Dynamics of two interacting dipoles

We study the deterministic spin dynamic of two interacting magnetic moments with anisotropy and dipolar interaction under the presence of an applied magnetic field, by using the Landau–Lifshitz equation with and without a damping term. Due to different kinds of interactions, different time scales appear: a long time scale associated with the dipolar interaction and a short time scale associated with the Zeeman interaction. We found that the total magnetization is not conserved; furthermore, for the non-dissipative case it is a fluctuating function of time, with a strong dependence on the strength of the dipolar term. In the dissipative case there is a transient time before the total magnetization reaches its constant value. We examine this critical time as a function of the distance between the magnetic moments and the phenomenological damping coefficient, and found that it strongly depends on these control parameters.     

Anisotropic and large low-field magnetic entropy change in a La4/3Sr5/3Mn2O7 single crystal

We have studied the magnetocaloric effect (MCE) in a bilayered La_4/3Sr_5/3Mn₂O₇ single crystal with applied field along both ab-plane and c-direction. Due to the quasi-two-dimensional structure, the crystal exhibits a strong anisotropy in the MCE. The difference of magnetic entropy change between two crystallographic directions depends on external magnetic fields and has a maximum of 2 J/kg K. A large low-field magnetic entropy change, reaching 3.2 J/kg K for a magnetic field change of 15 kOe, is observed when the applied field is along ab-plane. This large low-field magnetic entropy change is attributed to the rapid change of magnetization in response to external magnetic fields in the easy magnetizing plane.     

Theoretical investigation of magnetic property in paramagnetic neodymium gallium garnet under high magnetic field

The magnetic property in neodymium gallium garnet (NdGaG) is studied by the quantum theory. The ground configuration split states are calculated taking into account the spin–orbit interaction and crystal field effect. Taking account of the Nd–Nd exchange interaction, a good agreement between experimental and theoretical values can be obtained for the variation of the magnetic moment with the external magnetic field under “extreme” conditions (low temperature and high magnetic field). Moreover, the temperature dependence of magnetic moment and the magnetic susceptibility χ is also discussed. Above 30 K, the magnetization (M) shows a linear field (H_e) dependence.     

Magnetic and magnetocaloric properties of the intermetallic compound TbNiAl

Magnetization measurements have been carried out on the intermetallic compound TbNiAl in applied fields up to 120 kOe. Temperature dependence of magnetization under zero-field-cooled and field-cooled conditions shows thermomagnetic irreversibility, which is attributed to magnetic frustration. With the increase of field, the irreversibility decreases and vanishes completely at high fields. Magnetocaloric effect has been calculated in terms of isothermal magnetic entropy change using magnetization isotherms obtained at various temperatures. The maximum entropy change is 13.8 J kg⁻¹ K⁻¹ near the ordering temperature for a field change of 50 kOe. The refrigerant capacity is found to be 494 J kg⁻¹ for the same field change and for a temperature difference of 52 K between the cold and the hot sinks.     

Equilibrium magnetic properties of dipolar interacting ferromagnetic nanoparticles

We use Monte Carlo simulations to study the influence of dipolar interaction on the equilibrium magnetic properties of monodisperse single-domain ferromagnetic nanoparticles. Low field magnetizations simulated in zero field cooling (ZFC)/field cooling (FC) procedures and field-dependent magnetization curves above the blocking temperatures show strong dependence on the concentration and the spatial arrangement (cubic or random) of the magnetic particles. The field-dependent magnetizations can not be simply described by the T^* model at relative low temperatures due to the interplay between anisotropy and dipolar interactions, as well as the spatial arrangement effect.     

Hysteresis in small arrays of interacting magnetic nanoparticles

The out-of-plane hysteresis loops of small arrays of magnetic nanoparticles, under the influence of an external field applied perpendicular to the array and the dipolar interaction are investigated. The particles are assumed to have a perpendicular anisotropy energy that tends to align the magnetic moments to be perpendicular to the array. The magnetization is found to exhibit a plateaux-and-jumps structure as the external field is swept up and down. These jumps are associated with jumps in the energy of the system, and correspond to transition from one configuration of the moment orientation to another. The energy of different configurations of the magnetic moments for a 3×3 array in the limit of weak dipolar interaction is analyzed, as a means to understand the hysteresis loop. These jumps are more pronounced in arrays of smaller sizes and when the dipolar interaction is weak. The configuration of magnetic moments at zero external field as the field is swept up and down is found to be highly sensitive to the dipolar interaction.     

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.     

磁性单层膜磁学性质的Monte Carlo模拟

采用类Ising模型,利用Monte Carlo方法研究了磁性单层膜中退磁性偶极作用和铁磁性交换作用对系统磁学性质的影响.结果显示,随着偶极相互作用的增加,系统在低温下的磁化出现平台现象,此时磁化曲线可分为2个阶段,在低外场下,温度升高,系统易磁化,在高外场下则反之.这种新奇的磁化行为导致系统的磁熵变在低温低外场下出现大于零的反常行为.在模拟过程中,对长程力作用采用了比较精确的处理方法.     

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.     

Perpendicular magnetic anisotropy of ultrathin FeCo alloy films on Pd(0 0 1) surface: First principles study

Using the full potential linearized augmented plane wave (FLAPW) method, thickness dependent magnetic anisotropy of ultrathin FeCo alloy films in the range of 1 monolayer (ML) to 5 ML coverage on Pd(0 0 1) surface has been explored. We have found that the FeCo alloy films have close to half metallic state and well-known surface enhancement in thin film magnetism is observed in Fe atom, whereas the Co has rather stable magnetic moment. However, the largest magnetic moment in Fe and Co is found at 1 ML thickness. Interestingly, it has been observed that the interface magnetic moments of Fe and Co are almost the same as those of surface elements. The similar trend exists in orbital magnetic moment. This indicates that the strong hybridization between interface FeCo alloy and Pd gives rise to the large magnetic moment. Theoretically calculated magnetic anisotropy shows that the 1 ML FeCo alloy has in-plane magnetization, but the spin reorientation transition (SRT) from in-plane to perpendicular magnetization is observed above 2 ML thickness with huge magnetic anisotropy energy. The maximum magnetic anisotropy energy for perpendicular magnetization is as large as 0.3 meV/atom at 3 ML film thickness with saturation magnetization of . Besides, the calculated X-ray magnetic circular dichroism (XMCD) has been presented.     

Magnetic properties of the Ce2Fe17−xMnx helical magnets up to high magnetic fields

Magnetic properties of the Ce₂Fe_17−xMn_x, x=0–2, alloys in magnetic fields up to 40 T are reported. The compounds with x=0.5–1 are helical antiferromagnets and those with 1<x?2 are helical ferromagnets or helical antiferromagnets at low and high T, respectively. Mn ions in the system carry average magnetic moment of 3.0±0.2 μ_B that couple antiparallelly to the Fe moments. Easy-plane magnetic anisotropy in the Ce₂Fe_17−xMn_x compounds weakens upon substitution of Mn for Fe. The absolute value of the first anisotropy constant in the Ce₂Fe_17−xMn_x helical ferromagnets decreases slower with increasing temperature than that calculated from the third power of the spontaneous magnetization. Noticeable magnetic hysteresis in the Ce₂Fe_17−xMn_x, x=0.5–2, helical magnets over the whole range of magnetic fields reflects mainly irreversible deformation of the helical magnetic structure during the magnetization of the compounds. A contribution from short-range order (SRO) magnetic clusters to the magnetic hysteresis of the helical magnets has been also estimated.     

基于伊辛模型的Fe0.5Mn0.1Al0.4 合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序 合金的磁化强度和磁熵变。首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场（温度）的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对 合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场h=0.14时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变 达到了正向最大值,极值的位置对应于体系的相变温度。     

基于伊辛模型的Fe_(0.5)Mn_(0.1)Al_(0.4)合金磁化强度和磁熵变蒙特卡洛模拟

基于伊辛模型的单自旋反转蒙特卡洛算法,考虑了粒子间的最近邻以及次近邻相互作用,研究了无序Fe0.5Mn0.1Al0.4合金的磁化强度和磁熵变.首先,强调了粒子间的次近邻相关作用对体系的磁性和热力学性质的影响,明确了次近邻相互作用系数,证实了低温合金阻挫的存在;其次,研究了在相变温度处(不同磁场下)磁化强度随外加磁场(温度)的变化情况以及磁性粒子对磁化强度的贡献,发现反铁磁性粒子Mn在低温区对Fe0.5Mn0.1Al0.4合金的相变起了主要作用,而高温区体系的相变是由铁磁性粒子Fe贡献的;最后,分析了体系在相变温度处磁熵变数值随外加磁场的变化情况以及磁熵变在不同的外磁场下随温度的变化情况,当外加磁场H=0.14(a.u.)时,Mn粒子在冻结温度处的平均磁化强度为零,体系处于最无序的状态,对应的磁熵变ΔS(0.1,0.14)达到了正向最大值,极值的位置对应于体系的相变温度.     

Magnetic dipolar interaction in ultrathin films: Structural and size effects

A previously introduced formalism for calculating magnetic dipolar anisotropy energy ΔU in atomic layered structures is further developed. Numerical results are presented for ultrathin films with different close-packed (face centered cubic (FCC) [1 1 1]) and non-close-packed (FCC [0 0 1] and body centered cubic (BCC) [0 0 1]) structures. Structural effects become apparent in the magnetocrystalline dipolar anisotropy energy ΔU_L when the ratio between the interlayer separation c and the 2D lattice constant a is changed. Despite the long-range character of the dipolar interaction, it is shown that the number of significantly interacting layers, conventially called coupled layers, is limited and depends on the structural aspect ratio c/a. The slope in the observed linear dependence between ΔU_L and the inverse of the film thickness t is explained by the number of the so-called coupled layers, and not by a surface contribution to volume values. Size effects appearing in ΔU are unambiguously distinguished from structural effects. Effective anisotropy energy ΔU_eff and ΔU are presented for Co [0 0 0 1] and Ni [0 0 1] ultrathin films. It is verified that the dipolar interaction makes an important contribution to ΔU_eff, but the spin reorientation transition is determined by non-dipolar interactions. The former favors the magnetization switching only when the size aspect ratio d/t, with d the characteristic lateral dimension of the film, is sufficiently small. Applications to other layered arrays of magnetic dipoles are straightforward.     

Stepwise magnetization of dispersed ferromagnets due to magnetic interparticle interactions

The main features of stepwise magnetization of dispersed ferromagnets caused by magnetic interparticle interactions are studied using a two-particle model. The ranges of values of the magnetic anisotropy constants of particles and of the dipole-dipole interaction between them are determined over which a reproducible jumpwise change in the magnetization of the system occurs in an external positive magnetic field. The proposed model is shown to explain the main specific features of the fine structure of the ferromagnetic resonance spectra.     

Anisotropy of the magnetocaloric effect in DyNiAl

We present study of the anisotropic magnetocaloric effect in DyNiAl. This compound crystallizes in the hexagonal ZrNiAl-type structure, orders magnetically below and undergoes a further magnetic phase transition at . The Dy-moments are aligned ferromagnetically along the hexagonal c-axis below T_C, the additional antiferromagnetic component develops within the basal plane below T₁. The magnetocaloric effect was evaluated from the magnetization measurements with field applied along the c-axis and perpendicular to it. Our data reveal a strong anisotropy of the magnetocaloric effect. The large effect occurs for field applied along the c-axis whereas the entropy change is small for the perpendicular field direction.     

Tunneling magnetoresistance in small dot arrays with perpendicular anisotropy

The tunneling magnetoresistance (TMR) of a small magnetic dot array with perpendicular anisotropy, is studied by using a resistor network model. Because of the competition between dipolar interaction and perpendicular anisotropy, the TMR ratio can be up to a maximum value (~26%) as predicted by a theoretical model. At moderate dipolar interaction strength, the perpendicular TMR ratio exhibits abrupt jumps due to the switching of magnetic moments in the array when the applied field (normal to the array plane) decreases from a saturation field. This novel character does not occur if the dipolar interaction between particles is quite strong. Furthermore, the effect of the array size N on TMR is also studied and the result shows that TMR ratio fluctuates when N increases for a moderate dipolar interaction strength. When the applied field h_e is parallel to the array plane, the in-plane TMR curve seems insensitive to the dipolar interaction strength, but the maximum TMR ratio (~26%) can also be obtained at h_e=0.     

Modifications in magnetic anisotropy of M—type strontium hexaferrite crystals by swift heavy ion irradiation.

Using vibrating sample magnetometery (VSM) 50 MeV Li³⁺ ion irradiation effects on magnetic properties of single crystals of SrGa_xIn_yFe_12−(x+y)O₁₉ (where x=0, 5, 7, 9; y=0, 0.8, 1.3, 1.0), are reported. The substitution of Ga and In in strontium hexaferrite crystals decreases the value of magnetization sharply, which is attributed to shifting of collinear magnetic order to a non-collinear one. Reduction of magnetization is also explained to be as a result of the occupation of the crystallographic sites of Fe³⁺ by Ga³⁺ and In³⁺. The Li³⁺ ion irradiation decreases the value of magnetization, irrespective of whether the crystals are Ga–In substituted or unsubstituted crystals of SrFe₁₂O₁₉. The result is interpreted in terms of the occurrence of a paramagnetic doublet in crystals replacing magnetic sextuplet as a result of irradiation. Substitution of Ga–In in Strontium hexaferrite decreases the value of anisotropy constant. Irradiation with Li³⁺ ions increases the values of anisotropy field for both substituted as well as unsubstituted crystals. Substitution with Ga–In also decreases the Curie temperature (T_c) but the irradiation with Li³⁺ ions does not affect the curie temperature of either Ga–In substituted or pure SrFe₁₂O₁₉ crystals.     

Magnetic properties of (Ga,Mn)As

A summary of experimental findings and theoretical modelling of micromagnetic properties of zinc-blende ferromagnetic semiconductor (Ga,Mn)As is presented. It is shown that the Zener p–d model explains quantitatively observed Curie temperatures in compensation free samples and that major strain-related effects are correctly accounted for, including the presence of the magnetization reorientation transition, observed as a function of hole concentration and temperature. It is evidenced that a presence of a small trigonal distortion could account for both the presence and properties of uniaxial in-plane magnetic anisotropy.     

Field-induced magnetic reorientation and effective anisotropy of a ferromagnetic monolayer within spin wave theory

The reorientation of the magnetization of a ferromagnetic monolayer is calculated with the help of many-body Green's function theory. This allows, in contrast to other spin wave theories, a satisfactory calculation of magnetic properties over the entire temperature range of interest since interactions between spin waves are taken into account. A Heisenberg Hamiltonian plus a second-order uniaxial single-ion anisotropy and an external magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the spin components (), which are calculated with the help of the spectral theorem. The knowledge of the orientation angle allows a non-perturbative determination of the temperature dependence of the effective second-order anisotropy coefficient. Results for the Green's function theory are compared with those obtained with mean-field theory (MFT). We find significant differences between these approaches. Received 6 April 1999 and Received in final form 9 July 1999