Theoretical methods for understanding advanced magnetic materials: The case of frustrated thin films

Materials science has been intensively developed during the last 30 years. This is due, on the one hand, to an increasing demand of new materials for new applications and, on the other hand, to technological progress which allows for the synthesis of materials of desired characteristics and to investigate their properties with sophisticated experimental apparatus. Among these advanced materials, magnetic materials at nanometric scale such as ultra thin films or ultra fine aggregates are no doubt among the most important for electronic devices.In this review, we show advanced theoretical methods and solved examples that help understand microscopic mechanisms leading to experimental observations in magnetic thin films. Attention is paid to the case of magnetically frustrated systems in which two or more magnetic interactions are present and competing. The interplay between spin frustration and surface effects is the origin of spectacular phenomena which often occur at boundaries of phases with different symmetries: reentrance, disorder lines, coexistence of order and disorder at equilibrium. These phenomena are shown and explained using of some exact methods, the Green's function and Monte Carlo simulation. We show in particular how to calculate surface spin-wave modes, surface magnetization, surface reorientation transition and spin transport.