Evolution of the resonance and incommensurate spin fluctuations in superconductingYBa2Cu3O<

Abstract

Polarized and unpolarized neutron triple-axis spectrometry was used to study the dynamical magnetic susceptibility χ ′′ (q, ω) as a function of energy (hω) and wave vector (q) in a wide temperature range for the bilayer superconductor YBa2Cu3O6+x with oxygen concentrations, x, of 0. 45, 0.5, 0.6, 0.7, 0.8, 0.93, and 0.95. The most prominent features in the magnetic spectra include a spin gap in the superconducting state, a pseudogap in the normal state, the much-discussed resonance, and incommensurate spin fluctuations below the resonance. We establish the doping dependence of the spin gap in the superconducting state, the resonance energy, and the incommensurability of the spin fluctuations. The magnitude of the spin gap (Esg) up to the optimal doping is proportional to the superconducting transition temperature Tc with Esg/kBTc = 3.8. The resonance, which exists exclusively below Tc for highly doped YBa2Cu3O6+x with x = 0.93 and 0.95, appears above Tc for underdoped compounds with x ≤ 0.8. The resonance energy (Er) also scales with kBTc, but saturates at Er ≈ 40 meV for x close to 0.93. The incommensurate spin fluctuations at energies below the resonance have structures similar to that of the single-layer superconducting La2−xSrxCuO4. However, there are also important differences. While the incommensurability (δ) of the spin fluctuations in La2−xSrxCuO4 is proportional to Tc for the entire hole-doping range up to the optimal value, the incommensurability in YBa2Cu3O6+x increases with Tc for low oxygen doping and saturates to δ = 0.1 for x ≥ 0.6. In addition, the incommensurability decreases with increasing energy close to the resonance. Finally, the incommensurate spin fluctuations appear above Tc in underdoped compounds with x ≤ 0.6 but for highly doped materials they are only observed below Tc. We discuss in detail the procedure used for separating the magnetic scattering from phonon and other spurious effects. In the comparison of our experimental results with various microscopic theoretical models, particular emphasis was made to address the similarities and differences in the spin fluctuations of the two most studied superconductors. Finally, we briefly mention recent magnetic field dependent studies of the spin fluctuations and discuss their relevance in understanding the microscopic origin of the resonance.

Quantum spin excitations through the metal-to-insulator crossover inYBa2Cu3O6+y

“…3(a). While the χ ′′ (Q, ω) at 55 K increases linearly withhω, consistent with the energy dependence of the normal state dynamics susceptibility in other metallic ground state YBCO 7,8,10 Fig. 3(e) gives Q-scans along the [H, H, 2] direction, which is the position expected for the central diffusive mode 15 .…”

“…However, the S(Q, ω) peak intensity for hω = 1 meV is larger at T = 55 K than that at 5 K. To further study the low energy spin fluctuations, we measured the energy dependence of the scattering at the peak Q = (0.5, 0.5, 1.8) and background Q = (0.36, 0.36, 1.8) positions for the acoustic mode 6,7,8,9,10 . The scattering function S(Q, ω) at different temperatures can then be estimated by subtracting the background scattering from the peak position as shown in Fig.…”

“…For YBa 2 Cu 3 O 6+y (YBCO) with y ≥ 0.5, the prominent features in spin fluctuations spectra at the superconducting state include a collective magnetic excitation known as the "resonance" mode, which is sharp in energy and centered at the AF ordering wavevector Q = (1/2, 1/2), and a superconducting spin gap 4,5,6,7,8,9,10,11 . The magnetic excitation spectra show an "hourglass"-like dispersion with the resonance at the saddle point 9,10,11 .…”

“…The magnetic excitation spectra show an "hourglass"-like dispersion with the resonance at the saddle point 9,10,11 . The energies of the mode (E R ) and the spin gap (E gap ) track T c 's as y is varied, and the opening of the spin gap below T c is compensated in part by the spectral weight gain of the resonance 4,5,7,8,9,10 . In the case of optimally doped La 2−x Sr x CuO 4 (LSCO), inelastic neutron scattering measurements reveal that spin excitations also display an hourglass dispersion with a spin gap and incommensurate resonance below T c 4,5,12,13 .…”

Magnetic Excitation in Lightly-Doped Bi2.4Sr1.6CuO6+y

“…The incommensurability (δ), which corresponds to the half distance between a pair of IC peaks, linearly increases with the hole concentration (p) and the IC wavevector changes from [110] to [100]/[010] direction in the tetragonal notation at p∼0.06. These observations are quite similar to the results for LSCO, but different from those for YBCO [4][5][6] , suggesting that the doping evolution of spin correlation is classified by the number of CuO 2 planes between the block layers. In this study, to gain further insights into the universality in the spin correlations in doped cuprate oxide, we measured the spin excitation in the SG phase of Bi 2.4 Sr 1.6 CuO 6+y (Bi2201) with p ∼ 0.06 up to a relatively high energy region (∼30 meV).…”