We have studied the structural and spectral properties of the classical system consisting of a finite number of charged particles, moving in two dimensions (2D), and interacting through a screened Coulomb potential and held together by an anisotropic harmonic potential. It is known that for the bare Coulomb interaction, the system crystallizes in well defined ordered configurations in which the particles are distributed in shells. However, we have found that the occupation of the shells changes considerably as a function of the screening parameter, and for large screening, the shell structure disappears and the particles form a Wigner lattice. We have shown that the eigenmodes of the system stiffen with increasing screening. By increasing the anisotropy of the confining potential, we were able to drive the system from 2D to 1D; this change occurs through a series of structural transitions. These transitions are reflected in the mode spectrum which collapses into a narrower frequency region with increasing anisotropy.

Electron-pinned defect dipoles, in the form of highly stable triangle-diamond and/or triangle-linear dopant defect clusters with well defined relative positions for Ti reduction, are present in rutile In + Ta co-doped TiO2 for the colossal permittivity and low loss.

Using Path Integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2d Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d 3 He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for rs ≤ 175±10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.PACS Numbers: 73.20Dx, 67.8Jd The uniform system of electrons is one of the basic models of condensed matter physics. In this paper, we report on the first exact calculations of the spin Hamiltonian in the low density 2 dimensional Wigner crystal (2dWC) near melting. This system is realized experimentally with electrons confined at an semiconductor MOS-FET's and heterostructures [1], and for electrons on the surface of liquid helium [2].A homogeneous charged system is characterized by two parameters: the density given in terms of r s = a/a 0 = (m * /mǫ)(πa 2 0 ρ) −1/2 and the energy in effective Rydbergs Ry * = (m * /m e ǫ 2 )Ry where m * is the effective mass and ǫ the dielectric constant. Figure 1 summarizes the 2d phase diagram. At low density (large r s ) the potential energy dominates over the kinetic energy and the system forms a perfect triangular lattice, the Wigner crystal [3]. Tanatar and Ceperley [4] determined that melting at zero temperature occurs at r s ≃ 37 ± 5. Recent calculations [5] have shown that the low temperature phase is free of point defects for densities with r s ≥ 50 but defects may be present very near melting. At densities for r s ≥ 100 the melting is classical, and occurs for temperatures T melt = 2Ry/(Γ c r s ) where Γ c ≈ 137 [6].We determine the spin-spin interaction in the Wigner crystal, using Thouless' [8] theory of exchange. According to this theory, in the absence of point defects, at low temperatures the spins will be governed by a Hamiltonian of the form:where the sum is over all cyclic (ring) exchanges described by a cyclic permutation P , J P is its exchange frequency andP spin is the corresponding spin exchange operator. Path Integral Monte Carlo (PIMC) as suggested by Thouless [8] and Roger [9]has proved to be the only reliable way to calculate these parameters. The theory and computational method have been tested thoroughly on the magnetic properties of bulk helium obtaining excellent agreement with measured properties [10]. Rather surprisingly, it has been found [11] that in both 2d and 3d solid 3 He, exchanges of 2, 3 and 4 particles have roughly the same order of magnitude and must all be taken into account. This is known as the multiple spin exchange model(MSE). A WKB calculation of the exchange frequencies in the 2dWC by Roger [9] predicted that the three electron J 3 nearest neighbor exchange would dominate, leading to a ferromagnetic(F) ground state. It has be...