We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

Photoelectrochemical (PEC) cells offer the ability to convert electromagnetic energy from our largest renewable source, the Sun, to stored chemical energy through the splitting of water into molecular oxygen and hydrogen. Hematite (α-Fe(2)O(3)) has emerged as a promising photo-electrode material due to its significant light absorption, chemical stability in aqueous environments, and ample abundance. However, its performance as a water-oxidizing photoanode has been crucially limited by poor optoelectronic properties that lead to both low light harvesting efficiencies and a large requisite overpotential for photoassisted water oxidation. Recently, the application of nanostructuring techniques and advanced interfacial engineering has afforded landmark improvements in the performance of hematite photoanodes. In this review, new insights into the basic material properties, the attractive aspects, and the challenges in using hematite for photoelectrochemical (PEC) water splitting are first examined. Next, recent progress enhancing the photocurrent by precise morphology control and reducing the overpotential with surface treatments are critically detailed and compared. The latest efforts using advanced characterization techniques, particularly electrochemical impedance spectroscopy, are finally presented. These methods help to define the obstacles that remain to be surmounted in order to fully exploit the potential of this promising material for solar energy conversion.

Solar Water Splitting: Progress Using Hematite (α‐Fe2O3) Photoelectrodes

Physical Review B

Multiferroic magnetoelectric composite systems such as ferromagnetic-ferroelectric heterostructures have recently attracted an ever-increasing interest and provoked a great number of research activities, driven by profound physics from coupling between ferroelectric and magnetic orders, as well as potential applications in novel multifunctional devices, such as sensors, transducers, memories, and spintronics. In this Review, we try to summarize what remarkable progress in multiferroic magnetoelectric composite systems has been achieved in most recent few years, with emphasis on thin films; and to describe unsolved issues and new device applications which can be controlled both electrically and magnetically.

Recent Progress in Multiferroic Magnetoelectric Composites: from Bulk to Thin Films

A surface magnetoelectric effect is revealed by density-functional calculations that are applied to ferromagnetic Fe(001), Ni(001), and Co(0001) films in the presence of an external electric field. The effect originates from spin-dependent screening of the electric field which leads to notable changes in the surface magnetization and the surface magnetocrystalline anisotropy. These results are of considerable interest in the area of electrically controlled magnetism and magnetoelectric phenomena.

/pdf/surface-magnetoelectric-effect-in-ferromagnetic-metal-films-57a2zr0i5w.pdf

Surface magnetoelectric effect in ferromagnetic metal films.

The existence of multiple ferroic orders in the same material and the coupling between them have been known for decades. However, these phenomena have mostly remained the theoretical domain owing to the fact that in single-phase materials such couplings are rare and weak. This situation has changed dramatically recently for at least two reasons: first, advances in materials fabrication have made it possible to manufacture these materials in structures of lower dimensionality, such as thin films or wires, or in compound structures such as laminates and epitaxial-layered heterostructures. In these designed materials, new degrees of freedom are accessible in which the coupling between ferroic orders can be greatly enhanced. Second, the miniaturization trend in conventional electronics is approaching the limits beyond which the reduction of the electronic element is becoming more and more difficult. One way to continue the current trends in computer power and storage increase, without further size reduction, is to use multi-functional materials that would enable new device capabilities. Here, we review the field of multi-ferroic (MF) and magnetoelectric (ME) materials, putting the emphasis on electronic effects at ME interfaces and MF tunnel junctions.

Multi-ferroic and magnetoelectric materials and interfaces

Based on first-principles calculations, we demonstrate the impact of the electric polarization on electron transport in ferroelectric tunnel junctions (FTJs). Using a $\mathrm{Pt}/{\mathrm{BaTiO}}_{3}/\mathrm{Pt}$ FTJ as a model system, we show that the polarization of the ${\mathrm{BaTiO}}_{3}$ barrier leads to a substantial drop in the tunneling conductance due to changes in the electronic structure driven by ferroelectric displacements. We find a sizable change in the transmission probability across the $\mathrm{Pt}/{\mathrm{BaTiO}}_{3}$ interface with polarization reversal, a signature of the electroresistance effect. These results reveal exciting prospects that FTJs offer as resistive switches in nanoscale electronic devices.

/pdf/effect-of-ferroelectricity-on-electron-transport-in-pt-batio-4rdvhxrq4c.pdf

Effect of Ferroelectricity on Electron Transport in Pt / BaTiO 3 / Pt Tunnel Junctions

It is predicted that magnetic anisotropy of a thin magnetic film may be affected by the polarization of a ferroelectric material. Using a Fe∕BaTiO3 bilayer as a representative model and performing first-principles calculations, we demonstrate that a reversal of the electric polarization of BaTiO3 produces a sizable change in magnetic anisotropy energy of Fe films. Tailoring the magnetic anisotropy of a nanomagnet by an adjacent ferroelectric material may yield entirely new device concepts, such as electric-field controlled magnetic data storage.

/pdf/tailoring-magnetic-anisotropy-at-the-ferromagnetic-3xno7ca96c.pdf

Tailoring magnetic anisotropy at the ferromagnetic/ferroelectric interface

/pdf/magnetoelectric-effect-at-the-fe-3-o-4-batio-3-001-interface-2pssqtt3er.pdf

Julian P. Velev

Papers

Surface magnetoelectric effect in ferromagnetic metal films.

Multi-ferroic and magnetoelectric materials and interfaces

Effect of Ferroelectricity on Electron Transport in Pt / BaTiO 3 / Pt Tunnel Junctions

Tailoring magnetic anisotropy at the ferromagnetic/ferroelectric interface

Magnetoelectric effect at the Fe 3 O 4 /BaTiO 3 (001) interface: A first-principles study