No abstract

We propose a statistical method to estimate densities of states (DOS) and thermodynamic functions of very large Hamiltonian matrices. Orthogonal polynomials are defined on the interval between lower and upper energy bounds. The DOS is represented by a kernel polynomial constructed out of polynomial moments of the DOS and modified to damp the Gibbs phenomenon. The moments are stochastically evaluated using matrixvector multiplications on Gaussian random vectors and the polynomial recurrence relations. The resulting kernel estimate is a controlled approximation to the true DOS, because it also provides estimates of statistical and systematic errors. For a given fractional energy resolution and statistical accuracy, the required cpu time and memory scale linearly in the number of states for sparse Hamiltonians. The method is demonstrated for the two-dimensional Heisenberg anti-ferromagnet with the number of states as large as 226. Results are compared to exact diagonalization where available.

We present the results of a theoretical model describing electrical spin injection from a spin-polarized contact into a nonmagnetic semiconductor. The model includes the possibility of interface resistance due, for example, to a tunnel barrier at the contact/semiconductor heterojunction, and shows that such interface resistance can be critical in determining spin injection properties. With no interface resistance spin injection is very weak for contacts with typical metallic resistivities. For higher bulk resistivity contacts, such as doped semiconductors, or for completely spin-polarized contacts, strong spin injection is possible without significant interface resistance. However the spin polarization must be extremely close to complete for contacts with metallic resistivities. A tunnel barrier with spin-dependent interface resistance can greatly enhance spin injection. An insulating tunnel barrier with a spin-polarized contact, and a ferromagnetic insulator tunnel barrier, both have spin-dependent interface resistance, and provide two promising approaches to achieve significant electrical spin injection. The model is consistent with a variety of experimental observations, identifies the basic physics problems that must be addressed to achieve a high degree of spin injection, and suggests systematic strategies to achieve strong spin injection.

No abstract

No abstract