# Research Highlights

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

Markus Eisenbach^{1} , Chenggang Zhou*^{1}, Donald M. Nicholson^{1}, Gregory Brown^{2}, Jeff Larkin^{3} , Thomas C. Schulthess^{1,4}

^{1}, Chenggang Zhou*

^{1}, Donald M. Nicholson

^{1}, Gregory Brown

^{2}, Jeff Larkin

^{3}, Thomas C. Schulthess

^{1,4}

**1**Oak Ridge National Laboratory, Oak Ridge, TN 37831,

**2**Florida State University, Florida

**3**Cray Inc..

**4**ETH Zurich, ..

### 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.

Sham potential and moment and the frozen potential rotated potential. The black arrow on the right illustrates that the moment associated with the rotated potential need not align with the rotated potential. The dashed line on the right indicates that the rotated potential will differ by small amounts from the actual Kohn-Sham potential. |

### 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.

Switching in (100) rhombohedral ferroelectrics can proceed in 4 equivalent states, which cannot be selected without broken symmetry.

Phase field modeling allows the deterministic switching mechanisms to be deciphered. Tip motion can be used to stabilize the preferred polarization state (color) at an existing domain wall (left) or in a uniform domain (right).

The unnormalized logarithmic Wang-Landau density of states ln g(E) for a periodic system of 16 iron atoms. | The unnormalized logarithmic Wang-Landau density of states ln g(E) for a periodic system of 250 iron atoms. |

### 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

### References

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