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.

The Nineteenth Century Law of the Sea and the British Abolition of the Slave Trade

This study focuses on British attempts during the nineteenth century to outlaw the Atlantic Slave Trade internationally, for which it was successful, after seventy-five years of effort. It considers the lack of willingness to allow Great Britain, at the Congress of Vienna and during the Concert of Europe, to establish a universal treaty outlawing the slave trade. As a result, this mandated a change in British tactics, which would ultimately prove to be successful – the establishment of a web of bilateral agreements which came to included all maritime powers. The study then moves on to consider the evolution of these bilateral agreements while highlighting the relationship between Great Britain and States (Brazil, France, Portugal and the United States) which were obstinate in their willingness to join this bilateral regime. Finally, consideration is given to the move towards the establishment of the 1890 General Act of Brussels; and thus the conclusion of the decades long British foreign policy objective of a universal instrument meant to suppress the Atlantic Slave Trade.

ARTICLE: On the Curious Disappearance of Human Servitude from General International Law

The following study considers the fragmentation of law which occurred in 1956 with regard to the law on servitude. As States were unwilling to go as far as the Universal Declaration on Human in establishing that "no one shall be held in [...] servitude", the negotiators of the 1956 Supplementary Conventions moved to expunge the very term 'servitude' from the text and to replace it with the phrase 'institutions and practices similar to slavery' which could then be abolished 'progressively and as soon as possible'. The negotiation history of the 1956 Convention clear demonstrate that the Universal Declaration on Human was the elephant in the room and that it ultimately lead to a fragmentation of the law as between general international law manifest in the 1956 Supplementary Convention on the one hand and international human rights law on the other. It is for this reason that, for instance the 2001 UN and 2005 Council of Europe trafficking conventions mention both 'practices similar to slavery' and 'servitude' as types of human exploitation to be suppressed in their definition of 'trafficking in persons'.