The two-dimensional quantum Heisenberg antiferromagnet at zero temperature, with locally frustrating magnetic defects, is studied. We consider two types of defects---an isolated ferromagnetic bond (FMB) and a quantum impurity spin, coupled symmetrically to the two sublattices. A technique is developed to study strong defect-environment interaction. In the case of a FMB we find that, contrary to the previous linear spin-wave result, the local magnetization stays finite even for strong frustration. For an antiferromagnetic coupling of a quantum impurity spin with its environment, we find a local change in the ground state. All our calculations are compared with numerical results from exact diagonalization.The two-dimensional quantum Heisenberg antiferromagnet at zero temperature, with locally frustrating magnetic defects, is studied. We consider two types of defects---an isolated ferromagnetic bond (FMB) and a quantum impurity spin, coupled symmetrically to the two sublattices. A technique is developed to study strong defect-environment interaction. In the case of a FMB we find that, contrary to the previous linear spin-wave result, the local magnetization stays finite even for strong frustration. For an antiferromagnetic coupling of a quantum impurity spin with its environment, we find a local change in the ground state. All our calculations are compared with numerical results from exact diagonalization.

arXiv:cond-mat/9712281Physical review. B, Condensed matterOct 1, 199814 citations

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

Andreas Lüscher, Oleg P. Sushkov

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.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.

arXiv:cond-mat/0408598Physical Review BFeb 23, 200516 citations

From enhanced to reduced quantum antiferromagnetism by tuning a magnetic impurity

Julian Engel, Stefan Weßel

Based on quantum Monte Carlo simulations, we study the local-order-parameter modulations induced by a magnetic impurity that couples to a single moment of a two-dimensional quantum antiferromagnet. A strong antiferromagnetic coupling of the impurity spin reduces the antiferromagnetic order in the host beyond the next-nearest-neighbor sites of the impurity spin, whereas on the next-nearest neighbors the order increases, similar as for an embedded vacancy. We show that for weak and intermediate couplings to the impurity spin, the local antiferromagnetic order is enhanced throughout the host magnet. We compare our numerical findings to analytical results from a recent perturbative approach based on spin-wave theory.Based on quantum Monte Carlo simulations, we study the local-order-parameter modulations induced by a magnetic impurity that couples to a single moment of a two-dimensional quantum antiferromagnet. A strong antiferromagnetic coupling of the impurity spin reduces the antiferromagnetic order in the host beyond the next-nearest-neighbor sites of the impurity spin, whereas on the next-nearest neighbors the order increases, similar as for an embedded vacancy. We show that for weak and intermediate couplings to the impurity spin, the local antiferromagnetic order is enhanced throughout the host magnet. We compare our numerical findings to analytical results from a recent perturbative approach based on spin-wave theory.

Physical Review BSep 9, 20095 citations

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.