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Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and
magnetic properties Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
, such as metal-insulator transitions,
heavy fermion In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons in unfilled electron bands. Electrons are one type of fermion, and when they are found in such materials, th ...
behavior,
half-metal A half-metal is any substance that acts as a conductor to electrons of one spin orientation, but as an insulator or semiconductor to those of the opposite orientation. Although all half-metals are ferromagnetic (or ferrimagnetic), most ferroma ...
licity, and spin-charge separation. The essential feature that defines these materials is that the behavior of their
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s or
spinon Spinons are one of three quasiparticles, along with holons and orbitons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero. The ele ...
s cannot be described effectively in terms of non-interacting entities. Theoretical models of the electronic (
fermionic In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
) structure of strongly correlated materials must include electronic (
fermionic In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
)
correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
to be accurate. As of recently, the label
quantum materials Quantum materials is an umbrella term in condensed matter physics that encompasses all materials whose essential properties cannot be described in terms of semiclassical particles and low-level quantum mechanics. These are materials that present s ...
is also used to refer to strongly correlated materials, among others.


Transition metal oxides

Many
transition metal oxides An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the E ...
belong to this class which may be subdivided according to their behavior, ''e.g.'' high-Tc, spintronic materials,
multiferroics Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase: * ferromagnetism – a magnetisation that is switchable by an applied magnetic field * ferroelectricity – an electric polarisa ...
,
Mott insulator Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures). These insulators fail to be correctly described by band ...
s, spin Peierls materials,
heavy fermion In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons in unfilled electron bands. Electrons are one type of fermion, and when they are found in such materials, th ...
materials, quasi-low-dimensional materials, etc. The single most intensively studied effect is probably
high-temperature superconductivity High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previ ...
in doped
cuprate Cuprate loosely refers to a material that can be viewed as containing anionic copper complexes. Examples include tetrachloridocuprate ( uCl4sup>2−), the superconductor YBa2Cu3O7, and the organocuprates (e.g., dimethylcuprate u(CH3)2sup>∠...
s, e.g. La2−xSrxCuO4. Other ordering or magnetic phenomena and temperature-induced
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
s in many transition-metal oxides are also gathered under the term "strongly correlated materials."


Electronic structures

Typically, strongly correlated materials have incompletely filled ''d''- or ''f''- electron shells with narrow energy bands. One can no longer consider any
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
in the material as being in a "
sea The sea, connected as the world ocean or simply the ocean, is the body of salty water that covers approximately 71% of the Earth's surface. The word sea is also used to denote second-order sections of the sea, such as the Mediterranean Sea, ...
" of the averaged motion of the others (also known as
mean field theory In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...
). Each single
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
has a complex influence on its neighbors. The term ''strong correlation'' refers to behavior of electrons in solids that is not well-described (often not even in a qualitatively correct manner) by simple one-electron theories such as the
local-density approximation Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT) that depend solely upon the value of the electronic density at each point in space (and not, ...
(LDA) of
density-functional theory Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body s ...
or Hartree–Fock theory. For instance, the seemingly simple material NiO has a partially filled 3''d'' band (the Ni atom has 8 of 10 possible 3''d''-electrons) and therefore would be expected to be a good conductor. However, strong
Coulomb repulsion Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
(a correlation effect) between ''d'' electrons makes NiO instead a wide-
band gap In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in ...
insulator. Thus, ''strongly correlated materials'' have electronic structures that are neither simply free-electron-like nor completely ionic, but a mixture of both.


Theories

Extensions to the LDA (LDA+U, GGA, SIC, ''GW'', etc.) as well as simplified models Hamiltonians (e.g. Hubbard-like models) have been proposed and developed in order to describe phenomena that are due to strong electron correlation. Among them,
dynamical mean field theory Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure ...
(DMFT) successfully captures the main features of correlated materials. Schemes that use both LDA and DMFT explain many experimental results in the field of correlated electrons.


Structural studies

Experimentally, optical spectroscopy, high-energy electron spectroscopies
resonant photoemission
and more recently resonant inelastic (hard and soft) X-ray scattering (
RIXS Resonant inelastic X-ray scattering (RIXS) is an X-ray spectroscopy technique used to investigate the electronic structure of molecules and materials. Inelastic X-ray scattering is a fast developing experimental technique in which one scatters hi ...
) and
neutron spectroscopy Neutron scattering is a spectroscopic method of measuring the atomic and magnetic motions of atoms. Inelastic neutron scattering observes the change in the energy of the neutron as it scatters from a sample and can be used to probe a wide variety of ...
have been used to study the electronic and magnetic structure of strongly correlated materials. Spectral signatures seen by these techniques that are not explained by one-electron density of states are often related to strong correlation effects. The experimentally obtained spectra can be compared to predictions of certain models or may be used to establish constraints to the parameter sets. One has for instance established a classification scheme of transition metal oxides within the so-called Zaanen–Sawatzky–Allen diagram.


Applications

The manipulation and use of correlated phenomena has applications like
superconducting magnets A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. In its superconducting state the wire has no electrical resistance and therefore can conduct much ...
and in magnetic storage (CMR) technologies. Other phenomena like the metal-insulator transition in VO2 have been explored as a means to make smart windows to reduce the heating/cooling requirements of a room. Furthermore, metal-insulator transitions in Mott insulating materials like LaTiO3 can be tuned through adjustments in band filling to potentially be used to make transistors that would use conventional field effect transistor configurations to take advantage of the material's sharp change in conductivity. Transistors using metal-insulator transitions in Mott insulators are often referred to as Mott transistors, and have been successfully fabricated using VO2 before, but they have required the larger electric fields induced by ionic liquids as a gate material to operate.


See also

*
Electronic correlation Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Ato ...
*
Emergent behavior In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole. Emergence ...


References


Further reading

* * * * * * *


External links

* {{DEFAULTSORT:Strongly Correlated Material Materials science Condensed matter physics Quantum mechanics Magnetism