Quantitative analysis of shadow x-ray magnetic circular dichroism photoemission electron microscopy

Shadow x-ray magnetic circular dichroism photoemission electron microscopy is a recent technique, in which the photon intensity in the shadow of an object lying on a surface may be used to gather information about the three-dimensional magnetization texture inside the object. Our purpose here is to lay the basis of a quantitative analysis of this technique. We first discuss the principle and implementation of a method to simulate the contrast expected from an arbitrary micromagnetic state. Textbook examples and successful comparison with experiments are then given. Instrumental settings are finally discussed, having an impact on the contrast and spatial resolution: photon energy, microscope extraction voltage and plane of focus, microscope background level, electric-field related distortion of three-dimensional objects, Fresnel diffraction, or photon scattering.

Figure 1

XAS and XMCD with shadows. (a) Shadow XMCD (top) on a ${\mathrm{Fe}}_{20}{\mathrm{Ni}}_{80}$ cylindrical wire with a modulation of diameter, from 400 to 150 nm (bottom: schematic of wire, the arrows depicting the direction of magnetization). The direction of the beam is indicated by the upper-left wavy arrow. Notice the inversion of surface contrast at the back side of the wire, when its diameter is the largest (left side). (b) Schematic for the dual surface and volume contrast on the basis of the test case of magnetization parallel to the x-ray beam. The curves below represent the polarization-dependent x-ray intensity at the absorption peak as the x rays propagate through the wire section. (c) Red: Absorption spectra on the wire across the Fe and Ni L edges, normalized to the background signal (absorption on the supporting Si surface). Blue: Inverted and normalized spectra measured in the shadow.

Figure 2

Collecting the photoelectrons. (a) Illustration of electrons escaping the magnetic object. $\theta$ is the angle between the imaging axis and the secondary electron emission direction ${\mathbf{e}}^{-}$. (b) Illustration of the distortion of the photoelectron trajectory due the electric field extracting electrons into the microscope column (see Sec. 5).

Figure 3

Flow chart of the analysis method. Key acquisition and simulation steps for the quantitative analysis of shadow XMCD-PEEM images.

Figure 4

Description of interpolation methods. The system considered as an example is a cylindrical nanowire. Panel (a) shows the method to model the x-ray beam. The red line stands for the x-ray beam that crosses the tetrahedron elements (in white, from the finite-element discretization). (b) The photon beam, and the wire on the regularly gridded supporting surface. (c) Scheme of a triangle to illustrate in 2D the method of the areal coordinates for interpolating magnetization along each ray.

Figure 5

Illustration of XMCD-PEEM post-processing on two test cases. The first test case is (a) uniform magnetization across the wire and parallel to the x-ray beam; the second case (b) is orthoradial curling. The lower part presents the photon density and XMCD for each case at the surface of the wire (yellow background) and in the shadow (pink background). The modeled wire is suspended above the surface, so the entire shadow is visible. Note that the lateral scale is expanded by a factor $1/sin\left({16}^{\circ }\right)\approx 3.6$ in the shadow, thanks to the grazing incidence.

Figure 6

Comparison of experiment and simulation for the Bloch-point wall. (a) Experimental and (b) simulated contrasts at the surface and in the shadow (respectively left and right in both images) at the Fe L3 edge for a wire of diameter 90 nm. This diameter has been determined from the XAS of the wire shadow. (c) Micromagnetic simulation of a Bloch-point wall, used as an input for simulating the contrast. (d) Cross sections for (a) and (b). The inset shows the XAS (dotted line) and XMCD (full line) spectra for the experimental contrasts (a).

Figure 7

Role of the absorption coefficient on the contrast. (a) LEEM image of a wire with diameter 120 nm and (b) left end of the wire, with both experimental and simulated XMCD contrast at the Fe L3 edge, revealing a curling micromagnetic configuration. [(c)–(f)] Experimental XMCD contrast of this wire. [(g)–(j)] The XMCD contrast computed from the same experimental XAS but from which the background level has been removed. Simulated XMCD-PEEM images [(k) and (m)] and their profiles [(l) and (n)] for a 90-nm-diameter wire with a Bloch point wall and different absorbtion coefficients (see Table 2). For (c), (d), (g), and (h) the contrast is 6%; it is 9% for (f) and (j) and 5% for (e) and (i).

Figure 8

Role of the plane of focus and the start voltage. XMCD contrast taken at the Fe L3 edge and with start voltage $2.1\mathrm{eV}$, with focus (a) on the surface and (b) on the wire. (c) The XAS superimposed with wire and shadow areas as a guide to the eye. (d) XMCD with a focus on the surface and start voltages $2.0\mathrm{eV}$ and (e) $2.8\mathrm{eV}$. (f) XAS on the wire and the shadow versus the start voltage.

Figure 9

Scattering effects. Wire image of the intensity for (a) the XMCD and (b) the XAS. (c) The wire and shadow zones on the XAS images. Plot (d) presents the intensity at the cross sections shown in (a) and (b). Dotted lines are guides to the eyes and limit the wire (left) and shadow areas (right).

Figure 10

Signal-to-noise ratio. Schematic to describe the notations used in the calculation (see text).