Uniaxial Crystalline Anisotropy Research Articles

Angular and linear momentum of excited ferromagnets

The angular momentum vector of a Heisenberg ferromagnet with isotropic exchange interaction is conserved, while under uniaxial crystalline anisotropy the projection of the total spin along the easy axis is a constant of motion. Using Noether's theorem, we prove that these conservation laws persist in the presence of dipole-dipole interactions. However, spin and orbital angular momentum are not conserved separately. We also define the linear momentum of ferromagnetic textures. We illustrate the general principles with special reference to the spin transfer torques and identify the emergence of a non-adiabatic effective field acting on domain walls in ferromagnetic insulators.

Optimization of perpendicular magnetic anisotropy tips for high resolution magnetic force microscopy by micromagnetic simulations

Magnetic Force Microscopy (MFM) tip coated with perpendicular magnetic anisotropy film (PMA tip) is one of the choices for high resolution imaging at low scan height (SH), since it has negligible tip–sample interaction related to its stable magnetic state, sharp, and small tip stray field. In this work, detailed micromagnetic studies are carried out to understand the effect of geometrical and magnetic parameters including the cone angle θ of the PMA tip, intergrain exchange constant \(A_{2}^{*}\), saturation magnetization M s and uniaxial crystalline anisotropy constant K 1 of the tip coating on the MFM tip resolution. To evaluate the resolution performance of the optimized PMA tip, MFM images of high-density granular recording media and patterned media are simulated. We find that, for the PMA tip and its coating, a cone angle in a range of 36.9∘ to 53.1∘, a saturation M s of 700 emu/cm3, a large uniaxial crystalline anisotropy constant K 1 (>4.9×106 erg/cm3) and a high intergrain exchange constant \(A_{2}^{*}\) of (0.3–1.0)×10−6 erg/cm are optimized conditions for high resolution imaging. The optimized PMA tip has an excellent performance on imaging of high-density thin film media (bit size of 8×16 nm2) at low SH of 2–8 nm and bit pattern media with a pitch of 50 nm, edge-edge spacing of 5–15 nm at SH of 8–15 nm.

Quantitative analysis of interaction between domain walls and magnetic nanoparticles

We have studied the potential energy and effective field induced by the presence of a single superparamagnetic particle above a magnetic domain wall in a 5 nm ferromagnetic film (Ms = 800 emu/cm3) with uniaxial crystalline anisotropy (Ku < 107 erg/cm3). The wall width, wall type (head-to-head, Néel, and perpendicular Bloch), film dimensions, particle height, and external applied field are found to affect the performance of particle sensing systems. Results and optimization strategies derived from this model are presented. The calculated change in depinning field (ΔHdp) is compared against experimental data and micromagnetic simulation. This comparison provides justification for further development in terms of integration with micromagnetic simulations.

Effects of crystalline and elastic anisotropies on coercivity of longitudinally oriented CoCrPt thin films grown on CrW underlayer

The longitudinal CoCrPt thin films have been prepared on CrW underlayer at room temperature. The dependence of CoCrPt’s structure and magnetic properties on the Pt content was investigated. The addition of platinum element in the CoCrPt magnetic layer increases the lattice constant and longitudinal coercivity of the CoCrPt thin films. The coercivity mechanism of the CoCrPt thin film is analyzed by using the micromagnetic models, with careful discussions of the uniaxial crystalline anisotropy and the magnetostriction. It is found that the magnetostriction effects play an important role on the coercivity mechanisms when the Pt content is more than 15 at. % Pt concentrate.

Effect of discrete track medium at high areal density

The degradation of SNR caused by the higher uniaxial crystalline anisotropy field (Hk) of medium and small write fields of narrower write width is one of the problems for achieving higher areal density. The SNR dependence on Hk of a medium with different write fields of head using the discrete track medium (DTM) is investigated by using micromagnetics simulation. As a result, the curves of SNR as a function of Hk have peak values. In DTM, the peak values of SNR are almost constant at any Hk of the medium and different write fields. Higher SNR is realized even at low Hk and small write field in DTM.

Energy barrier and effective thermal reversal volume in columnar grains

A method to determine the minimum energy path between two stable states in a magnetic system is used to investigate magnetic reversal of an irregularly shaped columnar grain. The method describes the magnetization reversal process initiated by thermal excitations in zero applied field or fields below the intrinsic switching field. In addition to the energy barrier, an effective volume V eff is calculated as a function of material exchange interaction, uniaxial crystalline anisotropy, and particle length. The minimum energy barrier paths follow that of intrinsic switching where with decreasing exchange the reversal modes go from uniform rotation to end nucleation and subsequent expansion to reversal by vortex excitation. The effective reversal volume decreases with decreasing exchange and increasing crystalline anisotropy. Decreasing the particle length also decreases the effective volume once the length becomes less than the excitation length. A very simple analytic wall model nicely indicates these trends. Analysis of measured thermal reversal fields for CrO 2 and Fe explain the inferred effective volumes in these particles.

Magnetic properties of Fe/ZnSe and Fe/GaAs heterostructures investigated by ferromagnetic resonance and SQUID measurements

(0 0 1) Fe-films on GaAs and ZnSe substrates show steps in the hysteresis. For Fe on GaAs, which exhibits small damping in FMR (9–70 GHz), the step is attributed to the critical ratio, 0.58, of the uniaxial in-plane and crystalline anisotropy. For the 60 nm Fe-film on ZnSe, the step in the hysteresis loop is caused by different anisotropy at the top and bottom surfaces.

Frequency pulling effects in the quasi-two-dimensional ferromagnet54Mn−Mn(COOCH3)2⋅4H2Ostudied by nuclear orientation techniques

Continuous wave NMR thermally detected by nuclear orientation has been used to investigate the magnetic properties and spin dynamics of the quasi-two-dimensional ferromagnet ${}^{54}\mathrm{Mn}\ensuremath{-}\mathrm{Mn}({\mathrm{COOCH}}_{3}{)}_{2}\ensuremath{\cdot}4{\mathrm{H}}_{2}\mathrm{O}.$ The system exhibits a frequency pulling effect due to the indirect Suhl-Nakamura interaction between nuclear spins and the electronic spin excitation spectrum is related to the coupling strength of the nuclear spins. The temperature dependence of the frequency pulling effect was measured for the two crystalline sublattices Mn1 and Mn2 in low magnetic field. The spectra show a structure not predicted theoretically. The current theory is valid only for $I=1/2$ with uniaxial crystalline anisotropy fields. The theory of frequency pulling has been extended here to the case of $I>~1/2$ and nonuniaxial crystalline anisotropy fields and the resonant frequencies and linewidths have been calculated as a function of temperature. The new theory and data agree well in terms of the magnitude and temperature dependence of the frequency pulling. Discrepancies are likely due to simplifying assumptions when calculating the electronic magnon spectrum. Classical and quantum numerical simulations confirm qualitatively the predictions of the model.

Determination of a zero-field splitting parameter D in Mn 12Ac below 20 K

Molecular magnet Mn 12Ac has a large molecular spin S=10. The uniaxial crystalline anisotropy splits the energy levels in zero magnetic field into 10 doublets and one singlet. The simplest Hamiltonian in magnetic field H z for this symmetry is H=−DS z 2−gμ B μ 0HS z . The zero-field splitting parameter D has been determined from measured M( H) in weak magnetic field at different temperatures. The approximate value is D=0.7 K .

Surface-induced low-field instability of antiferromagnetic multilayers

We discuss the surface-induced low-field instability of the antiferromagnetic phase of magnetic multilayers. The threshold field is calculated analytically for multilayers of arbitrary thickness containing an even number of layers. We show that the threshold is given by ${H}_{\mathrm{SSF}}=\sqrt{{H}_{e}{H}_{a}{+H}_{a}^{2}},$ where ${H}_{e}$ and ${H}_{a}$ are the effective exchange and anisotropy fields. The effective anisotropy field ${H}_{a}$ may include both uniaxial and fourfold crystalline anisotropy. Numerical simulations of the equilibrium phases, based on a self-consistent effective field method, are used to obtain the magnetization pattern. We find that thick uniaxial multilayers display a three-stage transition from the antiferromagnetic to the field-aligned phases, whereas in thin multilayers the transition is from the antiferromagnetic to a nearly spin-flop structure, which gradually aligns with the applied field. If the films composing the multilayer have uniaxial and crystalline anisotropy, the magnetization profile in the multilayer and the nature of the transition depend on the relative values of the uniaxial and crystalline anisotropies.

Magnetic viscosity in high-density recording

For future ultrahigh-density magnetic recording, the magnetic viscosity in thin-film media will become an issue due to the drastic reduction in grain size. An algorithm combining a Monte Carlo method and molecular dynamics was employed to study the thermal effects in thin-film media. The component of the field perpendicular to the plane defined by the axes of shape anisotropy and uniaxial crystalline anisotropy makes it necessary to use the three-dimensional energy surface to find the minimum energy barrier. This barrier is used to sample the reversal rate and the elapsed time. Hysteresis loops for various KuV/kT ratios and sweep times are simulated. Isolated and di-bit transitions are written, taking into account thermally assisted switching. After the head field is turned off, the subsequent thermal decay is computed for time spans as long as 6 months. Significant aftereffect is found for grain volumes about twice that for ordinary superparamagnetism.

Magnetization processes in small ferromagnetic particles with inhomogeneous demagnetizing field and uniaxial anisotropy

A numerical micromagnetic method was used to calculate the magnetization processes in small rectangular parallelepipeds with uniaxial crystalline anisotropy and inhomogeneous demagnetizing fields. With the material parameters of the Fe 14Nd 2B phase the temperature dependence of the nucleation field was calculated for a particle size of 10 μm. The microstructural parameters describing the nucleation field were determined. They are in excellent agreement with measurements on Fe 14Nd 2B sintered magnets. The stable remanent state was calculated for different ratios of the anisotropy and the magnetostatic energy for arbitrary materials. The critical radius for single domain particles was determined by comparing the stable equilibrium states. The demagnetization curve for particles with low and high crystalline anisotropy compared to the stray field energy were calculated. The crossover from hard magnetic to soft magnetic behavior was investigated. The shape of the demagnetization curve as well as the coercivity changes drastically.

Computer simulation of magnetization reversal: The effect of shape and uniaxial crystalline anisotropy

The Landau–Lifshitz–Gilbert equation has been used to compare the hysteresis loops and magnetization-reversal mechanisms of a cubic particle, with uniaxial crystalline anisotropy, and a 2:1-aspect-ratio elongated particle. The switching fields of these particles were 700 Oe. The cubic particle exhibited a square hysteresis loop, but the elongated particle had a nonsquare hysteresis loop due to the tilting of spins in the surface layers. Magnetization reversal for the elongated particle was initiated at the surface layers. For the cubic particle the reversal was initiated at an edge of the particle and spread through to the central elements. Differences between the hysteresis loops and reversal mechanisms, for the different particles, are attributed to the different nature of the magnetic anisotropies.

Size dependence of the nucleation field of rectangular ferromagnetic parallelepipeds

A numerical micromagnetic model based on the finite difference method was used to calculate the nucleation field H N of a rectangular ferromagnetic parallelepiped as a function of the edge length d . The inhomogeneous equilibrium states of the magnetization M s and the magnetic stray field H s were calculated in the range 0.01 μm < d < 100 μm. The particle was assumed to have uniaxial crystalline anisotropy, the easy axis being perpendicular to the lateral edge. The nucleation field H N was found to decrease with increasing particle size d . For d = 100 μm approximately half of Brown's ideal value 2 K 1 / M s was obtained. The reversal process can be divided into two parts: For 0 < H ext < H N reversible inhomogeneous rotation processes occur. At the corners of the particle the stray field H s leads to partial demagnetization even before H N is approached. For H ext = H N an irreversible reversal process occurs. The metastable state transforms into the stable one. The hysteresis curve is nearly rectangular. In the vicinity of the corners the magnitude of H s is less than 5.6π M s .

Ferromagnetic Crystalline Anisotropy of Pd1-xFexAlloys. III. \(0.38\lesssim{x}\lesssim0.5\), L10-Type Ordered Phase

The uniaxial magnetic crystalline anisotropy of Pd 1- x Fe x in tetragonal L1 0 -type ordered phase (\(0.38\lesssim{x}\lesssim0.50\)) was obtained from magnetization curves of quasi-single crystal samples in a magnetic field up to 100 kOe. The first anisotropy constant K u1 at 4.2 K of stoichiometric composition ( x =0.5) was estimated to be 2.1×10 7 erg/cm 3 . The constants of x =0.42 and 0.38 were 1.5×10 7 and 0.8×10 7 erg/cm 3 , respectively. From the present result the most evident magnetic field dependence of torque curve found in x =0.42 (reported in Part II) was attributable to the difficulty to suppress the ordered atomic arrangement due to the highest order-disorder transition temperature of this sample. K u2 was much smaller than K u1 for all compositions.

Magnetization reversal in CoCr perpendicular thin films

Computer simulation has been utilized to study magnetization reversal processes in CoCr perpendicular films. The model is based on the columnar structure of the film. Each column is considered to be a single crystal with perpendicular uniaxial crystalline anisotropy. The model assumes that each column is always uniformly magnetized even during its magnetization reversal. The gyromagnetic equation of motion with phenomenological Landau–Lifshitz damping is utilized to describe the magnetization rotation of this coupled system. The study focuses on the collective magnetization reversal modes of the particles due to magnetostatic interactions and intergranular exchange coupling. Low nucleation fields occur which are characterized by a planar chain nucleation mode. This yields coercivities equal to or less than the crystalline anisotropy field 2K/M. It is argued that, due to this collective process, the uniform rotation reversal mechanism for the individual particles in the film is energetically more favorable than nonuniform reversal, such as curling. Intercolumn exchange coupling significantly reduces the coercivity and an increase of the exchange coupling strength changes the magnetization behavior from ‘‘particulate’’ to ‘‘continuous.’’

Magnetization processes in ferromagnetic cubes

A cubic discretization procedure of the micromagnetic energy functional is used to carry out numerical studies of the magnetization process in ferromagnetic cubes. Equilibrium magnetization configurations and their switching behavior are calculated for particle sizes in the range from 100 to 550 Å. In the model calculations the particles are assumed to have uniaxial crystalline anisotropy with an anisotropy constant of 18 500 erg/cm3, a saturation magnetization of 370 emu/cm3, and an exchange constant of 10−6 erg/cm. For particle sizes smaller than 520 Å the remanent state has a flowerlike magnetization configuration. Beyond 520 Å this state is replaced by a vortex structure about the easy axis. For particles smaller than 450 Å switching occurs by approximately uniform rotation of the flower state. The switching fields are larger than the corresponding Stoner–Wohlfarth value. Beyond 450 Å the application of an external field leads to the formation of a vortex configuration. The switching of the vortex configuration involves rotation of the vortex axis at a reduced value of the switching field. The angular dependence of the coercive field is calculated for particle sizes of 200, 400, and 550 Å.

Catastrophe model for micromagnetics.

It is shown that transition at the Curie point and uniaxial crystalline anisotropy exhibit catastrophes which have the same morphology as well-known elementary catastrophes like the cusp and the swallowtail. It is possible to understand micromagnetics as conflict between attractors of dynamical systems. Catastrophe theory allows great geometrical insight into the mathematical background of micromagnetics. It appears as a geometrical study of metastability that can have general significance.

Magnetization reversal for barium ferrite particulate media

A perpendicularly oriented Ba ferrite particulate medium was investigated with regard to the magnetization reversal process. Coercivity and remanence coercivity for the medium were found to be decreasing and increasing functions, respectively, of the angle between the easy axis and the applied field. The angular dependence of remanence coercivity, being supported by the rotational hysteresis integral value, implies that the magnetization reversal process for the medium is incoherent. A fanning model for the two aligned particles with uniaxial crystalline anisotropy, was developed. This model yields variable angular dependencies of coercivity for varying ratios of a crystalline anisotropy field (H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</inf> to a dipole-dipole interaction field (H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> ). Taking an appropriate H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</inf> /H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> value, the model can predict the angular dependence of coercivity and remanence coercivity for the medium.

Distinctive characteristics of barium ferrite media

Barium ferrite magnetic recording media have demonstrated the capability of achieving much higher recording densities than other particulate media. Even though the best performance is obtained with perpendicularly oriented media, longitudinally oriented and non-oriented Ba-ferrite media also exhibit exceptional recording characteristics. These media have very distinctive magnetic and switching field (SFD) characteristics, exhibiting very small SFD values, almost rectangular remanence loops (indicating no irreversible losses over a wide range of reverse fields), and minor loops very close to the major loop until the driving field becomes almost equal to the coercivity. These unique magnetic and switching field characteristics can explain the very low or negligible demagnetization losses (including recording demagnetization) which we observe in Ba-ferrite media and which result in their outstanding recording performance. The fundamental reasons for these unique magnetic and switching field properties are the predominant high uniaxial crystalline anisotropy of the platelets and their single domain character. On the negative side, the high anisotropy field is directly implicated as the main reason behind the marginal overwrite modulation which characterizes these media.