Resonant inelastic X-ray scattering
Encyclopedia
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 high energy, x-ray
photons inelastically off matter. It is a photon-in/photon-out spectroscopy
where one measures both the energy and momentum change of the scattered photon. The energy and momentum lost by the photon are transferred to intrinsic excitations of the material under study and thus RIXS provides information about those excitations. The RIXS process can also be described as a Resonant X-ray Raman
or Resonant X-ray Emission process.
RIXS is a resonant technique because the energy of the incident photon is chosen such that it coincides with, and hence resonates with, one of the atomic x-ray absorption edges of the system. The resonance can greatly enhance the inelastic scattering cross section, sometimes by many orders of magnitude
The RIXS event can be thought of as a two-step process. Starting from the initial state, absorption of an incident photon leads to creation of an excited intermediate state, that has a core hole. From this state, emission of a photon leads to the final state. In a simplified picture the absorption process gives information of the empty electronic states, while the emission gives information about the occupied states. In the RIXS experiment these two pieces of information come together in a convolved manner, strongly perturbed by the core-hole potential in the intermediate state.
RIXS studies can be performed using both soft and hard x-ray
s.
In principle RIXS can probe a very broad class of intrinsic excitations of the system under study—as long as the excitations are overall charge neutral. This constraint arises from the fact that in RIXS the scattered photons do not add or remove charge from the system under study. This implies that, in principle RIXS has a finite cross section for probing the energy, momentum and polarization dependence of any type of electron-hole excitation: for instance the electron-hole continuum and exciton
s in band metals and semiconductors, charge transfer and crystal field excitation
s in strongly correlated material
s, lattice excitations
and so on. In addition magnetic excitations are also symmetry-allowed in RIXS, because the angular momentum
that the photons carry can in principle be transferred to the electron's spin
moment.
of a spectral feature is determined by the life-times of initial and final states. In x-ray absorption and non-resonant emission spectroscopy, the resolution is often limited by the relatively short life-time of the final state core-hole. As in RIXS a high energy core-hole is absent in final state, this leads to intrinsically sharp spectra with energy and momentum resolution determined by the instrumentation. At the same time, RIXS experiments keep the advantages of x-ray probes, e.g., element specificity.
In contrast to elastic x-ray scattering, radiative inelastic x-ray scattering is a weak process, with a small cross section. RIXS experiments therefore require a high-brilliance x-ray source, and are only performed at synchrotron
radiation sources.
In direct RIXS, the incoming photon promotes a core-electron to an empty valence band state. Subsequently an electron from a different state decays and annihilates the core-hole. The hole in the final state may either be in a core level at lower binding energy than in the intermediate state or in the filled valence shell. Some authors refer to this technique as resonant x-ray emission spectroscopy (RXES). The distinction between RIXS, resonance x-ray Raman and RXES in the literature is not strict.
The net result is a final state with an electron-hole excitation, as an electron was created in an empty valence band state and a hole in a filled shell. If the hole is in the filled valence shell, the electron-hole excitation can propagate through the material, carrying away momentum and energy. Momentum and energy conservation require that these are equal to the momentum and energy loss of the scattered photon.
For direct RIXS to occur, both photoelectric transitions—the initial one from core to valence state and succeeding one to fill the core hole—must be possible. These transitions can for instance be an initial dipolar transition of 1s → 2p followed by the decay of another electron in the 2p band from 2p → 1s. This happens at the K-edge of oxygen, carbon and silicon. A very efficient sequence often used in 3d transition metals is a 1s → 3d excitation followed by a 2p → 1s decay.
Indirect RIXS is slightly more complicated. Here, the incoming photon promotes a core-electron to an itinerant state far above the electronic chemical potential. Subsequently the electron in this same state decays again, filling the core-hole. Scattering of the x-rays occurs via the core-hole potential that is present in the intermediate state. It shakes up the electronic system, creating excitations to which the x-ray photon loses energy and momentum. Because the number of electrons in the valence sub-system is constant throughout the process.
X-ray spectroscopy
X-ray spectroscopy is a gathering name for several spectroscopic techniques for characterization of materials by using x-ray excitation.-Characteristic 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 high energy, x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
photons inelastically off matter. It is a photon-in/photon-out spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
where one measures both the energy and momentum change of the scattered photon. The energy and momentum lost by the photon are transferred to intrinsic excitations of the material under study and thus RIXS provides information about those excitations. The RIXS process can also be described as a Resonant X-ray Raman
Resonance Raman spectroscopy
Resonance Raman spectroscopy is a specialized implementation of the more general Raman spectroscopy.- Overview :As in Raman spectroscopy, RR spectroscopy provides information about the vibrations of molecules, and can also be used for identifying unknown substances. RR spectroscopy has found wide...
or Resonant X-ray Emission process.
RIXS is a resonant technique because the energy of the incident photon is chosen such that it coincides with, and hence resonates with, one of the atomic x-ray absorption edges of the system. The resonance can greatly enhance the inelastic scattering cross section, sometimes by many orders of magnitude
The RIXS event can be thought of as a two-step process. Starting from the initial state, absorption of an incident photon leads to creation of an excited intermediate state, that has a core hole. From this state, emission of a photon leads to the final state. In a simplified picture the absorption process gives information of the empty electronic states, while the emission gives information about the occupied states. In the RIXS experiment these two pieces of information come together in a convolved manner, strongly perturbed by the core-hole potential in the intermediate state.
RIXS studies can be performed using both soft and hard x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s.
Features
Compared to other scattering techniques, RIXS has a number of unique features: it covers a large scattering phase-space, is polarization dependent, element and orbital specific, bulk sensitive and requires only small sample volumes:- In RIXS one measures both the energy and momentum change of the scattered photon. Comparing the energy of a neutron, electron or photon with a wavelength of the order of the relevant length scale in a solid—the interatomic lattice spacing in the order of ÅngströmÅngströmThe angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
s -- it is obvious that an x-ray photon has much more energy than a neutron or electron. The scattering phase space (the range of energies and momenta that can be transferred in a scattering event) of x-rays is therefore without equal. In particular, high-energy x-rays carry a momentum that is comparable to the inverse lattice spacing of typical condensed matter systems so that, unlike Raman scatteringRaman scatteringRaman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....
experiments with visible or infrared light, RIXS can probe the full dispersion of low energy excitations in solids. - RIXS can utilize the polarizationPhoton polarizationPhoton polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized...
of the photon: the nature of the excitations created in the material can be disentangled by a polarization analysis of the incident and scattered photons, which allow one, through the use of various selection rules, to characterize the symmetry and nature of the excitations. - RIXS is element and orbital specific: chemical sensitivity arises by tuning to the absorption edges of the different types of atoms in a material. RIXS can even differentiate between the same chemical element at sites with inequivalent chemical bondings, with different valencies or at inequivalent crystallographic positions as long as the x-ray absorption edges in these cases are distinguishable. In addition, the type of information on the electronic excitations of a system being probed can be varied by tuning to different x-ray edges (e.g., K, L or M) of the same chemical element, where the photon excites core-electrons into different valence orbitals.
- RIXS is bulk sensitive: the penetration depth of resonant x-ray photons is material and scattering geometry- specific, but typically is on the order of a few micrometreMicrometreA micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
in the hard x-ray regime (for example at transition metal K-edgeK-edgeK-edge describes a sudden increase in the attenuation coefficient of photons occurring at a photon energy just above the binding energy of the K shell electron of the atoms interacting with the photons. The sudden increase in attenuation is due to photoelectric absorption of the photons...
s) and on the order of 0.1 micrometreMicrometreA micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
in the soft x-ray regime (e.g. transition metal L-edgeMetal L-edgeMetal L-edge XAS is an experimental technique that involves the excitation of a metal 2p electron to unfilled metal d orbitals...
s). - RIXS needs only small sample volumes: the photon-matter interaction is relatively strong, compared to for instance the neutron-matterNeutron scatteringNeutron scattering,the scattering of free neutrons by matter,is a physical processand an experimental technique using this processfor the investigation of materials.Neutron scattering as a physical process is of primordial importance...
interaction strength. This makes RIXS possible on very small volume samples, thin films, surfaces and nano-objects, in addition to bulk single crystal or powder samples.
In principle RIXS can probe a very broad class of intrinsic excitations of the system under study—as long as the excitations are overall charge neutral. This constraint arises from the fact that in RIXS the scattered photons do not add or remove charge from the system under study. This implies that, in principle RIXS has a finite cross section for probing the energy, momentum and polarization dependence of any type of electron-hole excitation: for instance the electron-hole continuum and exciton
Exciton
An exciton is a bound state of an electron and hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and some liquids...
s in band metals and semiconductors, charge transfer and crystal field excitation
Crystal field excitation
Electronic transition between two orbitals of an atom that is situated in a crystal field environment. For example, dd-transitions on a copper atom that is surrounded by an octahedron of oxygen atoms....
s in strongly correlated material
Strongly correlated material
Strongly correlated materials are a wide class of electronic materials that show unusual electronic and magnetic properties, such as metal-insulator transitions or half-metallicity...
s, lattice excitations
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
and so on. In addition magnetic excitations are also symmetry-allowed in RIXS, because the angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
that the photons carry can in principle be transferred to the electron's spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
moment.
Resolution
The energy and momentum resolution of RIXS do not depend on the core-hole that is present in the intermediate state. In general the natural linewidthSpectral linewidth
The spectral linewidth characterizes the width of a spectral line, such as in the electromagnetic emission spectrum of an atom, or the frequency spectrum of an acoustic or electronic system...
of a spectral feature is determined by the life-times of initial and final states. In x-ray absorption and non-resonant emission spectroscopy, the resolution is often limited by the relatively short life-time of the final state core-hole. As in RIXS a high energy core-hole is absent in final state, this leads to intrinsically sharp spectra with energy and momentum resolution determined by the instrumentation. At the same time, RIXS experiments keep the advantages of x-ray probes, e.g., element specificity.
In contrast to elastic x-ray scattering, radiative inelastic x-ray scattering is a weak process, with a small cross section. RIXS experiments therefore require a high-brilliance x-ray source, and are only performed at synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...
radiation sources.
Direct and Indirect RIXS
Resonant Inelastic x-ray Scattering processes are classified as either direct or indirect. This distinction is useful because the cross-sections for each are quite different. When direct scattering is allowed, it will be the dominant scattering channel, with indirect processes contributing only in higher order. In contrast, for the large class of experiments for which direct scattering is forbidden, RIXS relies exclusively on indirect scattering channels.In direct RIXS, the incoming photon promotes a core-electron to an empty valence band state. Subsequently an electron from a different state decays and annihilates the core-hole. The hole in the final state may either be in a core level at lower binding energy than in the intermediate state or in the filled valence shell. Some authors refer to this technique as resonant x-ray emission spectroscopy (RXES). The distinction between RIXS, resonance x-ray Raman and RXES in the literature is not strict.
The net result is a final state with an electron-hole excitation, as an electron was created in an empty valence band state and a hole in a filled shell. If the hole is in the filled valence shell, the electron-hole excitation can propagate through the material, carrying away momentum and energy. Momentum and energy conservation require that these are equal to the momentum and energy loss of the scattered photon.
For direct RIXS to occur, both photoelectric transitions—the initial one from core to valence state and succeeding one to fill the core hole—must be possible. These transitions can for instance be an initial dipolar transition of 1s → 2p followed by the decay of another electron in the 2p band from 2p → 1s. This happens at the K-edge of oxygen, carbon and silicon. A very efficient sequence often used in 3d transition metals is a 1s → 3d excitation followed by a 2p → 1s decay.
Indirect RIXS is slightly more complicated. Here, the incoming photon promotes a core-electron to an itinerant state far above the electronic chemical potential. Subsequently the electron in this same state decays again, filling the core-hole. Scattering of the x-rays occurs via the core-hole potential that is present in the intermediate state. It shakes up the electronic system, creating excitations to which the x-ray photon loses energy and momentum. Because the number of electrons in the valence sub-system is constant throughout the process.
Applications
- High-temperature superconductorsHigh-temperature superconductivityHigh-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...
, e.g., cuprates. - Semiconductors, e.g. Cu2O.
- Colossal magnetoresistanceColossal magnetoresistanceColossal magnetoresistance is a property of some materials, mostly manganese-based perovskite oxides, that enables them to dramatically change their electrical resistance in the presence of a magnetic field...
Manganites. - MetalloproteinsProteinProteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
, e.g., the oxygen-evolving complex in Photosystem IIPhotosystem IIPhotosystem II is the first protein complex in the Light-dependent reactions. It is located in the thylakoid membrane of plants, algae, and cyanobacteria. The enzyme uses photons of light to energize electrons that are then transferred through a variety of coenzymes and cofactors to reduce...
. - CatalysisCatalysisCatalysis is the change in rate of a chemical reaction due to the participation of a substance called a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. A catalyst may participate in multiple chemical transformations....
, e.g. s. - WaterWaterWater is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
.