Phenomenological theory of spin excitations in La- and Y-based cuprates

Abstract

Motivated by recent inelastic neutron scattering experiments on La-based cuprates and based on the fermiology theories, we study the spin susceptibility for La-based (e.g., ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$) and Y-based (e.g., $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$) cuprates, respectively. The spin excitation in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ is dominated by a sharp resonance peak at the frequency $40\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ in the superconducting state. Below and above the resonance frequency, the incommensurate (IC) peaks develop and the intensity of the peaks decreases dramatically. In the normal state, the resonant excitation does not occur and the IC peaks are merged into commensurate ones. The spin excitation of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ is significantly different from that of Y-based ones, namely, the resonance peak does not exist due to the decreasing of the superconducting gap and the presence of the possible spin-stripe order. The spectra are only enhanced at the expected resonance frequency (about $18\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$) while they are still incommensurate. On the other hand, another frequency scale is also revealed, namely, the spectra are commensurate and show local maximum at the frequency of $55\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. We elaborate all the results based on the Fermi surface topology and the $d$-wave superconductivity and suggest that the spin-stripe order is also important in determining the spin excitation of La-based cuprates. A coherent picture for the spin excitations is presented for Y-based and La-based cuprates.