Spin dynamics in lightly doped La$_{2-x}$Sr$_x$CuO$_4$: Relaxation function within the $t - J$ model

TL;DR

This paper develops a relaxation function theory for doped 2D Heisenberg antiferromagnets within the $t-J$ model, explaining experimental spin relaxation data in lightly doped La$_{2-x}$Sr$_x$CuO$_4$.

Contribution

It derives a fourth frequency moment expression for the relaxation shape function considering all wave vectors, incorporating AF and hole correlations, and explains experimental relaxation rates.

Findings

Spin diffusion significantly influences relaxation rates.

Main contribution to $^{63}(1/T_1)$ arises from AF fluctuations.

Theory matches temperature and doping dependence of experimental data.

Abstract

The relaxation function theory of doped two-dimensional $S=1/2$ Heisenberg antiferromagnetic (AF) system in the paramagnetic state is presented taking into account the hole subsystem as well as both the electron and AF correlations. The expression for fourth frequency moment of relaxation shape function is derived within the $t-J$ model. The presentation obeys rotational symmetry of the spin correlation functions and is valid for all wave vectors through the Brillouin zone. The spin diffusion contribution to relaxation rates is evaluated and is shown to play a significant role in carrier free and doped antiferromagnet in agreement with exact diagonalization calculations. At low temperatures the main contribution to the nuclear spin-lattice relaxation rate, $^{63}(1/T_1)$, of plane $^{63}$Cu arises from the AF fluctuations, and $^{17}(1/T_1)$, of plane $^{17}$O, has the contributions from the wavevectors in the vicinity of $(\pi,\pi)$ and small $q \sim 0$. It is shown that the theory is able to explain the main features of experimental data on temperature and doping dependence of $^{63}(1/T_1)$ in the paramagnetic state of both carrier free La$_2$CuO$_4$ and doped La$_{2-x}$Sr$_x$CuO$_4$ compounds.