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15 May 2003

Volume 93, Issue 10, pp. 5855-8792

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Increased efficiency and accuracy in micromagnetic calculations of switching astroids

M. R. Scheinfein and A. S. Arrott

J. Appl. Phys. 93, 6802 (2003); http://dx.doi.org/10.1063/1.1557271 (3 pages) | Cited 7 times

Online Publication Date: 9 May 2003

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The “path method” is introduced to use results of one or a few full Landau–Lifshitz–Gilbert dynamical micromagnetic calculations to predict switching diagrams for magnetic elements in random access memories. The utility of the method is demonstrated for an element in the form of a trapezoidally distorted generalized ellipse, where the symmetry produces the C state in the absence of applied fields. The element switches by almost uniform rotation of the S-state configuration in the presence of an adequate bias field. The path method relies on the empirically observed insensitivity of the magnetization patterns in a switching process to the amount by which the field exceeds that necessary for switching. © 2003 American Institute of Physics.
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75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
75.50.Ss Magnetic recording materials

Geometric integration of the Gilbert equation

A. W. Spargo, P. H. W. Ridley, and G. W. Roberts

J. Appl. Phys. 93, 6805 (2003); http://dx.doi.org/10.1063/1.1557274 (3 pages) | Cited 2 times

Online Publication Date: 9 May 2003

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Geometric integration refers to numerical methods which aim to preserve the qualitative and geometric features of a differential equation after discretization. In micromagnetics, the magnetization vector M represents a statistical average of magnetic moments, the magnitude of which should be conserved in time. In general, the midpoint scheme preserves the modulus of solutions on the sphere due to intrinsic quadratic invariance. This method has previously been implemented in various forms to solve the Landau–Lifshitz and Landau–Lifshitz–Gilbert equations within finite-difference formulations. In this article, it is shown that an explicit Euler method will overestimate ∣M∣ while an implicit Euler method will make an underestimate, whereas the midpoint method conserves ∣M∣ up to round-off error. The midpoint scheme is then utilized within a variational finite-element formulation of the Gilbert equation. Numerical stability and error control are discussed using the reversal of a cobalt nanoparticle as an example calculation. © 2003 American Institute of Physics.
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02.60.Jh Numerical differentiation and integration
02.30.Cj Measure and integration
75.40.Mg Numerical simulation studies
75.50.Tt Fine-particle systems; nanocrystalline materials
61.46.-w Structure of nanoscale materials
02.30.Hq Ordinary differential equations
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
75.30.Cr Saturation moments and magnetic susceptibilities
02.30.Xx Calculus of variations
02.70.Dh Finite-element and Galerkin methods
75.50.Cc Other ferromagnetic metals and alloys

Simple iterative calculation of micromagnetic kernels

D. M. Apalkov and P. B. Visscher

J. Appl. Phys. 93, 6808 (2003); http://dx.doi.org/10.1063/1.1543881 (3 pages)

Online Publication Date: 9 May 2003

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To calculate the magnetostatic field in a micromagnetic calculation, it is customary to use a stored “kernel,” which is the average field in a cubic cell due to a uniform magnetization in some other cell. This can be calculated from a dipole approximation if the cells are far apart, but is obtained from a table of stored kernels for a finite set of small cell-separation vectors. The kernel is usually calculated numerically or analytically, either of which is laborious and error-prone. We have found an iterative method that requires almost no coding beyond what is already present in a micromagnetic code, and converges much more rapidly than finite-element integration. © 2003 American Institute of Physics.
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41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

Comparison of analytical solutions of Landau–Lifshitz equation for “damping” and “precessional” switchings

G. Bertotti, I. Mayergoyz, C. Serpico, and M. Dimian

J. Appl. Phys. 93, 6811 (2003); http://dx.doi.org/10.1063/1.1557275 (3 pages) | Cited 14 times

Online Publication Date: 9 May 2003

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The analytical solutions to the Landau–Lifshitz equation for “damping” and “precessional” switchings of materials with uniaxial anisotropy are found. These solutions lead to the expressions for the switching times and critical fields. Comparison of these two distinct modes of switching is presented. © 2003 American Institute of Physics.
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75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
75.30.Gw Magnetic anisotropy

Finite temperature micromagnetics and magnetic measurements of submicron patterned permalloy thin films

James G. Deak

J. Appl. Phys. 93, 6814 (2003); http://dx.doi.org/10.1063/1.1555334 (3 pages) | Cited 4 times

Online Publication Date: 9 May 2003

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Micromagnetic simulation using the deterministic Landau–Lifshitz–Gilbert (LLG) equation is inadequate for predicting the coercivity of submicron patterned thin films. The discrepancy results because the deterministic LLG equation only provides a zero-temperature description of the magnetization processes of a ferromagnetic material. In order to properly simulate the coercivity, the stochastic LLG equation, which includes thermal effects through a fluctuating magnetic field, must be used. Direct comparison of measurements of the coercivity of arrays of submicron patterned permalloy thin films with simulation has been used to show that the second-order Heun scheme is adequate for this purpose. In addition, the simulated temperature dependence of the magnetization of the patterned bits tracks the measured dependence. © 2003 American Institute of Physics.
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75.70.Rf Surface magnetism
75.70.Ak Magnetic properties of monolayers and thin films
75.50.Bb Fe and its alloys
75.50.Vv High coercivity materials
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
75.40.Mg Numerical simulation studies

Transition state in magnetization reversal

G. Brown, M. A. Novotny, and Per Arne Rikvold

J. Appl. Phys. 93, 6817 (2003); http://dx.doi.org/10.1063/1.1543882 (3 pages) | Cited 3 times

Online Publication Date: 9 May 2003

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We consider a magnet with uniaxial anisotropy in an external magnetic field along the anisotropy direction, but with a field magnitude smaller than the coercive field. There are three representative magnetization configurations corresponding to three extrema of the free energy. The equilibrium and metastable configurations, which are magnetized approximately parallel and antiparallel to the applied field, respectively, both correspond to local free-energy minima. The third extremum configuration is the saddle point separating these minima. It is also called the transition state for magnetization reversal. The free-energy difference between the metastable and transition-state configurations determines the thermal stability of the magnet. However, it is difficult to determine the location of the transition state in both experiments and numerical simulations. Here it is shown that the computational Projective Dynamics method, applied to the time dependence of the total magnetization, can be used to determine the transition state. From large-scale micromagnetic simulations of a simple model of magnetic nanowires with no crystalline anisotropy, the magnetization associated with the transition state is found to be linearly dependent on temperature, and the free-energy barrier is found to be dominated by the entropic contribution at reasonable temperatures and external fields. The effect of including crystalline anisotropy is also discussed. Finally, the influence of the spin precession on the transition state is determined by comparison of the micromagnetic simulations to kinetic Monte Carlo simulations of precession-free (overdamped) dynamics. © 2003 American Institute of Physics.
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75.60.Jk Magnetization reversal mechanisms
75.75.-c Magnetic properties of nanostructures
75.30.Kz Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.)
75.50.Ww Permanent magnets
75.30.Gw Magnetic anisotropy
65.40.G- Other thermodynamical quantities
75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
75.50.Tt Fine-particle systems; nanocrystalline materials

Equivalence of sweep-rate and magnetic-viscosity dynamics

R. Skomski, R. D. Kirby, and D. J. Sellmyer

J. Appl. Phys. 93, 6820 (2003); http://dx.doi.org/10.1063/1.1557276 (3 pages) | Cited 4 times

Online Publication Date: 9 May 2003

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The irreversible response of magnetic materials to magnetic fields of arbitrary time dependence is investigated by a master-equation approach. The magnetization reversal is expressed in terms of renormalized magnetization modes, and the resulting set of two-level master equations is solved by direct integration. The theory applies not only to linear energy-barrier laws but also to the physically more reasonable case where the activation energy is a nonlinear function of the applied field. Particular emphasis is on the relation between sweep-rate and magnetic-viscosity dynamics. Other regimes, such as oscillating magnetic fields, can be mapped onto sweep-rate dynamics. Magnetic-viscosity and sweep-rate experiments reflect the same fundamental magnetization processes, but energy barriers probed by dynamic experiments are smaller by about 20%. © 2003 American Institute of Physics.
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75.60.Lr Magnetic aftereffects
75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)
75.60.Jk Magnetization reversal mechanisms

Analytical and experimental study of identification of Preisach–Néel-type models for magnetic nanoparticle systems

I. D. Borcia, M. Cerchez, Al. Stancu, L. D. Tung, and L. Spinu

J. Appl. Phys. 93, 6823 (2003); http://dx.doi.org/10.1063/1.1557277 (3 pages) | Cited 1 time

Online Publication Date: 9 May 2003

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This article describes an identification methodology for a Preisach–Néel model based on a nonlinear Stoner–Wohlfarth energy barrier hypothesis. In the identification, one uses data from a set of remanent curves, the major hysteresis loop at two different temperatures below the blocking temperature and the zero-field-cooled and field-cooled magnetization curves. This identification scheme was experimentally applied to a system of Co ferrite nanoparticles with an average diameter of 3 nm. The quality of the identification procedure is analyzed and the differences between the experimental and computational results are discussed. © 2003 American Institute of Physics.
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75.50.Tt Fine-particle systems; nanocrystalline materials
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects

Analysis of spectral noise density of hysteretic systems driven by stochastic processes

I. Mayergoyz and M. Dimian

J. Appl. Phys. 93, 6826 (2003); http://dx.doi.org/10.1063/1.1543883 (3 pages) | Cited 5 times

Online Publication Date: 9 May 2003

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A technique for computing spectral noise density of hysteretic systems driven by stochastic inputs is discussed. This technique is based on the mathematical machinery of stochastic processes on graphs. Computational results illustrating this technique are presented. © 2003 American Institute of Physics.
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05.40.Ca Noise
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