Pseudogap term in the magnetic response of cuprate superconductors

Abstract

This paper presents a joint analysis of inelastic neutron scattering (INS) and nuclear magnetic resonance data on superconducting cuprates, with the aim of a detailed characterization of the dynamical susceptibility ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$ at low frequencies and at temperatures ranging from ${T}_{c}$ up to room temperature. Using the well-known relation between $1/{T}_{1}$ and ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$, the analysis shows that the temperature dependence of the nuclear relaxation rate $1/{T}_{1}$ is controlled by a combination of dynamic spin-spin correlations between pairs of fluctuating moments in the CuO${}_{2}$ plane and a time constant proportional to the integral of ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$ over the Brillouin zone. INS data on ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$ for ${\text{La}}_{1.86}{\text{Sr}}_{0.14}{\text{CuO}}_{4}$ (LSCO) and ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{6.5}$ (YBCO6.5) are seen to obey $\ensuremath{\omega}/T$ scaling above a transition temperature, then fall to very low values at low temperatures. Thus, there is no evidence in such data for magnetic pseudogap effects, which are known to be quite pronounced in YBCO6.5, but somewhat muted in LSCO. Our analysis of ${T}_{1}$ data shows, however, that above the transition temperature noted above there occurs the onset of another term in ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$, which comes to dominate $1/{T}_{1}$ at room temperature and above. We call this term ``the pseudogap term'' ${\ensuremath{\chi}}_{P}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$. The onset of ${\ensuremath{\chi}}_{P}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$ coincides with the entry into a quantum-critical regime dominated by stripes, but could also be derived from low-energy fluctuations resulting from nearby phase transitions characterized by other types of order, such as ring currents. For YBCO6.5 this onset is at ${T}_{c}\ensuremath{\sim}62\phantom{\rule{0.28em}{0ex}}\text{K}$, but for LSCO, it occurs 20--30 K higher than ${T}_{c}$. We model the $q$-space behavior of ${\ensuremath{\chi}}_{P}^{\ensuremath{'}\ensuremath{'}}(\stackrel{P\vec}{q},\ensuremath{\omega})$ and discuss its prospects for observation via INS. The occurrence of the foregoing effects is suggested to be widespread among the superconducting cuprates.