Estudo de interações competitivas e anisotropia em sistemas magnéticos

Abstract

We studied the efect of competitive interactions and anisotropies in the Heisenberg model in diferent situations. Initially, we treat the antiferromagnetic Heisenberg model of spin S = 1 with competitive interactions between next J1 and next-nearest J2 neighbors (Heisenberg model J1 J2) and easy plane anisotropy in a cubic lattice with interactions J3 between adjacent planes. We use the self-consistent harmonic approximation to calculate the phase transition temperature from paramagnetic phase to the ordered phase at low temperature. We also obtained at zero temperature, the critical value of the easy plan anisotropy that separates the region of small D values, from the quantum paramagnetic phase for large D values. We found a disordered phase at zero temperature which may be a possible candidate to spin liquid phase. In the following work, we use the Schwinger bosons mean eld theory to study the efect of competitive interactions J1 and J2 in the ferrimagnetic Heisenberg isotropic model of spins 1 and 1/2 in one and two dimensions. In one dimension, we have also considered the eect dimerization beyond competitive interactions. We compute sublattices magnetizations, the antiferromagnetic branch gap and free energy at zero temperature. The long-range order is seen as a consequence of Schwinger boson condensation. Finally , we study the Heisenberg model on the square lattice with spin S = 1, considering interactions of next-nearest neighbors. We use the generalized Schwinger bosons mean eld theory to analyze the properties of the paramagnetic phase at zero temperature. We compute some quantities as the quadrupole structure factor, which is characteristic of a disordered phase called nematic phase. We calculated the gap and free energy of nematic phase.