How does one determine the magnetization state and hysteresis loop corresponding to one of the ferromagnetic (FM) layers located at a given depth in a stack of FM/non-FM layers by means of the magneto-optical Kerr effect? For this purpose the representation of the Kerr effect in the complex rotation-ellipticity plane is introduced. A depth sensitivity function controlling the Kerr effect is defined and its dependence on the photon energy and angle of incidence is studied. A general way to determine the in-depth location of the FM layer, from which the Kerr signal originates, is proposed. In the case of a FM bilayer structure, previous proposed solutions are discussed within a unified formalism. For a system with three or more FM layers two approaches are proposed to extract selectively the magneto-optical signals originating at individual FM layers: the parallel Kerr vector and cascade numerical projection methods. These methods are successively checked experimentally on simple multilayer structures. Finally, on the basis of the developed approaches a readout solution for multivalued magneto-optical recording in a four-storage-layer structure is proposed.

For a better understanding of optical interactions in magnetic layered structures we establish general expressions of both polar Kerr and Faraday first-order magneto-optical (MO) effects. The approach presented here enables the MO response of an arbitrary magnetic layer system to be analytically expressed with an accuracy practically equal (less than ${10}^{\mathrm{-}4}$ deg) to that of the full matrix calculations usually employed for modeling MO effects in magnetic multilayers. The formulas for any particular structure are obtained from general MO expressions by introducing associated reflection and transmission coefficients. This procedure is justified here in the simple case of an ultrathin magnetic film sandwiched between two nonmagnetic layers. These accurate expressions are further simplified for ultrathin magnetic films and the limitations of this approximation discussed. The simplified formulas are then used to analyze MO polar Kerr and Faraday data in well-defined Au (5 nm)/Co/Au (25 nm) structures, grown on float glass substrates. The Co layer thicknesses are chosen in the range 0.4–2.0 nm to preserve a perpendicular magnetic anisotropy. The simplified expressions, as well as the numerical modeling of the trends in MO spectra with a variation of the overlayer or buffer layer thicknesses, show that the shape of the polar Kerr effect spectrum is mainly dependent upon the optical properties of the Au buffer layer whereas the observed MO amplitudes are reduced consistently with the absorption of the Au overlayer.

Quadratic or second-order magneto-optic effects in reflection significantly effect in-plane magnetization measurements. While the magneto-optic effects linear in magnetization are independent of orientation of cubic crystal axes, the amplitude and sign of the quadratic effects change significantly under crystal rotation. Theoretical formulas for the magneto-optic effects have been derived using a permittivity tensor including terms quadratic in magnetization. A method for separation of the diagonal and off-diagonal quadratic magneto-optic tensor components ${\mathrm{(G}}_{11}{\mathrm{-G}}_{12})$ and ${\text{2G}}_{44}$ is proposed. The theory was completed by an experimental observation of the quadratic effect anisotropy in an epitaxial Fe layer prepared on a MgO substrate. The influence of the magnetization components on the magneto-optic vector magnetometry is discussed for an interface, a single layer, and exchange coupled bilayer system for a general magnetization direction including the quadratic magneto-optic effect anisotropy.

This paper is devoted to magnetic and structural properties of anisotropic γ-Fe2O3 superparamagnetic particles dispersed in a transparent xerogel matrix. The effect of frozen anisotropy axes and magnetic texture, induced by a magnetic field applied during the solidification of the matrix on the in-field magnetization process, is studied by alternating gradient force magnetometry and first and second order magneto-optical effects. The changes of magnetization curves with respect to the ferrofluid solution at the same particle concentration are interpreted on the basis of an existing statistical approach extended to systems with particle size distribution, which has to be taken into account for real samples. A very good agreement between the experiment and theory was achieved for a log-normal distribution of diameters which well resembles that deduced from electron microscopy observations in different imaging modes. This structural analysis states the parameter values used in calculations and confirms the relevance of basic assumptions of the model for the specimens studied. The experimental results and the related theoretical discussion should be of use to understand magnetic properties of other magnetically textured superparamagnetic systems.