Photoemission
X-ray photoemission spectroscopy (XPS) and ultraviolet photoemission spectroscopy (UPS): Uses x-ray or UV light to eject electrons from sample and analyzes the energy of the ejected electrons. This gives the energies of the core levels of the constituents relative to the vacuum, which encodes the valence state of the elements. Sample in vacuum. Surface-sensitive, very useful for determining chemical composition. Can be combined with etching to do depth profiling of composition.
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Inverse photoemission spectroscopy (IPES): Low energy (< 20 eV) electrons interact with low-lying unoccupied electronic states, sometimes generating emitted photons. Probes states above the Fermi level of materials.
Photoemission electron microscopy (PEEM): With a scannable optical source, it is possible to map spatial nonuniformity in photoemitted electrons.
Angle-resolved photoemission spectroscopy (ARPES): Uses incident x-rays or UV at precisely known energy and momenta to eject electrons from sample; hemispherical analyzer is used to measure energy and momenta of ejected electrons with high precision (energy resolution can be as sharp as 1 meV in synchrotron facilities). Sample in ultrahigh vacuum, typically requires surfaces cleaved in vacuo. This is the primary technique for measuring electronic band structure. Like all photoemission techniques, it works best on conductive samples to avoid charging problems. Variations include spin-polarized ARPES (polarization of detected electrons is found) and time-resolved ARPES (optical pump followed by time-delayed x-ray/UV pulse to do the photoemission). There is also a related technique in terms of hardware called momentum-resolved EELS, where incident electrons of known energy and momentum are bounced off the material of interest and their final energy and momenta are measured.
Neutrons
Neutron diffraction: Neutron scattering, requires beam of monoenergetic neutrons (prepared from a reactor via moderation + diffraction off a known crystal to act as a monochromator) (or broad-band neutrons but with time-of-flight to assess neutron energy). Sensitive to lattice structure (nuclei). Magnetic dipole interactions with electrons allows neutron diffraction to be sensitive to magnetic order. Variations: cold neutrons (prepared by scattering off cryogenic material) for higher sensitivity to magnetic systems; polarized neutrons, with polarized detection for higher sensitivity to magnetic systems. Because neutron scattering cross-sections are generally small, neutron scattering historically requires large quantities (many milligrams) of material, and single-crystal diffraction is typical (with magnetic structure measurements requiring careful alignment of sample material via XRD first). High brightness sources are improving the situation. Another challenge: some elements and isotopes have large absorption cross-sections for neutrons and thus cannot readily be measured via neutron scattering. A positive flipside of this is that neutron scattering is very sensitive to hydrogen and lithium, of interest in batteries and other energy-related applications.
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Inelastic neutron scattering (INS): Momentum- and energy-resolved neutron scattering, with change in neutron energy and momentum recorded. Similar in spirit to ARPES, for mapping out dispersion relations of excitations within the sample material. This is the primary method of tracing out phonon dispersions in solids, as well as the means of identifying and quantifying magnons. Spin-polarized INS is possible, though any neutron scattering technique that requires preparation or detection of neutrons in particular spin states is more demanding (takes longer, requires higher initial flux) because of loss of neutrons during preparation and detection.
Neutron reflectometry: Diffraction of reflected neutrons, rather analogous to EBSD, though also sensitive to magnetic scattering.
Small-angle neutron scattering (SANS): Analogous to SAXS, but with grazing-incidence neutrons. Strongly sensitive to light elements (because they have bigger neutron scattering cross-sections) and magnetic structure.
Optical spectroscopy
Note that many optical techniques can be combined with microscopy to achieve spatial resolution and mapping of responses over sample surfaces. A good review article on some of these is this.
UV/Vis/IR absorption: A sample is illuminated in a transmission geometry with broadband light, and by measuring the transmitted spectrum, electronic transitions can be identified and band structure can be constrained. Selection rules constrain what transitions can be seen.
Fourier transform infrared (FTIR) spectroscopy and microscopy: Using a broadband mid- to far-IR light source and incorporating the sample into one arm of an interferometer, it is possible to measure absorption out to longer wavelengths (10 μm, e.g.). Good for identifying “infrared active” (e.g. involving polar displacements) low energy vibrational modes in solids.
Ellipsometry and spectroscopic ellipsometry: Incident light of known wavelength, measuring reflected light from a surface as a function of angle of incidence (and wavelength of incident light, in the spectroscopic case). Allows determination of dielectric function/index of refraction, interpretation through modeling. Great for quantifying layer thicknesses for dielectric multilayers.
THz spectroscopy: Using THz sources and detection, can look at transmission and reflection in the mm-wave (very far IR; not quite the microwave). Great for identifying vibrational modes, low-energy excitations as in superconductivity and some magnetic states. CW sources now exist for THz using quantum cascade lasers. Time-resolved THz (THz time-domain spectroscopy) is often used, as broadband THz pulses can be created using pulsed lasers and photoconductive antennas.
Optical conductivity: By measuring real and imaginary parts of the dielectric function (through light scattering, ellipsometry, absorption measurements) and using the Kramers-Kronig relations, it is possible to infer the frequency-dependent conductivity σ(ω), which can reveal a lot about dynamics of charged excitations.
Faraday rotation: In transmission, the polarization of light can be rotated due to magnetization of the sample. Provides information about magnetic structure of materials.
Magneto-optic Kerr effect (MOKE): In reflection, the polarization of light can be rotated due to magnetization of the sample.
Raman spectroscopy: This is inelastic light scattering, often applied to molecules or optical phonons in solids. An incoming photon of angular frequency ω0. Elastic scattering is called Rayleigh scattering. If the photon excites a vibration or another excitation of energy ℏω, the (“Stokes”) scattered photon comes out with frequency ω0 – ω. If the system is already excited, the (“anti-Stokes”) scattered photon can grab energy from the excitation and come out with frequency ω0 + ω. Raman scattering can take place if the polarizability tensor of the system α depends on the displacements of the atoms. In Raman spectroscopy of solid crystalline materials, with polarization control of the incoming light and known incident angle vs. the crystallographic orientation, it is possible to gain insight into dispersion of excitations. Detection is usually done with a grating spectrometer + CCD or CMOS camera. Variation: magnetoRaman, where sample is in an applied magnetic field.
Brillouin light scattering: Inelastic light scattering at quite low energy transfers, better suited for looking at acoustic phonons, magnons, etc. in solids. Energy transfers are sufficiently small that detection is usually done with an interferometer.
Photoluminescence (PL): Optical spectroscopy in which incident light electronically excites the sample, and the sample then emits photons of energies characteristic of the electronic excitations. This is a standard way to characterize excitons and related excitations in semiconductors. Variations include time-resolved PL (to look at dynamics of excitations and their lifetimes) using pulsed excitation and timed detection; and two-photon PL (TPPL), in which high intensity lower energy excitation is used to nonlinearly excite the sample. (Nonlinear optical processes depend critically on symmetries of the underlying material.) When applied to molecular systems (or semiconductor nanocrystals) in the context of chemistry, PL is often referred to as fluorescence spectroscopy.
Electronic transport
I-V characterization: Measuring the current as a function of voltage (or voltage as a function of current). Depending on the material involved, considerable information may be inferred from such data.
Magnetoresistance/magnetoconductance: Measuring electrical resistance or conductance as a function of applied magnetic field and temperature. Conductance measurements = source a voltage, measure a current. Resistance measurements = source a current, measure a voltage. Best practice, if possible, is to perform a 4-terminal (or more) measurement, with current sourced via two leads and voltages measured with other leads. Since an ideal voltage probe draws no current, contact resistances do not interfere with the voltage measurement.
Differential conductance/differential resistance: For differential conductance (dI/dV), the applied bias includes a small ac voltage in addition to an applied dc voltage Vdc, and an ac measurement (via a lock-in amplifier) allows the detection of the ac contribution to the current; this allows measurement of dI/dV as a function of Vdc. Similarly, for differential resistance (dV/dI), the applied bias includes a small ac current in addition to an applied dc current Idc, and an ac measurement via lock-in allows detection of the ac contribution to the voltage; this allows measurement of dV/dI as a function of Idc. Note that differential resistance measurements are appropriate for examining candidate superconductors, when it is possible that the sample may support nonzero current with zero voltage.
Hall effect: By measuring longitudinal and transverse resistance (Rxx ≡ Vxx/Ix, Rxy ≡ Vxy/Ix) in the presence of a perpendicular magnetic field Bz, it is possible to infer the sign of the charge carriers, charge mobility, and carrier density (assuming an isotropic single-band conductor).
Tunneling spectroscopy: In a tunnel junction (between a conducting sample and a normal metal probe electrode), at zero temperature the differential tunneling conductance dI/dV is proportional to the electronic density of states of the probe at its Fermi energy and the density of states of the sample at E = EF,sample-eVdc, where Vdc is the bias voltage of the probe relative to the sample. (For a superconducting probe, the probe density of states is very sharp but is also shifted relative to the normal state EF because of the superconducting energy gap.)
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Inelastic electron tunneling spectroscopy (IETS): Conventionally, in tunneling spectroscopy, when the bias energy scale eVdc crosses the energy ℏω required to inelastically excite an excitation of the sample, this adds a possible path for electron transport. The result is a kink in I-V, equivalently a step in dI/dV vs. Vdc, and therefore a peak in d2I/dV2 (at positive Vdc) at Vdc=ℏω/e. A real excitation of the sample should result in antisymmetric d2I/dV2 features at Vdc=± ℏω/e. This approach has been used to identify vibrations in molecules, optical phonons in solids, and also magnetic excitations in solids. The IETS features are broadened by the finite electronic temperature (kBT), so cryogenic temperatures are best suited for this technique.
Thermodynamic and thermal measurements
Specific heat: Adding a small amount of thermal energy to a sample via a heater and measuring the temperature rise of the sample using a local thermometer. Because of the relationship between specific heat and entropy (Cp = (1/T)(∂S/∂T)|p), the specific heat as a function of temperature may be used to infer entropy. First-order phase transitions show up as a huge feature in specific heat vs temperature, since the entropy is discontinuous across a first-order transition. Second-order phase transitions show up as a singular feature (discontinuity) in heat capacity vs temperature because (∂S/∂T) is discontinuous across such a transition, and will show critical fluctuations approaching the transition temperature. Specific heat of metals is linear in T at low temperatures and is used to infer the electronic density of states at the Fermi level.
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Differential scanning calorimetry (DSC): Temperature is measured as heat input to the sample is scanned. Intended to reveal phase changes within the material.
Thermal conductivity: A known thermal energy current is applied through a sample, and the temperature drop across the sample is measured using local thermometers. This is a measure of the transport of energy by all mobile excitations in the material. In conductors, charge carriers are expected to transport an amount of energy proportional to their specific heat, leading in metals to the Wiedemann-Franz relation.
Thermal expansion: Changes in sample dimensions as a function of temperature are measured, giving insights into material structure and bonding. Typically, thermal expansion relates to the anharmonicity of the interatomic potential, and it is related therefore to nonlinearities in the properties of phonons (see the Grüneisen parameter).
Thermopower/Seebeck coefficient: Absolute Seebeck response = the change in voltage across a sample is measured as a function of the temperature difference imposed across the sample. Electronic excitations (and phonons) tend to diffuse away from the hot side. Seebeck response sign generally depends on sign of the charge carriers (electron-like or hole-like). The Seebeck response in a conductor is proportional to the energy dependence of the conductivity (and hence the mean free path) of the carriers.
Nernst-Ettingshausen effect: In a Hall-like geometry, the transverse voltage across a sample Vxy is propertional to the temperature gradient along the sample dT/dx and the mutually perpendicular magnetic field Bz, so that the Nernst coefficient is defined as ν = (Exy/Bz)/(dT/dx). This gives information about the transverse scattering of heat-carrying excitations in the presence of a magnetic field.
Magnetic measurements
Magnetization: Measurements of M vs H may be performed using SQUID-based and other magnetometers, though knowledge of sample dimensions and geometry are required. Characteristic features of M are expected for certain material types. For example, near zero field, a superconductor is expected to show perfect diamagnetism. Often measurements are also made of M vs T at fixed H, comparing field-cooled and zero-field-cooled responses. Saturation of M vs H at low temperatures and high fields can reveal the magnetic state of elements hosting local magnetic moments.
Vibrating sample magnetometry (VSM): a particular type of magnetometer that vibrates the sample back and forth through pickup coils.
AC susceptibility: An oscillating component of H is applied and the change in M is measured.
Nuclear magnetic resonance (NMR): liquid (for molecules) or solid-state. Applied magnetic field provides Zeeman energy splitting for spin states of nuclei, radio frequency pulse sequences (and continuous wave methods) used to determine nuclear spin properties (and because of hyperfine couplings, provides information about electronic states). Specific effects in superconductors (Knight shift). Care must be taken with conducting samples, as microwaves don’t necessarily penetrate into the bulk of the material.
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR): Applied magnetic field provides Zeeman energy splitting for spin states of electrons, microwave pulse sequences (and continuous wave methods) are applied to do spectroscopy of these. Best in insulating materials with unpaired electrons. Particularly handy in determining the g factors for local magnetic moments, which is affected by crystal fields (local chemical bonding environment) at the local spin-carrying atoms.
Ferromagnetic resonance (FMR): Conventionally, a radio frequency/microwave drive is applied to make the ferromagnetic magnetization M of a material precess around an external magnetic field. Gives information about the magnetization dynamics and damping. Recently, FMR in small devices has been driven via spin currents (from the spin Hall effect/spin-orbit torques or spin transfer torques).
Mossbauer spectroscopy: This is really a nuclear physics-based technique, but given that the most famous Mössbauer material is iron, it has relevance for magnetism. Gamma-ray spectroscopy using the Mössbauer effect (collective recoil or lack thereof of the entire lattice rather than individual atoms), gives extremely precise energetic information about nuclear environment of the particular isotopes, including hyperfine interactions.
Muon spin spectroscopy (μSR): Muons produced via an accelerator are implanted or transmitted through a material of interest. Decay of positive muons leads to emission of positrons, with directional asymmetry of emission related to the spin state of the muon. These measurements this give information about the magnetic environment within the material. Does not require pulsed fields.
Other techniques to assess composition
Secondary ion mass spectrometry (SIMS): Material is sputtered away from the sample, and the fragments are analyzed using mass spectrometry (e.g., ionized fragments are accelerated and curved in a magnetic field for detection, to determine their charge to mass ratio).
Inductively coupled plasma mass spectrometry (ICP-MS): Using an inductively coupled plasma source to ionize sample material for MS.
Atomic emission spectroscopy (AES): Material is heated or otherwise excited, and the emission spectra of the products is measured. Modern version of old approach of looking at the color of flame produced by a bit of material.
Rutherford backscattering spectrometry (RBS): Ions (protons, alpha particles) are fired at the sample material and back-scattered ions are detected; can give depth-dependent compositional information.
Thermogravitic analysis (TGA): Destructive technique. The sample is placed in a sensitive balance and heated through its decomposition, and the sample is weighed as the temperature is swept. Different breakdown products will be produced at different temperatures. Often combined with mass spectrometry to determine the molecular weight of the evolved products.
