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 L-component switching at H = 5 Oe. The switching of T-component at H = 40 Oe begins to appear at θ = 41.5°, but the L-component still dominates the switching. With increasing incident angle (θ = 47.5°), the T-component 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 T-component dominates the hysteresis loop. For SP-enhanced MOKE, at θ = 41° and θ = 41.5°, the T-component is negligible. At larger angles, θ = 47.5° and θ = 52.5°, the T-component becomes enhanced but remains at a relatively low level as compared to the L-component. This important observation demonstrates the large variation of L- and T-component in MSHG, which is absent in MOKE. There is no such huge effect for MSHG under normal reflection geometry or MSHG under Kretschmann-Raether configuration with S-polarized fundamental field. The T- and L- magnetic contrast for two-jump 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 p-polarization). The magnetic contrasts can be expressed as:

where k_T and k_L are the ratios of magnitude between the magnetic and non-magnetic MSHG response for T- and L-magnetization 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 non-magnetic MSHG response for T- and L-magnetization components, respectively. We note that when k_T = 0, the expression for C_L becomes identical to the one for the one-jump MSHG hysteresis loop measured in the L-geometry. Furthermore, k_T and φ_T can only be obtained from the two-jump 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 L-magnetization 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 non-magnetic 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 T-magnetization components are normal to each other, C_T and C_L display opposite trends.

References:

1. Wei Zheng, Aubrey T. Hanbicki, Berend T. Jonker, and Gunter Lüpke, Control of Magnetic Contrast with Nonlinear Magneto-Plasmonics, Nature Scientific Reports 4, 6191 (2014).

Funding: DOE