Michael J. Donahue

Exchange energy representations in computational micromagnetics

Abstract In order to solve Browns equations, which describe a continuous medium, computational micromagnetic modeling requires a discrete representation of the magnetization M(r) , and a discrete representation of the derivatives of M(r) must be chosen. This choice may be made through an explicit choice of interpolation or through the choice of numerical representation of Browns equations. In this paper we describe some alternative representations of the exchange energy on a square 2-D grid, and test these representations through comparison with analytical results for magnetization spirals and with simulations testing vortex and domain wall mobility.

Integrated microfluidic isolation platform for magnetic particle manipulation in biological systems

We have developed a micromachined fluid-cell platform that consists of patterned magnetic thin-film elements supported on a thin silicon–nitride membrane. In the presence of an external magnetic field, the field gradients near the magnetic elements are sufficiently large to trap magnetic particles that are separated from the patterned films by a 200 nm thick nitride membrane. The two main applications of this fluid-cell platform are to provide a means to control and position magnetic microparticles, which can be tethered to biological molecules, and also to sort superparamagnetic microparticles based on their size and magnetic susceptibility. We determine the characteristic trapping forces of each trap in the array by measuring the Brownian motion of the microparticle as a function of applied external field. Typical force constants and forces on the superparamagnetic particles are 4.8×10−4±0.7×10−4 N/m and 97±15 pN, respectively.

Artifacts in magnetic resonance imaging from metals

Metallic biomedical implants, such as aneurysm clips, endoprostheses, and internal orthopedic devices give rise to artifacts in the magnetic resonanceimage(MRI) of patients. Such artifacts impair the information contained in the image in precisely the region of most interest, namely near the metallic device. Ferromagnetic materials are contraindicated because of the hazards associated with their movement during the MRI procedure. In less‐magnetic metals, it has been suggested that the extent of the artifact is related to the magnetic susceptibility of the metal, but no systematic data appear to be available. When the susceptibility is sufficiently small, an additional artifact due to electrical conductivity is observed. We present an initial systematic study of MRI artifacts produced by two low susceptibility metals, titanium (relative permeability μ r ≊1.0002) and copper (μ r ≊0.99998), including experimental, theoretical, and computer simulation results.

Domain wall traps for low-field switching of submicron elements

In magnetic random access memory, power consumption depends on the coercivity of the magnetic elements in the memory cells. In this article a new method is described that uses a “domain wall trap” element shape to reduce both the coercivity and the dependence of coercivity on element size in submicron magnetic elements. Micromagnetic simulations of a shaped permalloy element show coercivity less than one tenth the coercivity calculated for a rectangular permalloy element of the same size. The switching times for the domain wall traps are shown to be comparable to those of rectangular elements.

Velocity of transverse domain wall motion along thin, narrow strips

Micromagnetic simulation of domain wall motion in thin, narrow strips leads to a simplified analytical model. The model accurately predicts the same domain wall velocity as full micromagnetic calculations, including dependence on strip width, thickness, and magnitude of applied field pulse. Domain wall momentum and retrograde domain wall motion are both observed and explained by the analytical model.

Adiabatic domain wall motion and Landau-Lifshitz damping

Recent theory and measurements of the velocity of current-driven domain walls in magnetic nanowires have reopened the unresolved question of whether Landau-Lifshitz damping or Gilbert damping provides the more natural description of dissipative magnetization dynamics. In this paper, we argue that (as in the past) experiment cannot distinguish the two, but that Landau-Lifshitz damping, nevertheless, provides the most physically sensible interpretation of the equation of motion. From this perspective, (i) adiabatic spin-transfer torque dominates the dynamics with small corrections from nonadiabatic effects, (ii) the damping always decreases the magnetic free energy, and (iii) microscopic calculations of damping become consistent with general statistical and thermodynamic considerations.

Manipulation and sorting of magnetic particles by a magnetic force microscope on a microfluidic magnetic trap platform

We have integrated a microfluidic magnetic trap platform with an external magnetic force microscope (MFM) cantilever. The MFM cantilever tip serves as a magnetorobotic arm that provides a translatable local magnetic field gradient to capture and move magnetic particles with nanometer precision. The MFM electronics have been programmed to sort an initially random distribution of particles by moving them within an array of magnetic trapping elements. We measured the maximum velocity at which the particles can be translated to be 2.2mm∕s±0.1mm∕s, which can potentially permit a sorting rate of approximately 5500particles∕min. We determined a magnetic force of 35.3±2.0pN acting on a 1μm diameter particle by measuring the hydrodynamic drag force necessary to free the particle. Release of the particles from the MFM tip is made possible by a nitride membrane that separates the arm and magnetic trap elements from the particle solution. This platform has potential applications for magnetic-based sorting, manipulati...

Micromagnetic Calculation of the High Frequency Dynamics of Nano-Size Rectangular Ferromagnetic Stripes

Nano-size ferromagnetic dots, wires, and stripes are of great interest for future high speed magnetic sensors and ultrahigh density magnetic storage. High frequency dynamic excitation is one way to investigate the time scale of the magnetization reversal in submicron particles with lateral nanometer dimension. Macroscopic models like the Landau–Lifshitz (LL) model are often used to describe the switching process. However, these models do not take into account the nonuniformity of the magnetization structure. In this article dynamic micromagnetic calculations are used in determining the high frequency susceptibility of a 1 μm×50 nm×5 nm Permalloy stripe. The studied structure exhibits two resonance modes. The higher, primary peak is around 10 GHz and can be identified with the uniform resonance mode predicted by the macroscopic LL model. The low frequency peak is attributed to the splay of the magnetization distribution near the end of the stripe.

High-speed dynamics, damping, and relaxation times in submicrometer spin-valve devices

The dynamical response of spin-valve devices with linewidths of 0.8 μm has been measured after excitation with 160 ps magnetic impulses. The devices show resonant frequencies of 2–4 GHz which determine the upper limit of their operation frequency. The dynamical response can be fit with Landau–Lifshitz models to extract an effective uniform-mode damping constant, αum. The measured values of αum were between 0.04 and 0.01 depending on the magnitude of the longitudinal bias field. The appropriate damping coefficient for use in micromagnetic modeling, αmm, was extracted from the dynamical response with large longitudinal bias field. This value was used to model the switching of a 0.1 μm×1.0 μm magnetoresistive random access memory cell. The micromagnetic model included shape disorder that is expected to be found in real devices. The simulations showed that, while the magnetization reverses rapidly (<0.5 ns), it took several nanoseconds for the energy to be removed from the magnetic system. The switching energ...

Periodic boundary conditions for demagnetization interactions in micromagnetic simulations

A new method for the introduction of periodic boundary conditions to the self-magnetostatic (demagnetization) term in micromagnetic simulations is described, using an Ewald-like summation method in real space. The long-range character of the dipolar interactions is included without any distance cut-offs. The accumulated errors are carefully monitored to provide easy control of the quality of the results. This allows the calculations to be either accurate up to floating point limitations or less precise when computational speed requirements dominate. This method is incorporated into a full micromagnetic program, and comparisons are made to analytic results.