Ellipsometric Selective Sensitivity to Magnetic Nanostructures

Abstract

Recently, we have shown that the approach of depth sensitivity of magneto-optic ellipsometry can be generalized to selectivity from different materials in nanostructures. We use the condition number as the figure of merit to quantify the magneto-optic selectivity to two different magnetic contributions in magnetic nanostructure. The method is demonstrated on nanostructures containing magnetically hard Fe particles in surface layer of soft FeNbB amorphous ribbon. We separated both magnetic contributions from measurement of hysteresis loops using magneto-optic Kerr effect in longitudinal configuration. Magneto-optic selectivity is discussed and theoretical model on the basis of effective medium is compared with experimental data of longitudinal magneto-optic Kerr effect depending on angle of incidence.

Depth and material sensitivity in magneto-optic nanostructures

“…The loops confirm that the near-surface region is inhomogeneous and contain contributions of different phases [81]. By rotating the vector Φ tot with respect to the θ and axes two different phases showed in Figure 11(c) and (d) can be identified [60]. By rotating the vector Φ tot with respect to the θ and axes two different phases showed in Figure 11(c) and (d) can be identified [60].…”

“…The phase difference of MO effects from layers located at different depths comes from light propagation considerations (see equation (1) and related discussion). Note that the complex magneto-optical parameter (i.e., the off-diagonal dielectric tensor component related to the Voight Q constant) is extremely sensitive to a change of material composition, phase, or crystal structure [60]. Therefore, similar approach as described in Section 2, can be applied to separate the magneto-optic response coming different materials with distinct optical and MO parameters.…”

“…Using the Yeh's matrix formalism [12], the measured data for the angle of incidence varying from 0 • to 90 • were fitted and obtained for parameter values f 0 = 0.8, ∆d = 7 nm [60].…”

Selective sensitivity of ellipsometry to magnetic nanostructures

“…In our calculations we used the spectral norm [37,38] and the condition number is expressed from the ratio of the maximal σ max (A) and the minimal σ min (A) singular numbers obtained from the singular value decomposition of the matrix A. κ(A) is closed to 1 for well conditioned matrix and magnetic contributions are well separated. However, for large κ(A), the MO ellipsometry is not selectively sensitive to different magnetic phases [36].…”

“…The method is supported by modeling of the magneto-optic response based on the effective medium approximation and by hysteresis loop measurement of the multiferroic BiFeO 3 -CoFe 2 O 4 (BFO-CFO) self-assembled nanostructure. On the other hand, the longitudinal MO Kerr effect was applied to distinguish contribution of Fe nanocrystal from amorphous soft magnetic matrix in near-surface region of FeNbB amorphous ribbons [35,36].…”