Abstract
Magneto-optical Kerr effect (MOKE) spectroscopy in the -1st diffraction order with p-polarized incidence is applied to study arrays of submicron Permalloy wires at polar magnetization. A theoretical approach combining two methods, the local modes method neglecting the edge effects of wires and the rigorous coupled wave analysis, is derived to evaluate the diffraction losses due to irregularities of the wire edges. A new parameter describing the quality of the edges is defined according to their contribution in the diffracted MOKE. The quality factor, evaluated for two different samples, is successfully compared with irregularities visible on atomic force microscopy pictures.
Highlights
Optical-spectroscopic techniques play an important role in characterizing the quality of grating lithography [1,2,3]
It has been reported that the diffracted Magneto-optical Kerr effect (MOKE) (D-MOKE) hysteresis loops, i.e., the loops recorded on beams diffracted by gratings, can help to investigate the magnetization distribution in magnetic nanostructures
Two different theoretical approaches were chosen for modeling the D-MOKE response of the gratings, the rigorous coupled wave analysis (RCWA) implemented as the transfer-matrix approach for anisotropic media [21] and the local modes method (LMM), which is an approximate analytical method based on the far-field Fourier analysis of the lateral amplitudereflectance distribution assuming the saturated magnetization [17]
Summary
Optical-spectroscopic techniques play an important role in characterizing the quality of grating lithography [1,2,3]. Shallow gratings, with a small depth-to-period ratio, approximate analytical models neglecting the internal diffraction edge-effects were demonstrated as adequate to describe the D-MOKE response [9,10,11] Those models are based on the far-field Fourier analysis of the lateral amplitude-reflectance distribution and on the assumption of the optical and MO uniformity within depth. In this paper we demonstrate that the D-MOKE response can strongly be affected by the reduced quality of a laterally patterned structure, namely by random irregularities of the wireedge parts of the structure’s surface, which may cause both the approximate and rigorous models inaccurate The quality of such magnetic gratings is here evaluated by using one parameter identifying the amount of the edges’ internal-diffraction contribution to the DMOKE response in a broad spectral range
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