(Color online) (a) Helical spin structures of half a periodicity of a unit twist with right and left handednesses of four different orientations. The in-plane orientation of magnetization gradually changes in depth in a -thick Co layer. (b) shows the spectra vs for both the and , which are calculated from these various helical structures in a model layered structure of . Each inset shows the same calculations from a different but simple layered structure of . (c) shows the asymmetry ratio spectra (the difference of the two spectra normalized by their sum) for each pair of the counterpart and with the same orientation. In (d), the left and right panels show the asymmetry ratios for the pairs of and each of the different orientations of , , , of the same handedness, and those between the different orientations of the same handedness, respectively.
(Color online) Each pair shows the counterpart helical spin structures from which the same spectrum is obtained. Below each structure, the transverse and longitudinal components of the magnetizations distributed in depth are redrawn.
(Color online) (a) Helical spin configurations of with various periodicity. The repeating number of a complete 360° winding of a spin spiral in a given thickness varies as , 0.5, 1, 1.5, 2, 2.5, and 3. The spectra for a linear polarization from these spin structures are calculated at , as shown in (b), and their spectra with respect to in (c). The model-layered structure used is the same as that in Fig. 1, but the Co layer used in this calculation is thick.
(Color online) Top panels of (a) and (b) show the model spin configurations uniformly oriented through the entire Co thickness. The uniformly oriented are denoted as with each component of along -axis. In (a), varies as , , 0 with . In (b), varies as , , 0 with holding . The middle and bottom panels in (a) and (b) show the and spectra at as a function of , respectively, which are calculated from the spin configurations illustrated in the top panels with the same conditions used in Fig. 1.
(Color online) (a) Various spin configurations in which only the transverse component exists, i.e., and . The spins uniformly oriented toward the direction flip layer by layer to the opposite direction of , starting from the top. In this model, the layered structure is the same as that used in Fig. 1. The individual spins have a constant magnitude of through the entire Co layer in order to examine just the depth sensitivity to the transverse component. (b) the spectra versus calculated from each spin configuration illustrated in (a) for an incident linear polarization at , and their spectra with respect to .
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