INTRODUCTION (What? Why? and Potential Impact)
The confluence of new theoretical and algorithmic advances with rapidly expanding computational resources make now a particularly opportune time to initiate a major project involving magnetic materials modeling. Micro-magnetics, the phenomenological applied branch of magnetism, is able to model phenomena at ever smaller length scales, while a first principles electronic structure method, which provides a credible fundamental theory of magnetism, is able to treat complex and inhomogeneous systems involving an increasingly large number of atoms. An effective collaboration between these two, currently separate, communities would enable the incorporation of first principles input into micro-magnetics models thereby yielding microscopic physics based comprehension of the mechanisms that control the properties of real magnetic materials. Success would both advance our basic science understanding of a complex material system while having direct technological impact. Initial successes would permit the undertaking of fundamental studies of poorly understood essential magnetic phenomena such as defect induced domain wall pinning and nucleation. The enabling science would come from building the bridge that connects the underlying quantum mechanical mechanisms that are responsible for magnetism to the fundamental interactions that govern the observed macroscopic magnetic properties (e.g. permeability, coercivity and remanence) of real materials. The ultimate goal would be to enable accurate and reliable computational modeling that could then be used to improve material performance and aid the development of new materials within the $150B/year magnetic materials industry. Long term relevance to the DOE mission includes the possibility of finding magnetic materials with high coercivities, higher Curie temperatures, and larger energy products; in addition to lighter and more efficient magnetic materials for motors and transformers. In the magnetic recording industry ($>50B/year) the need for higher fidelity physics based modeling is especially acute. Here, impelled by market forces to achieve increases in the data storage capacity at an astounding rate of 60%/year, materials scientists are running into science roadblocks as the length scale of components continues to shrink. In other words, conventional phenomenological understanding of the macroscopic physics does not permit today's technology to be extrapolated to significantly smaller length scales.
SCIENCE ISSUES
The central scientific challenge of this project is to develop rigorous approaches to both refining and bridging the models that describe magnetic phenomena on different length scales. At the microscopic length scale, modern electronic structure techniques are capable of calculating fundamental magnetic properties (magnetic moments, exchange interactions, and in many cases magneto-crystalline anisotropy) of many materials. At a larger, but still relatively small length scale, spin dynamics (SD) calculations that treat only the spin degrees of freedom by using a Heisenberg model, have had some success in describing the statistical mechanics of moment re-orientations. At the macroscopic length scale, there have been significant advances in both developing and numerically solving a reasonable phenomenological continuum model that describes the "micro-magnetics" problem. It is the micro-magnetics calculations that contribute to evaluating the technologically relevant materials properties of a given system. Therefore to achieve the envisioned goal, it will be necessary to be able to take fundamental quantities (exchange interactions, anisotropy energies, etc.) calculated at the atomic level, e.g. near interfaces or defects and ultimately use them as input for a micro-magnetics model. In general there will be an intermediate model that describes the interactions between individual spins and the magnetic field, with the scientific challenge of linking the form of the model and the parameters in the model to the electronic structure calculations for real materials. The term "multiscale-modeling" is currently applied for many similar computational materials problems, where in general the mathematical model that describes the manifest phenomena changes with characteristic length scales. In this particular case, the achieving transition from atomic-scale results to the Landau-Lifshitz-Gilbert (LLG) equation used in micro-magnetics calculations seems highly feasible because of the similarity in the form of the SD and LLG Hamiltonians; i.e., both are Heisenberg-like, albeit on different length scales.
While the primary challenge is in bridging the length scales, there are several additional challenges to meet along the way to developing reliable and accurate methods that will be applicable to wide classes of materials. The application of first principles theory to study the dynamics of magnetic moments and their correlations at finite temperature is just emerging. Here, the basic precessional dynamics of the magnetic moment seems under control, but there are fundamental issues that are not in hand concerning the damping term that enters the equations of motion. There exist similar issues regarding the equivalent term in the micro-magnetics LLG equation as well as determining the connection between the two. At the quantum level, there is a tangential, but potentially significant, scientific issue. Whereas, transition metals and many of their alloys and compounds can be handled with reasonable reliability and accuracy, highly correlated, narrow band materials, such as transition metal oxides and rare earth materials, still require further development of more accurate approaches.
COMPUTATIONAL ISSUES
The computational requirements for studying magnetism with the large unit cells required to model defects and thermal properties are quite significant. However, many of the codes required to start this project are available, although not in one place. Parallel versions of the relevant first principles codes that scale as order-N already exist. Indeed, a code running a first principles SD calculation in iron won the 1998 Gordon Bell Award for the fastest real application (achieving more than 600 GFLOPS). Classical SD codes still require parallelization and scale-up. The generalization to three dimensions from the currently available two-dimensional micro-magnetics codes will greatly increase the complexity and will require the development of parallel algorithms. Integration of these diverse codes into a flexible problem-solving environment, able to access a wide range of computer resources from high-end MPP machines to work stations, would be highly desirable, but are quite non-trivial. There are numerous numerical issues in formulating and solving the resulting numerical models. For example, at the atomic scale, the equations of motion are extremely stiff. Another example is the need to develop effective capabilities for handling the very long-range dipolar interactions.
PARTNERING
The ideal team for the highest likelihood of success would include a wide range of expertise including first-principles calculations of magnetic structure, statistical mechanics and SD, micro-magnetics formulations and calculations. Expertise in first-principles approaches to narrow band materials would be highly desirable, because of the importance of highly correlated and f-band materials. There are numerous numerical and mathematical challenges in formulating and solving the models at the various length scales, which implies the need for applied mathematicians. Some of the obvious needs for mathematical developments include approaches to stiff equation solvers, fast Fourier transforms, fast-multipoles and possibly wavelets. The large-scale nature of the computational requirements necessitates the need for computational scientists with expertise in parallelization of codes, software engineering, and user interfaces. No one lab or organization has the expertise in all of these topics. Communication amongst such a diverse team will require significant attention. We envision web-based conferencing and the use of electronic notebooks, periodic meetings, extended visits between organizations and the sharing of students and postdocs.
IMPLICATIONS OF SUCCESS
The identification of a prototype project where there is a large and evolving experimental data base on well characterized model systems, where detailed electronic structure calculations are possible, and micro-magnetics codes are applicable, will play an important role in the success of the project. Here modeling of multi-layer spin-valves is an obvious candidate. A workshop bringing together the above communities would be able to identify the appropriate system to assure a certain level of success.
The primary scientific goal of this project is to further the fundamental understanding of how atomic scale structures in the material lattice affect bulk magnetic properties. A consequence of achieving this goal would be a modeling tool capable of integrating atomic level understanding of magnetic properties and interactions with structure and microstructure. Such a capability would allow the prediction of technologically relevant magnetic properties and the design of magnetic devices. There is already a truly critical need for such a tool in the magnetic storage industry, in particular for the design of magnetic media, magnetic read heads and magnetic random access memory cells. The enabling tool would also provide needed guidance for the design of magnetic sensors, magnetic isolators and other magneto-electronic devices. For example, there is a critical need for such a tool in the design of high moment, high remanence permanent magnet materials.
Beyond the realm of magnetics, we believe that this multiscale modeling approach, which involves interactions of one or two dimensional defects, e.g. domain walls, with microstructure may serve as a paradigm for other more difficult multiscale modeling programs, for example, relating of interatomic bonding to mechanical properties.
WHAT MIGHT SUCCESS LOOK LIKE?
Success would be the completion of robust codes (made available on the web) for calculating exchange parameters; for using Heisenberg models in various applications (e.g. finite temperature simulations); and for coupling to micro-magnetics codes. Success would be the development of a high-fidelity micro-mechanics model that was derived entirely from information that originated in first principles calculations, with no empiricism or phenomenology for at least one material system. Success would be the development of a robust capability that could reliably calculate atomistic, first principles parameters for various real materials (with selected defects), parameters that could in turn be used in micro-magnetic codes to accurately predict the magnetic properties of relevant bulk magnets. Success would be the utilization of the developed capability to help improve or perhaps even discover new magnetic materials or new designs to optimize device performance.