Scattering theory formalism for the magneto-optics of nanocorrugated ferromagnet surfaces

A theoretical formalism that allows analysis of the magneto-optical response of nanocorrugated ferromagnetic surfaces is presented and its validity checked with measurements in expressly fabricated structures. The formalism uses conventional scattering theory to find the expressions that account for the power scattered per unit area, and finds that for particular light-scattering directions and incidence polarizations the topographic and the magnetic contributions to the scattered light can be separated. By comparing theoretical and experimental results the magnetic state of the surfaces and its field evolution can be extracted.

Figure 1

(Color online) (A) Transversal MOKE geometry shown on an AFM image of the nanocorrugation: incident and scattered light $p$ polarized, external magnetic field applied perpendicular to the incidence plane and along the stripes’ long axis (the diffraction spots appear at the incidence plane). (B) Sample structure with the geometrical and optical parameters used in the theory

Figure 2

(Color online) Magneto-optical scattering ratio as a function of the scattering angle for 20° incidence angle. The lines are the theoretical results for (i) a magnetic surface on top of a nonmagnetic substrate (Co stripes on Au, termed type I); (ii) a nonmagnetic surface on top of a magnetic substrate (Cr stripes on Co, type II); and finally (iii) a magnetic surface on top of a magnetic substrate (Co stripes on Co, type III). The solid symbols are experimental results for the fabricated structures.

Figure 3

(Color online) Transverse Kerr hysteresis loops for the direct (reflected) and the first and second diffracted spots, measured at 20° incidence angle, for type I, type II, and type III structures. The easy magnetization axis of the Co layer is parallel to the stripes long axis.

Figure 4

(Color online) Experimental and simulated hysteresis Kerr loops for the reflected and first-order diffracted spots for two different orientations of the easy axis of the Co film with respect of the applied field. (A) easy axis parallel to the stripe long axis. (B) easy axis perpendicular to the stripe long axis. (a) Experimental reflected Kerr loops $\left(R\right)$, and first-order diffracted Kerr loops $\left(D_{-1}\right)$. (b) Simulated first-order diffracted Kerr loops. (c) Magnetic field dependence of the y component of the stripe magnetization.