Surface-and interface-sensitive optical techniques, such as optical secondharmonic generation (SHG), allow the buried interfacial structure of centrosymmetric materials to be explored through thin capping layers, and magnetic SHG (MSHG) extends this to magnetic interfaces. However, the variation of the MSHG intensity with magnetic field does not measure hysteresis loops directly, because the loops are displaced by an amount dependent on the crystallographic response and its phase difference with respect to the magnetic response, and also because there is a quadratic magnetization contribution to the SH intensity that may be significant. Two new procedures are reported for extracting hysteresis loops directly from the MSHG intensity. The first is applicable to all magnetic interfaces, including exchange-biased structures, where the saturation magnetization for positive and negative magnetic fields is equal and opposite. The second applies to all centrosymmetric hysteresis loops. These procedures correct for the quadratic response, allowing experimental geometries to be chosen that maximize the magnetic contribution, thus improving the signal-to-noise ratio and the sensitivity of the technique.

Low dimensional magnetic structures show interesting and novel phenomena such as oscillatory magnetic coupling and giant magnetoresistance. Magnetic second harmonic generation (MSHG) can provide unique information on magnetic surfaces and interfaces because, within the dipole approximation, broken spaceinversion symmetry at the surface or interface of centrosymmetric media, and broken time-reversal symmetry arising from the magnetization, are both required in order to observe a magnetic-field-dependent second harmonic response. However, the additional reduction in symmetry arising from the magetization produces many non-zero susceptibility tensor components, particularly in the case of vicinal, stepped surfaces of 1m symmetry, and care is needed in designing experiments that will produce readily interpretable results. Phenomenological expressions for the MSHG response from systems of 1m symmetry are presented, where combinations of input and output polarizations and magnetic field orientations allow the essential physics of these systems to be explored, particularly in relation to distinguishing terrace and step contributions to the magnetization from vicinal surfaces and interfaces.

The optical anisotropy of Au protected Fe layers grown on a vicinal W(110) surface has been investigated using reflectance anisotropy spectroscopy (RAS). Iron nanostripes formed at submonolayer coverage, as well as Fe layers up to 3 ML coverage, were protected by 12 and 16 nm gold caps and measured ex situ under ambient conditions. The RAS is dominated by structures originating in the interfacial W(110) region, modified by the absorption in the Au cap and possibly by uniaxial strain in the Au cap itself. The Fe nanostructures themselves do not produce a significant RAS signature but, nevertheless, differences with Fe coverage were identified and explained in terms of a simple isotropic Fe absorbing layer, together with strain relief in the W/Fe/Au interfacial region.

Aligned magnetic nanostructures grown on low symmetry interfaces are generally inhomogeneous, with different magnetic species, such as terrace and step atoms, contributing to the overall magnetic response from the interfacial regions. It is shown that the presence of different magnetic regions can be detected by means of normal incidence (NI) magnetic second-harmonic generation (MSHG). A phenomenological model of NI MSHG at magnetic interfaces of 1m symmetry is developed and a methodology is described for optimizing the signal-to-noise ratio of extracted hysteresis curves by adjusting the input polarization angle. Quadratic terms in the magnetization are properly accounted for, using recently published formulae. It is shown that, where more than one magnetic region is present, the shape of the extracted hysteresis curve, which contains contributions from the different magnetic regions, varies with the input polarization angle. The new approach is used to determine hysteresis loops from the various magnetic regions of Au-capped ultrathin Fe films grown on a vicinal W(110) substrate. The results for 0.75 ML Fe coverage are of particular interest, revealing distinct contributions from terrace and step Fe atoms. This experimental procedure and phenomenology opens up low symmetry magnetic interfaces and aligned nanostructures to characterization by means of MSHG.

It has been suggested that bond-hyperpolarizability models of optical second harmonic generation (SHG) may be simplified by assuming that the SH radiation originates from the anharmonic motion of bond charges strictly along bond directions [G. D. Powell, J. F. Wang, and D. E. Aspnes, Phys. Rev. B 65, 205320/1 (2002)]. This assumption allows more physical insight by connecting the SH response to the response of the bonds in a simple and direct manner. However, previous theoretical calculations of bond hyperpolarizabilities indicate that transverse components may be large [2]. The simplified model is modified here to account directly for the variation of the number of step bonds with vicinal angle. The results are promising but further work is required before general conclusions can be drawn about the role of the transverse components.