The magnetic properties across the martensitic transition in the Co38Ni34Al28 alloy

The magnetic properties of the Co₃₈Ni₃₄Al₂₈ alloy have been studied. The alloy exhibits a first order austenite-martensite phase transition in the temperature region between 155 and 247 K. A strain of 0.07% is produced across this phase transition. The Arrott plots obtained from the isothermal magnetic field dependence of magnetization indicate the presence of spontaneous magnetization both in the austenite and martensite phases, confirming the ferromagnetic character of the alloy up to room temperature. The temperature dependence of the high field magnetization indicates the presence of spin wave excitations, spin wave excitation gap and spin wave-spin wave interactions in the martensite phase. The magnetic anisotropy energy constant for the Co₃₈Ni₃₄Al₂₈ alloy is estimated both with the help of the standard law of approach to saturation of magnetization, and also from the field dependence of magnetization using the field for technical saturation of magnetization. The temperature dependences of these energy terms are compared. The estimated values of the magnetic anisotropy constant seem to be in agreement with the magnitude of the spin wave excitation gap estimated from the temperature dependence of high field magnetization.     

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     

Localized spin-wave resonance modes of ferromagnetic microstrips in the field of a magnetic probe

Some results of the micromagnetic modeling of forced magnetization oscillations in planar microstrips of NiFe with easy plane anisotropy and Co/Pt with perpendicular easy axis anisotropy in the field of a magnetic spherical probe are considered. It has been shown that the probe field provokes the appearance of a hedgehog–antivortex coupling state in the NiFe strips, due to its lateral components and a skyrmion magnetization state in the Co/Pt layer. These effects destroy spatial magnetization oscillations in the microstrips and lead to the appearance of additional resonances in the spectrum of oscillations corresponding to the modes localized in the probe field.     

Anisotropy of the magnetization and of the iron hyperfine field in R2Fe17 compounds

A single crystal of the hexagonal Y₂Fe₁₇ compound has been prepared. The exact composition, Y₂Fe_18.9 has been refined through X-rays measurements. A large anisotropy of the magnetization is associated with the large magnetocrystalline anisotropy. Mössbauer experiments have been performed at 4.2 K under high magnetic fields. A large anisotropy of the orbital contribution to the hyperfine field is reduced. This can explain the anomalies of the hyperfine field observed in Tm₂Fe₁₇ and ErFe₃ when magnetization reorientations occur with temperature.     

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.     

Temperature-induced magnetization reversal and ultra-fast magnetic switch at low field in SmFeO3

We have found that SmFeO₃, a family of rare-earth orthoferrites, exhibits temperature-induced magnetization reversal below the critical low-temperature along the a-axis of Pbnm symmetry. First-principles calculations demonstrate that this negative magnetization is mainly attributed to the competition between two magnetocrystalline anisotropy terms in the inequivalent magnetic sites of Sm³⁺ and Fe³⁺. Interestingly, the room temperature magnetization-field curve further shows an ultra-fast magnetization switch in the low-magnetic field, suggesting a potential applicability to high-speed magnetic switching devices.     

Many‐body Green's function theory for thin ferromagnetic films: exact treatment of the single‐ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many‐body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second‐ and fourth‐order uniaxial single‐ion anisotropy, and the magnetic dipole‐dipole coupling. The single‐ion anisotropy terms can be treated exactlyby introducing higher‐order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest‐order Green's functions. RPA‐like approximations are used to decouple the exchange interaction terms in both the low‐order and higher‐order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.     

Magnetization of nanomagnet assemblies: Effects of anisotropy and dipolar interactions

We investigate the effect of anisotropy and weak dipolar interactions on the magnetization of an assembly of nanoparticles with distributed magnetic moments, i.e., assembly of magnetic nanoparticles in the one-spin approximation, with textured or random anisotropy. The magnetization of a free particle is obtained either by a numerical calculation of the partition function or analytically in the low and high field regimes, using perturbation theory and the steepest-descent approximation, respectively. The magnetization of an interacting assembly is computed analytically in the range of low and high field, and numerically using the Monte Carlo technique. Approximate analytical expressions for the assembly magnetization are provided which take account of the dipolar interactions, temperature, magnetic field, and anisotropy. The effect of anisotropy and dipolar interactions are discussed and the deviations from the Langevin law they entail are investigated, and illustrated for realistic assemblies with the lognormal moment distribution.     

Study on the coercivity of granular solid iron

The iron granular solid, in which ultrafine iron particles are dispersed, has been prepared with both SiO₂ and Cu matrices using the sol-gel method. The structure and morphology of these granular solid samples are investigated by X-Ray Diffraction (XRD) and Transmission Electron Microscopy (TEM). The magnetic properties are measured using a vibrating sample magnetometer with 20 kOe maximum applied field. It is found that the coereivity decreases very slightly with temperature from 80 to 300 K for these Fe–SiO₂ and Fe–Cu granular solid samples with different average size of iron particles from 50 to 300 Å. The magnetic anisotropy has been obtained from the measured magnetization curves for these granular solid samples using the law of approach to saturation, and the obtained values of the effective magnetic anisotropy are all more than 10⁶ erg/cm³, which are larger than the value of the magnetocrystalline anisotropy for bulk iron. The coercivity vs temperature for these granular solid samples has been calculated using the Kneller and Luborsky theory, in which the magnetic anisotropy values obtained from the law of approach to saturation are used. The trends of the calculated coercivity as a function of temperature are in reasonable agreement with the observations.     

Spectral analysis of the precessional switching of the magnetization in an isotropic thin film

We study how a magnetic field step triggers the precessional switching of the magnetization in an isotropic thin film. Using a variational approach, we make an analytical estimate of the switching frequency. We compare it to more general analytical models, and to the results obtained numerically by direct integration of the equations of motion. We show that the periodic motions of the three magnetization components can be described satisfactorily with truncated Fourier expansions, indicating a relatively high spectral purity of the magnetic response. Our analytical expressions are simple enough to be physically transparent at first sight, in contrast to the results of the more elaborate models that treat also anisotropy.     

Anatomy of field effects on magnetization dynamics and spin transfer noise

Spin transfer-related phenomena in nanomagnets have attracted extensive studies. In this paper we shall focus on analysis of individual and combined effects of the external, anisotropy, and demagnetization fields on magnetization dynamics and spin transfer noise. It is found that individual roles of the external, anisotropy, and demagnetization fields, as well as the combined roles of external plus anisotropy fields and anisotropy plus demagnetization fields, do not change the behavior of current induced magnetization switching. Such magnetization reversal procedures are of low noise. Our dynamics and power spectral density calculations show that it is the demagnetization field that plays a major role in inducing spin transfer noise: the demagnetization field itself or in combination with the anisotropy field will result in wave-like switching; moreover, the demagnetization field, together with the external field (not too small), will lead to precession and hence the system would be in noisy states. Our modeling work for an elliptical Py alloy is qualitatively consistent with Cornell's experiment and simulation [Science 307 (2005) 228].     

复合多铁链的磁电耦合行为与外场调控

对含有界面磁电耦合的有限长铁电-铁磁多铁链体系进行了研究,基于矢量离散化思想,构建了描述其磁电性质的微观海森伯模型.利用传递矩阵方法获得了磁化强度、电极化强度、磁电化率等关键热力学量的解析表达式,重点探讨了界面磁电耦合、外场以及单离子各向异性对体系磁电耦合行为的影响和调控.研究结果表明,界面磁电耦合对体系的磁化强度和电极化强度均起促进作用.电场驱动下的电致磁电化率具有更强的磁电关联效应,预示着外电场能够有效地调控体系的磁性行为.而在磁致磁电化率中观察到的低温峰主要源于外磁场的诱导.此外,在高电场作用下体系比热容还呈现出有趣的三峰结构,这种三峰结构是自旋态的热激发以及电偶极矩的电场和温度共同激发导致的.     

Phase Transitions of Fel2 in high magnetic field parallel to the spin direction,static field up to 150 kOe,pulsed field up to 250 kOe

Study of parallel and perpendicular susceptibilities shows that ferrous iodide presents at low temperature an antiferromagnetic order, with spins oriented along the anisotropy axis (c axis).Phase transitions of Fel₂ in a magnetic field parallel to c axis are studied by help of magnetization measurements. At low temperature (2.2 K) saturation is reached only for a magnetic field of 140 kOe. Results obtained in high static fields (Bitter and supraconductive coils allowing respectively 140 and 150 kOe) and in pulsed field are presented.At low temperature, two successive first order phase transitions are observed at 46 and 120 kOe. In the intermediate phase, the magnetization presents two minor discontinuities. An original phase diagram is given.The complexity of the Fel₂ behavior, in parallel magnetic field shows that the magnetic structure is not the same as the two sublattices one characteristic of FeCl₂ and FeBr₂. An estimate of the principal exchange coupling parameters and a study by neutron diffraction measurements (to be published) confirm an original magnetic structure.     

Newtonian gravitational field theory

A field theory for gravitation is developed within the framework of the special theory of relativity. This is achieved by exploiting the similarity in mathematical structure of two relations which are found in both Newton's gravitational theory and Maxwell's electromagnetic theory. These relations are: (1) the law of force between the relevant physical entities (mass and electric charge), and (2) the equation of continuity (conservation of charge). The field equations describe the propagation of gravitational waves with the velocity of light in much the same way that Maxwell's field equations describe electromagnetic waves. Both fields have such similar mathematical structures that they are developed in parallel up to the point where their inherently different physical content cause their paths of evolution to diverge. At this stage, the field equations for both theories are determined. The physical significance of the field variables of both theories imposes a mathematical formalism which doesnot give rise to self-interactions. A calculation for the energy in the field of two particles representative of either the electromagnetic or gravitational field is shown to give the correct finite value. The reason that conventional calculations yield an infinite energy is readily seen to lie in the calculation of a physically meaningless quantity. The mathematical formalism required by the field theories is used to develop generalizations of the usual conservation laws. Two conservation laws are derived which are consequences of the consistent physical interpretation of the field variables. These laws do not appear in conventional theory. The approach followed here in developing the field theories leads to the appearance of forces dual to the well-known forces. Thus, for the electromagnetic field, we find a dual to the Lorentz force and, in the gravitational field, we find a dual to Newton's law of gravitation. These results are not due to the introduction of the fields, for they can be expressed in terms of the particle variables. They emerge from the consistent application of the physical interpretation of the particle and field variables. A basic physical principle, which underlies both theories, is best expressed by the statement: It is the interactions between the elements of a physical event and not the elements themselves which are the physical observables.     

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume——Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume--Capel model (BCM) in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.     

Oxygen effects on magnetic properties during annealing of sputtered Co-Gd-Mo films

Two sets of amorphous Co-Gd-Mo films with compensation temperatures below and above room temperature were annealed in various atmospheres. The changes in the net magnetization, the perpendicular anisotropy field and the uniaxial anisotropy constant were measured at room temperature after the annealing procedure. All the observed effects could be consistently explained by prefered oxidation of the Gd-“sublattice” atoms. Proper annealing allows one to obtain films with magnetic constants desired for device applications.     

Saturation Magnetization and Law of Approach to Saturation for Self-formed Ionic Ferrofluids Based on MnFe2O2 Nanoparticles

测量了MnFe₂O₄纳米微粒及其磁性液体在室温下的磁化曲线.微粒的中值粒径为13.67 nm. 磁性液体的比饱和磁化强度小于理论值.在高场范围(5～10 kOe)下,磁性液体趋于饱和时,其体积分数越大,磁化曲线的斜率越大. 这种饱和磁化强度性质和趋饱和律分别源自于无场时的环状自组装团聚体和场致团聚体. 场致团聚体是耗散结构,以致于其趋饱和磁化律不同于顺磁理论所描述的趋饱和律. 磁性液体中的大微粒导致了表观磁滞现象.     

Directed magnetic field induced assembly of high magnetic moment cobalt nanowires

A directed magnetic field induced assembly technique was employed to align two phase (h.c.p. + f.c.c.) cobalt nanoparticles in a mechanically robust long wire morphology. Co nanoparticles with an average size of 4.3 nm and saturation magnetization comparable to bulk cobalt were synthesized by borohydride reduction followed by size selection and magnetic field induced assembly. The coercivity of these nanowires was higher than their nanoparticle counterpart due to shape anisotropy. The experimental coercivity values of the nanowires were lower than the predictions of the coherent rotation, fanning and curling models of coercivity due to the preponderance of superparamagnetic particles with zero coercivity.     

On the magnetization of a thin-walled cylindrical sheath with a magnetic field from the Rayleigh range inside

In terms of the general theory of magnetization of thin-walled sheaths, magnetization of a thin-walled indefinitely long circular cylindrical sheath that is placed in an external magnetic field and experiences the action of an internal magnetic field from the Rayleigh range is considered. It is shown that the solution of the problem can be reduced to solving infinite sets of nonlinear equations in the coefficients of Fourier series representing the components of the magnetization and internal magnetic field strength that are averaged over the thickness of the sheath and tangent to its surface. Approximate solutions to these sets of equations are obtained, and expressions for the coefficients multiplying the first terms of the series are given.     

Nonlinear response of superparamagnetic particles to a sudden change of a high constant magnetic field

For a system of superparamagnetic particles in a high external constant magnetic field, a technique for calculating the nonlinear response to a sudden change in the field direction and magnitude is proposed. A set of momentary equations for the averaged spherical harmonics, which is derived from the Fokker-Planck equation for the magnetization-orientation distribution function is the basis of this technique. As an example, the nonlinear response of a system of particles with anisotropy of the easy-axis type is examined. For this case, a solution to the momentary equations is obtained by using matrix continued fractions. The magnetization relaxation time and the spectrum of the relaxation function are calculated for typical values of anisotropy, dissipation, and nonlinearity parameters. It is shown that the magnetization kinetics is essentially dependent on these parameters.