The two-dimensional Heisenberg model at zero temperature with a quantum S=1/2 impurity spin, coupled to one site, is studied. The ground state properties of the model are calculated for large coupling, in order to study the impurity-host spin local singlet formation and related local suppression of the magnetization in the host lattice. Analytic results are obtained by developing perturbation theory around the exactly solvable two-body (impurity plus neighbor) problem and compared with results obtained by exact diagonalization of small clusters. We find that perfect screening of the impurity is only achieved for infinitely large interaction, while at intermediate coupling the local magnetization is suppressed, but nonzero.
Local magnetic moments induced by a nonmagnetic impurity in the two-dimensional $t\ensuremath{-}J$ model are investigated by use of a Green function method in a finite-size system (50\ifmmode\times\else\texttimes\fi{}50=2500 sites). Local electron number and nearest-neighbor correlation functions are calculated self-consistently at each lattice point. A local electron number distribution shows that electrons form a bound state around an impurity site and the magnitude of the local moment is enhanced, whereas doped holes can be distributed only apart from the impurity site and destroy an antiferromagnetic spin configuration by their motion. This result is consistent with experimental results of Zn-doped high-
Tc superconductors.
We consider a finite two dimensional XY spin model. The model consists of a set of seven localized spin- 12 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external magnetic field. We study the effect of a single impurity spin coupled to its nearest neighbor through an exchange interaction J′ on the pairwise entanglement between the different spins in the lattice. We found that when the spin is located at a border site the entanglement between the impurity and its nearest neighbors increases monotonically with J′ reaching a saturation value that depends on the magnetic field strength h. On the other hand the entanglement with the next nearest spins shows a critical behavior where the entanglement increases and then decreases rapidly until it vanishes. The critical coupling value at which the entanglement vanishes increases as h increases. Studying the entanglement between two spins excluding the impurity show that while the entanglement between two spins coupled to the impurity reach a saturation value as J′ increases, it vanishes for spins not coupled to the impurity. Furthermore studying the effect of a central impurity show that the entanglement between nearest neighbor and next nearest neighbor spins reaches an asymptotic value as J′ increases. Interestingly it was demonstrated that the impurity can be used as a switch to control the entanglement between different spins in the lattice turning it on and off.
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.
In spin‐gapped quasi‐one‐dimensional antiferromagnets that do not show phase transitions down to zero temperature, impurities cause phase transitions by inducing local magnetic moments around them between which long‐range correlation is mediated by weak interchain couplings. We investigate the difference between the effects of non‐magnetic impurities and those of spin‐1/2 magnetic ones in the impurity‐induced transition temperatures and the staggered magnetization in the impurity‐induced ordered phase by the quantum Monte Carlo method. We find that the staggered correlation induced by spin‐1/2 impurities grows slower than that done by non‐magnetic ones as the system is cooled and approaches the ground state, while the transition temperature induced by the former is higher than that done by the latter. We argue that this is one of the characteristic aspects of the order‐by‐disorder phenomena in quantum systems.
Motivated by frustrated magnets and quasi-one-dimensional magnetic materials, we study the magnetic properties of one-dimensional (1D) Ising chains with nearest-neighbor (NN) and weaker next-to-nearest-neighbor (NNN) interactions in the presence of vacancy defects. The effect of a vacancy on the magnetic susceptibility of a spin chain is twofold: it reduces the length of the chain by an effective ``vacancy size'' and may also act as a free spin, a ``quasispin,'' with a Curie-type ${\ensuremath{\chi}}_{\text{quasi}}=\ensuremath{\langle}{S}^{2}\ensuremath{\rangle}/T$ contribution to the susceptibility. In chains with antiferromagnetic short-range order, the susceptibility of vacancy-free chains is exponentially suppressed at low temperatures, and quasispins dominate the effect of impurities on the chains' magnetic properties. For chains with antiferromagnetic NN interactions, the quasispin matches the value $\ensuremath{\langle}{S}^{2}\ensuremath{\rangle}=1$ of the Ising spins in the chain for ferromagnetic NNN interactions and vanishes for antiferromagnetic NNN interactions. For chains with ferromagnetic short-range order, quasispin effects are insignificant due to exponentially large low-temperature susceptibilities, and the dominant effect of a vacancy is effectively changing the length of the chain.