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In this project, we clearly separate the L and Tcomponent of MSHG by studying the anisotropy and the twojump hysteresis loops from a singlecrystal Fe film. Moreover, we developed formulas for the twojump switching loop to extract the ratios of magnitude and the phase differences between magnetic and nonmagnetic components for both L and TMSHG. This new effect enhances the sensing of magnetic switching, which has potential usage in quaternary magnetic storage systems because it enables the readout of all four magnetization states from crystalline iron with high contrast ratio, and it is also of interest for biochemical sensor applications due to its very high surface sensitivity and simple structure. Due to the cubic magnetic anisotropy, there are four magnetization states of the singlecrystalline Fe, which are two easy axes ([010] and [110]) and two hard axes ([110] and [110]). The twostep switching of the magnetic hysteresis loops of transverse and longitudinal components for MSHG and MOKE can be studied simultaneously. If a small external magnetic field is applied along the longitudinal direction, i.e. the hard axis [110], the magnetization can be easily switched between the easy axes along the longitudinal direction. But a large external magnetic field is necessary for the switching in the transverse direction. There is no magnetic contrast at the angle of total reflection (θ = 40°). For θ = 41°, ATR just begins, the hysteresis loop shows clear contrast with only the Lcomponent switching at H = 5 Oe. The switching of Tcomponent at H = 40 Oe begins to appear at θ = 41.5°, but the Lcomponent still dominates the switching. With increasing incident angle (θ = 47.5°), the Tcomponent becomes more enhanced, and eventually by θ = 52.5°, where the reflection is very small and close to the bottom of the ATR curve, the Tcomponent dominates the hysteresis loop. For SPenhanced MOKE, at θ = 41° and θ = 41.5°, the Tcomponent is negligible. At larger angles, θ = 47.5° and θ = 52.5°, the Tcomponent becomes enhanced but remains at a relatively low level as compared to the Lcomponent. This important observation demonstrates the large variation of L and Tcomponent in MSHG, which is absent in MOKE. There is no such huge effect for MSHG under normal reflection geometry or MSHG under KretschmannRaether configuration with Spolarized fundamental field. The T and L magnetic contrast for twojump hysteresis loop can be defined as: To elucidate the origin of the large variation in the MSHG contrast ratios, we studied C_{T} and C_{L} as a function of the angular position α of the analyzer (α = 0 corresponds to ppolarization). The magnetic contrasts can be expressed as: where k_{T} and k_{L} are the ratios of magnitude between the magnetic and nonmagnetic MSHG response for T and Lmagnetization components, both of which are composed of fundamental fields and corresponding effective susceptibility tensors. φ_{T} and φ_{L} are the phase differences between the magnetic and nonmagnetic MSHG response for T and Lmagnetization components, respectively. We note that when k_{T} = 0, the expression for C_{L} becomes identical to the one for the onejump MSHG hysteresis loop measured in the Lgeometry. Furthermore, k_{T} and φ_{T} can only be obtained from the twojump MSHG hysteresis loop, because the equations above become meaningless without k_{L} and α. The figure above shows the ratios of magnitude and phase differences as a function of incident angle under ATR condition for T and Lmagnetization components, respectively. The ratios k_{T} and k_{L} hardly change within experimental errors and hence cannot account for the large variation. In contrast, φ_{L} exhibits a large monotonic increase from 72° to 90° over the ATR range, while φ_{T} decreases from 88° to 77°. This trend is consistent with the large decrease of C_{L} and the steady increase of C_{T} with increasing incident angle under ATR. Therefore, the large variation of magnetic contrast originates from the change of relative phases caused by SP. The phase difference between magnetic and nonmagnetic components of MSHG signal is known to be related to the relative orientation of magnetization and the wave vector of fundamental fields. Since the L and Tmagnetization components are normal to each other, C_{T} and C_{L} display opposite trends. References:
Funding: DOE



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