion

Based on a single ion model, Hamiltonian of the simplest form about magnetocrystalline anisotropy for Tb3+ ion was solved by using the numerical method. The relation between the stabilization energy, crystal field coefficient B20 and the magnetic exchange interaction was studied as temperature approaches to 0 K. The results show that the stabilization energy contributed by Tb3+ is linear with crystal field coefficient B20 approximately, but it is insensitive to the change of magnetic exchange interaction for the strong magnetic substances such as TbCo5, Tb2Co17 and Tb2Fe14B compounds.