OTHER DESIGNATIONS: Soft x-ray emission spectroscopy (SXES), inelastic x-ray scattering (IXS), resonant x-ray inelastic scattering (RIXS), speckle patterns, small-angle x-ray scattering (SAXS).

PURPOSE: Soft x-ray scattering techniques employ the excitation of electrons in relatively shallow core energy levels (100–2000 eV) to probe the electronic structure and other properties of various kinds of matter. Problems addressed by soft x-ray spectroscopic techniques include:

• Strongly correlated materials
• Magnetic materials
• Environmental science
• Catalysis

HOW THE TECHNIQUE WORKS: Soft x-ray scattering is a photon-in/photon-out technique. The sample is illuminated with monochromatic soft x-rays and the scattered photons are detected over a small angular range. In the elastic scattering mode one measures the speckle diffraction pattern. In the inelastic mode the scattered photons are passed through a spectrometer and analyzed. Additional information is obtained in the resonant condition when the incident photon is near a core-level-energy absorption edge.

UNIQUENESS: Each element has its own set of characteristic core-electron energies, giving these techniques their elemental specificity. The tunability of synchrotron radiation is essential. Because of the low cross sections involved, SXES and RIXS are viable only at brilliant synchrotron sources.

EXAMPLES:

Learning How Magnets Forget
“Hole Crystal” Phase in the Spin Ladder of SCO
How Much Energy Does It Cost to Tilt a Hole?

Magnetic speckle pattern evolves from the featureless configuration in the magnetically saturated region
of the hysteresis curve to the annular shape characteristic of a two-dimensional liquid of
interacting domains at zero field.

A magnetic material immersed in an external magnetic field has a magnetization. As the external field cycles between positive and negative values, the magnetization traces out a hysteresis loop. While hysteresis underlies all magnetic data-storage technology, it is not understood at the microscopic level. Nevertheless, the magnetic disk drive industry has had a cumulative growth rate for the past decade that dwarfs even the celebrated Moore’s Law growth rate for microcircuits. A number of technological innovations have made this growth possible, including the use of thin layers of magnetic materials into which a certain amount of disorder has been introduced in a controllable way. Scientists have developed an x-ray analogue of the laser speckle well known to anyone who has seen the pattern created when laser light strikes a dusty mirror. They have used their technique to track quantitatively the evolution of magnetic domains as the magnetic layer cycles through various hysteresis loops, thereby directly probing how hysteresis unfolds at the microscopic level. They discovered that, contrary to the best current theories, the disordered magnetic storage materials partially remember their microscopic domain configuration, even after saturation.

M.S. Pierce, R.G. Moore, L.B. Sorensen, S.D. Kevan, O. Hellwig, E.E. Fullerton, and J.B. Kortright, “Quasistatic x-ray speckle metrology of microscopic magnetic return-point memory,” Phys. Rev. Lett. 90, 175502 (2003).

Experimental signature of a hole crystal phase for x-ray energies both off (top) and on (bottom) the ladder resonance.

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high-T_C) superconductors is one of the deepest problems in condensed matter physics. One candidate is the “stripe” phase in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the “spin ladder,” which consists of two coupled chains of magnetic ions connected by an array of rungs. Doped ladders have been predicted to exhibit both superconductivity and an insulating “hole crystal” phase in which the charge-carrying holes are localized through many-body interactions. One use of soft x-ray scattering is to identify such previously “hidden” electronic phases. Using a soft x-ray scattering technique in which scattering from holes is selectively enhanced more than a thousandfold, scientists have reported the existence of a hole crystal in the doped spin ladder of SCO (Sr₁₄Cu₂₄O₄₁). This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. The measurements confirmed theoretical predictions and supported the picture that proximity to charge-ordered states is a general property of superconductivity in copper oxides.

P. Abbamonte, G. Blumberg, A. Rusydi, A. Gozar, P.G. Evans, T. Siegrist, L. Venema, H. Eisaki, E.D. Isaacs, and G.A. Sawatzky, “Crystallization of charge holes in the spin ladder of Sr₁₄Cu₂₄O₄₁,” Nature 431, 1078 (2004).

In Raman scattering, the absorption and emission of an x-ray result in the excitation of the copper orbital from the ground state (blue) to an excited state with a different orientation (green).

One signature of the onset of superconductivity is the formation of electron pairs, but the electron-pairing mechanism for high-temperature superconductivity is one of the great unsolved problems of condensed-matter physics. The common feature of high-temperature superconductors is a set of parallel copper–oxygen planes. In these planes, each Cu²⁺ ion is surrounded by four oxygen atoms. The Cu²⁺ ions have an unoccupied electron orbital called a hole. We know from the angle dependence of x-ray absorption that this hole orbital is oriented in the plane with four lobes pointing toward the four neighboring oxygen atoms. Putting the hole in a differently oriented orbital costs energy. How large these energies are is a potentially important question for the theory of high-temperature superconductivity. If these energies are small (comparable to the thermal energy), excitations to these orbitals should be considered in whatever electron-pairing mechanism is operative in superconductivity. Scientists have used resonant x-ray Raman scattering to investigate electronic transitions within copper atoms in Sr₂CuO₂Cl₂, an insulating model compound for the copper-based high-temperature superconductors. Contrary to earlier conjecture, they found that these transitions have energies that are too high to be directly involved in the electron-pairing mechanism.

P. Kuiper, J.-H. Guo, C. Såthe, L.-C. Duda, J. Nordgren, J.J.M. Pothuizen, F.M.F. de Groot, and G.A. Sawatzky “Resonant x-ray Raman spectra of Cu dd excitations in Sr₂CuO₂Cl₂,” Phys. Rev. Lett. 80, 5204 (1998).