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

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 $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}g∕r$ for $1⪡r⪡1∕g$ and as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}1∕(g{r}^{3})$ for $r⪢1∕g$. Surprisingly the magnetization disturbance is inversely proportional to the coupling constant. The interaction between two impurities separated by a distance $r$ is $\ensuremath{\delta}ϵ\ensuremath{\propto}{g}^{2}∕r$ for $1⪡r⪡1∕g$ and $\ensuremath{\delta}ϵ\ensuremath{\propto}1∕{r}^{3}$ for $r⪢1∕g$. For large distances, the interaction is therefore universal and independent of the coupling constant. We have also found that the frequency of Rabi oscillations between two impurities is logarithmically enhanced compared to the decay width ${\ensuremath{\omega}}_{\mathrm{Rabi}}\ensuremath{\propto}{g}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(1∕\mathit{gr})$ at $1⪡r⪡1∕g$. This leads to a logarithmic enhancement for NMR and EPR line broadening. All these astonishing results are due to the gapless spectrum of magnetic excitations in the quantum antiferromagnet.