A Scalable Method for Ab Initio Computation of Free Energies in Nanoscale Systems

Markus Eisenbach  (Oak Ridge National Laboratory), Chenggang Zhou*  (Oak Ridge National Laboratory), Donald M. Nicholson  (Oak Ridge National Laboratory), Gregory Brown  (Florida State University), Jeff Larkin  (Cray Inc.), Thomas C. Schulthess  (Oak Ridge National Laboratory and ETH Zürich)

Achievement: A team led by Oak Ridge National Laboratory’s Markus Eisenbach was awarded the 2009 ACM Gordon Bell Prize, which honors the world’s highest-performing scientific computing applications.  Their code, the Wang-Landau Locally Self-consistent Multiple Scattering (WL-LSMS) for modeling magnetic structure  achieved 1.84 thousand trillion calculations per second (1.84 petaflops). WL-LSMS analyzes magnetic systems, in particular, the effect of temperature on those systems. By accurately revealing the magnetic properties of specific materials the project promises to enable the practical search for enhanced magnetic properties including stronger, more stable magnets, thereby contributing to advances in such areas as magnetic storage and the development of lighter, stronger motors for electric vehicles.

The WL-LSMS project initiated by T. Schulthess at the Center for Nanophase Materials Sciences (CNMS), was aimed toward making these types of advanced capabilities available to a broad scientific research community. Chenggang Zhou and Don Nicholson developed the necessary extensions to the WL-algorithm and LSMS respectively. Markus Eisenbach developed the combined WL-LSMS method, ran simulations, and evaluated results. Greg Brown, who was also funded by CNMS, performed key model-Hamiltonian simulations to help interpret the data. Markus Eisenbach was supported by CNMS/NTI at 25% in FY09 for the purpose of completing the final optimizations, which subsequently allowed the overall project submission into the GB finalist session.

Significance: The scientific calculation—known as WL-LSMS—allows researchers to directly and accurately calculate the temperature above which a material loses its magnetism—known as the Curie temperature. The WL-LSMS approach differs from earlier efforts because it sets aside empirical models and their attendant approximations to tackle the system through first-principles calculations. WL-LSMS combines two methods to achieve its goal. The first—known as locally self-consistent multiple scattering, or LSMS—applies density functional theory to solve the Dirac equation, a relativistic wave equation for electron behavior.  However, this approach only describes a system in its ground state at a temperature of absolute zero. By incorporating a Monte Carlo method known as Wang-Landau, which guides the LSMS application, technologically relevant temperatures can now be explored.

The work improves on previous advances in magnetic materials, in which materials research has led in the past century to more than a 50-fold increase in the magnetic strength of materials per volume and in the last decade to more than a 100-fold increase in the density of magnetic data storage. Other efforts that may benefit from the research include the design of more resilient steel, higher density magnetic storage of digital information, the development of future refrigerators that use magnetic cooling, and a rather broad set of applications in the soft materials arena.  Overall, this new capability demonstrates how advanced scientific computing can enable unique R&D in nanoscience.

Future Work: Future work will be focused on using this method for understanding a wide range of magnetic phenomena at finite temperature and toward using the WL method for addressing problems in soft materials modeling.

Acknowledgements: Thomas Schulthess, Chenggang Zhou, Gregory Brown, and Markus Eisenbach acknowledge the support of DOE Basic Energy Sciences, Division of Scientific User Facilities through the Center for Nanophase Materials Sciences and ORNL’s Ultrascale Computing Initiative within the Laboratory Directed Research and Development Program (LDRD) for initial code development and for subsequent scaling of the codes. Markus Eisenbach and Don Nicholson also acknowledge the support of the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy and ORNL’s Ultrascale Computing Initiative within its LDRD program. Jeff Larkin acknowledges the support of the Cray, Inc. Center for Excellence located at NCCS. This research used resources of the National Center for Computational Sciences at the Oak Ridge National Laboratory, which is supported by the Office of Sciences of the Department of Energy.

M. Eisenbach, C.-G. Zhou, D. M. Nicholson, G. Brown, J. Larkin, and T. C. Schulthess, A scalable method for ab initio computation of free energies in nanoscale systems, SC '09: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, Portland, OR, 2009.

C.-G. Zhou,  T. C. Schulthess, S. Torbrügge, and D. P. Landau, Wang-Landau algorithm for continuous models and joint density of states, Phys. Rev. Lett. 96 (2006), 120201.

Figure Caption: Top panel shows the magnetic statistical density of states of bulk iron computed via WL-LSMS. The bottom panel shows temperature dependent free energies as a function of magnetization for a 250 atom Fe cell.

* present address: J.P. Morgan Chase & Co