Boundary conditions in the simplest model of linear and second harmonic magnetooptical effects
Abstract
This paper is concerned with linear and nonlinear magnetooptical 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 magnetooptical 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 selfconsistency of the model is highlighted, relating to the existence of rescaling procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magnetooptical 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 ∞m, 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 fifthrank susceptibility tensor being invariant under the Curie group ∞∞m.
 Publication:

Physical Review B
 Pub Date:
 January 2002
 DOI:
 10.1103/PhysRevB.65.014432
 Bibcode:
 2002PhRvB..65a4432A
 Keywords:

 78.20.Ls;
 42.65.k;
 03.50.De;
 Magnetooptical effects;
 Nonlinear optics;
 Classical electromagnetism Maxwell equations