Resonant inelastic x-ray scattering on single magnons at oxygenKedges

Abstract

The recent discovery that resonant inelastic x-ray scattering can probe single-magnon (SM) dispersions in transition metal (TM) oxides when the x-ray energy is tuned to the TM L-edge, has put this technique on a par with inelastic neutron scattering. It is generally presumed that selection rules forbid SM-scattering at oxygen (O) K-edges. However, based on a symmetry analysis and exact diagonalization study, we show that SM-scattering at O K-edges becomes allowed when (i) spin-orbit coupling is present in the TM d-shell and (ii) inversion symmetry at the O-site is broken. For cuprates the resulting SM-amplitude is very weak but in iridates both prerequisites can amply be fulfilled.PACS numbers: 75.30. Ds,78.70.Ck,71.70.Ej Introduction -The theoretical prediction [1] and subsequent experimental observation [2,3] that the dispersion of magnetic excitations, in particular of elementary single-magnons, can be measured directly by resonant inelastic x-ray scattering (RIXS) has fundamentally changed the field of inelastic magnetic scattering [4]. It has for instance lead to the discovery of distinct paramagnons in a large family of high-temperature cuprate superconductors [3][4][5][6][7][8], and established the presence of strongly dispersive magnetic modes in a number of iridium oxides [9][10][11][12].All these efforts to extract the dispersion of elementary magnetic excitations from RIXS have focussed on the transition metal (TM) L-edge, where single spin-flip scattering is directly allowed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The microscopic origin of this type of magnetic scattering is rather straightforward. When energy in RIXS the incoming photon is tuned to a TM L-edge, an electron with spin σ is excited out of the atomic p-shell, deep inside the atomic core, into the TM d-shell. The core-hole that is created in this event can now flip its spin due its very large spin-orbit interaction. Subsequently a valence d electron with spin −σ can fill the core-hole and an outgoing x-ray is emitted. The net result of this RIXS process is a spin-flip transition σ → −σ in the TM d-shell, which is the same as the net result of inelastic neutron scattering involving this d-shell electron.When a K-edge is used instead of a L-edge, this direct spin-flip process is no longer allowed. This is because in K-edge RIXS an electron is excited from a core-shell with s-symmetry, for which spin-orbit coupling is simply absent. It thus appears that for RIXS at K-edges direct spin-flip scattering is forbidden and only higher order magnetic scattering processes -starting at double spin-flip (e.g. bi-magnon) scattering -are allowed [17][18][19]. Indeed bi-magnon scattering is observed both at TM [20,21] and oxygen (O) K-edges [22,23]. This apparent absence of single-magnon spin-flip scattering is unfortunate because the O K-edge is in a soft x-ray regime where the RIXS resolution is particularly high (even if in this situation only a limited part of momentum space is accessible) and oxygen anions are obviously ubiquito...

Dispersive magnetic and electronic excitations in iridate perovskites probed by oxygen K -edge resonant inelastic x-ray scattering

“…However, the symmetry analysis in Ref. [37] is only viable for q = 0 and π of a one-dimensional distorted Ir 1 -O 1 -Ir 2 -O 2 periodic arrangement [black dashed line in Fig. 1(a)], which is far from the situations for real iridate materials, such as the perovskite layered iridates (Sr 2 IrO 4 and Sr 3 Ir 2 O 7 ) bearing special interests.…”

“…Besides the dispersions, we find that the single magnons persist in the whole momentum space measured with undiminished spectral weight (Figs. 2 and 3), therefore sorting out the momentum dependence of the magnon intensity, which was not settled in previous studies [37,38].…”

“…4) [15][16][17][18]. Without any doubt, A and A can be attributed to single magnons, proving that O K RIXS is sensitive to single magnons in the iridates with strong SOC in the 5d shell and broken inversion symmetry at the oxygen sites [37]. The large magnon gap (∼90 meV) in Sr 3 Ir 2 O 7 was explained to be driven by the strong magnetic anisotropy associated with SOC [17,18].…”

“…This could allow single spin-flip processes at the O K edge. Indeed, Kim et al [37] proposed that single spin-flip excitations will be intense at the point for O K RIXS if strong SOC is present in TM d orbitals and space inversion symmetry at the oxygen sites is broken. However, the symmetry analysis in Ref.…”

“…We unambiguously observe the single-magnon dispersion of both samples, thus providing conclusive evidence for the capability of O K RIXS in probing single magnons in 5d TM oxides with large SOC. The collective excitonic quasiparticles dispersing between 0.4 and 0.6 eV at the Ir L 3 edge of Sr 2 IrO 4 [16] "dressed" by magnons [37] Fig. 1(g)].…”