Spin dynamics and magnetic correlation length in two-dimensional quantum Heisenberg antiferromagnets

TL;DR

This paper investigates spin dynamics and correlation lengths in 2D quantum Heisenberg antiferromagnets, showing experimental results align with several theoretical models and finding no crossover between quantum regimes.

Contribution

It provides detailed experimental analysis of spin dynamics in a new compound with smaller exchange constant, confirming theoretical predictions and challenging some existing models.

Findings

Excellent agreement between NMR relaxation rates and mode-coupling calculations

Correlation length behavior matches high-temperature expansions and quantum Monte Carlo results

No evidence of crossover between different quantum regimes as predicted by Non-Linear σ Model

Abstract

The correlated spin dynamics and the temperature dependence of the correlation length $\xi(T)$ in two-dimensional quantum ($S=1/2$) Heisenberg antiferromagnets (2DQHAF) on square lattice are discussed in the light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate (CFTD). In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of $\xi(T)$ is in agreement with high-temperature expansions, quantum Monte Carlo simulations and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the Non-Linear $\sigma$ Model, no evidence of crossover between different quantum regimes is observed.