Magnetic structure and diffracted magneto-optics of patterned amorphous multilayers

We present magneto-optical Kerr effect measurements of patterned arrays of ${\text{Co}}_{68}{\text{Fe}}_{24}{\text{Zr}}_8/{\text{Al}}_2{\text{O}}_3$ amorphous multilayers. The multilayers were patterned in two dimensions into two different arrangements of circular and ellipsoidal islands. Magnetization loops were recorded in a longitudinal geometry using both the specularly reflected beam as well as diffracted beams scattered off the patterned films. The magnetization of the patterned structures is significantly different from the magnetization of a continuous multilayer owing to the lateral confinement of the pattern and the introduction of additional dipolar coupling between the layers at the edges of the islands. By investigating the magnetic response at the different diffraction orders from the two different configurations of islands we are able to observe the magnetization at different length scales and determine the magnetic response of the circular and ellipsoidal islands individually.

Figure 1

(Color online) Atomic force microscopy images showing the patterns used in this investigation. The circular islands have a diameter of $1.5\mu \text{m}$ and the ellipsoidal islands a $1.5\mu \text{m}$ minor axis and a $4.5\mu \text{m}$ major axis. The shortest distance between the edges of the islands is $1.5\mu \text{m}$ resulting in a periodicity of $6\mu \text{m}$ for both patterns along both the [01] and [10] lattice directions, defined in the inset.

Figure 2

(Color online) Schematic drawing showing the longitudinal MOKE setup for recording magnetization loops at specularly reflected and diffracted beams. The applied magnetic field was aligned to the $x$ axis and the sample plane and the plane of incidence parallel to the $xy$ and $xz$ planes, respectively.

Figure 3

(Color online) Specular x-ray reflectivity and simulation for pattern $\alpha$ recorded at an energy of 8.8 keV. Layer thicknesses are found to be in excellent agreement with the nominal growth parameters.

Figure 4

(Color online) MOKE magnetization loops of a continuous multilayer film for the (a) easy and (b) hard directions of the imprinted anisotropy and for pattern $\alpha$ along the (c) [01] and (d) [10] lattice directions (similar results were obtained for pattern $\beta$). An inverted hysteresis, shown in the inset in graph (c), is observed at low fields and attributed to the demagnetizing field between layers. Blue and red lines (dark gray and light gray) represent the magnetization under increasing or decreasing applied magnetic field, respectively. The Kerr rotations for all the measured curves are normalized to their respective maximum values. The dashed lines in (c) and (d) show results of micromagnetic calculations.

Figure 5

(Color online) Results of micromagnetic calculations for individual circular islands for (a) the easy-axis direction and (b) the hard-axis direction. The arrows show the net magnetization vector for individual layers. The circles surrounding the magnetization vectors correspond to the maximum magnetization possible for each layer. In both cases an antiferromagnetic arrangement occurs between the layers. At remanence the magnetization vectors align to the easy axis. This is illustrated in (b) where an arrangement perpendicular to the applied field direction occurs.

Figure 6

Kerr microscopy image showing the remanent magnetization of pattern $\alpha$ after the field was applied along the [01] direction.

Figure 7

(Color online) A picture showing the distribution of diffraction spots for pattern $\alpha$ with the [01] direction parallel to the plane of incidence. Magnetization loops were recorded at the specularly reflected beam and at positive diffraction orders on the [01] and [10] principal axes.

Figure 8

(Color online) [(a) and (b)] The first-order magnetization loops for patterns $\alpha$ and $\beta$ along the [01] direction. (c) The magnetization of the circular islands obtained from the difference between the magnetization of patterns $\alpha$ and $\beta$. (d) The magnetization of the ellipsoidal islands obtained from the average of the first-order magnetizations. The Kerr rotation for all the measured curves is normalized to their respective saturation value except for the curve in (b) which is scaled according to results of numerical Fourier transform calculations. The dashed lines in (c) and (d) show results of micromagnetic calculations for the magnetization of individual structures. The insets in (a) and (b) show a standing-wave model illustrating the inversion of the circular island form factor between the two patterns.

Figure 9

(Color online) [(a) and (b)] The first- and second-order magnetization loops for pattern $\alpha$ along the [10] direction. (c) The magnetization of the circular islands obtained from the difference between the first- and second-order magnetization. (d) The magnetization of the ellipsoidal islands obtained from the average of the first- and second-order magnetization. The dashed lines in (c) and (d) show results of micromagnetic calculations for the magnetization of individual structures. Similar results were obtained for pattern $\beta$.

Figure 10

(Color online) Magnetization loops recorded at the second, third, and fourth diffraction order for both patterns $\alpha$ and $\beta$ measured with field and magnetization along both the [01] and [10] directions.