The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional planar rotator and XY models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster and over-relaxation techniques. The transition temperature Tc is determined as a function of vacancy density ρvac by calculations of the helicity modulus and the by finite-size scaling of the in-plane magnetic susceptibility. The results for Tc are consistent with those from the much less precise fourth-order cumulant of Binder. Tc is found to decrease monotonically with increasing ρvac, and falls to zero close to the square lattice percolation limit, ρvac ≈ 0.41 . The result is physically reasonable: the long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.

The dynamical behavior of anisotropic two dimensional Heisenberg models is still a matter of controversy. The existence of a central peak at all temperatures and a rich structure of magnon peaks are not yet understood. It seems that the central peaks are related, in some way, to structures like vortices. In order to contribute to the discussion of the dynamical behavior of the model we use Monte Carlo and spin dynamics simulations as well analytical calculations to study the behavior of vortices in the presence of nonmagnetic impurities. Our simulations show that vortices are attracted and trapped by the impurities. Using this result we show that if we suppose that vortices are not very much disturbed by the presence of the impurities, then they work as an attractive potential to the vortices explaining the observed behavior in our simulations. The anisotropic Heisenberg model (AHM) in two dimensions has received a lot of attention recently. Such attention is grounded in the fact that a large variety of models may be mapped in the AHM. It is an interesting model because it can support topological excitations, like solitons and vortices, which are present in several important phenomena. Topological defects are present in condensed matter systems such as superconductors, liquid crystals, superfluids, magnetic materials and several others. The knowledge of how such structures behave is essential for technological applications and an important condition for the understanding of many physical questions. Of great importance is the dynamical behavior of vortices in ordered structures. Knowing how vortices are pinned in superconductors is essential for applications such as magnetic levitation, improving magnetic resonance imaging devised for medical diagnosis and many others. Topological defects can be the signature left behind by the cosmological phase transitions, which occur while the universe expands and cools. Beside all of that, the study of the dynamics of the AHM model is interesting by itself. There are several questions not yet responded about the model. For example, the origin of the central peak in the dynamical structure factor observed in experiments and simulations is the source of several controversial interpretations. Its origin may be due to vortex motion 1,2,3 . However this point is still controversial 4,5 . The existence of some kind of impurity in the system may affect its properties in several ways. For example, solitons near a nonmagnetic impurity in 2D antiferromagnets cause observable effects in EPR experiments 6,7 . Lattice defects such as impurities and dislocations play a crucial role in disrupting order in solids.The main task of this letter is to consider the dynamical effects caused by impurities on topological defects. We will consider the classical two-dimensional magnetic (XY) model described byHere J is a coupling constant, S α (α = x, y, z) are the components of the classical spin vector S = (S x , S y , S z ) and the summation is over nearest-neighbor in a square lattice. The spin f...

We performed Monte Carlo simulations to calculate the Berezinskii-Kosterlitz-Thouless (BKT) temperature TBKT for the two-dimensional planar rotator model in the presence of nonmagnetic impurity concentration (ρ). As expected, our calculation shows that the BKT temperature decreases as the spin vacancies increase. There is a critical dilution ρc ≈ 0.3 at which TBKT = 0. The effective interaction between a vortex-antivortex pair and a static nonmagnetic impurity is studied analytically. A simple phenomenological argument based on the pair-impurity interaction is proposed to justify the simulations.

In this work we have used micromagnetic simulations to report four ways to build traps for magnetic skyrmions. Magnetic defects have been modeled as local variations in the material parameters, such as the exchange stiffness, saturation magnetization, magnetocrystalline anisotropy and Dzyaloshinskii-Moriya constant. We observe both pinning (potential well) and scattering (potential barrier) traps when tuning either a local increase or a local reduction for each one of these magnetic properties. It is found that the skyrmion-defect aspect ratio is a crucial parameter to build traps for skyrmions. In particular, the efficiency of the trap is compromised if the defect size is smaller than the skyrmion size, because they interact weakly. On the other hand, if the defect size is larger than the skyrmion diameter, the skyrmion-defect interaction becomes evident. Thus, the strength of the skyrmion-defect interaction can be tuned by the modification of the magnetic properties within a region with suitable size. Furthermore, the basic physics behind the mechanisms for pinning and for scattering is discussed. In particular, we discover that skyrmions move towards the magnetic region which tends to maximize its diameter; it enables the magnetic system to minimize its energy. Thus, we are able to explain why skyrmions are either attracted or repelled by a region with modified magnetic properties. Results here presented are of utmost significance for the development and realization of future spintronic devices, in which skyrmions will work as information carriers.

We investigate the influence of artificial defects ͑small holes͒ inserted into magnetic nanodisks on the vortex core dynamics. One and two holes ͑antidots͒ are considered. In general, the core falls into the hole; but, in particular, we would like to note an interesting phenomenon not yet observed, which is the vortex core switching induced by the vortex hole interactions. It occurs for the case with only one hole and for very special conditions involving the hole size and position as well as the disk size. Any small deformation in the disk geometry such as the presence of a second antidot completely changes the vortex dynamics, and the vortex core eventually falls into one of the defects. After trapped, the vortex center still oscillates with a very high frequency and small amplitude around the defect center.