Effective Field Theory for Layered Quantum Antiferromagnets with Non-Magnetic Impurities

TL;DR

This paper develops an effective field theory combining quantum non-linear sigma models and percolation theory to analyze magnetic properties of layered quantum antiferromagnets with non-magnetic impurities, revealing a quantum critical point below the percolation threshold.

Contribution

It introduces a novel combined theoretical framework to study impurity effects in layered quantum antiferromagnets, identifying a quantum critical point at lower doping levels.

Findings

Quantum critical point at x_c ≈ 0.305

Magnetization and correlation length behaviors match experimental data

Quantum fluctuations significantly influence magnetic properties

Abstract

We propose an effective two-dimensional quantum non-linear sigma model combined with classical percolation theory to study the magnetic properties of site diluted layered quantum antiferromagnets like La$_{2}$Cu$_{1-x}$M$_x$O$_{4}$ (M$=$Zn, Mg). We calculate the staggered magnetization at zero temperature, $M_s(x)$, the magnetic correlation length, $\xi(x,T)$, the NMR relaxation rate, $1/T_1(x,T)$, and the N\'eel temperature, $T_N(x)$, in the renormalized classical regime. Due to quantum fluctuations we find a quantum critical point (QCP) at $x_c \approx 0.305$ at lower doping than the two-dimensional percolation threshold $x_p \approx 0.41$. We compare our results with the available experimental data.