Materials, Methods, Microstructure, and Magnetism

G. Malcolm Stocks, Oak Ridge National Laboratory
Bruce N. Harmon, Ames Laboratory/Iowa State University
Michael Weinert, Brookhaven National Laboratory

Research Objectives

To develop first-principles quantum mechanical methods for addressing materials problems microscopically, especially the relationship between technical magnetic properties and microstructure. Towards this goal are major problems involving microstructure (independent of magnetism), magnetism (independent of microstructure), giant magneto-resistance, and thermal properties.

Computational Approach

A number of different first-principles techniques, including tight-binding molecular dynamics (TBMD), an iterative pseudopotential (IP) method, and the locally self-consistent multiple scattering (LSMS) method, are used to perform fundamental studies of the atomistic, electronic, and magnetic structure of microstructural defects in metals and semiconductors that involve the interactions between large numbers of atoms (TBMD 20,000 atoms, IP > 200, LSMS 250 to 3000 atoms). In addition, we are developing spin dynamics based on both model Hamilitonians and (local) spin density calculations as a fundamental theory of the magnetic properties of metals and alloys.

Accomplishments

A new constrained local moment (CLM) theory of non-equilibrium states in metallic magnets has been developed that places a recent proposal of our co-workers at Ames Laboratory for first-principles spin dynamics (SD) on firm theoretical foundations. In SD, non-equilibrium "local moments" (for example, in magnets above the Curie temperature, or in the presence of an external field) evolve from one time step to the next according to a classical equation of motion. As originally formulated, the instantaneous magnetization states that are being evolved were not properly defined within density functional theory. The CLM theory properly formulates SD within constrained density functional theory. Local constraining fields are introduced, the purpose of which is to force the local moments to point in directions required at a particular time step of SD. A general algorithm for finding the constraining fields has been developed.

The existence of CLM states has been demonstrated by performing calculations for large (up to 1458 atom) unit cell disordered local moment (DLM) models of bcc Fe above its Curie temperature. This DLM model can be considered prototypical of the state of magnetic order at a particular step in a finite temperature SD simulation of paramagnetic Fe. Figure 1 illustrates the calculated magnetic moments (arrows in the left frame) and constraining fields (spikes in the right frame) corresponding to a 512-atom DLM model of paramagnetic bcc Fe. Magnitudes of magnetic moments and constraining fields are color coded. These calculations represent significant progress towards the goal of full implementation of SD and a first-principles theory of the finite temperature and non-equilibrium properties of magnetic materials.

The record-setting computational performance we obtained during our work demonstrating the existence of CLM states for large unit cell models (up to 1024 atoms) resulted in our receiving the 1998 Gordon Bell Award for parallel processing applications. The calculations that resulted in our nomination were performed using the LSMS method extended to treat CLM states. The basic LSMS method is an O(N) local density approximation (LDA) method that was specifically designed for implementation on MPPs and for treating the quantum mechanical interactions between large numbers of atoms. The constrained non-collinear LSMS code showed near linear scale-up for system sizes from 2 to 1024 atoms per unit cell, utilizing 2 to 1024 processing elements (PEs). We obtained a performance of 657 gigaflops on a Cray T3E-1200 LC1024/512 at a U.S. government site, and 276 and 329 Gflops on T3E-900 and T3E-1200 LC512 machines at NERSC and Cray Research, respectively. After our award nomination, we obtained a performance of 1.02 teraflops during a CLM calculation of a 1458 atom/unit cell CLM state of paramagnetic Fe (a 9x9x9 repeat of the underlying bcc unit cell). The calculations were performed on a 1,480-processor Cray T3E at the manufacturer's facility in Minnesota.

The 7x7 reconstruction of the Si(111) surface is one of the most fascinating surface structures. The presence of adatoms is a unique feature of the 7x7 reconstruction as compared to other reconstructed structures on the semiconductor surface.

Figure 2. Calculated STM images of the adatom vacancy on the Si(111)-(7x7) surface in the energy window of 0.6 to 0.1 eV below the Fermi energy level.
Top: STM image of the perfect (7x7) reconstruction at a constant height of 4.5 Angstrom.
Middle: 7x7 reconstruction with an adatom vacancy at a constant height of 4.5 Angstrom.
Bottom: Image of the same vacancy at a lower height of 4.0 Angstrom.

Using the recently developed environment-dependent silicon tight-binding potential, we have studied the structures, energies, and electronic properties of the adatom vacancies on the Si(111)-7x7 surface. The results show that adatom vacancies on the edge of the 7x7 unit cell have formation energies lower than those on the corner of the unit cell by about 0.1 eV. These results are in good agreement with experimental observations. We also observed a sharp defect state located at 0.5 eV below Fermi energy level which arises from the new bonding state of a pair of backbone atoms around the vacancy. Simulation of STM images shows that this localized vacancy state gives a pair of bright spots in the STM picture located at the two backbone atoms associated with the vacancy. Figure 2 shows the calculated STM images of the adatom vacancy on the Si(111)-(7x7) surface in the energy window of 0.6 to 0.1 eV below the Fermi energy level.

Significance

The availability of powerful and accurate first-principles techniques permits the study of quantum interatomic interactions on a length scale not previously accessible, opening up the possibility of relating these fundamental interatomic interactions to the strength, ductility, transport and magnetic properties of materials. Applied to magnetic materials, these techniques should help establish the foundations for understanding the relationship between the technical magnetic properties (permeability, coercivity, remenance) of magnets and microstructure.

Publications

B. Ujfalussy, Xindong Wang, Xiaoguang Zhang, D. M. C. Nicholson, W. A. Shelton, G. M. Stocks, A. Canning, and B. L. Gyorffy, "High performance first principles method for complex magnetic properties," in Proceedings of the ACM/IEEE SC98 Conference, Orlando, Florida, November 7-13 (IEEE Computer Society, Los Alamitos, CA 90720-1264), CD-ROM (1998).

M. Alatalo, M. Weinert, and R. E. Watson, "Stability of Zr-Al alloys," Phys. Rev. B 57, R2009-R2012 (1998).

K. M. Ho, A. Shvartsburg, B. C. Pan, Z. Y. Lu, C. Z. Wang, J. Wacker, J. L. Fye, and M. F. Jarrold, "Structures of medium-sized silicon clusters," Nature 392, 582 (1998).