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

Magnetism and ferroelectricity are essential to many forms of current technology, and the quest for multiferroic materials, where these two phenomena are intimately coupled, is of great technological and fundamental importance. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The exciting new development is the discovery that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Such magnetic ferroelectricity, showing an unprecedented sensitivity to ap plied magnetic fields, occurs in 'frustrated magnets' with competing interactions between spins and complex magnetic orders. We summarize key experimental findings and the current theoretical understanding of these phenomena, which have great potential for tuneable multifunctional devices.

/pdf/multiferroics-a-magnetic-twist-for-ferroelectricity-40nmxke8g8.pdf

Multiferroics: a magnetic twist for ferroelectricity

BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

Physics and Applications of Bismuth Ferrite

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

Colossal magnetoresistance (CMR) phenomena are observed in the perovskite-type hole-doped manganites in which the double-exchange ferromagnetic metal phase and the charge–orbital ordered antiferromagnetic phase compete with each other. The quenched disorder arising from the inherent chemical randomness or the intentional impurity doping may cause major modifications in the electronic phase diagram as well as in the magnetoelectronic properties near the bicritical point that is formed by such a competition of the two phases. One is the phase separation phenomenon on various time-scales (from static to dynamic) and on various length-scales (from glass-like nano to grain-like micron). The other is the enhanced phase fluctuation with anomalous reduction in the transition temperatures of the competing phases (and hence in the bicritical-point temperature). The highly effective suppression of such a phase fluctuation by an external magnetic field is assigned here to the most essential ingredient of the CMR physics. Such profound and dramatic features as appearing in the bicritical region are extensively discussed in this paper with ample examples of the material systems specially designed for this purpose. The unconventional phase-controls over the competing phases in terms of magnetic/electric fields and photo-excitations are also exemplified.

https://iopscience.iop.org/article/10.1088/0034-4885/69/3/R06/pdf

Critical features of colossal magnetoresistive manganites

The detailed behavior of the phase transitions was mapped out for the series R${\mathrm{NiO}}_{3}$ as a function of the rare earth (R). A sharp insulator-metal transition is observed, which depends strongly on R.Forsmall$R it occurs at a higher temperature than the antiferromagnetic ordering (measured by muon-spin relaxation). By increasing either the temperature or the size of R, an insulator-metal transition is observed, most probably caused by the closing of the charge-transfer gap, induced by increase in the electronic bandwidth.

/pdf/systematic-study-of-insulator-metal-transitions-in-2x2sjurlrx.pdf

Systematic study of insulator-metal transitions in perovskites RNiO3 (R=Pr,Nd,Sm,Eu) due to closing of charge-transfer gap.

Synthesis, crystal structure, and properties of metallic PrNiO3: Comparison with metallic NdNiO3 and semiconducting SmNiO3

ONE of the main families of oxide superconductors comprises compounds with varying numbers of CuO2 sheets sandwiched between BiO or TIO bilayers1–5. The superconducting transition temperature (Tc) in these compounds increases with the number of CuO2 sheets; for example, Tc is 80–108 K for the double-sheet 2212 phase, and 110–125 K for the triple-sheet 2223 phase. Here we describe a new family of double-sheet copper oxide compounds with BiO or TIO bilayers, which can improve our understanding of the relationship between Tc and the CuO2 sheets. The new compounds, Bi2Sr2(Ln1–xCex)2Cu2O10+y, and Tl2Ba2(Ln1–xCex)2Cu2O10+y (where Ln is Sm, Eu or Gd), have double CuO2 pyramidal sheets between double BiO or TIO layered units, like the 2212 phase, but with a different arrangement of adjacent CuO2 sheets. The new bismuth compounds (Bi-2222) have a significantly lower Tc (∼30 K or less) than the 2212 or 2223 phases, even when the charge-carrier (hole) concentrations are comparable. So far, we have not found superconductivity in the Tl-2222 compounds.

P. Lacorre

Papers

Systematic study of insulator-metal transitions in perovskites RNiO3 (R=Pr,Nd,Sm,Eu) due to closing of charge-transfer gap.

Synthesis, crystal structure, and properties of metallic PrNiO3: Comparison with metallic NdNiO3 and semiconducting SmNiO3

New double-sheet copper oxide compounds with BiO or TlO bilayers