## Advanced numerical micromagnetics

## Thomas Schrefl

## Mid Term Report (FWF Project Y 132 PHY)

## Report on the first two years of funding

## 1.0 Objectives

The main object of the project is the realistic simulation of modern magnetic materials with a physically complete formalism. The development of new magnetic materials used for permanent magnets, data storage, or magnetic sensors is linked with the ability to make accurate predictions of their magnetic properties. Advanced numerical micromagnetic simulations are required to provide theoretical guidelines for the structural design of novel magnetic materials and devices.

The aim of the first two years of the project is the combination of micromagnetic theory with advanced numerical techniques for the solution of partial differential equations. Specific goals are the extension of the length- and time scales which are limited in standard micromagnetic solvers.

## 2.0 Results

Main objective of the first period of the project was the development of new numerical algorithms for large scale micromagnetic simulations. The following section summarizes the main achievements. Further details are given in the appendix (See "Gallery" on page 23.) and in the movie gallery on the CD.

## 2.1 Advanced numerical methods

## 2.1.1 Fast methods for long-range, magnetostatic interactions

Fast methods to compute the magnetostatic interactions are a crucial part in numerical micromagnetic simulations. The preferred algorithm to treat the magnetostatic interactions of distinct magnetic parts is a hybrid finite element / boundary element method. In order to reduce the storage and the CPU time required for the boundary element part, matrix compression techniques are applied. Whereas both a wavelet based method (Ref. 16 on page 15 or Ref. 22 on page 15) and a hierarchical summation technique (Ref. 61 on page 18) considerably reduce the storage requirements, only the hierarchical summation technique enables a substantial speedup of the computations. Using the hierarchical method it is possible to simulate the magnetostatic interactions in discrete storage media (Figure 1) and to treat moving magnetic parts (Section 11.2 on page 24).

## FIGURE 1. Snapshot of the magnetization states during the reversal of an array of island (bits) of a discrete media. The magnetostatic interactions between the islands are calculated using a hierarchical method. Red: magnetization up; blue: magnetization down.

## 2.1.2 Advanced time integration methods

The simulation of magnetic sensor elements require the solution of stiff systems of ordinary differential equations.Taking into account surface roughness and grain structures requires an inhomogeneous computational grid which in turn causes very small time steps for time integration. The time step required to obtain a stable solution of the Landau-Lifshitz Gilbert equation with an explicit time integration scheme has to be proportional to hh is the size of the spatial grid. Edge roughness and an irregular grain structure may cause small computational cells which leads to a small time step when an explicit time integration method is applied to solve the LLG equation. Time integration schemes which use backward differentiation formulas enable the simulation of large magnetic systems, taking into account the microstructure. Figure 2 shows the possible extension of the time scales due to the new algorithms.

## FIGURE 2. CPU time for different time integration methods during the reversal of a granular Co nano-element. The right hand side shows the remanent state and a transient state during reversal (red: magnetization up, blue: magnetization down).

## 2.1.3 Moving mesh algorithms

The different length scales involved in micromagnetic simulations may span several micro meters. In order to resolve domain walls a resolution in the nano-meter regime is required. On the other hand the sample geometry may approach micro meters. One approach to reduce the required simulation time is the implementation of an adaptive mesh refinement algorithm. The mesh is adjusted to the current magnetization distribution at each time step. Figure 3 shows a sequence of meshes during the domain wall motion in a magnetic nano-wire (Ref. 50 on page 17).

## FIGURE 3. Snapshots of the tetrahedral finite element mesh during the motion of a domain wall through a Co nano-wire with a diameter of 40 nm and a length of 600 nm.

## 2.1.4 Scalable micromagnetic solvers

The simulation of fully integrated magnetic systems that take into account all magnetic interactions of a device easily leads to large scale simulations involving millions of degrees of freedom. In order to perform the simulations on massively parallel computers, the current algorithms were adapted to achieve scalability. With a scalable algorithm the time to completion remains constant when both the problem size and the number of CPUs are doubled. These algorithms will be used to simulate the magnetic recording process in perpendicular media. Figure 4 shows the speedup (CPU time on a single processor / time to completion on n processors) and the time required for the different tasks of the parallel finite element / boundary element solver.

## FIGURE 4. Left: Speedup of the parallel micromagnetic solver as a function of the number of processors. Right: Partition of the total time to completion into the different tasks.

## 2.1.5 Methods for micromagnetics at non-zero temperature

Different approaches to treat magnetization processes at non-zero temperatures are compared. Basic questions like the influence of the spatial correlation length of the thermal and the relationship of a Langevin method and the hybrid Monte Carlo method were addressed (Ref. 42 on page 17 and Ref. 41 on page 21).

## 2.1.6 Antiferromagnetic / ferromagnetic structures

Antiferromagnets are used to stabilize domains in magnetic sensors such as read heads in magnetic recording. Traditionally, the effect of an antiferromagnet on a ferromagnetic layer is treated using a uniform bias field in micromagnetic simulation. This approach cannot explain the magnetic ripple structure observed experimentally in the ferromagnetic layer. A novel micromagnetic algorithm has been developed which treats both the ferromagnet and the antiferromagnet in a continuum approach. The new model enables a quantitative treatment of exchange bias, taking into account the granular structure of the antiferromagnetic layer (Ref. 60 on page 18).

## 2.2 Summary of achievements

- Fast numerical algorithms for micromagnetic simulations where successfully implemented and tested.
- The new methods provide a speed up of the micromagnetic simulations of granular media on a single CPU up to a factor of 100 as compared to the original micromagnetic solver at the start of the project.
- For the first time a fully integrated micromagnetic solver that can treat the magnetostatic interactions of moving magnetic parts has been developed.
- For the first time antiferromagnetic- / ferromagnetic structures can be simulated in an integrated approach, resolving magnetization processes within both, the ferromagnet and the antiferromagnet.
## 3.0 International Cooperations

## 3.1 Gerhard-Mercator University, Duisburg, Germany (U Nowak, D Hinzke)

## Thermal activation of small particles

With decreasing size of the elementary storage volumes, thermally activated magnetization reversal becomes an important issue in magnetic recording. Different numerical approaches to treat the thermal activation of small particles and wires were compared.

## 3.2 University of Glasgow (J Chapman)

## Magnetic imaging and micromagnetics

The detailed comparison of micromagnetic simulations and magnetic images obtained from Lorentz microscopy provides important details on the magnetization processes in magnetic sensor elements.

## 3.3 IBM Almaden Research Center, Almaden, CA, USA

(M E Schabes, B E Lengsfield)## Perpendicular magnetic recording

Numerical methods were developed to simulate a fully integrated magnetic recording process on perpendicular media, including the magnetization processes in the head, the data layer, and the soft underlayer.

## 3.4 IBM TR Watson Research Center, Yorktown, NY, USA

(D M Newns, W E Donath)## Scalable micromagnetic solvers

Micromagnetic simulation for massively parallel systems are developed. The aim of this collaboration is a micromagnetic solver which is scalable and shows an optimal speed up on parallel computers.

## 3.5 University of Western Australia, Perth

(R L Stamps, R C Woodward, D Crew)## Diluted Nd-Fe-B magnet

Small Nd2Fe14B particles embedded in a Nd-rich matrix show a coercive field close to the theoretical limit predicted by the Stoner-Wohlfarth theory. Micromagnetic simulations can explain the multidomain state which is found experimentally.

## FePt nanoparticles

Arrays of self assembled nano-particles are candidates for future ultra-high density recording media. Micromagnetic simulations reveal a possible mechanism for the observed remanence enhancement and reversible magnetization behavior.

## Ferromagnetic / Antiferromagnetic bilayers

The classical micromagnetic theory which describes magnetization processes in a continuum approach is extended to antiferromagnetic materials. The new theory is applied to study ferromagnetic/antiferromagnetic layer systems which are the basic structural units of magnetic sensors.

## 3.6 Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany

(K Nielsch)## Magnetic nano-wires

Magnetic nano-wires may be used in future magnetic storage and sensor applications. Numerical micromagnetics help to understand the influence of the granular structure of the wires on the magnetic properties.

## 3.7 Seagate Research, Pittsburgh, PA, USA

(R W Chantrell)## Vortices in thin film elements

Vortex formation and vortex motion is simulated using finite element micromagnetics. The results are compared with analytical models and thus provide a way to verify the micromagnetic algorithm.

## 4.0 Unexpected results

The implementation of a physically meaningful method to treat thermally activated magnetization processes turned out to be not straight forward. The currently most often used approach to include thermal activation into dynamic micromagnetic simulations is to add a random, thermal fluctuation field to the effective field (see Ref. 13 on page 15, Ref. 18 on page 15, Ref. 23 on page 15 and the references therein). This method was originally introduced by Brown [1] for a single domain particle with uniform magnetization.

The extension of Brown's method to the continuum theory of micromagnetism is not straight forward. Transition times and thermal averages were found to depend on both the spatial grid size and the time step (Ref. 42 on page 17). The proper spatial correlation length of the thermal noise is by no means obvious. Different approaches are used in the literature.The random, thermal field is either added separately to each atomic spin [2] or is assumed constant within one macroscopic grain [3].

- W. F, Brown, Jr., "Thermal fluctuations of a single domain particle, "Phys. Rev. 130 (1963)1677.
- D. Hinzke, U. Nowak, K. D. Usadel, "Thermally activated magnetization reversal in classical spin chainsInternational Symposium on Structure and Dynamics of Heterogeneous Systems," Editors: P. Entel and D.E. Wolf World Scientific (2000) pp.331
- J. Xue, R. H. Victora, "Micromagnetic Predictions for Thermally Assisted Reversal over Long Time Scales," J. Appl. Phys. 77 (2000) 3432.
## 5.0 Information on the funding

The personnel and equipment costs are listed below. The travel cost are about 10% to 15% of the total project costs.

## 5.1 Personnel

## 5.2 Equipment

## Outlook for the next period of the research project

## 6.0 Objectives and state of the art

The advanced micromagnetic algorithms developed within the first two years of the project enable simulations of systems as large as entire devices taking into account the structural characteristics of the material. The simulation of fully integrated magnetic systems which take into account all magnetic parts of the device and all their interactions are possible. The involved length scale will span from a nanometer resolution within a domain wall to an extension of the sample in the micrometer regime.

The proper and effective treatment of thermally activated magnetization processes remains an open and important issue. Especially, a good method to treat the long-term thermal stability has to be found. Recently proposed methods like a hyperdynamic scheme [1] or a path integral method [2] may not work in a system with many local minima and many possible paths between different states.

The rapid progress of magnetic storage technology makes predictions of future research topics unreliable. The current topical issues in the research community in the field of magnetic storage systems are highly driven by industrial developments and thus may change quickly. A high flexibility in the choice of the methods and the specific research area is important to make research of international interest. This situation provides also a chance for research performed at an university lab which can focus on a deeper understanding of the underlying physics. A prominent example are ferromagnetic / antiferromagnetic interfaces which are used in actual devices although a basic understanding of the underlying physical mechanism is still unclear [3].

This situation leads to the three distinct objectives for the second period of the project:

- Fully integrated simulation of the functional behavior of storage and sensor systems.
- Understanding the basic physics of thermally activated magnetization processes which in turn will enable a computational treatment of the magnetization reversal at non-zero temperatures.
- Rigorous analysis of numerical and experimental data in order to obtain a deeper understanding of the physics of modern magnetic materials.

- J. Xue, R. H. Victora, "Micromagnetic Predictions for Thermally Assisted Reversal over Long Time Scales," J. Appl. Phys. 77 (2000) 3432.
- W. E, W. Ren, E Vanden-Eojnden, "Optimal paths for metastable systems driven by noise", http://www.cims.nyu.edu/~eve2/optimalpath.pdf
- A. E. Berkowitz, K. Takano, "Exchange anisotropy - a review," J. Magn. Magn. Mater. 200 (1999) 552-570.
## 7.0 Tasks and workplan

## 7.1 Fully integrated micromagnetic simulations

This objective involves the following tasks:

- T1.1. Porting the scalable finite element / boundary element solver to massively parallel machines.
- T1.2. Integrating new software modules - like the simulation tool to treat antiferromagnets - into the parallel finite element / boundary element solver.
- T1.3. Production runs which focus on one specific device which is of high interest in the research community at the time when these investigations start.
## 7.2 Computational micromagnetics at non-zero temperature

The long term thermal stability of recording media and magnetic storage elements is a major issue for practical applications. Still predictive simulation tools which are based on rigorous description of the physical phenomena is missing.

- T2.1. Survey on the computational treatment of thermal activation in other fields of physics.
- T2.2. Address basic physical questions like the proper correlation length of the thermal noise or find new concepts which avoid these difficulties.
- T2.3. Test of newly proposed methods (see [1] and [2] on page 9) in simple test cases to learn about their validity.
- T2.4. Implementation of numerical schemes for non-zero temperature micromagnetics at large time scales.
## 7.3 Deep understanding of basic physical mechanism

The comparison of the results of micromagnetic simulations with experimental data (magnetic images and measurements) will provide a better knowledge of the physics behind modern magnetic materials.

- T3.1. Development of preprocessing tools that generate a finite element model which is close to the actual microstructure of samples used in magnetic imaging.
- T3.2. Magnetic imaging and measurements. This involves Lorentz microscopy of magnetic domain structures in thin film elements and permanent magnets.
- T3.3. Simulation of the samples measured in task T3.2.
- T3.4. Comparison of numerical and experimental results.
In addition to international collaborations, this tasks will be performed in close cooperation with the following projects within the working group on Magnetic Materials and Micromagnetics of the Institute for Solid State Physics at the Vienna University of Technology:

- Lorentz microscopy of pinning magnets at variable temperature, Austrian Science Fund-FWF P14899-PHY
- Self-assembled nanoparticles and nanopatterned arrays for high density magneto-recording (HIDEMAR), EC-5FPR Growth Project GRD1-2001-40316
## 7.4 Workplan

The work on all three tasks will start simultaneously at the beginning of the second project period. Currently the project leader, one post doc, two PhD students and one diploma student work within the project. The researchers are involved in the following subtasks and will keep working in this area for at least 12 month.

The work on the subtasks T1.2, T3.2, and T2.4 will start at the beginning of the 4th year of the project.

## 8.0 Information of the requested funding

## 8.1 Personnel

## 8.2 Requested equipment

## 8.3 Total costs for the second project phase

## 9.0 Future international cooperations

The cooperations (Ref. 3.0 on page 6) started in the first period of the project will continued. In addition collaborations with the following institutes will be established.

## 9.1 Laboratoire de Physique des Solides, Universite Paris-Sud, France

(J Miltat)## Non zero temperature micromagnetics.

Micromagnetics including thermal fluctuations is becoming a topic of increasing importance, as active magnetic devices become smaller and therefore come closer to the superparamagnetic limit. During this collaboration the validity of basic approaches to treat thermal fluctuations will be checked. Rok Dittrich will visit the Laboratoire de Physique des Solides for a period of three months.

## 9.2 Nihon University, Japan

(Y Uesaka)## Fast switching of recording media

Prof. Uesaka will visit our working group from February 17 to March 26. The joint research will focus on materials and systems for ultra-high data rates. Using micromagnetic simulations we will explore the limits for fast writing in high density recording media.

## 9.3 University of Twente, Enschede, The Netherlands

(J C Lodder)## Comparison of simulation and experiments.

Hermann Forster will visit the Systems and Materials for Information storage group which is part of the MESA+ research at the University of Twente. The objective of the research visit is a detailed comparison of numerical micromagnetic simulation and experimental data on single magnetic islands as used in discrete storage media.

## Appendix

## 10.0 Output

## 10.1 Publications

## 10.1.1 Invited reviews

- J. Fidler and T. Schrefl, "Micromagnetic modelling - the current state of the art," Journal of Physics D: Applied Physics 33, R135-R156 (2000). [PDF Full-Text]
- J. Fidler, R. W. Chantrell, T. Schrefl, M. Wongsam, and J. Fidler, "Micromagnetics I: Basic principles," Encyclopedia of Materials: Science and Technology, K. H. J. Buschow, R. W. Cahn, M. C. Flemings, B. Ilschner, E. J. Kramer, S. Mahajan (eds.), Elsevier, 2001, pp. 5642-5651. [PDF Full-Text]
- R. W. Chantrell, J. Fidler, T. Schrefl, and M. Wongsam, "Micromagnetics II: Finite element approaches," Encyclopedia of Materials: Science and Technology, K. H. J. Buschow, R. W. Cahn, M. C. Flemings, B. Ilschner, E. J. Kramer, S. Mahajan (eds.), Elsevier, 2001, pp. 5651-5661. [PDF Full-Text]
## 10.1.2 Book Chapters

- T. Schrefl, H. Forster, D. Suess, W. Scholz, V. D. Tsiantos and J. Fidler, "Micromagnetic simulation of switching events", in Advances in Solid State Physics, Bernhard Kramer (ed.), Springer Verlag, 2001, p. 623-635. [PDF Text], [PDF Figures]
- T. Schrefl, J. Fidler, D. Suess and V. Tsiantos, "Micromagnetic simulation of dynamic and thermal effects", in Advanced magnetic materials, Y. Liu, D.J. Sellmyer and D. Shindo (ed.), (2002), in press. [PDF Full-Text]
- T. Schrefl, D. Suess, W. Scholz, H. Forster, V. Tsiantos, and J. Fidler, "Finite element micromagnetics", in Lecture Notes in Computational Science and Engineering, Springer, in press. [PDF Full-Text]
## 10.1.3 Journals and conference proceedings

- T. Schrefl, J. Fidler, D. Suess and W. Scholz, "Hysteresis and switching dynamics of patterned magnetic elements", Journal Physica B-Condensed Matter 275, 55-58 (2000). [PDF Full-Text]
- T. Schrefl and J. Fidler, "Reversal modes and revesal times in submicron-sized elements for MRAM applications", Computational Materials Science 17 (2000) 490-495. [PDF Full-Text]
- B. Streibl, J. Fidler and T. Schrefl , "Domain wall pinning in high temperature Sm(Co,Fe,Cu,Zr)7-9 magnets," J. Appl. Phys. 87 (2000) 4765-4767. [PDF Full-Text]
- T. Schrefl, J. Fidler and M. Zehetmayer, "Micromagnetic simulation of 360 degree domain walls in thin Co-films," J. Appl. Phys. 87 (2000) 5517-5519. [PDF Full-Text]
- D. Suess, M. Dahlgren, T. Schrefl, R. Grössinger and J. Fidler, "Micromagnetic analysis of remanence and coercivity of nanocrystalline Pr-Fe-B magnets," J. Appl. Phys. 87 (2000) 6573-6575. [PDF Full-Text]
- W. Scholz, D. Suess, T. Schrefl and J. Fidler, "Micromagnetic simulation of structure-property relations in hard and soft magnets," Computational Materials Science 18 (2000) 1-6. [PDF Full-Text]
- W. Scholz, T. Schrefl, and J. Fidler, "Micromagnetic simulation of thermally activated switching in fine particles," J. Magn. Magn. Mater. 233, 296-304 (2001). [PDF Full-Text]
- J. Fidler, T. Schrefl and D. Suess, "Grain boundaries in high performance magnets, reasons for poor or excellent properties," Proc. of Workshop on Grain Boundaries, Institute of Materials, University of Birmingham, I.R. Harris and I.P. Jones (eds), The University Press, Cambridge, 2001, pp. 147-163. [PDF Full-Text]
- J. Bernardi, T.Schrefl, J. Fidler, T. Rijks, K.de Kort, V. Archambault, D. Pere, S. David, D. Givord, J.F. Sullivan, P. Smith, J.M.D. Coey, U. Czernik and M. Grönefeld, "Preparation, magnetic properties and microstructure of lean rare-earth permanent magnetic materials", J. Magn. Magn. Mater. 219 (2000) 186-198. [PDF Full-Text]
- T. Schrefl, D. Süss and J. Fidler, "Wavelet based matrix compression in numerical micromagnetics", Technical Proceedings of the Third International Concerence on Modeling and Simulation of Microsystems, March 27-29, 2000, San Diego, USA, Computational Publications, Boston, 429-431 (2000). [PDF Full-Text]
- T. Schrefl, J.Fidler and W. Scholz , "Modeling and limits of advanced HT-magnets", IEEE Trans. Magn. 36, 3394-3398 (2000). [PDF Full-Text]
- W. Scholz, T. Schrefl and J. Fidler, "Langevin micromagnetics of recording media using subgrain discretization" IEEE Trans. Magn. 36, 3189-3191 (2000). [PDF Full-Text]
- D. Suess, T. Schrefl and J. Fidler, "Micromagnetic simulation of high energy density permanent magnets", IEEE Trans. Magn. 36, 3282-3284 (2000). [PDF Full-Text]
- T. Schrefl, D. Suess, W. Scholz, J. Fidler, "Finite element simulation of hard magnetic properties", Proc. 19th Annual Conference on Properties and Applications of Magnetic Materials, Chicago, May 2000.
- J. Fidler, T. Schrefl and T. Matthias, "TEM study of novel Sm-Co based high temperature magnets" , Proc. European Electron Microscopy Conference EUREM 12, Brno, July 2000, Volume II, (2000) P154-P155.
- T. Schrefl, W. Scholz, D. Suess and J. Fidler, "Computational micromagnetics: Prediction of time dependent and thermal properties", J. Magn. Magn. Mater. 226-230, 1213-1219 (2001). [PDF Full-Text]
- W. Scholz, J. Fidler, D. Suess and T. Schrefl, ''Langevin dynamics of small ferromagnetic particles and wires'', Proc. 16th IMACS World Congress, Lausanne, August 2000, M. Deville, R. Owens (ed)., p. 161-9. [PDF Full-Text]
- V. D. Tsiantos, J. J. Miles, B.K. Middleton, Stiffness in Micromagnetic Simulations, 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation, August 21-25, 2000, Lausanne, Switzerland, p. 311-7. [PDF Full-Text]
- J. Fidler, T.Schrefl, S. Sasaki and D. Süss "The role of intergranular regions in sintered Nd-Fe-B magnets with (B.H)max>420kJ/m3 (52.5 MGOe)", Proc. XI. Int. Symp. on Magnetic Anisotropy and Coercivity in Rare Earth Transition Metal Alloys, H. Kaneko, M. Homma, M. Okada (ed.), The Japan Institute of Metals, Sendai, Japan, 2000, pp. S45-S54.
- T. Schrefl, J. Fidler and D. Süss, "Micromagnetic modelling of nanocomposite magnets", Proc. XI. Int. Symp. on Magnetic Anisotropy and Coercivity in Rare Earth Transition Metal Alloys, H. Kaneko, M. Homma, M. Okada (ed.), The Japan Institute of Metals, Sendai, Japan, 2000, pp. S57-S71. [PDF Full-Text]
- J. Fidler, T. Schrefl, D. Suess and W. Scholz, "Dynamic micromagnetic simulation of the configurational anisotropy of nanoelements", IEEE Trans. Magn. 37, 2058-2060 (2001). [PDF Full-Text]
- D. Suess, T. Schrefl, J. Fidler and V. Tsiantos, "Reversal dynamics of interacting circular nanomagnets", IEEE Trans Magn. 37, 1960-1962 (2001). [PDF Full-Text]
- T. Schrefl, J. Fidler, J.N. Chapman and K. J. Kirk, "Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions", J. Appl. Phys. 89, 7000 (2001). [PDF Full-Text]
- D. Suess, T. Schrefl and J. Fidler, "Reversal modes, thermal stability, and exchange length in perpendicular recording media", IEEE Trans Magn. 37, 1664-1666 (2001). [PDF Full-Text]
- V. Tsiantos, D. Suess, T. Schrefl and J. Fidler, "Stiffness analysis for the muMAG standard problem #4", J. Appl. Phys. 89, 7600 (2001). [PDF Full-Text]
- J. Fidler, T. Schrefl, W. Scholz and D. Suess, "Rotational Magnetization Processes in Meso- and Nanoscopic Magnets" in Proceedings 6th Int. Workshop on 1&2-dimensional Magnetic Measurement and Testing, Bad Gastein, Sept. 2000, published 2001, ed. H. Pfützner, pp. 163-171.
- V. D. Tsiantos, T. Schrefl and J. Fidler, "Cost-effective way to speed-up micromagnetic simulations in granular media", Applied Numerical Mathematics 39, 191-204 (2001). [PDF Full-Text]
- J. Fidler, T. Schrefl, W. Scholz and D. Suess, "Micromagnetic modelling and properties of nanocomposite magnets", Proc. of 22nd RISO Int. Symposium on Material Science, Science of metastable and nanocrystalline alloys, Roskilde, Denmark, 2001, pp 1-14.
- V. D. Tsiantos, T. Schrefl, J. Filder amd A.G. Bratsos, "Patterned Media: Stiffness of the micromagnetic simulations - Effective ways to speed-up the simulations", Proceedings of Conf. on Nonlinear evolution equations and wave phenomena: Computation and theory (IMACS), Athens, Georgia, USA, April 2001 (2001) in press.
- T. Schrefl, V. D. Tsiantos, D. Suess, W. Scholz, H. Forster and J. Fidler, "Micromagnetic simulations and applications", Proc. 5th Int. Workshop on mathematical methods in scattering theory and biomedical technology, (2001) in press. [PDF Full-Text]
- J. Fidler, T. Schrefl, W. Scholz, D. Suess and V.D. Tsiantos, "Micromagnetic simulation of magnetisation reversal in rotational magnetic fields", Journal Physica B-Condensed Matter 306, 112-116 (2001). [PDF Full-Text]
- V. D. Tsiantos, T. Schrefl, D. Suess, W. Scholz, J. Fidler and J.M. Gonzales, "Micromagnetic simulation of magnetization reversal in Co/Ni multilayers", Journal Physica B-Condensed Matter 306, 38-43 (2001). [PDF Full-Text]
- J. Fidler, T. Schrefl, D. Suess, W. Scholz and V.D. Tsiantos, "Micromagnetic simulation of the magnetic switching behaviour of mesoscopic and nanoscopic structures", Proc. EMRS 2001 Spring Meeting, Symposium on "Computational Materials Science across time and length scales", Strasbourg, France, June 2001, in press. [PDF Full-Text]
- H. Forster, T. Schrefl, D. Suess, W. Scholz, V.D. Tsiantos and J. Fidler, "Micromagnetic simulation of domain wall motion in magnetic nano-wires", J. Magn. Magn. Mater., in press. [PDF Full-Text]
- D. Suess, W. Scholz, T. Schrefl, and J. Fidler, "Fast switching of small magnetic particles", J. Magn. Magn. Mater., in press. [PDF Full-Text]
- V. D. Tsiantos, D. Suess, W. Scholz, T. Schrefl and J. Fidler, "Effect of spatial correlation length in Langevin micromagnetic simulations", J. Magn. Magn. Mater., in press.[PDF Full-Text]
- T. Matthias, G. Zehetner, J. Fidler, W. Scholz, T. Schrefl, D. Schobinger and G. Martinek, "TEM-analysis of Sm(Co,Fe,Cu,Zr)z magnets for high temperature applications", J. Magn. Magn. Mater., in press. PDF Full-Text]
- W. Scholz, J. Fidler, T. Schrefl and D. Suess, "Micromagnetic simulation of domain wall pinning in Sm(Co,Fe,Cu,Zr)z magnets", J. Magn. Magn. Mater., in press. [PDF Full-Text]
- J. Fidler and T. Schrefl, "Micromagnetic modelling and properties of nanocomposite magnets", Proc. of 22nd RISO Int. Symposium on Material Science, Science of metastable and nanocrystalline alloys, Roskilde, Denmark, Sept. 2001 (2001) in press.
- T. Matthias, G. Zehetner, W. Scholz, J. Fidler, T. Schrefl, D. Schobinger and G. Martinek,"TEM-Analysis of Sm(Co,Fe,Cu,Zr)z magnets for high temperature applications", Proc. Joint Austrian-German-Swiss Electron microscopy Conf., Sept. 2001, Innsbruck, (2001) in press.
- V. D. Tsiantos, T. Schrefl, D. Suess, W. Scholz, H. Forster and J. Fidler, "Time Integration Methods in Micromagnetic Simulations: Stiffness on Granular Media-Patterned Media and Proc. 5th Hellenic European Conference on Computer Mathematics & its Applications (HERMCA), Sept. 2001, Athens, Greece, (2001) in press.
- W. Scholz, D. Suess, T. Schrefl and J. Fidler, "Domain structures and domain wall pinning in arrays of elliptical NiFe nanoelements", J. Appl. Phys., in press. [PDF Full-Text]
- W. Scholz, J. Fidler, T. Schrefl, D. Suess, T. Matthias, "Micromagnetic 3D simulation of the pinning field in high temperature Sm(Co,Fe,Cu,Zr)z magnets", J. Appl. Phys., in press. [PDF Full-Text]
- H. Forster, T. Schrefl, D. Suess, W. Scholz, J. Fidler, and V. Tsiantos, "Domain wall motion in nano-wires using moving grids.", J. Appl. Phys. 91, in press. [PDF Full-Text]
- J. Fidler, T. Schrefl, V. Tsiantos and W. Scholz, "Ultrafast Switching of Magnetic Elements using a Rotating Field", J. Appl. Phys., in press. [PDF Full-Text]
- D. Suess, V. Tsiantos, T. Schrefl, W. Scholz, and J. Fidler, "Nucleation in polycrystalline nano elements using a preconditioned finite element method", J. Appl. Phys., in press. [PDF Full-Text]
- T. Schrefl, M. Schabes, B. Lengsfield, "Fast reversal dynamics in perpendicular magnetic recording media with soft underlayer", J. Appl. Phys. 91, in press. [PDF Full-Text]
- M. Schabes, B. Lengsfield, T. Schrefl, "Micromagnetic modelling of soft underlayer magnetization processes at bit transitions in perpendicular magnetic recording", IEEE Trans. Magn., in press.
- J. Fidler, T. Schrefl, V.D. Tsiantos, W. Scholz and D. Suess, "Fast switching behaviour of nanoscopic NiFe- and Co-elements", Computational Materials Science, in press.[PDF Full-Text]
- W. Scholz, H. Forster, J. Fidler, T. Schrefl, "Micromagnetic simulation of domain wall pinning and domain wall motion", Computational Material Science, in press. [PDF Full-Text]
- D. M. Newns, W. E. Donath, G. J. Martyna, M. E. Schabes, B. E. Lengsfield, T. Schrefl, "Performance of a Novel Algorithm for Perpendicular Magnetic Recording Simulation," Proceedings of The 3rd Workshop on Parallel and Distributed Scientific and Engineering Computing with Applications (PDSECA-02), in press.
- D. Suess, V. Tsiantos, T. Schrefl, J. Fidler, W. Scholz, H. Forster, R. Dittrich, J. Miles, "Time resolved micromagnetics using a preconditioned GMRES method," J. Magn. Magn. Mater., in press.
- D. Payer, D. Suess, T. Schrefl and J. Fidler, "Reversal processes in circular nanomagnets", J. Magn. Magn. Mater., submitted.
- D. Suess, W. Scholz, T. Schrefl, J. Fidler, R. Stamps, "Micromagnetic simulation of antiferromagnetic/ferromagnetic structures", IEEE Trans. Magn., submitted. [PDF abstract]
- R. Dittrich, W. Scholz, D. Suess, H. Forster, V. Tsiantos, T. Schrefl, J. Fidler, "Finite element simulation of discrete media with granular structure," IEEE Trans. Magn., submitted. [PDF Full-Text]
- H. Forster, T. Schrefl, J. Fidler, "Magnetization reversal in granular nanowires," IEEE Trans. Magn., submitted., [PDF Full-Text]
- T. Matthias, W. Scholz, J. Fidler, T. Schrefl, T. S. Rong, I. P. Jones, R. Harris, "Sm(Co,Fe,Cu,Zr)z magnets for high temperature applications: microstructural and micromagnetic analysis," IEEE Trans. Magn., submitted.
- J. Fidler, T. Schrefl, V. Tsiantos, H.Forster, D. Suess, W. Scholz, R. Dittrich, "FE simulation of fast switching behavior of granular nanoelements," IEEE Trans. Magn., submitted.
- D. C. Crew, Er. Girt,D. Suess,T. Schrefl, K. M. Krishnan,G.Thomas, and M.Guilot, "The effect of magnetic interactions between grains on reversal behavior in diluted Nd2Fe14B," Phys. Rev. B, submitted, [PDF Full-Text]
- D. Suess,T. Schrefl, J. Fidler, R. C. Woodward, T. G. St.Pierre, R. Street, S. Sun, C. Murray, L. Folks, B. Terris, "Reversal Processes in FePt Nanoparticle Arrays," IEEE Trans. Magn., submitted, [PDF Full-Text]
## 10.2 Invited talks and lectures

- Modeling and future trends of advanced magnets, Josef Fidler, Intermag 2000, Toronto, Candada, April 9, 2000.
- Finite element simulation of hard magnetic properties, Thomas Schrefl, Properties and Applications of Magnetic Materials Conference, Chicago, USA, May, 22, 2000.
- Computational micromagnetics: Prediction of time dependent and thermal properties, Thomas Schrefl, International Conference on Magnetism, Recife, Brasil, August 11, 2000.
- Coercivity and degree of alignment in sintered Nd-Fe-B magnets, Dieter Suess, University of Western Australia, Perth, September 10, 2000.
- Modeling of nanocomposite magnets, Thomas Schrefl, XVI International Worshop on Rare-Earth magnets and their Application, Sendai, Japan, September, 14, 2000.
- Micromagnetic modeling of time dependent phenomena, Thomas Schrefl, University of Electro-Communications, Tokyo, September 18, 2000.
- Fast switching and energy barriers in perpendicular media, Thomas Schrefl, Instituto de Magnetismo Aplicado, Madrid, November 16, 2000.
- Dynamic and thermal effects in micromagnetics, Thomas Schrefl, Instituto de Ciencia de Materiales de Madrid, November 21, 2000.
- Simulation dynamischer und thermischer Magnetisierungsvorgänge - Optimierung von Speicher und Sensorelementen, Thomas Schrefl, Institut für Experimentalphysik, Vienna University of Technology, 6. Dezember 2000.
- Numerical micromagnetics using finite elements, Thomas Schrefl, IBM Alamaden research center, San Jose, USA, January 19, 2001.
- Finite element micromagnetics, Thomas Schrefl, GAMM Workshop on computational electromagnetics, Kiel, Germany, January 27, 2001.
- Finite element simulation, Thomas Schrefl, Computational Material Science, Science-College-Seminar, Vienna University of Technology, March, 5, 2001.
- Simulation and design of magnetic materials, Thomas Schrefl, Computational Material Science, Science-College-Seminar, Vienna University of Technology, March, 12, 2001.
- Fast and thermal switching of small magnets, Thomas Schrefl, Spring meeting of the German Physical Society, Hamburg, March, 27, 2000.
- Finite element simulation of magnetization reversal in nanowires, Hermann Forster, Worksop on Magnetization reversal and electron transport in nanonstructures, Gerhard-Mercator University, Duisburg, Germany, April 27.
- Numerical micromagnetics, Thomas Schrefl, IBM Almaden Research Center, San Jose, CA, Mai 30, 2001.
- Micromagnetic simulation of domain wall motion in magnetic nano-wires, Thomas Schrefl, International Conference on Magnetic Nanowires, San Sebastian, Spain, June 21, 2001.
- Application of time resolved micromagnetism to small structures, Thomas Schrefl, Joint Summer workshop on "Mesomagnetism, Spin dynamics and Spin electronics, Santorin, Greece, July 1, 2001.
- Finite element micromagnetics: switching dynamics of magnetic elements and structures, Thomas Schrefl, 4th Joint UK Magnetics Worskshop, Cardiff University, July 10, 2001.
- Numerical micromagnetics: Recent advances and current limits, Thomas Schrefl, EPSRC Network meeting on theory and modeling in magnetism, Cardiff University, July 11, 2001.
- Dynamical magnetization switching, Dieter Suess, International workshop on "Ferromagnetic-semiconductor nanostructures", University of Regensburg, July, 26, 2001.
- Finite element approach to magnetic recording simulations, Thomas Schrefl, IBM TR Watson Research Center, York Town, N.Y., September 19, 2001.
- Adaptive mesh refinement in dynamic micromagnetic problems, Hermann Forster, Workshop on Magnetic Microstructures, Max Planck Institute for Mathematics in the Sciences, Leipzig, October 11, 2001.
- Micromagnetic simulations and applications, Thomas Schrefl, 5th International workshop on Mathematical Methods in Scattering Theory and Biomedical Technology, Greece, October 2001.
- Switching dynamics of magnetic nanoelements, Dieter Suess, University of Western Australia, Perth, November 22, 2001.
- Domain wall motion in nano-wires using moving grids, Hermann Forster, 46th Annual MMM Conference Seattle, Washington, November 13, 2001.
- Micromagnetic modelling of soft underlayer magnetization processes at bit transitions in perpendicular magnetic recording, Manfred Schabes, 1st North American Conference on Perpendicular Magnetic Recording, Miami, Florida, January 8, 2002.
## 10.3 Conference contributions

- T. Schrefl, D. Suess, J. Fidler, Wavelet Based Matrix Compression in Numerical Micromagnetics, Third International Conference on Modeling and Simulation of Microsystems, San Diego, California, U.S.A., March 27-29, 2000.
- T. Schrefl, W. Scholz, D. Suess, J. Fidler, Langevin micromagnetics of recording media using subgrain discretization, Intermag 2000, Toronto, Canada, April, 9, 2000.
- T. Schrefl, W. Scholz, D. Suess, J. Fidler, Micromagnetic simulation of high energy density permanent magnets, Intermag 2000, Toronto, Canada, April, 11, 2000.
- T. Schrefl, W. Scholz, J. Fidler, D. Süss, Langevin dynamics of small ferromagnetic particles and wires, 16th IMACS World Congress 2000 on Scientific Computing, Applied Mathematics and Simulation, Lausanne, August, 24, 2000.
- V. D. Tsiantos, J. J. Miles, B.K. Middleton, Stiffness in Micromagnetic Simulations, 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation, August 21-25, 2000, Lausanne, Switzerland.
- V. D. Tsiantos, J. J. Miles, and M. Jones, Preconditioned Krylov Subspace methods in Micromagnetic Simulations, 11-14 September 2000, Barcelona, Spain.
- J. Fidler, T.Schrefl, S. Sasaki and D. Suess, The role of intergranular regions in sintered Nd-Fe-B magnets with (B.H)max>420kJ/m3 (52.5 MGOe), Int. Symp. on Magnetic Anisotropy and Coercivity in Rare Earth Transition Metal Alloys, Sendai, Japan, September, 15, 2000.
- J. Fidler, T. Schrefl, D. Suess and W. Scholz, Dynamic micromagnetic simulation of the configurational anisotropy of nanoelements, Joint MMM-Intermag Conference, San Antonio, TX, January 9, 2001.
- D. Süss, T. Schrefl, J. Fidler and V. Tsiantos, Reversal dynamics of interacting circular nanomagnets, IEEE Trans Magn. (2001), January, 10, 2001.
- T. Schrefl, J. Fidler, J.N. Chapman and K. J. Kirk, Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions, Joint MMM-Intermag Conference, San Antonio, TX, January 10, 2001.
- D. Süss, T. Schrefl and J. Fidler, Reversal modes, thermal stability, and exchange length in perpendicular recording media, Joint MMM-Intermag Conference, San Antonio, TX, January 10, 2001.
- V. Tsiantos, D. Suess, T. Schrefl and J. Fidler, Stiffness analysis for the muMAG standard problem #4, Joint MMM-Intermag Conference, San Antonio, TX, January 11, 2001.
- D. Suess, H. Forster, W. Scholz, R. Dittrich, V. Tsiantos, T. Schrefl and J. Fidler, Numerical Methods in Micromagnetic Simulations, Joint Summer workshop on "Mesomagnetism, Spin dynamics and Spin electronics, Santorin, Greece, July 1, 2001 (poster). [PDF]
- R. Dittrich, W. Scholz, T. Schrefl, J. Fidler, D. Suess, H. Forster, V. Tsiantos, Thermal Activation in Micromagnetics, Joint Summer workshop on "Mesomagnetism, Spin dynamics and Spin electronics, Santorin, Greece, July 1, 2001 (poster). [PDF]
- D. Suess, W. Scholz, T. Schrefl, and J. Fidler, "Fast switching of small magnetic particles", JEMS'01 Conf. Grenoble August. 2001 (poster). [PDF]
- V.D. Tsiantos, W. Scholz, D. Suess, T. Schrefl and J. Fidler, Effect of spatial correlation length in Langevin micromagnetic simulations, JEMS'01 Conf. Grenoble August 2001.
- T. Matthias, G. Zehetner, J. Fidler, W. Scholz, T. Schrefl, D. Schobinger and G. Martinek, TEM-analysis of Sm(Co,Fe,Cu,Zr)z magnets for high temperature applications, JEMS'01 Conf. Grenoble August 2001 (poster).
- W. Scholz, J. Fidler, T. Schrefl, D. Suess and T. Matthias, Micromagnetic simulation of domain wall pinning in Sm(Co,Fe,Cu,Zr)z magnets, JEMS'01 Conf. Grenoble, August 2001 (poster). [PDF]
- T. Matthias, G. Zehetner, W. Scholz, J. Fidler, T. Schrefl, D. Schobinger, G. Martinek, TEM-Analysis of Sm(Co,Fe,Cu,Zr)z magnets for high temperature applications, Dreiländertagung für Elektronenmikroskopie, Innsbruck, Austria, September 11, 2001.
- J. Fidler, T. Schrefl, D.Suess and W. Scholz, Fast switching behaviour of nanoscopic NiFe- and Co-elements, Conference of the COST P3 Action "Simulation of Physical Phenomena in Technological Applications", Madrid, Spain, September 25, 2001.
- V. D. Tsiantos, T. Schrefl, D. Suess, W. Scholz, H. Forster and J. Fidler, Time Integration Methods in Micromagnetic Simulations: Stiffness on Granular Media-Patterned Media and , 5th Hellenic European Conference on Computer Mathematics & its Applications (HERMCA), Athens, Greece, September 20, 2001.
- W. Scholz, H. Forster, J. Fidler, T. Schrefl, Micromagnetic simulation of domain wall pinning and domain wall motion, Conference of the COST P3 Action "Simulation of Physical Phenomena in Technological Applications", Madrid, Spain, September 25, 2001.
- W. Scholz, D. Suess, T. Schrefl and J. Fidler, Domain structures and domain wall pinning in arrays of elliptical NiFe nanoelements, 46 Annual MMM Conference Seattle, Washington, November 13, 2001.
- W. Scholz, J. Fidler, T. Schrefl, D. Suess, T. Matthias, Micromagnetic 3D simulation of the pinning field in high temperature Sm(Co,Fe,Cu,Zr)z magnets, 46 Annual MMM Conference Seattle, Washington, November 16, 2001.
- J. Fidler, T. Schrefl, V. Tsiantos and W. Scholz, Ultrafast Switching of Magnetic Elements using a Rotating Field, 46 Annual MMM Conference Seattle, Washington, November 15, 2001 (poster). [PDF]
- D. Suess, V. Tsiantos, T. Schrefl, W. Scholz, and J. Fidler, Nucleation in polycrystalline nano elements using a preconditioned finite element method, 46th Annual MMM Conference Seattle, Washington, November 15, 2001 (poster). [PDF]
- D. M. Newns, W. E. Donath, G. J. Martyna, M. E. Schabes, B. E. Lengsfield, T. Schrefl, Performance of a Novel Algorithm for Perpendicular Magnetic Recording Simulation, 3rd Workshop on Parallel and Distributed Scientific and Engineering Computing with Applications (PDSECA-02), Fort Lauderdale, Florida, April 15-19, 2002.
- D. Suess, W. Scholz, T. Schrefl1, J. Fidler, R. Stamps, Micromagnetic simulation of antiferromagnetic/ferromagnetic structures, Intermag Conference, Amsterdam, Netherland, May 1, 2002.
- R. Dittrich, W. Scholz, D. Suess, H. Forster, V. Tsiantos, T. Schrefl, J. Fidler, Finite element simulation of discrete media with granular structure, Intermag Conference, Amsterdam, Netherland, May 2, 2002 (poster).
- H. Forster, T. Schrefl, J. Fidler, Magnetization reversal in granular nanowires, Intermag Conference, Amsterdam, Netherland, May 2, 2002.
- T. Matthias, W. Scholz, J. Fidler, T. Schrefl, T. S. Rong, I. P. Jones, R. Harris, Sm(Co,Fe,Cu,Zr)Z magnets for high temperature applications: microstructural and micromagnetic analysis, Intermag Conference, Amsterdam, Netherland, May 2, 2002.
- J. Fidler, T. Schrefl, V. Tsiantos, H.Forster, D. Suess, W. Scholz, R. Dittrich, FE simulation of fast switching behavior of granular nanoelements, Intermag Conference, Amsterdam, Netherland, May 2, 2002 (poster).
## 11.0 Gallery

In order to illustrate the simulation results the following animations can be viewed with the CD version of the midterm report.

## 11.1 Discrete storage media

Discrete media show great potential for future ultra-high density magnetic recording up to a storage density of 500 Gbit/intion reversal process of a continuous film, a single island, and magnetostatically interacting "bits" of a discrete media. (see R. Dittrich, W. Scholz, D. Suess, H. Forster, V. Tsiantos, T. Schrefl, J. Fidler, "Finite element simulation of discrete media with granular structure," IEEE Trans. Magn., submitted. [PDF Full-Text]).

Expansion of bubble domains in a continuous granular film in a constant applied field. The diameter of the columnar grains is 10 nm. The material parameters are that of CoCrPt. The magnetization is perpendicular to the film plane. Red: Magnetization up; blue: magnetization down. [movie]

Magnetization reversal of a single island of a discrete media. Gyromagnetic precession and domain wall motion influence the reversal process. The island consists of 49 grains. [movie]

Successive reversal of the islands in an array of bits. The external field increases with time. The misorientation of the anisotropy axes and the magnetostatic interactions cause a spread in the switching field of the individual islands. [movie]

## 11.2 Perpendicular magnetic recording

Perpendicular recording is a possible candidate to overcome thermal stability problems in conventional longitudinal media. The simulations of the writing process requires a fully integrated model of the data layer, the soft under layer, and the recording head. (see D. Suess, T. Schrefl and J. Fidler, "Reversal modes, thermal stability, and exchange length in perpendicular recording media", IEEE Trans Magn. 37, 1664-1666 (2001). [PDF Full-Text] and T. Schrefl, M. Schabes, B. Lengsfield, "Fast reversal dynamics in perpendicular magnetic recording media with soft underlayer", J. Appl. Phys. 91, in press. [PDF Full-Text]).

Magnetization reversal of a columnar grain in a perpendicular medium. If the column length exceeds 15 nm, the magnetization reversal process becomes nonuniform. A reversed domain nucleate and expands. Gyromagnetic precession dominates the reversal process. [movie]

Dynamic switching of the data layer and the soft underlayer. The data layer consists of 1000 grains with a grain diameter of 8 nm. The movie shows the magnetic moments in a slice plane through the model system (shown on the left) during magnetization reversal. [movie]

Simulation of the writing process on perpendicular media. Data layer, soft underlayer, and the head are included in the micromagnetic calculations. The head moves with constant velocity. The image on the left shows written bit transitions on a perpendicular recording media. [movie]

## 11.3 FePt Nanoparticles

Self assembled arrays of FePt particles have been studied as a possible candidate for ultrahigh density data storage. (see D. Suess,T. Schrefl, J. Fidler, R. C. Woodward, T. G. St.Pierre, R. Street, S. Sun, C. Murray, L. Folks, B. Terris, "Reversal Processes in FePt Nanoparticle Arrays," IEEE Trans. Magn., submitted, [PDF Full-Text])

For the simulations the diameter of one particle is assumed to be 4nm. Every sphere consists of three orthogonal uniaxial easy axes. The movie shows the reversal process of a three dimensional array of FePt particles after the application of an external field. [movie]

## 11.4 Microstructure of magnetic nano-elements

Small magnetic elements are the basic structural units of discrete storage media, magnetic sensors, or magnetic storage elements (MRAMS). Finite element micromagnetic simulations reveal the influence of the surface roughness and the grain structure on the switching field and the switching time (see D. Suess, V. Tsiantos, T. Schrefl, W. Scholz, and J. Fidler, Nucleation in polycrystalline nano elements using a preconditioned finite element method, 46th Annual MMM Conference Seattle, Washington, November 15, 2001 (poster). [PDF] and D. Suess, V. Tsiantos, T. Schrefl, W. Scholz, and J. Fidler, "Nucleation in polycrystalline nano elements using a preconditioned finite element method", J. Appl. Phys., in press. [PDF Full-Text]).

Magnetization reversal in an 80 nm x 400 nm x 25 nm Co element with zero anisotropy and flat surfaces. The image on the left shows remanent states and transient states during magnetization reversal (time t in ns after the application of an external field). The magnetization reversal involves the formation and movement of vortices. [movie]

Magnetization reversal in an 80 nm x 400 nm x 25 nm Co element with zero anisotropy and surface roughness. The image on the left shows remanent states and transient states during magnetization reversal (time t in ns after the application of an external field). Both the coercive field and the switching time decreases with respect to perfectly flat elements. [movie]

Magnetization reversal in polycrystalline Co element (grain diameter 8nm) with random anisotropy and surface roughness. The image on the left shows remanent states and transient states during magnetization reversal (time t in ns after the application of an external field). This element switches faster than the perfect elements. [movie]

## 11.5 Vortices in square and circular elements

Sensors and storage applications requires a well defined switching behavior of the individual nano-elements. A crucial issue is the formation and motion of vortices. The nucleation of vortices and their stability was investigated in square and circular nano-dots (see D. Suess, T. Schrefl, J. Fidler and V. Tsiantos, "Reversal dynamics of interacting circular nanomagnets", IEEE Trans Magn. 37, 1960-1962 (2001). [PDF Full-Text] and T. Schrefl, J. Fidler, J.N. Chapman and K. J. Kirk, "Micromagnetic simulation of domain structures in patterned magnetic tunnel junctions", J. Appl. Phys. 89, 7000 (2001). [PDF Full-Text]).

Vortex motion in a 200 nm x 200 nm x 20 nm NiFe nanoelement. After the application of an applied field the magnetic domain which has its magnetization parallel to field expands until the vortex reaches its new equilibrium position. [movie]

Vortex formation and vortex motion during the reversal of a NiFe circular nano-element. The dot diameter is 110 nm. The thickness is 15 nm. The larger and the thicker the dots the easier vortices are formed during magnetization reversal. [movie]

Magnetization reversal in patterned magnetic tunnel junctions. The magnetostatic interactions between the pinned layer and the free layer are calculated self consistently. The movies shows the reversal of the free layer when the external field is applied to the C-state. [movie]

## 11.6 Magnetic dot arrays

Interacting magnetic nano-elements might be used in future magnetic logic circuits and magnetic field sensors. The functional behavior of these devices relies on the magnetostatic interactions between the nano-magnets. The magnetostatic interactions can be easily calculated with a hybrid finite element boundary method. The time resolved simulations clearly show how the particles interact with each other. (see D. Suess, T. Schrefl, J. Fidler and V. Tsiantos, "Reversal dynamics of interacting circular nanomagnets", IEEE Trans Magn. 37, 1960-1962 (2001). [PDF Full-Text] and W. Scholz, D. Suess, T. Schrefl and J. Fidler, "Domain structures and domain wall pinning in arrays of elliptical NiFe nanoelements", J. Appl. Phys., in press. [PDF Full-Text]).

Circular nano dots may be used to construct logic magnetic gates [RW Cowburn, Science 287 (2000) 1466]. With finite element simulation it is possible to calculate the switching time and the details of the dynamic interaction process. Neighboring dots form partial flux closure structures during reversal. [movie]

The switching process of an array of elliptical elements was investigated. The long axis is 165 nm, the short axis is 55 nm and the thickness of the element is 10 nm. Depending on the position within the chain the different switching mechanisms occur. During reversal collective domain patterns which extend over two elements develop. [movie]

## 11.7 Magnetic nano-wires

Magnetic nano-wires are of great practical and theoretical interest. Future magneto-electronic devices and magnetic sensors may be based on the magnetoresistance of domain walls moving in nano-wires. The motion of the domain walls can be effectively simulated using a moving mesh finite element scheme. (see H. Forster, T. Schrefl, D. Suess, W. Scholz, J. Fidler, and V. Tsiantos, "Domain wall motion in nano-wires using moving grids.", J. Appl. Phys. 91, in press. [PDF Full-Text] and H. Forster, T. Schrefl, J. Fidler, "Magnetization reversal in granular nanowires," IEEE Trans. Magn., submitted., [PDF Full-Text])

Domain wall motion in a Co nano-wire with a length of 600 nm and a diameter of 40 nm. The domain with the magnetization parallel to the direction of the applied expands. [movie]

Change of the finite element mesh during the motion of the domain wall. The mesh is refined at the current wall position, whereas finite elements are taken out in regions where the wall has passed by. [movie]

Magnetization reversal in granular Co nano-wires. The hysteresis properties of an array of nano-wires can be successfully simulated if the finite element model is built according to the grain structure observed in transmission electron microscopy (MPI Stuttgart). Left: TEM image showing the grain structure; Calculated snapshot of the magnetization distribution of the granular Co nano-wire during magnetization reversal. The field is applied perpendicular to the long axis of the wire. [movie]

## Credits

Special thanks to Rok Dittrich, Josef Fidler, Hermann Forster, Wilm Donath, Byron Lengsfield, Thorsten Matthias, Dennis Newns, Ivan Rungger, Manfred Schabes, Werner Scholz, Bernhard Streibl, Dieter Suess, Vassilios Tsiantos

Micromagnetics and Magnetic Materials http://magnet.atp.tuwien.ac.at Voice: (+43) 1 58801 13729 Fax: (+43) 1 58801 13798 thomas.schrefl (at) tuwien.ac.at |