Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t\ensuremath{-}J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

Metal-insulator transitions

Since the discovery of superconductivity above 30 K by Bednorz and M\"uller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

Electronic structure of the high-temperature oxide superconductors

Ferromagnetic materials exhibit intrinsic `easy' and `hard' directions of the magnetization. This magnetic anisotropy is, from both a technological and fundamental viewpoint one of the most important properties of magnetic materials. The magnetic anisotropy in metallic magnetic multilayers forms the subject of this review article. As individual layers in a multilayer stack become thinner, the role of interfaces and surfaces may dominate that of the bulk: this is the case in many magnetic multilayers, where a perpendicular interface contribution to the magnetic anisotropy is capable of rotating the easy magnetization direction from in the film plane to perpendicular to the film plane. In this review, we show that the (in-plane) volume and (perpendicular) interface contribution to the magnetic anisotropy have been separated into terms related to mechanical stresses, crystallographic structure and the planar shape of the films. In addition, the effect of roughness, often inherent to the deposition techniques used, has been addressed theoretically. Several techniques to prepare multilayers and to characterize their growth as well as methods to determine the magnetic anisotropy are discussed. A comprehensive survey of experimental studies on the perpendicular magnetic anisotropy in metallic multilayers containing Fe, Co or Ni is presented and commented on. Two major subjects of this review are the extrinsic effects of strain, roughness and interdiffusion and the intrinsic effect of the crystallographic orientation on the magnetic anisotropy. Both effects are investigated with the help of some dedicated experimental studies. The results of the orientational dependence studies are compared with ab initio calculations. Finally, the perpendicular surface anisotropy and the in-plane step anisotropy are discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/59/11/002/pdf

Magnetic anisotropy in metallic multilayers

The structural properties of oxygen-deficient ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ have been determined by neutron powder diffraction for 0.07l\ensuremath{\delta}l0.91. The samples were produced by quenching into liquid nitrogen from controlled oxygen partial pressures at 520 \ifmmode^\circ\else\textdegree\fi{}C, and they exhibit a clearly defined ``plateau'' behavior of ${T}_{c}$ versus \ensuremath{\delta}. Superconductivity disappears at the orthorhombic-to-tetragonal transition that occurs near \ensuremath{\delta}=0.65. Structural parameters, including the copper-oxygen bond lengths, vary smoothly with \ensuremath{\delta} within each phase but exhibit different behavior in the superconducting and nonsuperconducting phases. These observations are consistent with a model in which superconducting behavior is controlled by charge transfer between the conducting two-dimensional ${\mathrm{CuO}}_{2}$ planes and the ${\mathrm{CuO}}_{\mathrm{x}}$ chains, which act as reservoirs of charge.

Structural properties of oxygen-deficient YBa2Cu3O7- delta.

We have previously shown that Tc for Bi2 (Sr, Ca)n+1CunO2n+4+δ (n=1, 2 and 3) varies with oxygen stoichiometry δ determined by annealing in a variety of oxygen partial pressures and temperatures. Annealing results are now also presented for several Tl-superconductors in the series Tlm(Ba, Sr)2Can−1CunO2n+m+2+δ, for both m=1 and 2, revealing two general results for this class of Bi or TI superconductors: (1) effects on Tc due to labile oxygen occur for all m=2 compounds but are absent in m = 1 compounds with Sr. m=1 compounds with Ba do have variable oxygen but the effects on the c-axis are the opposite to m=2 compounds. This suggests for the latter that the labile oxygen resides in interstitial sites within the Bi2O2 or Tl2O2 bi layers; (2) the hole concentration per Cu decreases in progressing from n = 1 to 2 to 3 in either class so that the parent n = 3 and n = 2 compounds lie respectively on the low- and high-hole concentration sides of the peak in Tc while the n = 1 compounds extend out into the non-superconducting domain at very high hole concentration.

/pdf/general-trends-in-oxygen-stoichiometry-effects-on-tc-in-bi-4gmly6ibdk.pdf

General trends in oxygen stoichiometry effects on Tc in Bi and Tl superconductors

We refined the crystal structures of four pseudotetragonal samples of ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CuO}}_{6+\mathrm{\ensuremath{\delta}}}$ with ${\mathit{T}}_{\mathit{c}}$'s of 0 (metallic), 48, 58, and 73 K by Rietveld analysis of time-of-flight neutron-powder-diffraction data. The presence of excess oxygen atoms located at an interstitial site between double TlO layers was confirmed. The change in oxygen content and the corresponding one in hole carrier concentration in this compound are caused by incorporation and release of the excess oxygen, whose amount is about 0.1 per formula unit for the metallic nonsuperconducting sample. The highest ${\mathit{T}}_{\mathit{c}}$ value of about 85 K in ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CuO}}_{6+\mathrm{\ensuremath{\delta}}}$ is achieved in the absence of excess oxygen. As the oxygen content is decreased, the c value increases, and apical ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions go away from the ${\mathrm{CuO}}_{2}$ layer, while ${\mathrm{Ba}}^{2+}$ ions approach it. It was also suggested that about 5% of a Tl site is substituted by Cu. A significant portion of hole carriers in this compound is attributed to substitution of Cu for Tl and incorporation of excess oxygen.

Neutron-diffraction study of Tl 2 Ba 2 CuO 6+δ with various T c 's from 0 to 73 K

The preparation condition of Tl 2 Ba 2 CuO 6 (2201 compound) and its properties including superconductivities and structural variations were studied. Preparation at relatively low heat-treatment temperatures produced the 2201 compound with an orthorhombic symmetry, while heat-treatment above 840°C produced a tetragonal symmetry. It was revealed that the appearance of superconductivity was independent of the structural symmetry, and was strongly affected by oxygen content. Decrease of oxygen content by quenching or Ar-annealing increased the superconducting transition temperatures up to about 70 K. A positive correlation between T c and the c -axis length was also found for all samples including both orthorhombic and tetragonal structures.

Variation in Tc, structure and oxygen content in Tl2Ba2CuO6 and their correlations

Preferentially oriented epitaxial Y‐Ba‐Cu‐O films were prepared on (100) SrTiO3 substrates by oxygen reactive ion beam sputtering. The epitaxial orientations were varied by controlling both substrate temperature and oxygen parital pressure. c‐axis oriented films tended to be formed at higher substrate temperatures (>620 °C) and lower oxygen pressures ( 3×10−3 Torr). The best Tc (end) of 82 K was observed in one of the c‐axis oriented film without post‐annealing. The tendency for preferential orientation can be well understood in terms of the lattice mismatch between the substrate and the film, the lattice constants of which depend on oxygen deficiency.

Preferentially oriented epitaxial Y‐Ba‐Cu‐O films prepared by the ion beam sputtering method

Crystal structures of the phases in the Tl-Ba-Ca-Cu-O system determined by powder X-ray diffraction were refined using Rietveld analysis. Three samples having the general composition Tl 2 Ba 2 Ca n −1 Cu n O 4+2 n where synthesized. These were Tl 2 Ba 2 Ca 2 Cu 3 O 10 ( n =3,2223 phase ) with a T c of 116 K, Tl 2 Ba 2 CaCu 2 O 8 ( n =2,2212 phase ) with a T c of 85 K, and Tl 2 Ba 2 CuO 6 ( n =1,2201 phase ) which did not exhibit superconductivity. The results of the Rietveld analysis revealed that as n increased the lattice parameter, a , and the interatomic distance Cu-O(2) became shorter, and the Tl-O and Ba-O layers showed a tendency to become flatter. Possible substitution of about 10% of the Ca-sites with Tl ions in the 2212 and 2223 phases was also suggested.

Rietveld analysis of Tl2Ba2Can−1CunO4+2n (n=1, 2 and 3) by powder x-ray diffraction

Effect of oxygen deficiency on crystal structure and superconductivity of Ba2YCu3O7-δ was studied by annealing and quenching experiments With increasing oxygen deficiency superconductivity was suppressed remarkably while axial ratio, a0/b0 in the orthorhombic phase approached to unity and c0 value increased Structural transformation from orthorhombic to tetragonal lattice took place in the temperature range, 950~980°C and maximum oxygen deficiency, δ=07 was observed for the tetragonal phase

Effect of Oxygen Deficiency on the Crystal Structure and Superconducting Properties of the Ba2YCu3Oy

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