Ivo Klik

Field orientations and sweep rate effects on magnetic switching of Stoner–Wohlfarth particles

Field angles and sweep rate dependence of coercivity of the Stoner–Wohlfarth (S‐W) particles are studied based on the decay‐rate model. An analytic expression of the hysteresis loops based on the model is obtained as a function of applied field for various frequencies at various field angles with respect to the easy axis. Variation of the coercivities versus the sweep rate (measurement frequency), field angles, anisotropy constant, activation volume, and the combination thereof, and the distribution of easy axis, etc., have been obtained. Comparison with the thermal‐equilibrium and S‐W hysteresis loops are made. Coercivities of such a system generally increase with increasing sweep rate, anisotropy constant and activation volume, etc., hence decreases with increasing sweeping period. As a function of the field angles, the coercivity curve turns flat with increasing field angles and sweeping period.

Structure and magnetic anisotropy of epitaxial fcc‐Co(110) and hcp‐Co(11̄00) films

Fcc‐Co(110) and hcp‐Co(1100) films of 200 A thickness were grown on MgO(110) and bcc‐Cr(211)/MgO(110), respectively, by the molecular beam epitaxy method. Reflection high energy diffraction was used to in situ characterize the crystal structure. Co films grown directly on MgO(110) were pseudomorphic fcc structure. Twofold symmetrical hcp‐Co(1100) films on top of the bcc‐Cr(211)/MgO(110) were grown and confirmed. The magneto‐optical Kerr effect (MOKE) was used to investigate the magnetic anisotropy of these films. The magnetization of these samples was found to be in‐plane. The magnetization of fcc‐Co films has cubic symmetry with texture induced uniaxial anisotropy. For hcp‐Co(1100)/bcc‐Cr(211) bilayer films, the magnetization was strongly anisotropic, but independent of the thickness of the Cr layer.

Hysteresis of binary clusters

A pair of parallel uniaxial particles with dipole‐dipole coupling has, for bond angles β=0 and π/2, up to four locally stable configurations: ↑↑, ↑↓, ↓↑, and ↓↓. Assuming thermal relaxation via coherent rotation and a periodic driving field we solve a master equation for the occupation probabilities of these states and find the coercivity and switching field distribution of the ensemble of coupled particles. For either value of the bond angle we compare numerical solutions of the master equation with approximate expressions based on extremal analysis and find good agreement between the two.

Reversible transverse susceptibility of particulate recording media

The response of a system to an infinitesimal perturbation becomes singular if the system changes its degree of metastability, i.e., if it has an inflection point. This theory is used to calculate the reversible transverse susceptibility χt of a single domain particle executing a major hysteresis loop under the influence of a field H(t) applied at an angle β to the easy axis. Thermal relaxation is taken into account and the response of the nonequilibrium system to the infinitesimal field h(t)=h sin ωt, h⊥H, is found. The resultant χt is studied as a function of β, temperature, and of the frequency Ω of the biasing field H.

Hysteresis and limiting cycles in a high frequency ac field

Numerical solutions of Brown’s Fokker-Planck equation are used to analyze the response of a superparamagnetic particle to an ac applied field. The nature of the response is governed by the rate of intrawell relaxation processes: At low driving frequencies they maintain the system close to a quasistationary state, and the response is Markovian. By contrast, probability redistribution effects taking place at high frequencies lead to a non-Markovian response mode which displays memory phenomena. The high frequency limiting cycles are analyzed in detail, and the transition to conventional low frequency hysteresis loops is discussed.

Eigenvalue spectrum of Brown's Fokker–Planck equation for coherent rotation of magnetization

Abstract The eigenvalues of Browns Fokker–Planck operator for coherent rotation of magnetization are computed for a bistable, axially symmetric system and their dependence on temperature and bias strength is studied. At zero bias the spectrum consists of alternating eigenvalue singlets and near triplets which split upon introduction of a small biasing field. Eigenvalue crossing sets in at a larger field bias and is found to be present also in an asymmetric single well eventhough it is absent from a symmetric single well. The possible origin of the eigenvalue crossing and the thermal relaxation rate are discussed.

Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilberts theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.

Enhancement of magnetoresistance in Co(11̄00)/Cr(211) bilayered films on MgO(110)

Epitaxial Co/Cr bilayered films have been successfully grown on the MgO(100) and MgO(110) substrates by molecular‐beam epitaxy. According to the reflection high‐energy electron‐diffraction and x‐ray‐diffraction measurements the crystal structure of the film depends on orientation of the buffer and substrate. Epitaxial growth of biaxial Co(1120)/Cr(100) on MgO(100) substrate and of uniaxial Co(1100)/Cr(211) on MgO(110) substrate has been confirmed. The anisotropy magnetoresistance (AMR) is strongly influenced by the orientation of the Cr buffer. In Co(1120)/Cr(100) on MgO(100) AMR is isotropic for all in‐plane fields. However, for Co(1100)/Cr(211) on MgO(110) we observed enhancement of AMR along the easy axis for temperatures below 150 K, while along the hard axis AMR has a local maximum at about 150 K. The easy axis data suggest that the longitudinal spin density wave of Cr and the crystal anisotropy of Co on Cr(211) plane dominate the enhancement of the AMR.

The coercivity of particle arrays

Thermal effects in an array of nonidentical, noninteracting single domain ferromagnetic particles are studied. Two sources of stochasticity are recognized within the array: the intrinsic stochastic nature of thermal relaxation and variations within the particles’ volume and orientation with respect to applied field, both are discussed in turn. We use the log‐normal volume distribution {∼(σV)−1exp[−ln2(V/V0)/(2σ2)]} and a cosν ψ angular distribution to calculate the mean coercivity Bc of a particle array. We find that Bc increases rapidly with increasing average volume <V≳=V0 exp(σ2/2) while for misaligned particles (ν≤∞) we observe a sudden decrease in Bc accompanied by a gradual loss of frequency dependence.

Fabrication and characterization of Co(11~00)/Mo(211) and Co(112~0)/Mo(100) bilayered films on MgO

Co/Mo bilayered films have been successfully grown on MgO(100) and MgO(110) substrates by molecular beam epitaxy. According to the reflection high energy electron diffraction and X-ray diffraction measurements the crystal structure of the film depends on the orientation of the buffer and substrate. The growth of biaxial Co(112~0)/Mo(100) on MgO(100) and of uniaxial Co(11~00)/Mo(211) on MgO(110) substrates has been confirmed. The anisotropic magnetoresistance (AMR) is strongly influenced by the Co orientation which is altered by growth on Mo/MgO(100) and MgO(110). In Co(112~0)/Mo(100) on MgO(110) AMR is isotropic for all in-plane fields. However, for Co(11~00)/Mo(211) on MgO(110) we observed enhancement of AMR along the easy axis at 10 K.