Dynamic spin susceptibility of superconducting cuprates: A microscopic theory of the magnetic resonance mode

TL;DR

This paper develops a microscopic theory for the dynamic spin susceptibility in superconducting cuprates, explaining the magnetic resonance mode observed in experiments through a detailed analysis of spin excitations and their damping mechanisms.

Contribution

It introduces a novel microscopic approach using the t-J model and Mori-type projection technique to explain the magnetic resonance mode in superconducting cuprates.

Findings

Resonance mode appears at low temperatures near Q = π(1,1).

Spin gap limits decay of spin excitations, enabling resonance observation.

Good agreement with neutron-scattering experiments on YBCO.

Abstract

A microscopic theory of the dynamic spin susceptibility (DSS) in the superconducting state within the t-J model is presented. It is based on an exact representation for the DSS obtained by applying the Mori-type projection technique for the relaxation function in terms of Hubbard operators. The static spin susceptibility is evaluated by a sum-rule-conserving generalized mean-field approximation, while the self-energy is calculated in the mode-coupling approximation. The spectrum of spin excitations is studied in the underdoped and optimally doped regions. The DSS reveals a resonance mode (RM) at the antiferromagnetic wave vector Q = \pi(1,1) at low temperatures due to a strong suppression of the damping of spin excitations. This is explained by an involvement of spin excitations in the decay process besides the particle-hole continuum usually considered in random-phase-type approximations. The spin gap in the spin-excitation spectrum at Q plays a dominant role in limiting the decay in comparison with the superconducting gap which results in the observation of the RM even above $T_c$ in the underdoped region. A good agreement with inelastic neutron-scattering experiments on the RM in YBCO compounds is found.