Magnetic Excitations of a Half-Filled Tl-based Cuprate

TL;DR

Cuprates offer a tunable platform to connect electron correlations with magnetic excitations in Mott insulators; this study introduces Tl$_2$Ba$_5$Cu$_4$O$_x$ (Tl2504) as a clean half-filled Tl-based cuprate and uses high-resolution RIXS to access long-lived magnons. A pronounced kink in the magnon dispersion is analyzed with a Hubbard–Heisenberg model incorporating a momentum-dependent renormalization $Z_c(k)$, yielding a universal relation between the interaction strength $U/t$ and the zone-boundary dispersion. Tl2504 shows a large zone-boundary magnon energy of about $E_{ZB}$ ≈ 100 meV and a ~1.8 eV ARPES gap, with $U/t$ ≈ 6.9 from the fit. The near-constant ratio between $E_{ZB}$ and $U/t$ across cuprates points to apical-oxygen geometry and interlayer screening as key controls of in-plane spin dynamics, suggesting maximal $T_c$ occurs at intermediate correlation strength that balances localization and itinerancy.

Abstract

Strong electron correlations drive Mott insulator transitions. Yet, there exists no framework to classify Mott insulators by their degree of correlation. Cuprate superconductors, with their tunable doping and rich phase diagrams, offer a unique platform to investigate the evolution of these interactions. However, spectroscopic access to a clean half-filled Mott-insulating state is lacking in compounds with the highest superconducting onset temperature. To fill this gap, we introduce a pristine, half-filled thallium-based cuprate system, Tl$_2$Ba$_5$Cu$_4$O$_{x}$. Using high-resolution resonant inelastic x-ray scattering, we probe long-lived magnon excitations and uncover a pronounced kink in the magnon dispersion, marked by a simultaneous change in group velocity and lifetime broadening. Modeling the dispersion within a Hubbard-Heisenberg approach, we extract the interaction strength and compare it with other cuprate systems. Our results establish a cuprate universal relation between electron-electron interaction and magnon zone-boundary dispersion. Superconductivity seems to be optimal at intermediate correlation strength, suggesting an optimal balance between localization and itinerancy.

Figures (4)

• Figure 1: Characteristic of single and double-layer Tl-based cuprates (a) Crystal structures of Tl2201 and Tl2504 (Cu-O bonds are indicated). (b,c) Low temperature RIXS spectra at $(h,0)=(0.38,0)$ measured with $\pi$ polarized incident light. Main orbital excitations are determined from fitting with Gaussians and are denoted by shaded areas. XAS profiles of Cu $L_3$ absorption edges, which correspond to the transitions from 2p to empty 3d states, are presented as insets. RIXS spectra were collected with incident light energy tuned to the maximum of the Cu $L_3$ edge. The RIXS spectrum for $p=0.25$ doped Tl2201 is adapted from Tam2022. (d,e) ARPES band maps taken along the nodal direction for metallic, overdoped Tl2201 ($p=0.25$) kramerPRB2019 and insulating Tl2504, respectively. The corresponding energy distribution curves in the right-hand panels were integrated within (d) $k_F-0.05>k>k_F+0.05$ with $k_F$ marked by a dashed line or (e) within the presented range of k.
• Figure 2: RIXS studies of undoped Tl2504 (a) Scattering geometry used for the RIXS experiment. $k_i$ and $k_f$ represent the momentum of the incident and scattered photons within the scattering plane (red shadow) perpendicular to the CuO$_2$ plane of the sample. The incident beam is polarized ($\pi$ or $\sigma$). (b) Reciprocal space probed by RIXS measurements. The gray dashed line represent the antiferromagnetic zone boundary (AFZB). (c-f) The low-energy region of normalized RIXS spectra fitted by four Gaussian components. A solid black line represents the sum of the fitting components. (g) Normalized RIXS spectra for the $\pi$-polarized beam recorded along three momentum trajectories defined by the colors in panel (b). The magnon contribution to RIXS spectra, based on fitting results, is indicated as a red shadow.
• Figure 3: Single-magnon dispersion in half-filled Tl2504 (a) Single-magnon dispersion and its inverse lifetime extracted from RIXS measurements performed with $\sigma$ and $\pi$ polarized light. The black arrow indicates simultaneous change of magnon energy and inverse lifetime. The gray dashed line represents the AFZB, while the azimuthal part of the dispersion is defined by $Q_1=0.5$. A blue dotted line represent the experimental energy resolution. (b) Comparison of magnon dispersion along $(h,0)$ and $(h,h)$ directions for selected cuprate systems. Solid lines are corresponding fits using the Hubbard model including renormalization factor (see text). Datasets for Tl2504 and LCO are shifted by a constant in energy scale, correspondingly by $0.8$ eV and $0.12$ eV. Data for LCO (SCO) has been adapted from headings_anomalous_2010 (wang_magnon_2024).
• Figure 4: Strength of electronic correlations From parametrization of magnon dispersions with a Hubbard model (see text), $U/t$ and $E_{\mathrm{ZB}}$ are extracted for various cuprate compounds. Fitting of magnon dispersions used data from Tl2504 (this work, star), LCO headings_anomalous_2010, Sr$_2$CuO$_2$Cl$_2$ (SCOC) plumb_high-energy_2014, Bi$_2$Sr$_{0.9}$La$_{1.1}$CuO$_6$ (Bi2201) peng_influence_2017, CCO martinelli_fractional_2022 and SCO wang_magnon_2024.