Magnetization curves of randomly oriented ferromagnetic single-domain nanoparticles with combined symmetry of magnetic anisotropy

The magnetization curves of randomly oriented nanoparticles with combined symmetry of magnetic anisotropy were studied. The composite mode of the Stoner–Wolfarth model has been used. In terms of this model each nanoparticle is characterized by random cubic crystalline magnetic anisotropy and by random uniaxial magnetic anisotropy. The series of simulated magnetization curves have been obtained. Each curve corresponds to different contributions of cubic and uniaxial magnetic anisotropy energy to the full energy of an individual nanoparticle k_u. Within this series we discuss the values of remnant magnetization, coercive force, both initial and maximal susceptibilities as the function of k_u. It is found that the magnetic properties are not monotonous functions of k_u. We discuss the possibility of comparing the calculated magnetization curves with the experimental curves in order to obtain new information on the magnetic constant.     

Cylindrical magnetization model for glass-coated microwires with circular anisotropy: Statics

The static magnetization profile of glass-coated microwires with effective circular anisotropy is investigated using micromagnetics. In this family of microwires, the ferromagnetic nucleus with an amorphous character presents a magnetic structure composed of an inner region with axial domains and an outer region with circular domains, due to magnetoelastic anisotropy. A one-dimensional micromagnetic model is developed, taking into account both the exchange and magnetoelastic anisotropy energies, and solved quasi analytically. The total energy, magnetization profiles and magnetization curves are investigated as a function of radius and anisotropy constant of the nucleus. This work represents a fundamental study of the magnetization process in these amorphous microwires and provides guidelines for the production of microwires with tailored magnetic properties. En passant, the nucleation problem in an infinite cylinder, introduced by W.F. Brown, is revisited.     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

Magnetische grenzflächen-anisotropie von amorphem Fe in kontakt mit nichtmagnetischen metallen

The magnetic properties of very thin ferromagnetic Fe films (1–10 atomic layers) in contact with nonmagnetic amorphous metals are investigated. Apart from the demagnetization energy, which supports a magnetization in the plane of the film, an energy of magnetic anisotropy occurs in the interlayer, which has the tendency to orient the magnetization perpendicular to the surface. The anomalous Hall effect of the ferromagnetic films is used to investigate their magnetic properties. From the measurements, we get the applied magnetic field B_s, which is necessary to orient the magnetization perpendicular to the film surface. In addition to a constant term, B_s is proportional to 1/d, which is typical of surface effects and yields the energy of the interface anisotropy. The value of this energy is strongly dependent on the nonmagnetic metal and is smaller for the system Pb/Fe than for Sn/Fe. Furthermore, the experimental results show no drastic reduction of the atomic magnetic moment in the surface layer.     

Magnetic interface-anisotropy of amorphous iron in contact with nonmagnetic metals

The magnetic properties of very thin ferromagnetic Fe films (1–10 atomic layers) in contact with nonmagnetic amorphous metals are investigated. Apart from the demagnetization energy, which supports a magnetization in the film plane, an energy of magnetic anisotropy occurs in the interlayer, which has the tendency to turn the magnetization perpendicular to the surface. The anomalous Hall effect of the ferromagnetic films is used to investigate their magnetic properties. From the measurements we get the applied magnetic fieldB _s , which is necessary to turn the magnetization perpendicular to the film surface.B _s is, besides a constant term, proportional to 1/d, which is typical of surface effects and yields the energy of the interface anisotropy. The value of this energy is strongly dependent on the nonmagnetic metal and is smaller for the system Pb/Fe than for Sn/Fe. Furthermore, the experimental results show no drastic reduction of the atomic magnetic moment in the surface layer.     

Magnetization plateau and quantum phase transitions in a spin-orbital model

A spin-orbital chain with different Landé g factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Landé g factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of the critical points. For the SU(4) spin-orbital model, explicit analytical expressions for the critical fields are derived, with excellent accuracy compared with numerics.Received: 8 January 2004, Published online: 8 June 2004PACS: 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Jm Quantized spin models     

Surface contribution to the anisotropy of magnetic nanoparticles

We calculate the contribution of the Néel surface anisotropy to the effective anisotropy of magnetic nanoparticles of spherical shape cut out of a simple cubic lattice. The effective anisotropy arises because deviations of atomic magnetizations from collinearity and thus the energy depends on the orientation of the global magnetization. The result is second order in the Néel surface anisotropy, scales with the particle's volume, and has cubic symmetry with preferred directions [+/- 1, +/-1 , +/-1].     

Spin kinetic Monte Carlo method for nanoferromagnetism and magnetization dynamics of nanomagnets with large magnetic anisotropy

The Kinetic Monte Carlo (KMC) method based on the transition-state theory, powerful and famous for simulating atomic epitaxial growth of thin films and nanostructures, was used recently to simulate the nanoferromagnetism and magnetization dynamics of nanomagnets with giant magnetic anisotropy. We present a brief introduction to the KMC method and show how to reformulate it for nanoscale spin systems. Large enough magnetic anisotropy, observed experimentally and shown theoretically in terms of first-principle calculation, is not only essential to stabilize spin orientation but also necessary in making the transition-state barriers during spin reversals for spin KMC simulation. We show two applications of the spin KMC method to monatomic spin chains and spin-polarized-current controlled composite nanomagnets with giant magnetic anisotropy. This spin KMC method can be applied to other anisotropic nanomagnets and composite nanomagnets as long as their magnetic anisotropy energies are large enough.      

Structure and magnetic properties of mechanically alloyed ferrite nanopowders

The morphology, structure parameters, and magnetic characteristics of mechanically alloyed magnetite and cobalt and magnesium spinel-ferrite nanopowders are investigated. The effect of the nanopowder particle size on the saturation magnetization of the spinel ferrites and the roles of the surface anisotropy and magnetoelastic energy in the formation of the magnetic anisotropy of the materials under study are discussed within the framework of a core-shell model. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 40–44, September 2006.     

Thickness dependent magnetization dynamics of perpendicular anisotropy Co/Pd multilayer films

We present the measurements of the picosecond magnetization dynamics of Co/Pd multilayer films. The dynamic magnetization properties of sputtered multilayer films were analyzed as a function of Co layer thicknesses and applied bias field. Both the eigenfrequencies of the magnetization precession in the multilayers and the associated Gilbert damping exhibit extreme sensitivity to the magnetic layer thickness on an atomic monolayer scale. The eigenfrequency increases more than threefold when the Co thickness decreases from 7.5 to 2.8 Å, mainly due to the changes in effective saturation magnetization and perpendicular anisotropy constant. A concomitant 2.6-fold increase in the damping of the oscillations is observed and attributed to stronger interface dissipation in thinner Co layers. In addition, we introduce a quasi-1D micromagnetic model in which the multilayer stack is described as a one-dimensional chain of macrospins that represent each Co layer. This model yields excellent agreement with the observed resonance frequencies without any free parameters, while being much simpler and faster than full 3D micromagnetic modeling.     

Effect of magnetic properties of soft magnetic phase on the energy product of an exchange-spring magnet

Research on exchange-spring magnets has focused on the microstructures of the materials.However,research has seldom been concerned with the effect of magnetic properties of soft magnetic phase on the energy product of an exchangespring magnet.In this paper,a simple one-dimensional numerical simulation is used to investigate this effect in a Nd2Fe14Bbased exchange-spring magnet.The results reveal that the larger the anisotropy constant,the stronger the exchange coupling,and the higher the magnetization of the soft magnetic4 phase,the larger the energy product of an exchange-spring magnet.This provides evidence for choosing a soft magnetic phase in an exchange-spring magnet.     

Influence of induced anisotropy on the processes of magnetization reversal of cobalt circular nanodots

The magnetic structure and the processes of magnetization reversal of individual cobalt nanodots and arrays of cobalt nanodots have been studied using the magneto-optical Kerr effect and magnetic force microscopy. Arrays of nanodots have been prepared by ion etching from a continuous cobalt film. Magnetic anisotropy is induced during deposition of the cobalt films. The nanodots have the diameter d = 600 nm and the period varying from 1.5d to 3.0d. Magnetic force microscopy images have shown that the induced magnetic anisotropy affects the orientation of magnetization of noninteracting nanodots and the direction of displacement of the magnetic vortex center in the nanodots coupled by the dipole-dipole interaction.     

Field dependent specific heat and longitudinal magnetization of the quantum magnet layer Cs2CuCl4: Anisotropy effects

We have addressed the specific heat and magnetization of an anisotropic spin-1/2 triangular Heisenberg antiferromagnet Cs₂CuCl₄ in the presence of magnetic field at finite temperature. We have investigated the behavior of thermodynamic properties by means of excitation spectrum in terms of a hard core bosonic representation. The effect of in-plane anisotropy on thermodynamic properties has also been studied via the bosonic model by Green’s function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the specific heat and longitudinal magnetization in the gapped field induced spin-polarized phase for various magnetic fields and anisotropy parameters. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various anisotropy parameters. Our results show temperature dependence of specific heat includes a peak so that its temperature position goes to higher temperature with increase of magnetic field. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum.     

In plane to out of plane magnetic reorientation transition in partially ordered FePd thin films

It is demonstrated that perpendicular magnetic anisotropy may be obtained with a room temperature growth process in ordered (FePd) alloys. Indeed, using atomic layer by atomic layer epitaxy, a partial chemical ordering into the L1₀ structure is obtained, with a corresponding intermediate perpendicular anisotropy (). These samples provide an appropriate template for the study of the magnetic reorientation from in plane to out of plane magnetization upon layer's thickness increase. VSM, transverse Kerr measurements and magnetic force microscopy have been used in order to determine the relevant magnetic parameters and the occurrence of the reorientation transition. Received 13 October 1998 and Received in final form 5 February 1999     

Three-and two-dimensional calculations for the interface anisotropy dependence of magnetic properties of exchange-spring Nd2Fe(14)B/α-Fe multilayers with out-of-plane easy axes

Hysteresis loops,energy products and magnetic moment distributions of perpendicularly oriented Nd2Fe(14)B/α-Fe exchange-spring multilayers are studied systematically based on both three-dimensional(3D)and one-dimensional(1D)micromagnetic methods,focused on the influence of the interface anisotropy.The calculated results are carefully compared with each other.The interface anisotropy effect is very palpable on the nucleation,pinning and coercive fields when the soft layer is very thin.However,as the soft layer thickness increases,the pinning and coercive fields are almost unchanged with the increment of interface anisotropy though the nucleation field still monotonically rises.Negative interface anisotropy decreases the maximum energy products and increases slightly the angles between the magnetization and applied field.The magnetic moment distributions in the thickness direction at various applied fields demonstrate a progress of three-step magnetic reversal,i.e.,nucleation,evolution and irreversible motion of the domain wall.The above results calculated by two models are in good agreement with each other.Moreover,the in-plane magnetic moment orientations based on two models are different.The 3D calculation shows a progress of generation and disappearance of vortex state,however,the magnetization orientations within the film plane calculated by the 1D model are coherent.Simulation results suggest that negative interface anisotropy is necessarily avoided experimentally.     

Bitter decoration and magneto-optical observations of vortex chains in high temperature superconductors

In tilted magnetic fields, vortices in anisotropic superconductors form one-dimensional arrangements, called vortex chains. We have visualized vortex chains by Bitter decoration and magneto-optical technique. The fundamental energy scale for the attractive interaction between pancake and Josephson vortices is evaluated by observing vortex chains under various conditions. We also explore how the vortex chains evolve when the large in-plane field is applied or when the anisotropy parameter of the system is changed     

Quantum spin model of a cubic ferromagnet in a magnetic field

The zero temperature phase diagram of a one-dimensional ferromagnet with cubic single ion anisotropy in an external magnetic field is studied. The mean-field approximation and the density-matrix renormalization group method are applied. Two phases at finite magnetic fields are identified: a canted phase with spontaneously broken symmetry and a phase with magnetization along the magnetic field. Both methods predict that the canted phase exists even for the single-ion anisotropy strong enough to destroy the magnetic order at zero magnetic field. In contrast to the mean-field theory, the density-matrix renormalization group predicts a reentrant behavior for the model. The character of the phase transition at finite magnetic field has also been considered and the critical index has been found. Received 9 May 2000 and Received in final form 5 July 2000     

Influence of the inhomogeneity of local magnetic parameters on the curves of magnetization in an ensemble of Fe<Subscript>3</Subscript>C ferromagnetic nanoparticles encapsulated in carbon nanotubes

Methods have been proposed and tested for analyzing local magnetic parameters in a system of single-domain ferromagnetic nanoparticles using their magnetization curves. The magnetic inhomogeneity in ensembles of Fe₃C nanoparticles encapsulated in carbon nanotubes has been investigated. It has been established that the Fe₃C nanoparticles encapsulated in carbon nanotubes are characterized by two-modal distribution functions of the local magnetic anisotropy energy. The particle distribution over the blocking temperature is reconstructed from the experimental temperature dependence of the coercive force. The allowance made for the inhomogeneity of the local magnetic parameters of the Fe₃C nanoparticles, which were studied by the proposed methods, explains the discrepancy between the magnetic anisotropy energy determined by the method of the magnetization approaching saturation and the magnetic anisotropy energy estimated from the coercive force of single-domain nanoparticles.     

Magnetization reversal of a single cobalt cluster using a RF field pulse

Technological improvements require the understanding of dynamical magnetization reversal processes at the nanosecond time scales. In this paper, we present the first magnetization reversal measurements performed on a single cobalt cluster (counting only a thousand of spins), using the micro-superconducting quantum interference device (SQUID) technique by applying a constant magnetic field combined with a radio-frequency (RF) field pulse. First of all, we present the different technical steps necessary to detect the magnetic reversals at low temperature (T=35 mK) of a well-defined nanoparticle prepared by low energy clusters beam deposition (LECBD). We previously showed that the three-dimensional (3D)-switching Stoner-Wohlfarth astroid represents the magnetic anisotropy of the nanoparticle. Then, an improved device coupled with a gold stripe line, allow us to reverse such macrospin, using a RF pulse. A qualitative understanding of the magnetization reversal by non-linear resonance has been obtained with the Landau-Lifschitz-Gilbert (LLG) equation.