Real-space study of the growth of magnesium on ruthenium

The growth of magnesium on ruthenium has been studied by low-energy electron microscopy (LEEM) and scanning tunneling microscopy (STM). In LEEM, a layer-by-layer growth is observed except in the first monolayer, where the completion of the first layer in inferred by a clear peak in electron reflectivity. Desorption from the films is readily observable at 400 K. Real-space STM and low-energy electron diffraction confirm that sub-monolayer coverage presents a moir\'e pattern with a 1.2 nm periodicity, which evolves with further Mg deposition by compressing the Mg layer to a 2.2 nm periodicity. Layer-by-layer growth is followed in LEEM up to 10 ML. On films several ML thick a substantial density of stacking faults are observed by dark-field imaging on large terraces of the substrate, while screw dislocations appear in the stepped areas. The latter are suggested to result from the mismatch in heights of the Mg and Ru steps. Quantum size effect oscillations in the reflected LEEM intensity are observed as a function of thickness, indicating an abrupt Mg/Ru interface.Comment: 21 pages, 10 figure

On a certain non-split cubic surface

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $$x_0(x_1^2 + x_2^2)=x_3^3$$ with a power-saving error term, which verifies the Manin-Peyre conjectures for this surface.Comment: v2. 18 pages, one author adde

Trade and Empire, 1700-1870

This paper surveys the rise and fall of the European mercantilist system, and the transition to the modern, well-integrated international economy of the 19th century. It also surveys the literature on the links between trade and economic growth during the period, and on the economic effects of empire.trade, empire, history

Trade and Empire, 1700-1870

This paper surveys the rise and fall of the European mercantilist system, and the transition to the modern, well-integrated international economy of the 19th century. It also surveys the literature on the links between trade and economic growth during the period, and on the economic effects of empire.trade, empire, history

Spontaneous chirality via long-range electrostatic forces

We consider a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of chiral helices, achiral rings or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns' size and pitch angle on the radius of the cylinder and salt concentration. We obtain a phase diagram by using numerical and analytic techniques. For pure Coulomb interactions, we find a ring phase for small radii and a chiral helical phase for large radii. At a critical salt concentration, the characteristic domain size diverges, resulting in macroscopic phase segregation of the components and restoring chiral symmetry. We discuss possible consequences and generalizations of our model.Comment: Revtex, 4 pages, 4 figure

Magnetism in nanometer-thick magnetite

The oldest known magnetic material, magnetite, is of current interest for use in spintronics as a thin film. An open question is how thin can magnetite films be and still retain the robust ferrimagnetism required for many applications. We have grown one-nanometer-thick magnetite crystals and characterized them in situ by electron and photoelectron microscopies including selected-area x-ray circular dichroism. Well-defined magnetic patterns are observed in individual nano-crystals up to at least 520 K, establishing the retention of ferrimagnetism in magnetite two-unit-cells thick.Comment: 5 pages, 4 figure