Magnetization reversal of microstructured kagome lattices

We report on a magneto-optical Kerr effect (MOKE) investigation of microstructured rectangular islands, which have been arranged on kagome lattices. The magnetization reversal was studied by regular longitudinal vector MOKE in specular geometry as well as in Bragg MOKE geometry, using the diffraction spots from the grating for hysteresis measurements. The magnetization at remanence is imaged by using magnetic force microscopy and x-ray photoemission electron microscopy. The measurements have been compared to the results of micromagnetic simulations, which allow a detailed interpretation of the experimental data. It is demonstrated that the magnetization reversal process in an external magnetic field strongly depends on the shape and the interparticle spacing between the islands. For the thorough understanding of the nontrivial dependence of magnetization reversal on the array geometry, the magnetic moments of the islands and the energy barriers for magnetization switching in individual elements have been theoretically analyzed. The performed analysis provides insight into the magnetostatic interactions and probability of switching paths taken by the particles arranged on lattices with kagome symmetry during the magnetization reversal process.

Figure 1

Scanning electron micrograph image of rectangular Fe islands placed between the nodes of kagome lattice $K1$. The lateral dimensions of the islands are $l=3.8\mu \mathrm{m}$ and $w=0.3\mu \mathrm{m}$, the height is $h=9.7\mu \mathrm{m}$, and the interparticle distance is $b=1.9\mu \mathrm{m}$. The kagome lattice can be separated into three sublattices, $S1$, $S2$, and $S3$, each of them consisting of a chain of rectangular islands. In the center of the marked positions, $A$, $B$, and $C$, the value of the stray field $H_{\mathit{stray}}$ is obtained from micromagnetic simulations. For further details, we refer to the text.

Figure 2

Sketch of the vector MOKE configuration to measure the Kerr rotation of (a) the $x$ component ${\theta }_x$ and (b) the $y$ component ${\theta }_y$.

Figure 3

Specular MOKE hysteresis loops showing the $x$ component of the four different kagome lattices in the orientation $\varphi =0°$.

Figure 4

Kagome lattice $K1$: Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) for the $x$ and $y$ components at the diffraction spots for $\varphi =0°$; only the ascending branches of the hysteresis loops are shown.

Figure 5

(Color online) Kagome lattice $K1$: Calculated magnetization distribution in the three sublattices $S1$, $S2$, and $S3$. The left panel is calculated for an external field $H_{\mathit{calc}}=0$, the right panel for a field $H_{\mathit{calc}}=33\mathrm{Oe}$ oriented parallel to the sublattice $S1$, which is referred to as the orientation $\varphi =0°$. The arrows indicate the net magnetization direction inside the rectangular islands.

Figure 6

Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) as in Fig. 4 but for kagome lattice $K2$.

Figure 7

(Color online) Calculated magnetization distribution for kagome lattice $K2$. For further details, see Fig. 5.

Figure 8

Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) as in Fig. 4 but for kagome lattice $K3$.

Figure 9

Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) as in Fig. 4 but for kagome lattice $K4$.

Figure 10

(Color online) Calculated magnetization distribution for kagome lattice $K3$. For further details, see Fig. 5.

Figure 11

(Color online) Calculated magnetization distribution for kagome lattice $K4$. For further details, see Fig. 5.

Figure 12

(Color online) Hysteresis loops $0x$ of each sublattice $S1$ (red), $S2$ (blue), and $S3$ (green) obtained from the simulations of the four kagome structures. The black line corresponds to the sum hysteresis loop.

Figure 13

Magnetic force microscopy image of kagome lattice $K4$ at remanence. The kagome lattice was saturated in a magnetic field at the orientation $\varphi =0°$ before the microscopy. The small arrows show the direction of the magnetization vector for some representative islands.

Figure 14

Kagome lattice $K1$: Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) for the $x$ and $y$ components at the diffraction spots for $\varphi =30°$; only the ascending branches of the hysteresis loops are shown.

Figure 15

(Color online) Kagome lattice $K1$: Calculated magnetization distribution in the three sublattices $S1$, $S2$, and $S3$. The left panel is calculated for an external field $H_{\mathit{calc}}=0$, the right panel for a field $H_{\mathit{calc}}=66\mathrm{Oe}$ oriented perpendicular to the sublattice $S2$, which is referred to as the orientation $\varphi =30°$. The arrows indicate the net magnetization direction inside the rectangular islands.

Figure 16

Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) similar to Fig. 14 but for kagome lattice $K2$.

Figure 17

(Color online) Calculated magnetization distribution similar to Fig. 15 but for kagome lattice $K2$.

Figure 18

Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) similar to Fig. 14 but for kagome lattice $K3$.

Figure 19

Measured (left panel) and calculated Bragg MOKE hysteresis loops (right panel) similar to Fig. 14 but for kagome lattice $K4$.

Figure 20

(Color online) Calculated magnetization distribution similar to Fig. 15 but for kagome lattice $K3$.

Figure 21

(Color online) Calculated magnetization distribution similar to Fig. 15 but for kagome lattice $K4$.

Figure 22

(Color online) Hysteresis loops $0x$ of each sublattice $S1$ (red), $S2$ (blue), and $S3$ (green) obtained from the simulations of the four kagome structures. The black line corresponds to the sum hysteresis loop.

Figure 23

(Color online) Magnetic force microscopy images of all four kagome lattices in remanence. The kagome lattices were first saturated in a magnetic field at the orientation $\varphi =30°$ as indicated, before taking the microscopy images.

Figure 24

Photoemission electron microscopy image of kagome lattices $K3$ and $K4$ in remanence. The kagome lattices were saturated in a magnetic field at the orientation $\varphi =30°$ as indicated, before taking the microscopy picture in remanence.

Figure 25

(Color online) Magnetization distribution of kagome lattice $K3$ for sample orientation $\varphi =30°$, showing the remanent state. The simulation was performed with a cell size of $25\mathrm{nm}$.

Figure 26

(Color online) (a) Magnetostatic energy of sublattices $S1$ (blue) and $S2$, $S3$ (green) for the sample orientation $\varphi =0°$. The energy levels of the onion state (upper inset) are shown on the left of the intermediate state (bottom insets) $E_{\mathit{im}}$ on the right hand side. The dashed lines schematically show the nucleation energy barriers. (b) Magnetostatic energy levels for the saturated and two possible remanent states at sample orientation $\varphi =30°$. Arrows indicate the direction of magnetization in sublattice $S2$.