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Invited article: Vector and Bragg Magneto-optical Kerr effect for the analysis of nanostructured magnetic arrays
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10.1063/1.2821148
/content/aip/journal/rsi/78/12/10.1063/1.2821148
http://aip.metastore.ingenta.com/content/aip/journal/rsi/78/12/10.1063/1.2821148
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The coordinate system of the nonmagnetic medium and the magnetic medium with refractive indices and , respectively. The direction of the magnetization of the magnetic medium is arbitrary.

Image of FIG. 2.
FIG. 2.

Schematic of the magneto-optic setup.

Image of FIG. 3.
FIG. 3.

(a) The intensity function [Eq. (9)] for , , , and . (b) The power spectrum of the signal calculated with FFT, and (c) the phase of the FFT.

Image of FIG. 4.
FIG. 4.

Definition of the sample rotation and the angle of the magnetization vector for the case of the longitudinal MOKE geometry measuring the component (top panel). In order to measure the component , the external magnetic field and the sample are rotated by 90°, such that the angle between the structure and the applied field is kept constant, but the magnetization component is in the scattering plane (bottom panel) (Ref. 22).

Image of FIG. 5.
FIG. 5.

Sketch of the diffraction pattern and nomenclature of the diffracted beams. Intermediate diffracted beams are not taken into account.

Image of FIG. 6.
FIG. 6.

Definitions of the various directions and angles mentioned in the text.

Image of FIG. 7.
FIG. 7.

(Color) Ascending branch of the hysteresis loop for the (black line) and the component (gray line) of the magnetization, and some selected calculated magnetization profiles.

Image of FIG. 8.
FIG. 8.

Real (black lines) and imaginary (gray lines) form factors for the (left panel) and the component (right panel) calculated for the periodicities .

Image of FIG. 9.
FIG. 9.

Real (black lines) and imaginary (gray lines) form factors for counterclockwise and clockwise vortex chiralities obtained at diffraction orders . Note that the chirality follows from the out-of-plane reflections.

Image of FIG. 10.
FIG. 10.

(Color) Ascending branch of the hysteresis loop for the (black line) and the component (gray line) of the magnetization, and some selected calculated magnetization profiles.

Image of FIG. 11.
FIG. 11.

Real (black lines) and imaginary (gray lines) form factors for the component calculated for two different periodicities as indicated in the figure (left panel: , right panel: ) and for different orders of diffraction.

Image of FIG. 12.
FIG. 12.

Measured (left) and calculated (right) Bragg-MOKE hysteresis curves of rectangular Fe islands described in Ref. 17. Only the diffraction order (30) is shown as an example. The hysteresis curves have been normalized to saturation magnetization. Solid (dashed) line represents increasing (decreasing) magnetic field.

Image of FIG. 13.
FIG. 13.

The left plots show the ascending branch of the hysteresis loops both for the (black line) and and the component (gray line) of the magnetization. The right plots show the component of the magnetization as a function of the component; thus, the plots describe the path of the magnetization vector. The calculations are performed for two different anisotropy values, (top panel) and (bottom panel). For further explanations the reader is referred to the text.

Image of FIG. 14.
FIG. 14.

Real (black lines) and imaginary (gray lines) form factors for the (left panel) and the component (right panel) calculated for the periodicities and the anisotropy constants .

Image of FIG. 15.
FIG. 15.

Real (black lines) and imaginary (gray lines) form factors for the (left panel) and the component (right panel) calculated for the periodicities and and the anisotropy constants .

Image of FIG. 16.
FIG. 16.

Definition of the angles and with respect to the longitudinal and vertical axes.

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/content/aip/journal/rsi/78/12/10.1063/1.2821148
2007-12-12
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Invited article: Vector and Bragg Magneto-optical Kerr effect for the analysis of nanostructured magnetic arrays
http://aip.metastore.ingenta.com/content/aip/journal/rsi/78/12/10.1063/1.2821148
10.1063/1.2821148
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