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

## TL;DR

This paper develops a phenomenological theory to explain the differences in spin excitations observed in La- and Y-based cuprates, linking experimental INS data with Fermi surface topology and superconductivity.

## Contribution

It provides a unified phenomenological framework explaining the distinct spin excitation spectra in La- and Y-based cuprates, emphasizing the role of spin-stripe order and Fermi surface effects.

## Key findings

- Y-based cuprates show a sharp 40 meV resonance peak in the superconducting state.
- La-based cuprates lack a resonance peak, showing incommensurate spectra at 18 meV and a local maximum at 55 meV.
- Spin excitations are influenced by Fermi surface topology, superconducting gap, and spin-stripe order.

## Abstract

Motivated by recent inelastic neutron scattering (INS) experiments on La-based cuprates and based on the fermiology theories, we study the spin susceptibility for La-based (e.g., La$_{2-x}$Sr$_x$CuO$_4$) and Y-based (e.g., YBa$_2$Cu$_3$O$_y$) cuprates, respectively. The spin excitation in YBa$_2$Cu$_3$O$_y$ is dominated by a sharp resonance peak at the frequency 40 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 La$_{2-x}$Sr$_x$CuO$_4$ 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 meV) while it is still incommensurate. On the other hand, another frequency scale at the frequency 55 meV is also revealed, namely the spectra are commensurate and local maximum at this frequency. We elaborate all the results based on the Fermi surface topology and the d-wave superconductivity, and suggest that the spin-stripe order be 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.