Resolving the nature of electronic excitations in resonant inelastic x-ray scattering

Abstract

These authors contributed equally † rcomin@mit.edu 33]. In these materials, the orbital degrees of freedom are dynamically active (and often coupled to spin and charge), and contribute to the spectrum of low-energy excitations, thus complicating the interpretation of RIXS spectra. Most importantly, the polarization analysis, besides requiring additional experimental components, provides only limited information in these cases, since the scattering matrix for orbital excitations is typically more asymmetric (see Appendix A) than the charge and spin channels. These considerations underscore the importance to develop a systematic method to resolve the nature and character of individual excitations encoded in the RIXS spectra.RIXS is a 2 nd order interaction process governed by a polarization-dependent cross section which can be derived from the Kramers-Heisenberg formula [1,10]. Most importantly, in the RIXS process, the character of each excitation is uniquely imprinted onto a distinctive form of the scattering tensor, which is ultimately determined by the matrix elements of the interaction (electric dipole) operator. The scattering tensor can be partly resolved by measuring the RIXS signal as a function of the polarization of incident (σ in /π in : perpendicular/parallel to the scattering plane) and scattered (σ out /π out ) photon beams, for a total of four polarization channels (σ in -σ out , σ in -π out , π in -σ out , π in -π out ). Full polarization analysis is therefore often insightful [20,34,35] but ultimately insufficient to resolve the full (3×3) scattering tensor, especially in systems with complex orbital physics where all components are nonzero and the tensor is asymmetric.In this paper, we apply a special procedure to resolve the RIXS scattering tensor at a given momentum transfer, and correspondingly uncover the nature of excitations as a function of both energy and momentum. Our experimental approach relies on the use of an azimuthal scanning geometry where the sample is placed on a wedged holder as shown in Fig. 1(a). This geometry, owing to the collinearity of the azimuthal rotation axis to the direction of momentum transfer, ensures that the probed wavevector remains fixed (both in-plane Q and out-of-plane Q ⊥ components) for all values of the azimuthal angle (φ). At each azimuthal angle, a different combination of the tensor components are selected, so that the symmetry of scattering tensor is imprinted onto the azimuthal dependence of RIXS signal. This probing scheme is often used in resonant elastic X-ray scattering experiments and is here demonstrated for inelastic processes [36,37]. In our experiment, an ostensible variation of the RIXS signal can be observed as a function of φ and, most importantly, the intensity modulation is different for each spectral component, reflecting the symmetry of the underlying scattering tensor (Fig. 1(b)). We applied this method to resolve the charge, spin, and orbital nature of elastic scattering, magnon and multimagnon, and dd excitations in cuprate compou...

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

“…Moreover, in both cases the lowest lying d − d excitation has an energy by ca. 1.5 eV higher than the ground state orbital even in SC samples [88], in agreement with Table I. The above discussion shows that the orbital excitations in the cuprates have relatively high energies, suggesting that the electrons close to the Fermi surface are clearly of a single 3d-band character.…”

High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb α−Li2IrO3

“…The intensity variation as a function of Q || is predominantly due to polarization effects which enter into the RIXS cross-section. This effect has been studied in some detail by Kang et al [54], and shall not be discussed further here.…”

Polarization-resolved Cu L3 -edge resonant inelastic x-ray scattering of orbital and spin excitations in NdBa2Cu3O7−<

“…When performed at the Cu L 3 -edge (2p 3/2 → 3d transition) it enables momentumdependent studies of low-and medium-energy excitations of superconducting cuprates [5][6][7][9][10][11][12] . RIXS spectra contain a variety of excitations spanning over a wide range of energies, from phonons below 100 meV [13][14][15] , to magnetic excitations up to 500 meV in cuprates 5,6 , to orbital (dd, crystal field) 9,11,[16][17][18][19][20][21][22] and charge transfer [23][24][25][26] excitations in the eV range. Moreover, the elastic and quasi-elastic intensities collected in RIXS spectra carry information on charge density waves or charge orders and associated excitations 10,[27][28][29] .…”