Effects of size and surface anisotropy on thermal magnetization and hysteresis in the magnetic clusters

Based on Monte Carlo simulation, the spin configurations, thermal magnetization and hysteresis loops of the clusters coated by the surface shell with radial anisotropy are studied. Interestingly, a new multidomain containing a few of subdomains whose easy directions are along those of the configurational anisotropy, a magnetization curve in steps and a first order phase transition from the single domain to the multidomain in the thermal and field magnetization processes, are found, which is as a result of the interplay of the configurational anisotropy, the size effect, the surface anisotropy, the applied field and the thermal fluctuation. In this first order transition, we find a critical temperature, a critical surface anisotropy and a critical size. The simulated temperature dependence of the coercivity of the cluster with the surface anisotropy can be fitted by H_c (T)=H_c (0)(1-C_αT^α) with low value of α, which explains well the experimental results of the nanoparticles. Moreover, it is found that the hysteresis loops and coercivity are strongly affected by the cluster size and the thickness of the surface layer.     

Molecular Dynamics Simulation of Icosahedral Transformations in Solid Cu-Co Clusters

We study the icosahedral transformations of solid Cu Co clusters with different initial configurations by using molecular dynamics with the embedded atom method. It is found that the formation of symmetric icosahedral cluster is strongly related to the atomic number and initial configuration. The transformation originates from the surface into the interior of the cluster and is a structural change which is rapid and diffusionless. The icosahedral clusters with any composition and configuration, such as core-shell or three-shell duster, can be prepared by the means of solid-solid phase transition in bimetallic clusters.     

稳态Cu-Zr二十面体团簇电子结构的密度泛函研究

采用第一原理对以Cu为心的低能稳态Cu_nZ_(r13-n)(n=6,7,8,9)二十面体团簇的电子结构进行计算,结果表明:同一化学组分下,以Cu为心的Cu-Zr二十面体团簇中出现的同类原子聚集现象可以增强团簇的稳定性,降低费米能级(EF)上的电子数N(EF),这为低能稳态团簇拥有较小的N(EF)提供了深层次的理论解释.进一步的差分电子密度与Mulliken布居分析得知,Cu-Zr二十面体中共价键与离子键共存,成键态与反键态共存,且团簇在形成时壳层Zr与中心Cu原子是电子的提供者,壳层Cu是电子的获得者.该电荷转移方向是金属玻璃中以Cu为心的Cu-Zr二十面体团簇普遍遵循的规律,不随团簇的化学序参数及化学组分的变化而变化.计算的红外振动谱为实验上准确表征不同二十面体原子团提供了一种新的思路.     

Magnetization and configurational anisotropy in magnetic clusters: Monte Carlo simulation

Based on the Monte Carlo simulation, the magnetic properties of the clusters, e.g. magnetization, Curie temperature, hysteresis, coercivity, natural angle and energy distribution etc., have been calculated. It has been found that, for the pure ferromagnetic cluster, the T^3/2 Bloch law is well satisfied at low temperature (T < 0.5 T_C) and B_sur is equal to 3 B_bulk. Meanwhile, there are clear indications that B increases drastically with the reducing atomic number Nwhich is consistent with the experimental facts. The results have been evalucted using the Bloch exponent law in the approximate crystalline approximation. It has also been demonstrated that the size dependence of the Curie temperature can be described by finite-size scaling theory. The investigation of the hysteresis and the spin configurations in different magnetization processes reveals the existence of an easy magnetization direction and anisotropy. The thermal coercivity for the clusters with zero and finite uniaxial anisotropy matches the experimental results well. The simulated results for the natural angle and energy distribution in the clusters prove further the existence of the configurational anisotropy in the clusters. It has been discussed that the natural angle and energy distribution influence the hysteresis of a cluster.Received: 10 September 2003, Published online: 15 March 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.40.Mg Numerical simulation studies - 75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)     

Magnetism of Fe clusters formed by buffer-layer assisted growth on Pt(997)

The growth and magnetism of nanometer size Fe clusters on stepped Pt surfaces is investigated by scanning tunneling microscopy (STM) and magneto-optical Kerr effect measurements (MOKE). The clusters are formed on xenon buffer layers of varying thickness and then brought into contact with the substrate by thermal desorption of the Xe. The cluster size is controlled by the thickness of the Xe layer. It is found that clusters of diameter smaller than the Pt terrace width of 2 nm are aligned along the step edges of the Pt(997), thus forming linear cluster chains. In this arrangement, the clusters are ferromagnetic with an easy axis in the direction along the surface normal. If the cluster diameter is larger than the terrace width then the alignment along the step edges is not observed and rather large agglomerates are found which are randomly distributed over the surface. Despite their increased volume, such agglomerates are superparamagnetic with in-plane easy magnetization axis. The enhanced magnetic anisotropy energy in the smallest clusters is originating from hybridization effects at the Fe-Pt interface.     

Superparamagnetism in small Fe clusters on Cu(111)

Fe clusters of 105±2 atoms/cluster were mass selectively deposited onto Cu(111) at cryogenic temperatures. XMCD was used to measure temperature and direction dependent magnetization curves. The clusters are superparamagnetic at the lowest temperature measured (10 K). Their magnetization curves are consistent with magnetic moments of ≈2.5μ_B per atom which are thus enhanced over the bulk values. Within experimental accuracy, the clusters do not present magnetocrystalline anisotropy in the temperature range of 10 K to 60 K.     

Two-dimensional magnetic cluster growth with a power-law interaction

A two-dimensional cluster model in which the morphology of clusters depends on power-law magnetic interactions that decay with distance r as a r^−α law is introduced. The growth algorithm is a generalization of diffusion-limited aggregation (DLA) model. The particles with spin degree diffuse on a square lattice and each spin is allowed to flip under a Monte Carlo probability. The simulation shows that, for the antiferromagnetic coupling, the spins of the particles in clusters tend to be oriented alternately. For the ferromagnetic coupling, however, the spin distribution depends on the exponent α: for large value of α, domains with different sizes are observed in the clusters; while for small α, during the earlier stage of the growth process, the clusters exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the clusters, the spin states of all particles are similar. The magnetization and system energy of the clusters as well as their evolutions with the growth parameters are also studied in detail.     

Competition between face-centered cubic and icosahedral cluster structures

The binding energy of atoms in icosahedral and face-centered-cubic clusters is calculated numerically for pairwise Morse-potential interactions between atoms and for clusters containing from 561 to 923 atoms, which corresponds to gradual filling of the sixth layer of the icosahedral cluster. Perturbation theory is used to calculate the cluster binding energy, in which the small parameter is the ratio of the interaction energy between non-nearest neighbor atoms to the interaction energy between nearest neighbors. Values of the Morse interaction potential parameter are found for which the energies of clusters with different structures coincide. Under the conditions used in these computations, the strain energy of a cluster can be neglected. Although the contribution of the interaction energy between non-nearest neighbors to the total cluster energy is small, it turns out to be important in finding the level crossing parameter. Zh. éksp. Teor. Fiz. 112, 1082–1090 (September 1997)     

Magnetization reversal processes in layered high-temperature superconductors with ferromagnetic impurities

The self-consistent interaction of a vortex system of a high-temperature superconductor and ferromagnetic impurities, including single impurities and their clusters, has been considered in the model of a layered high-temperature superconductor. For different temperatures and concentrations of ferromagnetic impurities, the magnetization reversal loops have been calculated by the Monte Carlo method taking into account an ensemble of ferromagnetic particles with different orientations of their easy magnetization axes with respect to the direction of an external magnetic field and for different magnetic anisotropy energies. It has been demonstrated that there is a nonlinear interaction of the high-temperature superconductor with ferromagnetic impurities, in which the initially thermodynamically reversible character of the magnetization reversal of the ferromagnetic ensemble can become irreversible. For a periodic lattice of clusters of ferromagnetic impurities, the magnetization curves of the high-temperature superconductor have been calculated for different sizes and configurations of the clusters. It has been revealed that, when extended defects are oriented parallel to the direction of the entrance of vortices in the sample, the length of the defects does not affect the remanent magnetization. It has been shown that the inclusion of the interaction between the magnetic moments inside the impurity cluster leads to a decrease in the magnetization reversal loop, the coercivity, and, accordingly, the energy loss due to magnetization reversal.     

Novel metal-encapsulated caged clusters of silicon and germanium

We report the recent findings of metal (M) encapsulated clusters of silicon from computer experiments based on ab initio total energy calculations and a cage shrinkage and atom removal approach. Our results show that using a guest atom, it is possible to wrap silicon in fullerenelike (f) structures, as sp² bonding is not favorable to produce empty cages unlike for carbon. Transition M atoms have a strong bonding with the silicon cage that are responsible for the compact structures. The size and structure of the cage change from 14 to 20 Si atoms depending upon the size and valence of the M atom. Fewer Si atoms lead to relatively open structures. We find cubic, f, Frank-Kasper (FK) polyheral type, decahedral, icosahedral and hexagonal structures for M@Si_n with n = 12-16 and several different M atoms. The magic behavior of 15 and 16 atom Si cages is in agreement with experiments. The FK polyhedral cluster, M@Si₁₆ has an exceptionally large density functional gap of about 2.35 eV calculated within the generalized gradient approximation. It is likely to give rise to visible luminescence in these clusters. The cluster-cluster interaction is weak that makes such clusters attractive for cluster assembled materials. Further studies to stabilize Si₂₀ cage with M = Zr, Ba, Sr, and Pb show that in all cases there is a distortion of the f cage. Similar studies on M encapsulated germanium clusters show FK polyhedral and decahedral isomers to be more favorable. Also perfect icosahedral M@Ge₁₂ and M@Sn₁₂ clusters have been obtained with large gaps by doping with divalent M atoms. Recent results of the H interaction with these clusters, hydrogenated silicon fullerenes as well as assemblies of clusters such as nanowires and nanotubes are briefly presented.     

Theoretical and experimental study of Fe/Cr nanometric quasiperiodic multilayers

An experimental and theoretical study of magnetization curves of Fe/Cr nanometric magnetic films grown with the structure of the quasiperiodic Fibonacci sequence is presented. Fe ferromagnetic films with interfilm exchange coupling provided by intervening Cr non-ferromagnetic layers were grown on MgO (100) by dc magnetron sputtering at 300 ^°C. The magnetization curves were investigated using the magneto-optical Kerr effect with the external field applied along the easy axis. The theoretical approach for this system is based on a realistic phenomenological model that includes the following contributions to free magnetic energy: Zeeman, cubic magneto-crystalline anisotropy, as well as bilinear and biquadratic exchange energies. Our numerical results are in very good agreement with the experimental data.     

Unsupported lead clusters and electron diffraction

A beam of Pb clusters is produced with the inert gas aggregation method and probed by electron diffraction. Analysis of the diffraction patterns indicates that average cluster size can vary between 3 and 7 nm, according to nucleation conditions. The diffraction patterns from beams with larger average cluster size are very similar to patterns calculated from model decahedron clusters, while those for smaller cluster size do not appear to have simple geometrical face-centred cubic, decahedral, or icosahedral structure. Received 30 November 2000     

Magnetization of Gd cluster: Anomalous thermal behavior

Theoretical studies of the temperature (T) dependence of magnetization of Gd₁₃ clusters have been carried out within a classical Heisenberg model using Monte-Carlo simulations. It is shown that for a broad range of values of , defined as the ratio between competing ferro and anti-ferro magnetic couplings, the cluster magnetization increases with T in the low T region, as seen in experiment. The clusters are also shown to exhibit a wide distribution of moments at a given T, which broadens significantly with increasing T. It is suggested that this may affect the observed magnetic behavior of magnetic clusters in Stern-Gerlach experiments. Received 29 May 1999 and Received in final form 5 September 1999     

Domain morphology in ultrathin ferromagnetic films with perpendicular magnetization

We determine the minimal domain structure for the equilibrium thickness of stripes as well as for the minimal energy of the domain configuration in ultrathin films of ferromagnetically coupled spins, where the easy direction of magnetization is perpendicular to the film. It is found that the equilibrium thickness of stripes and walls depend on the exchange energy. The normalized anisotropy, f, depends on interplay between the magnetic and anisotropy energies and is almost independent of the exchange energy inside the wall. The results are compared with the experimental data for thin Ag/Fe/Ag (0 0 1) films and a good coincidence is obtained between both results.     

Monte carlo simulation of magnetization and coercivity of free magnetic clusters

Based on Monte Carlo method, the oscillatory behaviour of the average magnetic moment as a function of the cluster sizes and the temperature dependences of magnetic moment with different sizes have been studied. It is found that the oscillations superimposed on the decreasing moment are associated with not only the geometrical structure effects but also the thermal fluctuation. The hystereses and thermal coercivities for free clusters with zero and finite uniaxial anisotropies have been calculated. The simulated thermal dependence of the coercivity is consistent with the experimental result, but does not fit the T^α law in the whole temperature range. It is evident that an easy magnetization direction and an anisotropy resulting from the spin configurations exist in the free clusters with the pure exchange interaction, which is also proved by the natural angle and energy distribution of clusters. A systematic theoretical analysis is also made to establish the relationship between natural angle and coercivity.     

Surface tensions and stress tensors of liquid and solid clusters by molecular dynamics

Surface tension and pressure (stress) tensors of Lennard-Jones clusters, in the size range 200 ~ 2700 atoms/cluster, formed from evaporating liquid droplets were calculated in a Molecular Dynamics simulation. Icosahedral clusters have a much larger surface tension than decahedral, fcc, and hcp ones, meanwhile asymmetric icosahedral clusters have a lower surface tension. Fcc and hcp clusters have a very small surface tension. Decahedral clusters have a surface tension closer to that of fcc and hcp ones than to that of icosahedral ones, though both icosahedral and decahedral structures have five fold symmetry axis. Binary component clusters have a higher surface tension than single component ones.     

Dynamics simulation on interaction of intense laser pulses with atomic clusters

Under classical particle dynamics, the interaction process between intense femtosecond laser pulses and icosahedral noble-gas atomic clusters was studied. Our calculated results show that ionization proceeds mainly through tunnel ionization in the combined field from ions, electrons and laser, rather than the electron-impact ionization. With increasing cluster size, the average and maximum kinetic energy of the product ion increases. According to our calculation, the expansion process of the clusters after laser irradiation is dominated by Coulomb explosion and the expansion scale increases with increasing cluster size. The dependence of average kinetic energy and average charge state of the product ions on laser wavelength is also presented and discussed. The dependence of average kinetic energy on the number of atoms inside the cluster was studied and compared with the experimental data. Our results agree with the experimental results reasonably well.     

Anisotropic explosions of hydrogen clusters under intense femtosecond laser irradiation

We report on measurements of ion energy distributions from hydrogen clusters irradiated by intense laser pulses of duration 40 and 250 fs. Contrary to the predictions of a simple Coulomb explosion model, we observe a pronounced spatial anisotropy of the ion energies from these explosions with the highest energy ions ejected along the laser polarization direction. The origin of the anisotropy is distinct from that previously seen in clusters of high Z atoms such as Ar and Xe. Furthermore, a measured increase in H+ ion energy when longer, lower intensity pulses are employed suggests that multiple-pass, vacuum heating of the cluster electrons is important in the deposition of energy by the laser.     

Electronic structure and magnetism in 4d-transition metal clusters

We analyze the stability of magnetic states obtained within the tight-binding model for cubooctahedral (O_h) and icosahedral (I_h) clusters of early 4d (Y, Zr, Nb, Mo, and Tc) transition metals. Several metastable magnetic clusters are identified which suggests the existence of multiple magnetic solutions in realistic systems. A bulk-like parabolic behavior is observed for the binding energy of O_h and I_h clusters as a function of the atomic number along the 4 d-series. The charge transfer on the central atom changes sign, while the average magnetic moments present an oscillatory behavior as a function of the number of d electrons in the cluster. Our results are in agreement with other theoretical calculations. Received: 20 November 1997 / Received in final form: 9 March 1998 / Accepted: 30 March 1998