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

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

The progress toward major applications of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$-type high-${T}_{c}$ superconductors has been hindered by low critical current densities (${J}_{c}$) and their significant deterioration in weak magnetic fields. The present work demonstrates that these problems can successfully be overcome through proper microstructural control using molten oxide processing. Melt-textured growth of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ from a supercooled melt created an essentially 100% dense structure consisting of locally aligned, long, needle-shaped grains (typically 40--600 \ensuremath{\mu}m in length). The needles appear to have their long axes parallel to the conduction plane (basal plane) of the orthorhombic structure, with a low-angle orientation change between adjacent grains. This new microstructure, which completely replaces the previous granular and random structure of the sintered precursor, exhibits a dramatically higher transport ${J}_{c}$ (7400 A/${\mathrm{cm}}^{2}$ at 77 K) than the typical sintered materials (${J}_{c}$=150--600 A/${\mathrm{cm}}^{2}$). Even more significant is the much reduced field dependence of ${J}_{c}$(\ensuremath{\approxeq}1000 A/${\mathrm{cm}}^{2}$ at H=1 T as compared to \ensuremath{\approxeq}1 A/${\mathrm{cm}}^{2}$ in the sintered structure), indicating that the coupling between grains is much stronger in the new structure. The mechanism responsible for the suppressed weak-link behavior in the melt-textured material is inferred to be the combined effects of the densification, alignment of crystals, and formation of cleaner grain boundaries.

Melt-textured growth of polycrystalline YBa2Cu3O7- delta with high transport Jc at 77 K.

The development of an optically transparent yet electrically conductive material made with a composite structure having preferentially arranged conductive paths is described. The medium contains many vertically aligned but laterally isolated chains of ferromagnetic spheres dispersed in a sheet of transparent polymer. The sheet material transmits more than 90 percent of the incident light and is highly conductive only in the thickness direction. When suitably modified, the material exhibits on-off electrical switchability at a certain threshold pressure. These characteristics confer potential usefulness for visual communication devices such as write pads or touch-sensitive screens.

https://science.sciencemag.org/content/sci/255/5043/446.full.pdf

Optically transparent, electrically conductive composite medium.

Bulk YBa2Cu3O7-δ superconductors, under certain processing conditions such as melt texturing, exhibit a very high dislocation density of 109 to 1010 per square centimeter. In addition, the density of low-angle grain boundaries in such samples can be significantly increased (to less than 700-nanometer spacing) through a dispersion of submicrometer-sized Y2BaCuO5 inclusions. These defect densities are comparable to those in high critical current thin films as revealed through scanning tunneling microscopy, and yet the critical current densities in the bulk materials (at 77 kelvin and a field of 1 tesla for example) remain at a 104 amperes per square centimeter level, about two orders of magnitude lower than in thin films. The results imply that these defect density levels are not significant enough to explain the difference in flux pinning strength between the thin film and bulk materials. The observation of spiral-like growth of the superconductor phase in bulk Y-Ba-Cu-O is also reported.

https://science.sciencemag.org/content/sci/253/5018/427.full.pdf

Dislocations and Flux Pinning inYBa2Cu3O7-δ

A new simple synthesis route was used to produce the ‘124’ superconductor YBa 2 Cu 4 O 8 . The method utilizes YBa 2 Cu 3 O 7 powder (‘123’) as a precursor, which is then converted to the 124 superconductor by reaction with a stoichiometric amount of CuO through normal grinding and sintering, without the need for high oxygen pressure processing. Sintered bars of the 124 superconductor exhibited a T c of ∼ 75 K in resistivity and AC magnetic susceptibility measurements. Transport critical current density was measured to be ∼ 150 A/cm 2 at 60 K, and showed a strong field dependence. This behavior, in combination with a relatively high J c (magn.) of 4 × 10 4 A/cm 2 at 60 K and H = 0.9 T, is indicative of Josephson weak links at grain boundaries, which is similarly observed in the 123 phase. It is also noted that the intragrain J c in the twin-free 124 superconductor is about the same as that in the twinned 123 superconductor at ∼ 15 degrees below their respective T c .

Thomas Henry Tiefel

Papers

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

Melt-textured growth of polycrystalline YBa2Cu3O7- delta with high transport Jc at 77 K.

Optically transparent, electrically conductive composite medium.

Dislocations and Flux Pinning inYBa2Cu3O7-δ

Synthesis and properties of the YBa2Cu4O8 superconductor