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.

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.

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.

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.

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.

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.

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.

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.

Exchange couplings in magnetic films

Recent advances in the study of exchange couplings in magnetic films are introduced.To provide a comprehensive understanding of exchange coupling,we have designed different bilayers,trilayers and multilayers,such as anisotropic hard/soft-magnetic multilayer films,ferromagnetic/antiferromagnetic/ferromagnetic trilayers,[Pt/Co]/NiFe/NiO heterostructures,Co/NiO and Co/NiO/Fe trilayers on an anodic aluminum oxide（AAO） template.The exchange-coupling interaction between soft-and hard-magnetic phases,interlayer and interfacial exchange couplings and magnetic and magnetotransport properties in these magnetic films have been investigated in detail by adjusting the magnetic anisotropy of ferromagnetic layers and by changing the thickness of the spacer layer,ferromagnetic layer,and antiferromagnetic layer.Some particular physical phenomena have been observed and explained.

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.

Investigation on Magnetic Properties of Exchange Coupled Transition Metal Complexes──I. Application of the Kambe's Theory

Magnetic susceptibility of a series of dinuclear Ⅴ(Ⅳ) . Co(Ⅱ) and Mn(Ⅲ) complexes has been measured in the temperature range of 1. 5 ～300K. The isotropic Heisenberg theory has been applied to study the temperature-dependent behaviour of the magnetic susceptibility of these complexes and a corresponding program for fitting the experimental results has been set up on a VAX 11/785 computer. Conclusions can be drawn that the three complexes studied are all anti-ferromagnetically coupled with coupling constants -4. 4 , -115. 2 , and - 8. 4 cm￣(-1) for Ⅴ(Ⅳ) . Co(Ⅱ) ,and Mn(Ⅲ) complexes, respectively.

Anisotropic exchange coupling interaction between hard-hard magnetic grains in sintered SrFe_(12)O_(19)ferrites

Exchange coupling interaction in sintered magnetic materials is generally isotropic.In this study,the anisotropic exchange coupling interaction was found in sintered oblate cylindrical SrFe_(12)O_(19)(SrM)specimens obtained by the SrM nanopowders synthesized via a hydrothermal method.According to Henkel plots,the exchange coupling interaction between hard-hard magnetic grains was found in both as-pressed and sintered specimens.However,the exchange coupling interaction can only be found in the in-plane direction but not in the out-of-plane direction for thel sintered specimens.By building a model of a grain configuration,this anisotropy of the exchange coupling interaction was ascribed to the vertically arranged plate-like SrM grains with micrometers in width but nanometers in thickness,which was confirmed by morphologies of cross sections in fractured specimens.

Magnetic Properties and Molecular Field Analysis of (Ce,Nd)_2(Fe,Si,Mn)_(17) Compounds

The temperature dependent magnetization of the (Ce,Nd) 2(Fe,Si,Mn) 17 intermetallic compounds were measured and analyzed by molecular field theory (MFT). The relationship between T C and the intrasublattice coupling interactions was discussed. The two sublattice MFT model can well describe the temperature dependence of the magnetization for all the compounds investigated. Ce ion in (Ce,Nd) 2Fe 17 compounds does not simply dilute the magnetic structure, but is likely present in a mixed valence state. The substitution of Si for Fe strongly raises T C and the mean Fe moment remains unchanged for Ce 2(Si,Fe) 17 compounds, and the 3d exchange coupling constant J FF increases linearly. Mn decreases T C of Nd 2(Mn, Fe) 17 compound by reducing J FF .

Exciton dynamics in luminescent carbon nanodots： Electron-hole exchange interaction

The electron-hole exchange interaction significantly influences the optical properties of excitons and radiative decay. However, exciton dynamics in luminescent carbon dots （Cdots） is still not clear. In this study, we have developed a simple and efficient one-step strategy to synthesize luminescent Cdots using the pyrolysis of oleylamine. The sp^2 clusters of a few aromatic rings are responsible for the observed blue photoluminescence. The size of these clusters can be tuned by controlling the reaction time, and the energy gap between the π-π＊ states of the sp^2 domains decreases as the sp^2 cluster size increases. More importantly, the strong electron-hole exchange interaction results in the splitting of the exciton states of the sp^2 clusters into the singlet-bright and triplet-dark states with an energy difference ΔE, which decreases with increasing sp^2 cluster size owing to the reduction of the confinement energy and the suppression of the electron-hole exchange interaction.

Structure and Transport Behaviors of Nanograin La_(0.8)Sr_(0.2)Mn_(1-x)Al_xO_3

The influence of aluminum doping at Mn-site in nanograin compound La0.8Sr0.2MnO3 was investigated based on X-ray diffraction, scanning electron microscope and resistivity measurement, in the light of structure and transport properties. The results showed that Al doping was favorable to the globurizing of powders and grain size uniformity, however, depressed the particles growth. The resistivity of system increased rapidly and the metal-insulator transition temperature (TIM) and room temperature magnetoresistance decreased as the aluminum concentration increased. In the T>TIM region, the current carriers were moving in variable range transition mode. The resistivity of La0.8Sr0.2Mn1-xAlxO3 for x=0.05 and 0.1 satisfied metal model in the T<TIM region. The characteristics of the transport behavior for aluminum doping were analyzed in terms of destroying the double exchange channel of Mn3+-O-Mn4+, distortion of the cell lattice and change of powder particles size and shape.

Composition Dependent Magnetic Coupling in Fe-Cr Alloy Cluster Arrays

Dense arrays of Fe-Cr alloy clusters with different Cr ratios were fabricated by gas-phase cluster beam deposition. The complex multiphase structure and various coupling effects in the cluster arrays were studied. A lattice mismatched tetragonal-like morphology of the Fe-Cr alloy cluster was observed at large Cr ratio. An exchange bias effect was observed and was shown to be dependent on the proportion of the Cr components in the alloy. With the increase of the Cr composition, the exchange bias field became smaller and stronger dipolar interactions between the clusters developed. Residual coercivity and magnetization, which were more remarkable in the tetragonal-like clusters, were observed above the ferromagnetic-superparamagnetic transition temperature. The experimental results of the coercive field and the bias field at different temperatures demonstrated that the tetragonal-like clusters had better thermal stability and greater anisotropy.