Observation of spin-conserving two-spinon continuum in the $S$=1/2 antiferromagnetic chain system Sr$_2$CuO$_3$ using Cu $K$-edge resonant inelastic x-ray scattering

TL;DR

This work demonstrates that Cu $K$-edge RIXS can observe spin-conserving two-spinon excitations in the one-dimensional $S=1/2$ antiferromagnetic chain Sr$_2$CuO$_3$ by detecting spectral weight below the charge-transfer gap that maps onto the spin-exchange dynamical structure factor $S^{ex}(q,\omega)$. Using an 18-site extended Hubbard model and exact diagonalization, the authors show that the Cu $K$-edge RIXS intensity $I(q,\omega)$ reproduces the two-spinon continuum predicted by $S^{ex}(q,\omega)$, with a momentum dependence that peaks near the zone-midpoint ($q\approx1/4$) and diminishes toward the zone center and boundary. The study highlights the Cu $K$-edge as a selective probe of $\Delta S=0$ magnetic excitations in 1D systems, complementary to INS and Cu $L_3$-edge RIXS, and demonstrates that polarization-resolved RIXS can help separate spin-conserving from spin-flip channels via symmetry arguments. These results establish Cu $K$-edge RIXS as a powerful tool for investigating fractionalized spin dynamics in low-dimensional quantum magnets.

Abstract

We report a Cu $K$-edge resonant inelastic x-ray scattering (RIXS) study of spin excitations in the $S$=1/2 antiferromagnetic chain system Sr$_2$CuO$_3$. The spectral weight observed below the charge-transfer gap appears in two-spinon continuum, indicating the fractionalization of a spin-conserving ($ΔS = 0$) magnetic excitation into two-spinon states. The intensity of these excitations reaches a maximum near the midpoint between the center and the boundary of the Brillouin zone, and decreases toward the zone boundary; this behavior contrasts with that of the spin-flip ($ΔS = 1$) excitations typically observed via inelastic neutron scattering or Cu $L_3$-edge RIXS. The momentum dependence of the intensity is described by the spin-exchange dynamical structure factor. A phenomenological analysis of the symmetry between the polarization and the $d$ orbital explains the resonance condition for the two-spinon excitations.

Figures (5)

• Figure 1: Fractionalization of elementary excitations in the one-dimensional spin chain. (a) Removal of an electron by photon irradiation breaks into a holon (H) and a spinon (S). (b) A single spin-flip excitation ($\Delta S = 1$) splits into two spinons. (c) A double spin-flip and total spin-conserving excitation ($\Delta S = 0$) is also fractionalized into two spinons. The wavy vertical line represents an antiferromagnetic domain boundary where the nearest-neighbor spins are aligned in parallel.
• Figure 2: Polarization-dependent x-ray absorption spectra of Sr$_2$CuO$_3$. Each spectrum has two peaks near the absorption edge and they correspond to the well-screened (w) and poorly-screened (p) core-hole final states. The inset shows a one-dimensional array of Cu-O plaquettes along with the crystallographic axes.
• Figure 3: Cu $K$-edge RIXS spectra of Sr$_2$CuO$_3$ taken at $q = 1/4$. The incident photon energy ($E_\mathrm{i}$), incident photon polarization (${\boldsymbol \epsilon}_{\rm i}$), absolute momentum transfer $\bm{Q}$ are shown in each figure, where ${\bm x}$, ${\bm y}$ and ${\bm z}$ represent the unit vectors along the crystallographic ${\bm a}$, ${\bm b}$ and ${\bm c}$ directions, respectively. The scattering geometry and crystal orientation are shown in the inset, in which $\bm{k}_\mathrm{i}$ and $\bm{k}_\mathrm{f}$ denote the incident and scattered photon wavevector, respectively.
• Figure 4: Momentum dependence of the Cu $K$-edge RIXS spectra of Sr$_2$CuO$_3$. The incident photon energy is $E_i=8982.5$ eV, and the absolute momentum transfer is $\bm{Q}=(0,q,3.56).$ The monochromator is Si(333) for (a)--(b) and Si(400) for (c)--(h). The filled circles are the raw spectra. In (a)--(g), the black solid lines represent the tail of the elastic scattering, and the open circles show the spectra after subtracting the tail. The horizontal gray bars indicate the energy range of the two-spinon continuum broadened by the experimental energy resolution. The spectrum in (h) is identical to that in (c), but plotted with different scales for energy loss and intensity to highlight the lineshape of tail of the elastic scattering. A small bump, indicated by an asterisk, appears at –0.3 eV and causes a spurious peak in the subtracted spectra in (c)–(g).
• Figure 5: (a) and (b) Calculated RIXS spectra below 1 eV (black solid lines) and the spin-exchange dynamical structure factor (red broken lines) in an 18-site extended Hubbard model. The parameters used in the calculation are given in the text. The $\delta$-function (vertical lines) is convoluted with the Lorentzian broadening of $0.2t$. The intensity of each spectrum is normalized relative to the weight of the lowest-energy excitation at $q=5/18$, and the original intensity in (b) is approximately 5.5 times larger than that in (a). (c) X-ray absorption spectrum of the model. Lorentzian broadening of $t$ is applied. The arrows indicate the incident photon energy for the calculation of RIXS in (a) and (b).