We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Multiferroic magnetoelectrics are materials that are both ferromagnetic and ferroelectric in the same phase. As a result, they have a spontaneous magnetization that can be switched by an applied magnetic field, a spontaneous polarization that can be switched by an applied electric field, and often some coupling between the two. Very few exist in nature or have been synthesized in the laboratory. In this paper, we explore the fundamental physics behind the scarcity of ferromagnetic ferroelectric coexistence. In addition, we examine the properties of some known magnetically ordered ferroelectric materials. We find that, in general, the transition metal d electrons, which are essential for magnetism, reduce the tendency for off-center ferroelectric distortion. Consequently, an additional electronic or structural driving force must be present for ferromagnetism and ferroelectricity to occur simultaneously.

Why Are There so Few Magnetic Ferroelectrics

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

3.6.1. Polishing and Cleaning 2663 3.6.2. Vacuum and Heat Treatments 2664 3.6.3. Carbon Electrode Activation 2665 3.7. Summary and Generalizations 2666 4. Advanced Carbon Electrode Materials 2666 4.1. Microfabricated Carbon Thin Films 2666 4.2. Boron-Doped Diamond for Electrochemistry 2668 4.3. Fibers and Nanotubes 2669 4.4. Carbon Composite Electrodes 2674 5. Carbon Surface Modification 2675 5.1. Diazonium Ion Reduction 2675 5.2. Thermal and Photochemical Modifications 2679 5.3. Amine and Carboxylate Oxidation 2680 5.4. Modification by “Click” Chemistry 2681 6. Synopsis and Outlook 2681 7. Acknowledgments 2682 8. References 2682

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Advanced carbon electrode materials for molecular electrochemistry.

Colossal magnetoresistance1—an unusually large change of resistivity observed in certain materials following application of magnetic field—has been extensively researched in ferromagnetic perovskite manganites. But it remains unclear why the magnetoresistive response increases dramatically when the Curie temperature (T C) is reduced. In these materials, T C varies sensitively with changing chemical pressure; this can be achieved by introducing trivalent rare-earth ions of differing size into the perovskite structure2,3,4, without affecting the valency of the Mn ions. The chemical pressure modifies local structural parameters such as the Mn–O bond distance and Mn–O–Mn bond angle, which directly influence the case of electron hopping between Mn ions (that is, the electronic bandwidth). But these effects cannot satisfactorily explain the dependence of magnetoresistance on T C. Here we demonstrate, using electron microscopy data, that the prototypical (La,Pr,Ca)MnO3 system is electronically phase-separated into a sub-micrometre-scale mixture of insulating regions (with a particular type of charge-ordering) and metallic, ferromagnetic domains. We find that the colossal magnetoresistive effect in low-T C systems can be explained by percolative transport through the ferromagnetic domains; this depends sensitively on the relative spin orientation of adjacent ferromagnetic domains which can be controlled by applied magnetic fields.

Percolative phase separation underlies colossal magnetoresistance in mixed-valent manganites

A negative isotropic magnetoresistance effect more than three orders of magnitude larger than the typical giant magnetoresistance of some superlattice films has been observed in thin oxide films of perovskite-like La0.67Ca0.33MnOx. Epitaxial films that are grown on LaAIO3 substrates by laser ablation and suitably heat treated exhibit magnetoresistance values as high as 127,000 percent near 77 kelvin and ∼1300 percent near room temperature. Such a phenomenon could be useful for various magnetic and electric device applications if the observed effects of material processing are optimized. Possible mechanisms for the observed effect are discussed.

http://science.sciencemag.org/content/sci/264/5157/413.full.pdf

Thousandfold Change in Resistivity in Magnetoresistive La-Ca-Mn-O Films

Vertically aligned yet laterally spaced nanoscale TiO2 nanotubes have been grown on Ti by anodization, and the growth of MC3T3-E1 osteoblast cells on such nanotubes has been investigated. The adhesion/propagation of the osteoblast is substantially improved by the topography of the TiO_2 nanotubes with the filopodia of growing cells actually going into the nanotube pores, producing an interlocked cell structure. The presence of the nanotube structure induced a significant acceleration in the growth rate of osteoblast cells by as much as ∼300–400%.

Significantly accelerated osteoblast cell growth on aligned TiO2 nanotubes.

Growth of nano-scale hydroxyapatite using chemically treated titanium oxide nanotubes.

Colossal magnetoresistance in excess of 106% has been obtained (at 110 K, H=6 T) in epitaxially grown La–Ca–Mn–O thin films. The as‐deposited film exhibits a substantial magnetoresistance value of 39 000%, which is further improved by heat treatment. The magnetoresistance is found to be strongly dependent on film thickness, with the value reaching the maxima at ∼1000 A thickness, and then reduced by orders of magnitude when the film is made thicker than ∼2000 A. This behavior is interpreted in terms of lattice strain in the La–Ca–Mn–O films.

Thickness dependence of magnetoresistance in La–Ca–Mn–O epitaxial films

We show a fully integrated, on-chip, vacuum microtriode fabricated via silicon micromachining processes using carbon nanotubes as field emitters. The triode is constructed laterally on a silicon surface using microelectromechanical systems (MEMS) design and fabrication principles. The technique incorporates high-performance nanomaterials in a MEMS design with mature solid-state fabrication technology to create miniaturized, on-chip power amplifying vacuum devices, which could have important and far-reaching scientific and technological implications.

Li-Han Chen

Papers

Thousandfold Change in Resistivity in Magnetoresistive La-Ca-Mn-O Films

Significantly accelerated osteoblast cell growth on aligned TiO2 nanotubes.

Growth of nano-scale hydroxyapatite using chemically treated titanium oxide nanotubes.

Thickness dependence of magnetoresistance in La–Ca–Mn–O epitaxial films

On-chip vacuum microtriode using carbon nanotube field emitters