Ferromagnetic resonance in metal films with angular dispersion of magnetic anisotropy

The specific features of the ferromagnetic resonance spectra of metal magnetic films due to the cubic crystalline anisotropy and induced uniaxial magnetic anisotropy have been studied using the statistical model of noninteracting blocks. It has been demonstrated that the inclusion of the angular dispersion of the fields of these magnetic anisotropies leads to a shift, asymmetry, and broadening of the integral resonance curve and to characteristic angular dependences of the resonance field and the resonance line width.     

Energy barrier distributions for magnetic nanoparticles with competing cubic and uniaxial anisotropies

We report in this study the effect of the competition between cubic and uniaxial anisotropies on the magnetic properties of magnetic nanoparticles. We have employed Monte Carlo simulations in our calculations and we have seen that the observed behavior is very different for the cases where easy uniaxial axes are completely random oriented or parallel to an external magnetic field. We have also calculated the effective energy barrier distribution probed during the isothermal magnetic relaxation and a two peak structure is observed only for a random orientation of uniaxial axes.     

外应力场下铁磁/反铁磁双层膜系统中的自旋波

采用自由能极小的方法研究了铁磁/反铁磁双层膜系统在外应力场下的一致进动自旋波性质，即铁磁共振现象. 本模型中铁磁层很薄可看成单畴结构，但具有单轴磁晶各向异性和立方磁晶各向异性；而反铁磁层仅具有单轴磁晶各向异性，但其厚度趋于半无穷. 推导出了该系统的铁磁共振频率和频谱宽度的解析式. 结果表明，外应力场和界面交换耦合或反铁磁磁强度仅在弱磁场下对系统的铁磁共振有影响，且系统的铁磁共振行为按磁场强度可分为两支，其区分弱磁场和强磁场的临界场依赖于外应力场的方向. 另一方面，应力场方向的改变可借助于反铁磁层磁畴变化对铁磁层磁晶各向异性轴有影响. 关键词： 铁磁/反铁磁双层膜 界面耦合强度 铁磁共振 应力场     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Ferromagnetic resonance of nonstoichiometric zinc ferrite and cobalt-doped zinc ferrite nanoparticles

Ferromagnetic resonance spectra of zinc ferrite and cobalt doped zinc ferrite nanoparticles, measured at various temperatures, exhibit an invariant point at a given field. This makes it possible to determine the equation relating the resonance field shift to the peak-to-peak linewidth. When particles are frozen in a matrix in a magnetic field, the anisotropy constant of the material can be derived from the angular variation of the resonance field. This procedure is useful to determine the thermal dependence of the anisotropy constant, but is shown to require various freezing temperatures experiments to estimate the accuracy of the deduced anisotropy constant values. It is also shown that the angular dependence of the resonance field is similar for a uniaxial (zinc ferrite) and cubic (zinc ferrite containing 40% cobalt ions) anisotropy. This unexpected result is explained by the weakness of the texturation, leading to a distribution in easy axes directions.     

铁磁和反铁磁双层膜中铁磁共振的研究

采用微磁学理论研究了铁磁/反铁磁双层膜中的铁磁共振现象.本模型将铁磁薄层抽象为一个单晶,具有立方磁晶各向异性和单轴磁晶各向异性,而反铁磁层视为厚度趋近于半无穷,且只有单轴磁晶各向异性.推导出了该系统的铁磁共振频率和频率谱宽度的解析式.数值计算表明,铁磁共振模式分两支,取决于立方磁晶各向异性.而界面的交换耦合,是磁易轴具有单向性的起因.     

On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

外应力场下铁磁/反铁磁双层膜系统中的交换偏置

采用自由能极小的方法研究了铁磁/反铁磁双层膜系统在外应力场下的交换各向异性.本模型中铁磁层具有单轴磁晶各向异性和立方磁晶各向异性，而反铁磁层仅具有单轴磁晶各向异性，但其厚度趋于半无穷.理论上解析地给出了系统的等效交换偏置和钉扎角(它显示了反铁磁层对铁磁层磁化的钉扎作用)与外应力场之间的关系.数值计算表明：系统的等效交换偏置与外磁场的方向有关，而与其大小无关；然而外应力场的大小和方向均对系统的等效交换偏置有影响，其根源在于外应力场的大小和方向都影响着钉扎角. 关键词： 铁磁/反铁磁双层膜 交换偏置 钉扎角 应力场     

Spin-wave resonance as a tool for probing surface anisotropies in ferromagnetic thin films: Application to the study of (Ga,Mn)As

In this paper we provide a concise review of present achievements in the study of spin-wave resonance (SWR) in ferromagnetic semiconductor (Ga,Mn)As thin films. The theoretical treatment of the experimental SWR data obtained so far concentrates specifically on the spherical surface pinning (SSP) model, in which the surface spin pinning energy is expressed by configuration angles (the out-of-plane polar angle $?$ and the in-plane azimuthal angle $\phi$) defining the direction of surface magnetization in the considered thin film. The model is based on a series expansion of the surface spin pinning energy; the terms in the series represent the respective pinning contributions from the cubic anisotropy as well as uniaxial anisotropies. Comparing theory with the reported experimental studies of SWR in thin films of the ferromagnetic semiconductor (Ga,Mn)As, we find that besides the first-order cubic anisotropy, higher-order cubic anisotropies (in the second and third orders) as well as uniaxial anisotropies (perpendicular in the first and second orders, and in-plane diagonal) occur on the surface of this material. We use our results to plot a 3D hypersurface visualizing the angle dependence of the surface spin pinning energy in configurational space. An advantage of this spatial representation is that the shape of the obtained hypersurface allows us to predict new SWR effects that have not yet been observed experimentally. Prospective experimental studies for the verification of this surface pinning model would bring new insight into the surface anisotropy phenomenon in (Ga,Mn)As thin films and help complete the knowledge in this field, the shortage of which in the literature available to date is becoming bothersome.     

Role of anisotropy on the domain wall properties of ferromagnetic nanotubes

In this paper we investigate the role of magneto-crystalline anisotropy on the domain wall (DW) properties of tubular magnetic nanostructures. Based on a theoretical model and micromagnetic simulations, we show that either cubic or uniaxial magneto-crystalline anisotropies have some influence on the domain wall properties (wall size, propagation velocity and energy barrier) and then on the overall magnetization reversal mechanism. Besides the characterization of the transverse and vortex domain wall sizes for different anisotropies, we predict an anisotropy dependent transition between the occurrence of transverse and vortex domain walls in tubular nanowires. We also discuss the dynamics of the vortex DW propagation gradually increasing the uniaxial anisotropy constant and we found that the average velocity is considerably reduced. Our results show that different anisotropies can be considered in real samples in order to manipulate the domain wall behavior and the magnetization reversal process.     

Ferromagnetic resonance in arrays of highly anisotropic nanoparticles

We present in this study computational simulations of the ferromagnetic resonance response of magnetic nanoparticles with a uniaxial anisotropy considerably larger than the microwave excitation frequency (in field units). The particles are assumed to be randomly oriented in a two dimensional lattice, and are coupled by dipolar interactions through an effective demagnetization field, which is proportional to the packing fraction. We have included in the model fluctuations in the anisotropy field (H_K) and allowed variations in the demagnetizing field. We then analyzed the line shape and line intensity as a function of both fields. We have found that when H_K is increased the line shape changes drastically, with a structure of two lines appearing at high fields. The line intensity has a maximum when H_K equals the frequency gap and decreases considerably for larger values of the anisotropy. The effects of fluctuations in H_K and variations in the packing fraction have been also studied. Comparison with experimental data shows that the overall observed behavior is dominated by the particles with lower anisotropy.     

Determination of anisotropy constants of protein encapsulated iron oxide nanoparticles by electron magnetic resonance

Angle-dependent electron magnetic resonance was performed on 4.9, 8.0, and 19 nm iron oxide nanoparticles encapsulated within protein capsids and suspended in water. Measurements were taken at liquid nitrogen temperature after cooling in a 1 T field to partially align the particles. The angle dependence of the shifts in the resonance field for the iron oxide nanoparticles (synthesized within Listeria-Dps, horse spleen ferritin, and cowpea chlorotic mottle virus) all show evidence of a uniaxial anisotropy. Using a Boltzmann distribution for the particles’ easy-axis direction, we are able to use the resonance field shifts to extract a value for the anisotropy energy, showing that the anisotropy energy density increases with decreasing particle size. This suggests that surface anisotropy plays a significant role in magnetic nanoparticles of this size.     

The origin of noncollinear anisotropies and asymmetric magnetization reversal in FM/AFM bilayer system

The effects of the magnitude of the uniaxial anisotropy of a ferromagnet and the cooling field on the noncollinearity between uniaxial anisotropy and induced unidirectional anisotropy in a ferromagnet/antiferromagnet bilayer system are investigated. A diagram of noncollinear anisotropies and relative negative (positive) exchange bias field dependence upon cooling field and uniaxial anisotropy of the ferromagnet is obtained. The numerical result shows that the emergence of noncollinear anisotropies originates from the action of the cooling field and uniaxial anisotropy of the ferromagnet. The noncollinearity strongly depends on the magnitude of cooling field and uniaxial anisotropy of the ferromagnet. Moreover, the effect of noncollinear anisotropies and applied field on asymmetric magnetization reversal is also investigated. Amazingly, when the magnetic field is applied collinearly with unidirectional anisotropy, the hysteresis loop of ferromagnet/antiferromagnet bilayers is always symmetric even if there are noncollinear anisotropies. Our results indicate that the asymmetry of the hysteresis loop only originates from the noncollinearity between the induced unidirectional anisotropy and the applied field, rather than from the noncollinearity between the uniaxial and unidirectional anisotropies.     

Spin configurations in the absence of an external magnetic field in a magnetic bilayer with in-plane cubic or uniaxial anisotropies

The spin configurations in the absence of an external magnetic field have been systematically investigated for a magnetic bilayer system consisting of two ferromagnetic layers separated by a non-magnetic layer with interlayer exchange coupling. Based on a phenomenological model, the conditions for the existence of collinear and non-collinear spin structures were derived for three kinds of magnetic bilayers with different combinations of in-plane cubic and uniaxial anisotropies for the two ferromagnetic layers. The phase diagrams of the spin configurations at zero field were drawn, taking into account the lowest-order anisotropy parameters of both the ferromagnetic layers. The values of the canting angle have been derived analytically and then numerically plotted.     

Dynamical study of remanent magnetization in nanoparticles

For collections of noninteracting nanoparticles, we study the reduced static remanent magnetization, m_R, produced by the removal of a saturating magnetic field. We show that, except for special cases such as easy uniaxial anisotropy, m_R depends on both the ramp-down rate of the field and the energy dissipation rate of the spin dynamics. Using the Landau–Lifshitz equation, we illustrate this result with explicit dynamical calculations of m_R for cubic and for mixed cubic–uniaxial anisotropies.     

Theoretical investigation of ferromagnetic resonance in a ferromagnetic thin film with external stress anisotropy

We use the ferromagnetic resonance(FMR)method to study the properties of ferromagnetic thin film,in which external stress anisotropy,fourfold anisotropy and uniaxial anisotropy are considered.The analytical expressions of FMR frequency,linewidth and the imaginary part of magnetic susceptibility are obtained.Our results reveal that the FMR frequency and the imaginary part of magnetic susceptibility are distinctly enhanced,and the frequency linewidth or field linewidth are broadened due to a strong external stress anisotropy field.The hard-axis and easy-axis components of magnetization can be tuned significantly by controlling the intensity and direction of stress and the in-plane uniaxial anisotropy field.     

Effect of thermal annealing on the magnetic anisotropy of GaMnAs ferromagnetic semiconductor

We have systematically investigated the influence of annealing on the magnetic anisotropy properties of GaMnAs film using an epilayer with a Mn concentration of 6.2%. The GaMnAs epilayer was grown by molecular beam epitaxy and the planar Hall effect measurement was used to monitor the magnetic anisotropy of the film. We found significant annealing-induced changes in the magnetic anisotropy properties of the GaMnAs film that depended on the annealing conditions. For example, the cubic anisotropy that gave a four-fold symmetry of magnetic easy axes decreased while the uniaxial anisotropy that gave a two-fold symmetry of magnetic easy axes increases in the samples annealed temperature below 300 °C. In particular, the uniaxial anisotropy along the [010] direction in as-grown GaMnAs film changed to the [100] direction by rotating by 90° after the sample was annealed at 300 °C for 3 h. This investigation thus indicates that the magnitude and the direction of the magnetic anisotropy in the GaMnAs film can be effectively controlled by choosing an appropriate annealing time and temperature.     

Analysis of antiferromagnetic resonance in KNiF3

We have compared theoretical calculations of the temperature dependence of the antiferromagnetic resonance field for KNiF₃, a cubic crystal, with the experimental data obtained by other authors. We have discussed the applicability to the cubic case of Kittel's equations for a uniaxial system. We have used experimental values from the literature for the magnetic susceptibilities and anisotropy in the expression for the antiferromagnetic resonance field.     

外应力场下铁磁/反铁磁双层膜系统的铁磁共振性质

从系统能量出发，采用Smith和Beljers理论方法研究了铁磁/反铁磁双层膜系统在外应力场下的铁磁共振现象.本模型中铁磁薄层具有单轴磁晶各向异性和立方磁晶各向异性，而反铁磁层非常薄因而其能量可忽略.推导出了该系统的铁磁共振频率和频谱宽度的解析式.结果表明：外应力场仅在低磁场下对具有立方磁晶各向异性系统的铁磁共振有影响，且区分弱磁场和强磁场的临界场依赖于外应力场的方向. 关键词： 铁磁/反铁磁双层膜 交换偏置 铁磁共振 应力场     

Development of magnetic anisotropies in ultrathin epitaxial films of Fe(001) and Ni(001)

Ultrathin films, bcc Fe(001) on Ag(001), fcc Fe(001) on Cu(001) and Fe/Ni(001) bilayers on Ag, were grown by molecular beam epitaxy. A wide range of surface science tools were employed to establish the quality of epitaxial growth. Ferromagnetic resonance and Brillouin light scattering were used to extract the magnetic properties. Emphasis was placed on the study of magnetic anisotropies. Large uniaxial anisotropies with easy axis perpendicular to the film surface were observed in all ultrathin structures studied. These anisotropies were particularly strong in fcc Fe and bcc Fe films. In sufficiently thin samples the saturation magnetization was oriented perpendicularly to the film surface in the absence of an applied field. It has been demonstrated that in bcc Fe films the uniaxial perpendicular anisotropy originates at the film interfaces. In situ measurements indentified the strength of the uniaxial perpendicular anisotropy constant at the Fe/vacuum, Fe/Ag and Fe/Au interfaces asK _us = 0.96, 0.63, and 0.3 ergs/cm² respectively. The surface anisotropies deduced for [bulk Fe/noble metal] interfaces are in good agreement with the values obtained from ultrathin films. Hence the perpendicular surface ansiotropies originate in the broken symmetry at abrupt interfaces. An observed decrease in the cubic anisotropy in bcc Fe ultrathin films has been explained by the presence of a weak 4th order in-plane surface anisotropy,K _1S=0.012 ergs/cm². Fe/Ni bilayers were also investigated. Ni grew in the pure bcc structure for the first 3–6 ML and then transformed to a new structure which exhibited unique magnetic properties. Transformed ultrathin bilayers possessed large inplane 4th order anisotropies far surpassing those observed in bulk Fe and Ni. The large 4th order anisotropies originate in crystallographic defects formed during the Ni lattice transformation.