Colossal Magneto Resistance
In October 2001, Apple Computer announced its new audio device, the iPod. This first generation device (on the left above) measured 4.02” x 2.43” x 0.78” and held 5Gb of data/music. Almost six years later, the iPod (right above) has grown to 160Gb of storage, while its overall size has decreased to 4.1” x 2.4” x .55”.
The iPod uses a compact disk driver as a storage media. The tremendous advances in storage capacity/density are due to increased understanding of the magnetic properties of metal oxides that exhibit “gigantic” or “colossal” magnetoresistance effects (CMR). Therefore, an understanding of CMR is important in data storage applications. One of the models for understanding CMR is quantum Monte-Carlo (QMC) simulations on a lattice.
In QMC simulations, each atom of the lattice is visited and the probability of a change (or event) is computed from all the eigenvalues of the Hamiltonian matrix. If a change is accepted, several entries in the Hamiltonian matrix are changed. After the entries are changed, all eigenvalues must be recomputed. A direct computation of all eigenvalues at every step is prohibitively expensive and limits the model to small 15 by 15 lattices. This model size imposes a limitation on the kinds of physical phenomena that can be studied. Oak Ridge National Laboratory is developing a method based on fast multipole method to incrementally update the eigenvalues from previously computed eigen-decomposition that is an order of magnitude faster than repetitive computation.
This algorithm will allow us to model larger 24 by 24 lattices. The move from 15 by15 to 24 by 24 will allow researchers to develop more complete and accurate understandings of the properties of materials which may have only been seen previously in partial form or influenced by finite system sizes.
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