Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction

The dependences of spin wave resonance(SWR)frequency on the surface anisotropy field,interface exchange coupling,symmetry,biquadratic exchange(BQE)interaction,film thickness,and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green’s function method.A remarkable increase of SWR frequency,except for energetically lower two modes,can be obtained in our model that takes the BQE interaction into account.Again,the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio.It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films.In addition,for bilayer ferromagnetic films,the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system.These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.

The exchange interaction between neighboring quantum dots:physics and applications in quantum information processing

Electron spins confined in semiconductor quantum dots(QDs)are one of potential candidates for physical implementation of scalable quantum information processing technologies.Tunnel coupling based inter exchange interaction between QDs is crucial in achieving single-qubit manipulation,two-qubit gate,quantum communication and quantum simulation.This review first provides a theoretical perspective that surveys a general framework,including the Helter−London approach,the Hund−Mulliken approach,and the Hubbard model,to describe the inter exchange interactions between semiconductor quantum dots.An electrical method to control the inter exchange interaction in a realistic device is proposed as well.Then the significant achievements of inter exchange interaction in manipulating single qubits,achieving two-qubit gates,performing quantum communication and quantum simulation are reviewed.The last part is a summary of this review.

Dynamic modeling of cavitation bubble clusters:Effects of evaporation,condensation,and bubble-bubble interaction

We present a dynamic model of cavitation bubbles in a cluster,in which the effects of evaporation,condensation,and bubble-bubble interactions are taken into consideration.Under different ultrasound conditions,we examine how the dynamics of cavitation bubbles are affected by several factors,such as the locations of the bubbles,the ambient radius,and the number of bubbles.Herein the variations of bubble radius,energy,temperature,pressure,and the quantity of vapor molecules are analyzed.Our findings reveal that bubble-bubble interactions can restrict the expansion of bubbles,reduce the exchange of energy among vapor molecules,and diminish the maximum internal temperature and pressure when bursting.The ambient radius of bubbles can influence the intensities of their oscillations,with clusters comprised of smaller bubbles creating optimal conditions for generating high-temperature and high-pressure regions.Moreover,an increase in the number of bubbles can further inhibit cavitation activities.The frequency,pressure and waveform of the driving wave can also exert a significant influence on cavitation activities,with rectangular waves enhancing and triangular waves weakening the cavitation of bubbles in the cluster.These results provide a theoretical basis for understanding the dynamics of cavitation bubbles in a bubble cluster,and the factors that affect their behaviors.

Stacking-dependent exchange bias in two-dimensional ferromagnetic/antiferromagnetic bilayers

A clear microscopic understanding of exchange bias is crucial for its application in magnetic recording, and further progress in this area is desired. Based on the results of our first-principles calculations and Monte Carlo simulations,we present a theoretical proposal for a stacking-dependent exchange bias in two-dimensional compensated van der Waals ferromagnetic/antiferromagnetic bilayer heterostructures. The exchange bias effect emerges in stacking registries that accommodate inhomogeneous interlayer magnetic interactions between the ferromagnetic layer and different spin sublattices of the antiferromagnetic layer. Moreover, the on/off switching and polarity reversal of the exchange bias can be achieved by interlayer sliding, and the strength can be modulated using an external electric field. Our findings push the limits of exchange bias systems to extreme bilayer thickness in two-dimensional van der Waals heterostructures, potentially stimulating new experimental investigations and applications.

Effect of annealing time on the exchange coupling interactions and microstruc-ture of nanocomposite Pr_(7.5)Dy_1Fe_(71)Co_(15)Nb_1B_(4.5) ribbons

The influence of annealing time on the magnetic properties and microstructure of nanocomposite Pr7.5Dy1Fe71Co15Nb1B4.5 ribbons was systematically investigated by the methods of vibrating sample magnetometer （VSM）, X-ray diffraction （XRD） and high resolution transmission electron microscopy （HRTEM）. Interaction domains derived from strong exchange coupling interactions between hard and soft magnetic grains were imaged using magnetic force microscopy （MFM）. Maximum remanence, intrinsic coercivity, and maximum energy product values were obtained in the ribbons annealed at 700℃ for 15 min, which were composed of Pr2（Fe, Co）14B, α-（Fe, Co）, and slight Pr2（Fe, CO）17 phases. Although Jr, Hci, and （Bn）max decreased gradually with further increase of annealing time, it is emphasized that comparatively high Jr and Hci and （BH）max were obtained in a wide annealing time period of 15 to 360 min. The shape of initial magnetization curves and hysteresis loops change as a function of annealing time, indicating different magnetization reversal routes, which can be fully explained by the corresponding microstructure.

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.

Solitary excitations in one-dimensional ferromagnetic spin chains with biquadratic exchange interaction

By using the traveling wave method, the solutions of the elliptic function wave and the solitary wave are obtained in a ferromagnetic spin chain with a biquadratic exchange interaction, a single ion anisotropic interaction and an anisotropic nearest neighbour interaction. The effects of the biquadratic exchange interaction and the single ion anisotropic interaction on the properties （width, peak and stability） of the soliton are investigated. It is also found that the effects vary with the strengths of these interactions.

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.

The curve of ion exchange ratio(%)-pH of the interaction between suspended particles with Cd(Ⅱ) in the Yellow River

The curve of ion exchange ratio(%) pH of the interaction between suspended particles with Cd(II) in the Yellow River was studied. The effects of lysine on this curve have been also investigated. The results showed that (1) Cadmium in Cd(OH) + form in the suspended particles exchanges with the cations. The exchange ratio of Cd 2+ is nearly at its greatest value in the range of pH (8.0—8.5) in natural aquatic system; (2) Ion exchange ratio decreases as the concentration of Cd 2+ raises from 8.9×10 -6 mol/L to 2×8.9×10 -6 mol/L; (3) At the lysine concentration of 6 8×10 -6 mol/L, it can promote the ion exchange ratio; (4) Adsorption of the suspended particles to cadmium is weaker in seawater and Jin Sha River than in the Yellow River.

Analyses of crystal field and exchange interaction of Dy_3Ga_5O_(12) under extreme conditions

This paper theoretically investigates the effects of crystal field and exchange interaction field on magnetic properties in dysprosium gallium garnet under extreme conditions （low temperatures and high magnetic fields） based on quantum theory. Here, five sets of crystal field parameters are discussed and compared. It demonstrates that, only considering the crystal field effect, the experiments can not be successfully explained. Thus, referring to the molecular field theory, an effective exchange field associated with the Dy-Dy exchange interaction is further taken into account. Under special consideration of crystal field and the exchange interaction field, it obtains an excellent agreement between the theoretical results and experiments, and further confirms that the exchange interaction field between rare-earth ions has great importance to magnetic properties in paramagnetic rare-earth gallium garnets.

Exchange Interactions and Ferromagnetism of Pr_(n+1)Co_(3n+5)B_(2n)-type Compounds

In present investigation exchange interactions of Pr_(n+1)Co_(3n+5)B_(2n)-type compounds have been evalu- ated in the light of molecular-field theory. The exchange interactions and ferromagnetism in these compounds are discussed in terms of lattice parameters and interatomic distance between Co atom.

Exchange interaction between vortex and antivortex

The dynamic properties of interacting vortex-antivortex pairs in thin film are studied by analytical calculations. An- alytical expressions for the magnetization vector distribution of vortex-antivortex pairs and the trivortex states are given. The magnetic states of the vortices are treated as having rigid structures, i.e., the vortex maintains its spin distribution when moving. The trajectories of the vortex cores are calculated by the Thiele＇s equation. It is found that the vortex-antivortex pair rotates around each other when they have opposite polarities, however, vortex and antivortex cores move along straight lines when they have the same polarity. The frequency of the rotation decreases with increasing the distance between the two cores of vortex-antivortex pair, and it has a lower value when a third vortex is introduced.

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.

Magnetic Ordering and Exchange Interaction of Laves Compounds Sm0.9Pr0.1(Fe1-xCox)2

Structure, magnetic properties and magnetostriction of Sm0.9Pr0.1(Fe1-xCox)2 compounds have been investigated by means of X-ray diffraction, a.c. initial susceptibility, extracting sample magnetometer, Mossbauer spec-troscopy and standard strain gauge techniques. The lattice parameter a of the MgCu2-type Laves compounds Sm0.9Pr0.1(Fe1-xCox)2 decreases nonlinearly with increasing Co concentration, deviating from the Vegard's law. Curie temperature Tc increases initially from 668 K for x=0 to 694 K for x=0.2 and then decreases to 200 K for x=1.0. The saturation magnetization Ms at temperatures 1.5 K, 77 K and 300 K have the same variation tendency as the composition dependence of Curie temperature, in consistence with rigid-band model. The easy magnetization direction (EMD) of Sm0.9Pr0.1(Fe1-xCox)2 lies along [111] direction in the range x<0.6, and changes to [110] for x=0.8, while Sm0.9Pr0.1Co2 stays in the paramagnetic state at room temperature. The composition dependence of the average hyperfine field,Hhf , demonstrates a similar variation tendency as that of the saturation magnetization Ms and Curie temperature Tc. The spontaneous magnetostricton Am increases with increasing Co content. The saturation magnetostriction λs decreases monotonically with increasing x, which is caused by the increase of magnetostriction constant λ100 with opposite sign to that of Am. A two-sublattice model has been proposed to understand the intermediate region between the [111] and [110] spin configurations, which can also be used to explain the temperature dependence of magnetization.

Generation of Quantum Vector States Using the Exchange Interaction

In this paper, I study the invariant subspaces of quantum states under SWAPα gates arising from the exchange interaction and their use in quantum computation. I investigate the generation and characterization of invariant-subspace vector-states that arise from such gates. I also state a condition for the locus of states that are accessible using the SWAPα gates, given an initial input state.

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.

Effect of Thickness on Magnetic Dipolar and Exchange Interactions in SmCo/FeCo/SmCo Thin Films

SmCo/FeCo/SmCo trilayer was deposited with two different thickness configurations for soft phase (FeCo);50 nm/10 nm/50 nm and 50 nm/25 nm/50 nm were deposited on Si (111) substrate and Ta (50 nm) seed layer by RF magnetron sputtering in a pressure, p, of 30 - 35 m Torr. After deposition the films were annealed under Ar atmosphere at temperature T equal to 923 and 973 for different times followed by quenching in water. X-ray diffraction patterns were obtained to identified phase presents and calculate average crystallite size. To study the effect of configuration thickness in soft phases, DC magnetic measurements were carried out;the measurements were done in the temperature interval of 300 - 50 K. Hysteresis loops collected at low temperatures exposed an increment in coercivity with the decrease of T and at same time, presented a “knee” in the second quadrant of the demagnetization curve, which suggests that the inter-layer exchange coupling becomes less effective, being more evident for sample with 50 nm/25 nm/50 nm thickness. Moreover, δM (H) plots were calculated from magnetic measurements at three different temperatures, T, equal to 300, 150 and 50 K, which corroborates that the dipolar interactions became stronger when thickness of soft phases increases. Finally, the thickness effect is attributed to the SmCo5 phase magnetocrystalline anisotropy constant, which is responsible for the exchange coupling length.

The role of charge-exchange processes in probing hydrogen plasma with a heavy ion beam

Charge-changing processes of low-charged ions,used in hydrogen plasma probing by the heavy ion beam probe method,are considered.Along with the ionization of beam ions by plasma electrons and protons,the charge-exchange processes of ions on H atoms and protons are also studied.It is shown that charge exchange of beam ions on plasma protons and H atoms,which is rarely taken into account,plays an important role in beam–plasma interaction.New data on the cross sections and rates of ionization and charge-exchange processes are presented for Tl+and Tl2+ions,which are frequently used for plasma diagnostics.Calculations are performed for hydrogen plasma temperatures Te=1 eV–10 keV and densities Ne=1012–1014 cm−3 at relatively low and high ion-beam velocities vb=0.2 and 1.0 a.u.,respectively.Special attention is paid to the determination of the electron temperatures at which the charge-exchange processes on H atoms and protons are important.Multiple ionization of beam ions by plasma electrons and protons is briefly discussed.