Long-range dynamics of magnetic impurities coupled to a two-dimensional Heisenberg antiferromagnet

TL;DR

This paper investigates the long-range effects of weakly coupled magnetic impurities in a 2D Heisenberg antiferromagnet, revealing inverse proportionality of disturbance to coupling and universal impurity interactions at large distances.

Contribution

It provides analytical expressions for impurity-induced magnetization disturbance and interactions, highlighting the inverse dependence on coupling and universality at large distances.

Findings

Magnetization disturbance scales as g/r for intermediate distances.

Impurity interaction scales as g^2/r at intermediate distances.

At large distances, the interaction becomes independent of the coupling constant.

Abstract

We consider a two-dimensional Heisenberg antiferromagnet on a square lattice with weakly coupled impurities, i.e. additional spins interacting with the host magnet by a small dimensionless coupling constant g<<1. Using linear spin-wave theory, we find that the magnetization disturbance at distance r from a single impurity behaves as g/r for 1<<r<<1/g and as 1/(gr^3) for r>>1/g. Surprisingly the disturbance is inversely proportional to the coupling constant! The interaction between two impurities separated by a distance r is proportional to g^2/r for 1<<r<<1/g and to 1/r^3 for r>>1/g. Hence at large distances, the interaction is universal and independent of the coupling constant. We also find that the frequency of Rabi oscillations between two impurities is proportional to g^2 ln(gr) at 1<<r<<1/g, logarithmically enhanced compared to the spin-wave width. This leads to a new mechanism for NMR, NQR and EPR line broadening. All these astonishing results are due to the gapless spectrum of the magnetic excitations in the quantum antiferromagnet.