Magnetic Anisotropy Coefficient Research Articles

Small polaron hopping and tunneling mechanisms in Ba0.9La0.1Fe12O19 hexaferrite ceramic at low temperatures

The correlation between dielectric relaxation and conduction mechanisms in the Ba0.9La0.1Fe12O19 ceramic hexaferrite, at temperatures below 100 K was investigated. The sample was prepared using the conventional solid-state reaction method. X-ray diffraction analysis indicated that the sample is composed of a hexagonal BaFe12O19 phase (lattice parameters a = 5.8778(6) Å and c = 23.170(3) Å) and a small proportion of hematite (α-Fe2O3). The average grain size is 1.48 ± 0.4 μm, with irregular hexagonal and agglomerated grains. The magnetic hysteresis curve shows characteristics typical of ferro and ferrimagnetic materials, with an effective magnetic anisotropy coefficient of 0.960×106 emu/cm3 and an anisotropy field of 1.587×104 Oe. A dielectric relaxation process is observed between 50 and 100 K, with an activation energy of 60.4 ± 0.4 meV and a characteristic relaxation time of 2.09 ×10−10 s, mainly attributed to the electrical behavior of the grains. Two conduction mechanisms were identified: small polaron tunneling (high temperatures and low frequencies) and correlated barrier hopping of electrons (low temperatures and high frequencies). The activation energy for free polaron formation, according to the Komine-Iguchi hopping polarization model, was 7.12 ± 0.02 meV. In the dielectric modulus relaxation process between 30 and 54 K, the activation energy was 40.8 ± 0.9 meV, with a characteristic relaxation time of 2.41×10−10 s. The small polaron conductivity in the grain region was 67.52 meV and 54.0 meV in the grain boundary region. The results highlight that the polarization and conduction mechanisms in this ceramic at low temperatures are dominated by small polaron hopping and tunneling, and emphasize the influence of La3+ doping on the structural, magnetic, and electrical properties of barium hexaferrite.

Spintronic virtual neural network by a voltage controlled ferromagnet for associative memory

Recently, an associative memory operation by a virtual oscillator network, consisting of a single spintronic oscillator, was examined to solve issues in conventional, real oscillators-based neural networks such as inhomogeneities between the oscillators. However, the spintronic oscillator still carries issues dissipating large amount of energy because it is driven by electric current. Here, we propose to use a single ferromagnet manipulated by voltage-controlled magnetic anisotropy (VCMA) effect as a fundamental element in a virtual neural network, which will contribute to significantly reducing the Joule heating caused by electric current. Instead of the oscillation in oscillator networks, magnetization relaxation dynamics were used for the associative memory operation. The associative memory operation for alphabet patterns is successfully demonstrated by giving correspondences between the colors in a pattern recognition task and the sign of a perpendicular magnetic anisotropy coefficient, which could be either positive or negative via the VCMA effect.

Solid phase epitaxy of perpendicular magnetic BaFe12O19 flexible sheets on a mica substrate

Epitaxial M-type BaFe12O19 flexible sheets, exhibiting RT perpendicular magnetization, were synthesized on mica substrates through the solid phase epitaxy method. The [110] and [001] directions of the BaFe12O19 layer were parallel to the [010] and [001] directions of the mica, respectively. In the synthesis process, amorphous BaFe12O19 films were firstly prepared on Al2O3-buffered mica (001) substrates and then annealed at 800 °C–900 °C in air for single crystallization. During optimization of the synthesis, we found that preparation of the buffer layer and controlling annealing temperature are important for obtaining the epitaxial sheet. The sheets exhibited perpendicular ferrimagnetism with large saturated magnetization (60 Am2 kg−1) and magnetic anisotropy coefficient (2.1 × 105 J m−3) at 300 K, together with flexibility.

Sub-volt switching of nanoscale voltage-controlled perpendicular magnetic tunnel junctions

Magnetic random-access memory (MRAM) based on voltage-controlled magnetic anisotropy in magnetic tunnel junctions (MTJs) is a promising candidate for high-performance computing applications, due to its lower power consumption, higher bit density, and the ability to reduce the access transistor size when compared to conventional current-controlled spin-transfer torque MRAM. The key to realizing these advantages is to have a low MTJ switching voltage. Here, we report a perpendicular MTJ structure with a high voltage-controlled magnetic anisotropy coefficient ~130 fJ/Vm and high tunnel magnetoresistance exceeding 150%. Owing to the high voltage-controlled magnetic anisotropy coefficient, we demonstrate sub-nanosecond precessional switching of nanoscale MTJs with diameters of 50 and 70 nm, using a voltage lower than 1 V. We also show scaling of this switching mechanism down to 30 nm MTJs, with voltages close to 2 V. The results pave the path for the future development and application of voltage-controlled MRAMs and spintronic devices in emerging computing systems.

Elimination of the skyrmion Hall effect by tuning perpendicular magnetic anisotropy and spin polarization angle

The skyrmion Hall effect has been regarded as a critical issue in skyrmion future applications, which indicates that it causes skyrmions to deviate from the direction of the driving force and leads to the destruction of skyrmion at the sample edge. In the meanwhile, perpendicular magnetic anisotropy is a promising method to manipulate the skyrmion motion by adding a material with high crystalline anisotropy into an existing material. It has been also investigated that spin polarization angles also have an influence on the skyrmion motion directions. Here, we statistically study a bilayer nanostructure, where the skyrmion Hall effect would be eliminated by modifying perpendicular magnetic anisotropy coefficients and spin polarization angles. Our results may provide a useful method for the design of skyrmion based spintronics devices without skyrmion Hall effect, to meet the need for future high-density information storage applications.

Investigation of the unusual temperature dependence of magnetic anisotropy in nanocrystalline Fe96Zr4 films

We report on the temperature dependence of effective magnetic anisotropy in nanocrystalline Fe96Zr4 films fabricated by radio frequency sputtering. The temperature dependence of effective magnetic anisotropy presents an abnormal temperature dependence which found to increase with increasing temperature. This change was investigated using the law of approach to saturation and it was found that as the temperature increases from 20 to 280 K, the effective magnetic anisotropy coefficient increases from 1.44 × 103 J/m3 to 5.64 × 103 J/m3. This particular observation in increasing effective magnetic anisotropy with temperature was discussed by taking into account the stress-induced magnetic anisotropy contribution which becomes more dominant upon heating the film. It is shown that the magnetization reversal occurs through domain wall motion, which is influenced by the presence of inhomogeneities in the samples.

The first and the second-order magnetic anisotropy in a Fe/MgO system under electric field: a first-principles study

We studied the first- and the second-order magnetic anisotropy coefficients, K 1 and K 2, of Fe atomic monolayers on a MgO(001) substrate under an electric field by using first-principles calculations. Special attention has been paid to the effect of the Fe layer thickness and the Cr-capping layer on the electric field dependence of K 1 and K 2. The results show that for all the systems we studied the electric field derivatives of K 1 and K 2 have the opposite sign to each other as observed in recent experiments.

Structure of head-to-head domain wall in cylindrical amorphous ferromagnetic microwire and a method of anisotropy coefficient estimation

A model of head-to-head domain wall in the cylindrical amorphous ferromagnetic microwire is proposed by treating a class of exact particular solutions of Landau-Lifshitz-Gilbert equation in cylindrical coordinates, which are obtained for appropriate boundary conditions. It is shown that both the magnetic anisotropy coefficient value in the center of cross-section and the rate of its value change along the radius directly determine the domain wall structure. A flexural planar domain wall is visualized and analyzed under the influence of various parameters of the microwire. A method of anisotropy coefficient estimation is developed: the derived formula for mobility is used to evaluate values of anisotropy coefficient of the wire near its symmetry axis, the length of the head-to-head domain wall can be used for evaluation of radial dependence of anisotropy coefficient. For extraction of anisotropy coefficient the dynamic properties of the head-to-head domain wall propagation are investigated experimentally for microwires with different anisotropy coefficients: in stressed state and after partially stress removed state. The theory fit the measurements with linear dependence of the velocity on the magnetic field. The particular case of planar domain wall, corresponding to radial independent anisotropy coefficient, is also shown for a comparison.

Voltage-Assisted Magnetic Switching in MgO/CoFeB-Based Magnetic Tunnel Junctions by Way of Interface Reconstruction.

Engineering of interfacial structures has become important more than ever before to find new scientific observations and to create novel applications. Here, we show that the interface reconstructed by atomic layer-thick Mg insertion substantially improved the magneto-electrical properties of perpendicular magnetic tunnel junctions essential for modern spintronic applications. The 0.2-0.4 nm-thick Mg inserted between the MgO tunnel barrier and CoFeB ferromagnet restructured the interface in such ways as to protect the CoFeB from overoxidation, to strengthen the texture, to make the interfacial roughness smooth, and to relax the mechanical stress. Observed were great increases in the perpendicular magnetic moment and perpendicular magnetic anisotropy of the CoFeB by 2.1 and 1.8 times, respectively, which can be ascribed to the optimum interfacial condition because of the least possible chemical damage. The strong enhancement of (010) in-plane and (001) out-of-plane texture and of interfacial roughness led to a significant increase in the tunnel magnetoresistance by 4.4 times from 13.2 to 57.6% by the insertion. Most importantly, such optimum chemical and physical structures at the interface could modulate the perpendicular magnetic properties by an electric field. The electric field-controlled magnetic anisotropy coefficients became symmetrically bipolar to the electric field and were increased over 100 fJ/V·m, which is 6 times larger than one found before the Mg insertion. As a result, we could successfully demonstrate the voltage-induced magnetization switching of the perpendicular magnetic tunnel junctions with the help of an external magnetic field. Our findings will ignite further study on the new way of electrical control over magnetic switching and provide an essential ingredient to realize electric field-driven energy-effective magneto-electronic devices.

Single-particle mechanism of magnetostriction in magnetoactive elastomers.

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of magnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient K is much larger than the shear modulus µ of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.

Magnetic properties of nano-scale hematite, α-Fe2O3, studied by time-of-flight inelastic neutron spectroscopy.

Samples of nanoscale hematite, α-Fe2O3, with different surface geometries and properties have been studied with inelastic time-of-flight neutron scattering. The 15 nm diameter nanoparticles previously shown to have two collective magnetic excitation modes in separate triple-axis neutron scattering studies have been studied in further detail using the advantage of a large detector area, high resolution, and large energy transfer range of the IN5 TOF spectrometer. A mesoporous hematite sample has also been studied, showing similarities to that of the nanoparticle sample and bulk α-Fe2O3. Analysis of these modes provides temperature dependence of the magnetic anisotropy coefficient along the c-axis, κ1. This is shown to remain negative throughout the temperature range studied in both samples, providing an explanation for the previously observed suppression of the Morin transition in the mesoporous material. The values of this anisotropy coefficient are found to lie between those of bulk and nano-particulate samples, showing the hybrid nature of the mesoporous 3-dimensional structure.

Characterization of the elastic–plastic region in AISI/SAE 1070 steel by the magnetic barkhausen noise

The magnetic Barkhausen energy in the rolling and transversal directions of AISI/SAE 1070 annealed surfaces is studied. The measurements were made in the samples under applied tension in the elastic–plastic region for different angular directions. The outcomes evidence that the magnetic anisotropy coefficient can be used to characterize the linear and nonlinear elastic limits of the material under tensile stresses. The results also show that the area of the curve corresponding to the angular dependence of the number of Barkhausen jumps with average energy presents a maximum value that corresponds to the elastic limit of the sample.

Modification of interface magnetic anisotropy by ion irradiation on epitaxial Cu/Ni/Cu(002)/ Si(100) films

Various x-ray scattering and magnetic measurements were employed to reveal changes in intrinsic structural and magnetic properties on epitaxial Cu/Ni( t)/Cu(002)/Si(100) thin films (t520, 30, 60, and 90 A) before and after 1 MeV C 1 ion irradiation. Torque magnetometer and grazing incidence x-ray diffraction measurements were carried out to understand relation between magnetic and structural properties, respectively. X-ray reflectivity measurements were performed to characterize interface roughness and intermixing. It is observed that effective magnetic anisotropy values of ion-irradiated films are negative over the entire nickel thickness range and the dominant factor of the reorientation of magnetic easy axis from surface normal to surface parallel is reduction of the interface magnetic anisotropy coefficient in spite of decreased interface mixing after ion irradiation.

First-principles calculations of the magnetic anisotropy energy of Fe-V multilayers

The magnetic anisotropy energy (MAE) of ${\mathrm{Fe}}_{2}{\mathrm{V}}_{6},$ ${\mathrm{Fe}}_{3}{\mathrm{V}}_{5},$ and ${\mathrm{Fe}}_{4}{\mathrm{V}}_{4}$ multilayers are investigated using first-principles spin-polarized and relativistic band-structure calculations based upon the full-potential linearized muffin-tin-orbital method. A strong difference in the MAE and the easy axis of magnetization (calculated for the experimental lattice parameters) is observed between the three studied multilayer systems, with easy axes of (001), (110), and (100) for ${\mathrm{Fe}}_{2}{\mathrm{V}}_{6},$ ${\mathrm{Fe}}_{3}{\mathrm{V}}_{5},$ and ${\mathrm{Fe}}_{4}{\mathrm{V}}_{4},$ respectively. The MAE of the ${\mathrm{Fe}}_{2}{\mathrm{V}}_{6}$ and ${\mathrm{Fe}}_{4}{\mathrm{V}}_{4}$ multilayers agrees well with the experimental data. The origin of this difference of behavior is analyzed, via a study of the influence of the atomic volume as well as a relaxation study of the multilayers with respect to the tetragonal deformation. The important role played by the $c/a$ axial ratio, imposed by the alloying effects, is outlined. The magnetic anisotropy coefficients entering the expression of the MAE, as a function of the directional cosines, are extracted from a series of calculations for four independent spin directions. Finally, the band-filling effects on the MAE are analyzed as well as the different contributions in reciprocal space.

Symmetry-induced magnetic anisotropy in ultrathin planar striped Co films with and without Cu decoration

First-principles local density full potential linearized augmented plane wave method and state-tracking and torque approaches are employed for the theoretical determination of in-plane and off-plane magnetic anisotropy for both free standing planar Co stripes and the same film put on a Cu (100) substrate, with and without nonmagnetic Cu decoration. The easy magnetic axis is found to lie parallel to the stripes for clean Co stripes; the decoration with nonmagnetic Cu is found to switch the easy axis from parallel to perpendicular to the stripes. The magnetic anisotropy coefficients are determined and the magnetic behavior is related to, and explained in terms of, their electronic structures and the fundamental bonding properties of the constituent atoms.

Canonic dependences for single-ion anisotropy and magnetostriction on magnetization

The magnetic anisotropy coefficients and constants of single-ion origin as functions of magnetization have been computed and classified. They are valid for a whole class of untrivial theories and are thus universal or canonic within this class. The role of the anisotropy coefficients as a finite basis of functions spanning the variation of the constants with magnetization and, hence, with temperature and applied field is clarified. The ratio of the zero-temperature anisotropy constants is of crucial importance for the observed type of magnetization dependence of the first anisotropy constant when two basis functions are considered. The method is directly applicable to the analysis of magnetostriction of single-ion origin and serves to identify and quantify three generic types of variation of anisotropy and magnetostriction. It is demonstrated that a compensation point lambda S=0 for the macroscopic magnetostriction constant of amorphous ferromagnets may result from the competition between the lowest and the next-lowest single-ion contributions even if no two-ion contributions are considered. Prospective extensions of the method are given.

Temperature dependence of magnetic anisotropy and magnetostriction.

The first nonvanishing magnetic anisotropy coefficient is calculated as a function of temperature for any spin quantum number and all temperatures below the Curie temperature for the case of face-centered cubic symmetry within the random-phase approximation (RPA). A detailed and instructive comparison between the mean-field and the RPA predictions is carried out. The RPA magnetization curves are also given for spins Sg1/2. Most of the theoretical considerations are quite general as regards lattice type and even decoupling scheme and can thus be applied straightforwardly to other cases of interest. The progress reported here has been attained with the help of a simplified and improved parametric approach and of a recent calculation of the average occupation number of quasiparticle excitations within the RPA. In particular, this approach makes unnecessary the solving of integral equations so that the proposed procedure is especially simple and practically versatile in applications to any particular anisotropic material.

Analysis of single-domain particle flow orientation data

Rodlike single-domain particles tend to orient parallel to the streamlines in an extensional flow, resulting in anisotropy of the bulk magnetic permeability. The suspension is made to flow from a large chamber into a narrow tube which has an oscillator coil wound near its entrance. Particle orientation parallel to the magnetic field of the coil decreases the inductance. (Small changes in orientation can then be accurately measured with a countertimer.) Since both hydrodynamic orientation and Brownian motion depend on the shape characteristics of the particle, the orientation data provide information about the ‘‘effective-particle’’ shape. The gradients of the inductance with respect to flowrate, in the limits of high and low flowrate, are used to calculate relative changes in the effective-particle rotary diffusion coefficient. This method is demonstrated with a γ-Fe2O3 suspension over a wide range of surfactant concentration. Changes in the particle magnetic properties calculated from the flow orientation data are consistent with an increase in the magnetic anisotropy coefficient by the adsorbed surfactant.

Formation and magnetic properties of ultrafine spinel ferrites

Investigations of the formation and magnetic properties of Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δ</inf> Co <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-δ</inf> Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> formed in alkaline aqueous solution by the coprecipitation method are covered. The lattice constant of these ferrites apparently reduced with decreasing average particle size below about 500 Å. The coercive force ratio of MnFe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> and Co-Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> is 1 to 50 and equal to that of the crystal magnetic anisotropy coefficient K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> of sintered ferrites. As the average particle size became larger, the coercive force and the apparent remanence increased linearly, and superparamagnetic critical size was determined. The sizes range, for example, from 50 to 100 Å for CoFe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> and from 150 to 200 Å. for MnFe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> . From the correlation between the average particle size and their magnetization, the limit size of ferromagnetic critical particle was also determined. Results obtained in this experiment are approximately in accord with Néel's Version of the theory on thermal fluctuation aftereffect of magnetic fine particles.

Temperature-dependent crystal field effects in the spin-wave spectrum of terbium

A variational principle for the free energy is applied to the Hamiltonian for terbium in the ferromagnetic region to study the effect of interactions among spin waves having their origin in the strong crystalline electric fields. At high temperatures this `crystal field renormalization' has the effect of multiplying the crystal field parameters appearing in the spin-wave energies of the non-interacting theory by powers of the reduced magnetization. The powers are found to be close to those associated with the corresponding magnetic anisotropy coefficients. This leads to an appreciable temperature dependence of the spin-wave energies which, after allowing for exchange renormalization, appears to be in reasonable agreement with the inelastic neutron scattering results of Moller and Houmann. The ferromagnetic resonance measurements of Bagguley and Liesegang and of Stanford and Young have also been analysed and found to be consistent with this picture.