Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

The duty of loyalty in the cooperative law. A comparative study

Among the duties of the government bodies’ members of the different entities, which are connected to the good government, the duty of loyalty must be underlined. This duty, derived from the good-faith duty, obliges to act in the interest of the entity in case of conflict of interest, and to subordinate one’s own interests, except when there is an authorisation. Loyalty duty is applicable both to managers, who must manage the entity’s interest, and to partners, according to the common purpose derived from the company contract. This duty, at the same time, includes some particular rules, referred to transparency, remuneration, prohibition of competition, self-contracting... This essay compares the regulation of the duty of loyalty and its realizations in the different Cooperative Laws in Spain, both referring to the managers and to the partners, comparing this, at the same time, with the regulation of these aspects in companies’ general legislation, an in the Spanish Corporate Enterprises Act in particular, in order to obtain a general view of the issue, a necessary basis to go more deeply into it, and suggesting some preliminary conclusions or assessments.

Wall thickness dependence of the scaling law for ferroic stripe domains

The periodicity of 180 degrees. stripe domains as a function of crystal thickness scales with the width of the domain walls, both for ferroelectric and for ferromagnetic materials. Here we derive an analytical expression for the generalized ferroic scaling factor and use this to calculate the domain wall thickness and gradient coefficients ( exchange constants) in some ferroelectric and ferromagnetic materials. We then use these to discuss some of the wider implications for the physics of ferroelectric nanodevices and periodically poled photonic crystals.