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

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

We review recent experimental work falling under the broad classification of colossal magnetoresistance (CMR), which is magnetoresistance associated with a ferromagnetic-toparamagnetic phase transition. The prototypical CMR compound is derived from the parent compound, perovskite LaMnO 3. When hole doped at a concentration of 20–40% holes/Mn ion, for instance by Ca or Sr substitution for La, the material displays a transition from a high-temperature paramagnetic insulator to a low-temperature ferromagnetic metal. Near the phase transition temperature, which can exceed room temperature in some compositions, large magnetoresistance is observed and its possible application in magnetic recording has revived interest in these materials. In addition, unusual magneto-elastic effects and charge ordering have focused attention on strong electron–phonon coupling. This coupling, which is a type of dynamic extended-system version of the Jahn–Teller effect, in conjunction with the double-exchange interaction, is also viewed as essential for a microscopic description of CMR in the manganite perovskites. Large magnetoresistance is also seen in other systems, namely Tl 2Mn2O7 and some Cr chalcogenide spinels, compounds which differ greatly from the manganite perovskites. We describe the relevant points of contrast between the various CMR materials.

REVIEW ARTICLE: Colossal magnetoresistance

Electrical signals are produced by a pressure-responsive device, such signals being indicative of the position of locally applied pressure. The device comprises a position sensor assembly which comprises a composite layer medium including electrically conductive magnetic particles in a nonconductive matrix material. The particles are aligned into chains extending across the thickness of the layer, and chains include a non-conductive gap which is bridged upon application of sufficient pressure. The medium is sandwiched between sheet electrodes, and the resulting assembly may be transparent as is advantageous in writing pad and touch-sensitive screen applications. The pressure-responsive device is suitable, e.g., as an input device in graphics information systems, in combination with transmission and display facilities.

Pressure-responsive position sensor

A fine-scale dispersion of Y2BaCuO5 (“211”) particles ( ∼8000 A average diam.) within the YBa2Cu3O7-δ supercondu ctor (“123”) has been achieved by local melt-texture processing of off-stoichiometric Y-Ba-Cu-O prepared by the aerosol decomposition technique. The presence of such fine particles significantly reduces the thickness of the superconductor plate to below ∼ 7000 A. The plate thickness almost linearly with 211 particle size. The observed scaling relationship is most likely caused by the 211 inclusions serving as effective nucleation sites for 123 crystallization as well as restricting the plate coarsening below the peritectic temperature. The submicron-sized 211 particles tend to reduce microcracks and segregation of impurity phases at the plate boundaries, however, their effect on flux pinning appears to be insignificant.

Microstructure and properties of the Y-Ba-Cu-O superconductor with submicron “211” dispersions

Grain-growth enhancement in the YBa2Cu3O7−δ superconductor by silver-oxide doping

Electrical interconnections are made by means of a layer or sheet medium comprising chains of magnetically aligned, electrically conducting particles in a nonconducting matrix material. End particles of chains protrude from a surface of the medium, thereby enhancing electrical contact properties of the medium. The medium can be used for temporary as well as permanent connections; in the latter case the use of a nonconductive adhesive material is convenient for physical attachment to contacts on both sides of the medium.

Electrical interconnection by a composite medium

Superconducting properties of the YBa 2 Cu 3 O 7−δ compound with partial rare earth substitution (20 atomic pct substitution for yttrium) have been studied. Among the 14 rare earth elements investigated, La, Ce and Pr caused suppression in T c , while other elements had no effect. Some of the rare earths (Sm, Gd, Eu), when partially substituted for Y, resulted in a slight improvement in intragrain J c (flux pinning) as measured magnetically. Although the rare earth elements have widely different ionic radii, all the (RE) Ba 2 Cu 3 O 7−δ phases have been found to be soluble in YBa 2 Cu 3 O 7−δ with no detectable segregation observed by SEM and energy dispersive X-ray analysis.

Thomas Henry Tiefel

Papers

Pressure-responsive position sensor

Microstructure and properties of the Y-Ba-Cu-O superconductor with submicron “211” dispersions

Grain-growth enhancement in the YBa2Cu3O7−δ superconductor by silver-oxide doping

Electrical interconnection by a composite medium

Superconducting properties of YBa2Cu3O7−δ with partial rare earth substitution