Michael J. Donahue: Presentations

Additional material is available on my publications page.

• Event: HMM 2009, Gaithersburg, MD
  Date: 13-May-2009
  Title: OD-4: Quasi-stable vortex magnetization structures in nanowires with perpendicular anisotropy
  Authors: K.M. Lebecki and M.J. Donahue
  PDF (1 760 452 bytes).
  

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• Event: Intermag 2009, Sacramento, CA
  Date: 5-May-2009
  Title: AS-09: Parallelizing a micromagnetic program for use on multi-processor shared memory computers
  Authors: M.J. Donahue
  Abstract, Publication, PDF (437 075 bytes).
  

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• Event: MMM 2008, Austin, TX
  Date: 14-Nov-2008
  Title: GS-02: Exploiting effective field time derivative information to improve accuracy of a norm-preserving Landau-Lifshitz solver
  Authors: D.G. Porter and M.J. Donahue
  PDF (100 248 bytes).
  

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• Event: MMM 2008, Austin, TX
  Date: 12-Nov-2008
  Title: Session XB: Open Forum on Micromagnetic Modeling: Finite Difference Micromagnetics
  Author: M.J. Donahue
  PDF (1 208 223 bytes).
  

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• Event: MMM 2007, Tampa, FL
  Date: 6-Nov-2007
  Title: AP-21: Precession axis modification to a semianalytical Landau-Lifshitz solution technique
  Authors: D.G. Porter and M.J. Donahue
  Abstract, Publication, PDF (188 255 bytes).
  

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• Event: 6th International Symposium on Hysteresis Modeling and Micromagnetics HMM-2007, Naples, Italy
  Date: 4-Jun-2007
  Title: Accurate computation of the demagnetization tensor
  Author: M.J. Donahue
  Abstract: Analytic formulae for computing the demagnetizing (self-magnetostatic) field between uniformly magnetized rectangular prisms are commonly used in the stray field computation of finite-difference based micromagnetic simulations. These formulae are amenable to Fast Fourier Transform methods, allowing efficient evaluation of this long-range interaction. Unfortunately, the numerical behavior of these formulae is poor, with significant and increasing loss of accuracy due to catastrophic cancellation as the distance between the prisms grows.
  PDF (538 894 bytes).
  

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• Event: 10th Joint MMM/Intermag Conference, Baltimore, MD
  Date: 11-Jan-2007
  Title: Micromagnetics on curved geometries using rectangular cells: error correction and analysis
  Authors: M.J. Donahue and R.D. McMichael
  Abstract, Publication, PDF (380 475 bytes), Gzip-compressed PostScript (271 820 bytes).
  

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• Event: Micromagnetics: Experiments, Modeling, and Mathematical Theory Workshop, Bonn, Germany
  Date: 5-Sep-2006
  Title: Micromagnetics on curved geometries using rectangular cells: error correction and analysis
  Authors: M.J. Donahue and R.D. McMichael
  Abstract: Rectangular meshes are convenient in micromagnetics because they allow the self-magnetostatic field to be efficiently computed using Fast Fourier Transform (FFT) techniques. However, geometric edges that are curved or rotated off the coordinate axes result in partially filled cells or stair-step edges that produce errors in the self-magnetostatic field computation. This talk will discuss two local edge correction methods that are compatible with FFT-based far field self-magnetostatic computations. The first correction method is based on a simple empirical formula in the form of an edge cell anisotropy. The second is a flexible, fully three-dimensional adjustment computed using the standard self-magnetostatic algorithms but applied to a local, refined mesh. To evaluate these correction methods, we use a quantitative measure that is based on calculating an edge mode resonance for different orientations of an edge with respect to the rectangular mesh. Applied to a 350 nm Permalloy square, we find up to a 50% frequency shift for the uncorrected approach, but less than a 4% shift with either of the discussed correction methods.
  PDF (1 114 589 bytes), Gzip-compressed PostScript (783 7 bytes).
  

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• Event: MMM 2005, San Jose California
  Date: 1-Nov-2005
  Title: CV-11: Magnetization normalization methods for Landau-Lifshitz-Gilbert
  Authors: D.G. Porter and M.J. Donahue
  Abstract: Exact solutions of the Landau-Lifshitz-Gilbert (LLG) equation have constant magnetization magnitude. Numerical solvers working in Cartesian coordinates fail to preserve this quantity. It is common practice to re-normalize magnetization between time steps, but this can produce errors. For example, consider a single spin precessing with no damping about a fixed applied field. A first-order Euler integration step always ends outside the unit sphere, increasing the angle between the spin and the applied field. Renormalization along the new magnetization direction results in an increase to the system energy, resulting not only in errors to energy dissipation rates but also potentially leading to numerical instabilities. Similar problems arise with higher order integration schemes, although to a lesser degree. However, an energy-neutral renormalization---one that adjusts the spin perpendicular to the precession axis---does not suffer from this problem. This poster describes such a renormalization method, and illustrates the results in simple one spin and complex multi-spin examples. A supplemental approach is also presented, where an additional term is introduced to the LLG equation that explicitly directs the magnetization magnitude toward its proper value. This additional term comes into effect only if the spin magnitude deviates from 1, so exact solutions remain unchanged.
  PDF (116 311 bytes), Gzip-compressed PostScript (69 561 bytes).
  

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• Event: HMM 2005, Budapest Hungary
  Date: 31-May-2005
  Title: TO1-4: Vortex head-to-head domain walls and their formation in onion-state ring elements
  Authors: M.H. Park, Y.K. Hong, S.H. Gee, B.C. Choi, and M.J. Donahue
  Abstract: Vortex head-to-head (HTH) domain walls in Ni₈₀Fe₂₀ ring elements were studied using MFM and micromagnetic simulations. Two types of vortex HTH domain walls, single- and double-vortex, were observed to be stable in the onion configuration at remanent state, depending on the geometry. Micromagnetic simulations of the wall formation process showed that once the vortex core nucleated the exchange energy began to decrease, accompanied by an increase in the width of the wall. Vortex nucleation in the 65 nm thick ring was found to be much faster than in the 40 nm thick ring element due to its higher initial magnetostatic energy density.
  PDF (2 654 901 bytes), Gzip-compressed PostScript (5 792 377 bytes).
  

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• Event: HMM 2005, Budapest Hungary
  Date: 30-May-2005
  Title: MP2-2: Micromagnetic Calculations of Eddy Currents with Time-Varying Fields
  Authors: L. Yanik, E. Della Torre, and M.J. Donahue
  Abstract: This paper extends a recently presented program for solving the eddy current problem in a limited geometry, by investigating the effect of time-varying fields. When the applied field was turned off, the wall motion slowed by several orders of magnitude, but since the wall energy could be reduced by reducing the amount of wall, it continued to move, albeit much more slowly . Reversing the applied field had the effect of nucleating the opposite kind of wall which propagated inward and eventually annihilated the previous wall.
  PDF (322 653 bytes), Gzip-compressed PostScript (197 730 bytes).
  

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• Event: MMM 2004, Jacksonville Florida
  Date: 8-Nov-2004
  Title: AR-14: Micromagnetic and Analytic Study of Small Zigzag Sensors
  Authors: M.J. Donahue, F. da Silva, and D.P. Pappas
  Abstract: Zigzag shaped elements are studied as prototypes for low field magnetic sensors. The elements are composed of rectangular blocks of size L x L/2 x 20 nm, where L varies from 500 nm to 50 nm. The shape anisotropy of the blocks causes the magnetization to scissor back and forth between blocks with tilt angle θ relative to the long axis of the full element. Results from micromagnetic simulations indicate that the sensitivity to applied fields decreases with the element size, and effectively vanishes when the block size L is below 100 nm. As the part size is reduced, the exchange field becomes proportionally stronger, resulting in a decreased tilt angle. A simple analytic model shows the sensitivity to be ΔR sinθ sin²θ/H_k, where ΔR/R₀ is the AMR ratio and H_k is the effective anisotropy, i.e., the sum of the exchange and shape anisotropy in each subblock. This response function exaggerates the effect of the reduced tilt angle: at θ = 45°, the sensitivity is 92% of the maximum obtained at 55°, but the sensitivity drops to 40% of the maximum by 25°. The rejection ratio (i.e., the insensitivity to fields applied in the perpendicular plane) is studied in a similar fashion.
  PDF (1 633 043 bytes), Gzip-compressed PostScript (937 139 bytes).
  

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• Event: MMM 2004, Jacksonville Florida
  Date: 8-Nov-2004
  Title: BF-02: Micromagnetic Eddy Currents in Conducting Cylinders
  Authors: E. Della Torre, L. Yanik, M.J. Donahue, and E. Cardelli
  Abstract: Recently interest has been expressed in introducing eddy currents into micromagnetic problems. We have developed a micromagnetic program to solve for the dynamic magnetization in conducting cylinders as a test bed for determining errors in these programs. This involves solving the coupled problems of eddy current and magnetization calculation. Applying a magnetic field along the wire but opposite to the magnetization creates a Bloch wall that moves inwards and generates eddy currents that impedes its progress. This model permits one to determine the effect of wall bending on its characteristics, since its curvature increases as it approaches the center of the wire. The results of this model properly reduce to earlier published results for a zero thickness wall.
  PDF (84 588 bytes), Gzip-compressed PostScript (151 278 bytes).
  

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• Event: IFIP Workshop on the Changing Face of Mathematical Software, Washington, DC
  Date: 3-Jun-2004
  Title: Standard Problems and Public Code for Micromagnetics
  Author: M.J. Donahue
  Abstract: Advances in magnetic devices such as recording heads, field sensors and magnetic non-volatile memory are dependent on microstructural details for high performance. Magnetization processes can be modeled by micromagnetics, which is a continuum theory applicable at the nanometer scale. In 1995, the micromagnetic modeling activity group (muMAG) was formed at NIST to address fundamental issues in micromagnetic modeling through promotion of community standard problems and development of a micromagnetic public code. The standard problem suite currently consists of four problems, covering both equilibrium and dynamic aspects of micromagnetics. A fifth problem, dealing with thermal effects, is under development. The public code (OOMMF) is an extensible collection of applications written in C++ and Tcl/Tk. Use of OOMMF has been acknowledged in over 100 refereed journal publications. This talk will discuss results and lessons from the standard problem suite, and provide an overview of the OOMMF architecture and extension mechanisms.
  PDF (1 393 474 bytes), Gzip-compressed PostScript (1 241 150 bytes).
  

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• Event: SIAM Conference on Mathematical Aspects of Materials Science, Los Angeles, CA
  Date: 23-May-2004
  Title: Motion of Magnetic Domain Walls in Thin, Narrow Strips
  Authors: M.J. Donahue and D.G. Porter
  Abstract: In thin, narrow strips of ferromagnetic material, magnetic domains orient parallel to the long axis of the strip. In-plane transverse walls form at the junction between oppositely directed domains. Micromagnetic simulations show that a magnetic field applied along the strip axis induces domain wall motion primarily through precession about the strip demagnetizing fields. A simple model is presented that quantitatively agrees with results from the full micromagnetic model, including domain wall momentum and retrograde motion.
  PDF (374 398 bytes), Gzip-compressed PostScript (206 247 bytes).
  

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• Event: µMAG meeting, Anaheim, CA
  Date: 7-Jan-2004
  Title: OOMMF: Where is it, where is it going?
  Authors: M.J. Donahue
  PDF (1 025 088 bytes), Gzip-compressed PostScript (433 307 bytes).
  

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• Event: 9th Joint MMM/Intermag Conference, Anaheim, CA
  Date: 6-Jan-2004
  Title: BR-12: Velocity of Transverse Domain Wall Motion Along Thin, Narrow Strips
  Authors: D.G. Porter and M.J. Donahue
  An extended version of this presentation can be found above.
  Abstract, PDF (272 652 bytes), Gzip-compressed PostScript (101 007 bytes).
  

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• Event: MCSD Seminar, NIST, Gaithersburg MD
  Date: 16-Sept-2003
  Title: Exchange Energy Formulations for Micromagnetics
  Authors: M.J. Donahue and D.G. Porter
  Abstract: Micromagnetics is a continuum theory that models behavior of magnetic materials at the nanometer scale. Typically, four component energies are considered: Zeeman (applied magnetostatic), demagnetization (self-magnetostatic), crystalline anisotropy, and exchange. The exchange energy represents the adjacent spin-spin interaction that gives rise to ferromagnetism. Defined in terms of the gradient of the magnetization components, it is especially sensitive to discretization details in a numerical implementation. This talk examines several discretization methods for the exchange energy term, and presents results on convergence rates, boundary conditions, and iterative stability. Effects of the discretization method on vortex mobility and Néel wall collapse are also presented.
  PDF (606 455 bytes), Gzip-compressed PostScript (706 452 bytes).
  

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• Event: HMM 2003, Salamanca Spain
  Date: 28-May-2003
  Title: WA-03: Exchange Energy Formulations for 3D Micromagnetics
  Authors: M.J. Donahue and D.G. Porter
  An extended version of this talk is above.
  Abstract, Publication, PDF (171 143 bytes), Gzip-compressed PostScript (198 242 bytes).
  

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• Event: HMM 2003, Salamanca Spain
  Date: 28-May-2003
  Title: WD-08: A Test Bed for a FDTD Micromagnetic Program with Eddy Currents
  Authors: L. Yanik, E. Della Torre, and M.J. Donahue
  Abstract, Publication, PDF (409 994 bytes), Gzip-compressed PostScript (677 294 bytes).
  

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• Event: Applied Math Lab Seminar, New York University
  Date: 10-Apr-2003
  Title: Exchange Energy Formulations for 3D Micromagnetics
  Authors: M.J. Donahue and D.G. Porter
  A revised and updated version of this talk can be found above.
  PDF (983 072 bytes), Gzip-compressed PostScript (1 259 770 bytes).
  

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• Event: MMM 2002, Tampa Florida
  Date: 13-Nov-2002
  Title: CC-03: Defect Related Switching Field Reduction in Small Magnetic Particle Arrays
  Authors: M.J. Donahue, G. Vértesy and M. Pardavi-Horvath
  Abstract, Publication, PDF (386 375 bytes), Gzip-compressed PostScript (1 587 906 bytes).
  

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• Event: MMM 2002, Tampa Florida
  Date: 12-Nov-2002
  Title: BC-02: Comparison of Exchange Energy Formulations for 3D Numerical Micromagnetics
  Authors: M.J. Donahue and D.G. Porter
  Abstract: Exchange energy is one of the canonical terms in micromagnetic theories. Because it is derived from the derivative of the magnetization vector, it is especially sensitive to the numerical representation selected. In this work we compare three discretized exchange formulations for 3D numerical micromagnetics on rectangular grids: the first is derived from the magnetization at a cell and at each of its 6 nearest neighbors; the second uses a trilinear interpolation on the 26 nearest neighbors; the third uses 12 neighboring points, 2 forward and 2 backward along lines parallel to the grid axes. Convergence studies on analytic 1D domain walls show that the 12 neighbor method is of higher order than the other two, so this method can attain a specified accuracy with a coarser grid. Similar results are observed on studies of 3D vortex structures in small cubes of soft magnetic material, as in muMAG Standard Problem 3. The effect of the exchange representation on the motion of magnetic structures is also important. Vortex cores tend to move preferentially towards locations between grid nodes, requiring extra applied field to overcome this discretization induced artifact. We find that the 12-neighbor method exhibits somewhat greater vortex pinning on coarse grids than the others, but at finer discretizations, where the vortex core is resolved, this formulation exhibits considerably less pinning.
  PDF (117 684 bytes), Gzip-compressed PostScript (127 532 bytes).
  

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• Event: NIST Nanotechnology Open House, Gaithersburg Maryland
  Date: 20-Jun-2002
  Title: Micromagnetic Modeling
  Authors: M.J. Donahue
  Abstract: Micromagnetics is the study, modeling and simulation of magnetic materials and their behavior at the nanometer scale. The micromagnetic modeling activity group, muMAG, was formed in 1995 as part of the NIST Center for Theoretical and Computational Materials Science (CTCMS) to address fundamental issues in micromagnetic modeling. This talk will provide an overview of the two main facets of muMAG, the Standard Problem suite and the OOMMF micromagnetic public code.
  PDF (739 061 bytes), Gzip-compressed PostScript (959 541 bytes).
  

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• Event: Intermag 2002, Amsterdam, The Netherlands
  Date: 2-May-2002
  Title: GR-02, Analysis of Switching in Uniformly Magnetized Bodies
  Authors: M.J. Donahue and D.G. Porter
  Abstract, Publication, PDF (147 766 bytes), Gzip-compressed PostScript (154 440 bytes).
  

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• Event: MMM 2001, Seattle Washington
  Date: 13-Nov-2001
  Title: AF-04, High Resolution Study of Discretization Effects in µMAG Standard Problem No. 1
  Authors: M.J. Donahue and D.G. Porter
  Abstract: A fine detail, 3D micromagnetic study has been made of magnetization reversal in muMAG Standard Problem No. 1, a 2 µm x 1 µm x 20 nm rectangle of Ni₈₀Fe₂₀. In the remanent state, closure domains form 90° walls with the single domain in the central portion of the part. As the applied field is reversed, these walls seed the creation of 180° Néel walls running perpendicular to the long axis of the sample, starting on one edge and terminating in a half vortex situated approximately halfway to the opposite edge. If the magnetization discretization is too coarse, magnetostatic forces overpower the exchange field and temporarily collapse the wall, which reforms as a cross-tie and now full vortex. Magnetization reversal proceeds by growth of the domain formed between the cross-tie and vortex. Conversely, if the discretization is fine enough, then in sufficiently strong reversing fields the equilibrium state with 180° Néel walls is found to be unstable---if the symmetry about the center point is broken, then reversal occurs by growth of one of the edge domains. Included in this material is a multiscale approach to self-magnetostatic field calculation.
  PDF (1 361 659 bytes), Gzip-compressed PostScript (1 195 881 bytes).
  

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• Event: HMM 2001, Ashburn Virginia
  Date: 21-May-2001
  Title: Poster III-5, OXS: An Extensible Public Domain Solver for Micromagnetics
  Authors: M.J. Donahue and D.G. Porter
  Digest, PDF (2 374 334 bytes), Gzip-compressed PostScript (2 604 874 bytes).
  

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• Event: Scientific Object Oriented Programming Users Group (Scoop), NIST, Gaithersburg Maryland
  Date: 6-Feb-2001
  Title: An Introduction to the OOMMF eXtensible Solver Class Architecture
  Author: M.J. Donahue
  Abstract: Micromagnetics is the modeling of magnetic behavior of materials at the nanometer scale. OOMMF (Object Oriented MicroMagnetic Framework) is a project in MCSD/ITL developing micromagnetic programs and tools in Tcl/Tk and C++. This talk provides a brief overview of the OOMMF project, and then shifts focus to the class structure of the OXS 3D solver currently in development. I discuss in particular detail the Oxs_Ext class, which is designed to provide a uniform framework for program modification and extension. I also give an explicit example showing what is involved in adding a new energy term using this mechanism, and discuss the architectural issues involved in designing this framework.
  PDF (626 780 bytes), Gzip-compressed PostScript (505 299 bytes).
  

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• Event: The 8th Joint MMM-Intermag Conference, San Antonio, Texas
  Date: 10-Jan-2001
  Title: EW-11: Non-uniform Thickness in Two-dimensional Micromagnetic Simulation
  Authors: D.G. Porter and M.J. Donahue
  Abstract, Publication, PDF (1 340 700 bytes), Gzip-compressed PostScript (1 526 904 bytes).
  

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• Event: The 8th Joint MMM-Intermag Conference, San Antonio, Texas
  Date: 9-Jan-2001
  Title: DF-13: Micromagnetic Calculation of the High Frequency Dynamics of Nano-Size Rectangular Ferromagnetic Stripes
  Authors: O. Gérardin, H. Le Gall, M.J. Donahue and N. Vukadinovic
  Abstract, Publication, PDF (417 223 bytes), Gzip-compressed PostScript (613 828 bytes).
  

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• Event: AMRI seminar, University of New Orleans
  Date: 30-Oct-2000
  Title: Micromagnetic Dynamics in Thin Films
  Author: M.J. Donahue
  Abstract: Dynamic micromagnetic computations are increasingly important for rate-sensitive applications such as magnetic memory. In this talk I give a brief overview of micromagnetics, and then discuss new solutions to muMAG Standard Problem No. 4, which details magnetization switching behavior in a 500 x 125 x 3 nm NiFe particle under Landau-Lifshitz-Gilbert dynamics. We find two reversal modes, depending on the relative orientation of the applied field with the initial magnetization state. One mode proceeds by simple propagation of end domains toward the sample center, but the other involves counter-rotating domains, 360 degree walls and complex dynamics on fine length scales. I also present computational and theoretical results describing the functional dependence of the resonance frequency and susceptibility to the applied field in the neighborhood of a switching event.
  
  • Main slides: PDF (1 012 353 bytes), Gzip-compressed PostScript (776 523 bytes)
  • Magnetization reversal snapshots: PDF (1 366 271 bytes), Gzip-compressed PostScript (1 580 964 bytes)

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• Event: OOMMF Workshop 2000, Gaithersburg Maryland
  Date: 18-August-2000
  Authors: M.J. Donahue, D.G. Porter, R.D. McMichael and J. Eicke
  Titles:
  • Background (PDF 12 701 bytes, gzipped PostScript 28 882 bytes)
  • Installation and Architecture Overview (PDF 25 992 bytes, gzipped PostScript 15 567 bytes)
  • Details of 2D Solver (PDF 36 449 bytes, gzipped PostScript 30 450 bytes)
  • OOMMF eXtensible (3D) Solver (PDF 675 941 bytes, gzipped PostScript 102 164 bytes)

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• Event: µMAG Workshop, San Francisco California
  Date: 6-Jan-1998
  Title: OOMMF Micromagnetics Public Code Project
  Authors: M.J. Donahue, D.G. Porter, R.D. McMichael, J. Eicke and J. Blue
  PDF (251 810 bytes), Gzip-compressed PostScript (398 506 bytes).

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• Event: MMM 1995, Philadelphia Pennsylvania
  Date: Nov-1995
  Title: Artifacts in Magnetic Resonance Imaging from Metals
  Authors: L.H. Bennett, P.S. Wang, and M.J. Donahue
  Abstract, Publication, PDF (188 103 bytes), Gzip-compressed PostScript (343 590 bytes).

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• Event: NDE seminar, The Ohio State University, Columbus Ohio
  Date: 7-May-1991
  Title: Simulation of Radiographs
  Author: M.J. Donahue
  Abstract: This talk provides an overview with examples of a radiograph simulation package developed by the author as part of his Ph.D. dissertation work in the Welding Engineering Department of The Ohio State University. This package requires as input a text file defining a collection of simple objects (ellipsoids, cylinders, prisms, and intersections of these with half-spaces) having arbitrary orientations and X-ray absorption coefficients. The user also selects either parallel beam or cone beam X-ray source geometry. The output is a simulated radiograph. The talk also includes examples of tomographic reconstructions using the simulated radiographs, and a comparison with a reconstruction from actual radiographs.
  PDF (292 267 bytes), Gzip-compressed PostScript (889 979 bytes).