Phase diagram of magnetic nanodisks measured by scanning electron microscopy with polarization analysis

We use scanning electron microscopy with polarization analysis (SEMPA) to image the magnetic domain structures of individual ferromagnetic nanodisks with different diameters and thicknesses, and thereby determine the phase diagram of the magnetic ground states in these technologically important magnetic structures. Depending on the nanodisk dimensions, we observe magnetic structures based on one of three configurations: a single-domain in-plane, a single-domain out-of-plane, or a vortex state. By imaging the in-plane and out-of-plane magnetization components of identically prepared ${\text{Ni}}_{80}{\text{Fe}}_{15}{\text{Mo}}_5$ nanodisks with diameters that range from 35 to 190 nm and with thicknesses that range from 10 to 65 nm, we are able to locate phase boundaries between the three different phases and the triple point. The phase boundaries are not sharply defined, however. Near the boundaries and especially near the triple point, we observe disks in a mixture of the different metastable ground phases, and we observe variations of the basic states, such as a tilted vortex configuration. A magnetic phase diagram generated by a micromagnetic simulation is found to be in good qualitative agreement with the phase diagram determined by the SEMPA measurements. The ability to determine the magnetic phases in sub-100 nm nanodisks enables tailoring material properties and geometry of nanodisks for various potential applications.

Figure 1

Schematic illustration of the three basic nanodisk magnetic ground states: (a) in-plane state, (b) out-of-plane state, and (c) vortex state.

Figure 2

SEM image showing a low magnification overview of the patterned sample with nanodisk arrays of nine different diameters and continuously varying thickness. The insets show high magnification images from two arrays acquired at two sample tilts: (a)/(b) 65 nm thick $\times 35\text{nm}$ diameter nanodisks and (c)/(d) 65 nm thick $\times 90\text{nm}$ diameter nanodisks. Sample tilt is $0°$ in (a)/(c) and $45°$ in (b)/(d).

Figure 3

(Color online) Examples of SEMPA measurements from $1\mu \text{m}$ diameter $\times 25\text{-nm}$-thick permalloy disks. (a) Simultaneously measured images of the topography and the two in-plane ($M_x$ and $M_y$) magnetization components, and the corresponding, derived in-plane magnetization direction. The magnetization direction is represented by the colors shown in the inset color wheel. (b) Simultaneously measured images of the topography, the in-plane $\left(M_x\right)$ and the out-of-plane $\left(M_z\right)$ magnetization components from the central region of a disk with opposite chirality. The vortex chirality and polarity can therefore be measured simultaneously.

Figure 4

(Color online) Summary of the magnetic states observed in SEMPA images as a function of disk size and shape. Disk diameters were either 35, 45, 65, or 90 nm. Near the phase boundaries, multiple grouped symbols indicated that multiple states were observed for the same disk diameter and thickness. The dashed lines are taken from the main phase boundaries calculated by the OOMMF micromagnetic simulations [see Fig. 9a]. The numbers next to the data points refer to corresponding figures in this paper.

Figure 5

(Color online) SEMPA images of (a) in-plane magnetic states in 90 nm diameter $\times 10\text{-nm}$-thick disks and (b) out-of-plane magnetic states in 35 nm diameter $\times 65\text{-nm}$-thick disks. Simultaneously measured topography and either two in-plane, or one in-plane and the out-of-plane magnetization components are shown. From these components, (a) the in-plane magnetization angle and (b) the out-of-plane magnetization tilt angle in the $M_x$ and $M_z$ plane were derived. Note that the out-of-plane magnetic structure has a significant in-plane component which may indicate curling of magnetization near the top surface.

Figure 6

(Color online) SEMPA images of vortex magnetic states in 90 nm diameter $\times 35\text{-nm}$-thick disks. The in-plane magnetization direction is represented by the inset color wheel. The array contains vortex states with two different chiralities.

Figure 7

SEMPA images which show the transition with decreasing thickness from a vortex state in (a) to an in-plane state in (c). Disk thicknesses were (a) 48 nm thick, (b) 35 nm thick, and (c) 20 nm thick. Disk diameters were all 65 nm. In (b), a mixture of the two ground phases is observed near phase boundary.

Figure 8

SEMPA images of disks with sizes along the out-of-plane/vortex phase boundary. Disk thicknesses were (a) 35 nm, (b) 48 nm, and (c) 65 nm. Disk diameters were all 45 nm. In addition to showing the transition from (a) in-plane state to (c) out-of-plane state with increasing thickness, the images also reveal more complex magnetic states such as the tilted vortex states indicated by arrows in (b).

Figure 9

(Color online) Nanodisk magnetic state phase diagrams derived from OOMMF micromagnetic simulations. The phase diagrams show the boundaries between the three basic phases (in-plane: $\mathbf{I}$, out-of-plane: $\mathbf{O}$, and vortex phase: $\mathbf{V}$), and the color-coded, normalized out-of-plane magnetization component $\left(M_z\right)$. (a) Main phase boundaries (solid lines) between minimum-energy ground states. (b) Metastable phase boundaries (dashed lines) near the triple point [boxed region in (a)] that arise when more than one stable state was found. In the metastable regions the capital letters correspond to the magnetic ground phase while the small letters represent metastable phases.