Frustrated magnetic vortices in hexagonal lattice of magnetic nanocaps

Magnetic properties of hexagonal lattices of touching magnetic nanocaps fabricated by Co film deposition on a surface of polymethyl methacrylate colloidal crystals was studied as a function of both period (120–450 nm) and thickness (30–60 nm). Magnetization configurations and hysteresis loops of the samples were investigated by magneto-optic Kerr effect and magnetic force microscopy. Formation of frustrated hexagonal lattices of magnetic vortices was found in the system. Magnetic coupling of the nanocaps can be tuned by changing the thickness of the deposited magnetic film, leading to change of the magnetization loop. Micromagnetic simulations of hexagonal lattices of touching magnetic dots complement the experimental observations corroborating the influence of the lattice period and the intercap coupling on the possible magnetization configurations in the system.

Figure 1

(a),(b) SE images of the 30 nm Co film on the top of the colloidal crystals with the period 120 and 370 nm correspondingly. (c) Microphotography of the particles cross-section made by focused Ga${}^{+}$ ion beam. The image observed with backscattered electrons ($E=3$ kV), the Co coverage is visible as bright layer.

Figure 2

In-plane magnetization curves of the lattices of the Co nanocaps measured by the magnetooptic Kerr rotation. (a) Hysteresis loop of the 30-nm Co film deposited on the top of the PMMA colloidal crystal (the particle diameter is 340 nm). The loop corresponds to the vortex distribution of the magnetization in the caps. (b) Hysteresis loop of the 30-nm film deposited on the top of the PMMA colloidal crystal (the particle diameter is 120 nm). The loop corresponds to the single-domain distribution of the magnetization in caps. (c) Hysteresis loop of the 60-nm film deposited on the top of PMMA colloidal crystal (particle diameter 290 nm). The loop corresponds to the mixed states of the magnetization distribution in the system. (d) Hysteresis loop of the flat control Co film.

Figure 3

Experimental MFM images of the lattices of the Co nanocaps in different magnetic states at zero magnetic field. The length of the scale bar is equal to 400 nm. (a) MFM image of the lattice of the Co nanocaps (the particle diameter is 290 nm; Co thickness is 30 nm) at 200 Oe after magnetizing to the saturation at 1000 Oe. (b) The lattice of the magnetic vortices. (c) The lattice of single-domain states magnetized uniformly in the remanent state at zero magnetic field (the particle diameter is 120 nm; Co thickness is 30 nm). (d) The mixed distribution of the magnetization; both vortices and single-domain states are visible (the particle diameter is 290 nm; Co thickness is 60 nm). The particles with single-domain distribution produces two magnetic poles; the particles within vortex state produces less signal with centrally symmetric contrast.

Figure 4

Top and cross-section side schematic views of a Co layer coating the PMMA colloidal crystal surface for different coating thicknesses. The thicker coating caused larger overlapping.

Figure 5

The possible magnetization configurations numerically simulated on hexagonal lattices of overlapping magnetic nanodots. A part of the simulated lattice is shown. The lattice constant is 300 nm; dot diameter is 303 nm. Arrows represent the magnetization of $5\times 5$-nm cell of the computational grid, only 1/36 of arrows are shown. (a), (b), and (c) are vortex (the case with the minimal energy when only 1/3 of the interdot contacts are antiferromagnetically aligned), single-domain, and mixed distributions of the magnetization. Clockwise and anticlockwise vortices are denoted by green and blue colors, respectively; single-domain states are denoted by red color. (d) Unit cell of the simulated system. $a_c$ is the period of the lattice of the magnetic dots; $D$ is their diameter. $D>a_c$ to overlap the dots.

Figure 6

Calculated energies of the magnetic configurations for different ratios between magnetic disk diameter ($D$) and lattice constant ($a_c=300$ nm). Triangles denote the energy of the system with the dots in the single-domain states. Squares denote the energies of the frustrated lattices of the magnetic vortices for the configuration when all interdot contacts are antiferromagnetically aligned. The circles are for the lattice of the magnetic vortices configuration when 1/3 of the interdot contacts are antiferromagnetically aligned while 2/3 are aligned ferromagnetically. The solid square and the solid circle are for the maximum $D/a_c$ value when the corresponding vortex configurations remain stable. Stars denote the energies of different mixed configurations. The dashed lines are guides for the eyes.

Figure 7

Phase diagram of the magnetic states of the hexagonal lattice of the Co nanocaps. $a_c$ is the lattice period, $D$ is the magnetic dot diameter.Squares corresponds to the parameters when the the energies of the lattice of the magnetic vortices (with 1/3 of antiferromagnetically aligned interdot contacts) and uniformly magnetized single-domain states are equal. The open circles is for the parameters of the system the vortices begin to shifts from the central position. The solid circles is corresponds to the parameters values when the vortex lattice becomes unstable. The dashed lines are guides for eyes.