Exploring Quantum Materials with Resonant Inelastic X-Ray Scattering

Abstract

Understanding quantum materials -- solids in which quantum-mechanical interactions among constituent electrons yield a great variety of novel emergent phenomena -- is a forefront challenge in modern condensed matter physics. This goal has driven the invention and refinement of several experimental methods, which can spectroscopically determine the elementary excitations and correlation functions that determine material properties. This Perspectives article focuses on the future experimental and theoretical trends of resonant inelastic x-ray scattering (RIXS), which is a remarkably versatile and rapidly growing technique for probing different charge, lattice, spin, and orbital excitations in quantum materials. We provide a forward-looking introduction to RIXS and outline how this technique is poised to deepen our insight into the nature of quantum materials and their emergent electronic phenomena.

Figures (6)

• Figure 1: The Kramers-Heisenberg process for RIXS and the different excitations that it can probe. The RIXS process, shown in the center, involves the resonant absorption of an x-ray photon, creating an intermediate state with a core hole and a valence excitation, before the hole hole is filled via the emission of an x-ray photon. By measuring the energy and momentum change of the x-rays, one can infer the properties of the excitations created in the material. Around the outside, we illustrate the many different types of excitation that RIXS can probe, arranged clockwise in order of increasing energy scale, as denoted by the red-to-blue circular arrow.
• Figure 2: The charge excitation spectrum of correlated metals holds the key to understanding their anomalous electronic transport and symmetry breaking properties. (a) Electronic phase diagram of the cuprates showing the emergence of the unconventional or strange metal phenomenology from neighboring CDW, superconducting, and magnetic phases. (b) Conceptual picture of the charge excitations of cuprates, which reflect the properties of these unusual metalic states. At low momentum, cuprates feature plasmons, but at higher momentum, these decay to form a continuum in poorly understood ways. Cuprates also universally exhibit CDW symmetry breaking and correlations. (c) Plasmon dispersion and decay in Nd$_{2-x}$Ce$_x$CuO$_4$Hepting2018three. (d) Low-energy CDW excitations in La$_{2-x}$Ba$_x$CuO$_4$ above the CDW transition Miao2017high. Understanding these excitations can be key to comprehending unconventional metallicity.
• Figure 3: RIXS can access novel types of higher-order correlations functions that can help us identify QSL. (a) 1D Heisenberg spin chain. The AFM Heisenberg interaction $J>0$ acts equally on all three spin components. (b) Schematic diagram showing the phase space of fractionalized magnetic excitations in a spin chain. The darker shaded region is the 2-spinon continuum, and all shaded regions (both light and dark blue) represent the 4-spinon continuum Caux2006four. (c) Kitaev model where spins connected by an $x$-bond interact via their $x$-components and equivalent for the $y$- and $z$-bonds. (d) Experimental Ir $L_3$-edge RIXS data of the magnetic excitations along the chain direction in Ba$_4$Ir$_3$O$_{10}$ from Ref. Shen2022emergence. The dotted lines are the 2-spinon continuum boundary shown in panel (b). (e) Experimental RIXS spectra of a spin chain compound Sr$_2$CuO$_3$ obtained at the oxygen $K$-edge Schlappa2018probing. The dotted and dashed lines indicate the boundaries of the two- and four-spinon continua, respectively, as shown in panel (b). (f) Theoretical RIXS intensity of the Kitaev honeycomb model in the spin-conserving channel showing a strongly structured spectrum consistent with spin fractionalization Halasz2016resonant. The symmetry notation for the BZ is shown above the plot.
• Figure 4: Time-resolved RIXS will enable the discovery of transient phases without equilibrium analogs. (a) Sketch of a trRIXS experiment in which a material is perturbed by an optical pump and probed with short X-ray pulses Mitrano2020probing. (b) Ir $L$-edge trRIXS spectra of pseudospin excitations of Sr$_2$IrO$_4$ after excitation with near-infrared photons Dean2016ultrafast. (c) Cu L$_3$-edge trRIXS spectra of photoexcited La$_{2-x}$Ba$_x$CuO$_4$ showing prompt melting of the charge order (CO) quasielastic peak Mitrano2019ultrafast. (d) Ultrafast pump fields can lift (lower) in energy the intermediate doubly-occupied state of the exchange process by an amount proportional to the number of virtually absorbed (emitted) pump photons and alter the spin wave dispersion across the entire BZ Wang2021xray. $U$ is the onsite Coulomb repulsion, $t_{\textrm{eff}}$ the effective hopping amplitude, $\Omega$ the pump photon energy and $m$ the Floquet index Mitrano2020probingMitrano2020probingWang2021xray. (e) Photoexcited low-dimensional Mott insulators are predicted to exhibit an emergent condensate called $\eta$-pairing, i.e., a staggered superconducting phase with characteristic charge [$N(q,\omega)$], spin [$S(q,\omega)$], and superconducting [$SC(q,\omega)$] response functions Murakami2022exploring. (f) Photodoped Mott insulators and quantum magnets can evade thermalization to a hot metallic state and give rise to nonthermal states (prethermal and metastable) if their dynamics is constrained by approximate conservation laws or symmetries Murakami2023photoinduced.
• Figure 5: RIXS has unique assets for probing functional materials, such as the structure and propagation of novel magnetic excitons in van der Waals materials. (a) van der Waals heterostructures interacting with light, electric, and magnetic fields, which offer routes to swtiching between different electronic phases and the transduction of information. (b) Illustration of Frenkel, Hubbard, and Hund's excitons. (c) RIXS is sensitive to nominally dipole-forbidden excitations and can detect excitons, such as the 1.45 eV feature (circled in white) in the Ni $L_3$-edge spectra of NiPS$_3$Kang2020coherent.