Reversal mechanism, switching field distribution, and dipolar frustrations in Co/Pt bit pattern media based on auto-assembled anodic alumina hexagonal nanobump arrays

We fabricated a perpendicularly magnetized bit pattern media using a hexagonally close-packed auto-assembled anodic alumina template with 100 nm and 50 nm periods by depositing a Co/Pt multilayer to form an ordered array of ferromagnetic nanodots, so-called nanobumps. We used Hall resistance measurements and magnetic force microscopy to characterize the dot-by-dot magnetization reversal mechanism under applied field. The role of interdot exchange coupling and dipolar coupling are investigated. Then we focus on separating the various origins of switching field distribution (SFD) in this system, namely dipolar interactions, intrinsic anisotropy distribution, and template packing faults. Finally we discuss the influence of triangular dipolar frustrations on the energy stability of demagnetized and half-switched states based on an Ising model, including local exchange coupling. The impact of SFD and lattice defects lines between misoriented ordered domains on the magnetic configurations is studied in detail.

Figure 1

SEM images of nanobump arrays of a 100 nm period [(a) top and (b) tilted views, respectively] and a 50 nm period [(c) top view].

Figure 2

(a) Saturation magnetization vs applied field measured for a [Co(0.4 nm)/Pt(0.7 nm)] × 4 film at 300 K with out-of-plane (black solid squares) and in-plane (red open circles) field orientation. (b) Saturation magnetization (green solid squares) and anisotropy field (blue open triangles) vs temperature.

Figure 3

(a) EHE measurements for Co/Pt multilayers on a bumpy surface for $p$ = 100 nm measured at 20, 100, 200, and 300 K and for $p$ = 50 nm measured at 300 K (dotted line). The inset shows the variation of the coercive field with temperature; the experimental results (black curve) are compared with theoretical predictions (red curve). (b) Variation of coercivity as a function of the angle of the applied field measured at 20 K and 300 K for 100 nm lateral size bumps and at 300 K for 50 nm lateral size bumps with a Co/Pt multilayer deposited on top. The black continuous line is the prediction of switching field in the Stoner-Wohlfarth model.

Figure 4

(a) Derivative of EHE loops for Co/Pt multilayers on a 100 nm period bump surface measured at 20, 100, 200, and 300 K. The inset shows the double peak Gaussian fitting of the curve derived from the measurement made at 300 K for $p$ = 100 nm. (b) Variation of both peaks’ maximum and σ, the standard deviation, as a function of temperature for the first and second peaks shown in (a).

Figure 5

EHE measurement of out-of-plane major (black curve) and one minor loop (red dashed line) for Co/Pt nanobump array. Open red disks show the minor loop (red dashed line) upshifted. The large black and white dots are a scheme of magnetic configuration discussed in the text. Inset: derivative of the open red disks curve (upshifted minor loop) and of black curve (major loop). The arrows point out the difference of “easy switcher” switching field distribution as a function of their magnetic environment.

Figure 6

(a) EHE measurement of out-of-plane major and minor loops for Co/Pt nanobump array with $p$ = 100 nm. The percentage values correspond to the ratio of switched nanobumps during each loop. (b) Δ$H$($M$, Δ$M$) data (open circles) obtained from the partial reversal curves in (a) and compared with the fit (red solid line) of the Δ$H$($M$, Δ$M$) model. The quality of the fit is attested by the correlation coefficient $R^2=0.9689.$

Figure 7

1 μm × 1 μm MFM images obtained successively after saturation at +350 mT (a), under 0 mT to −300 mT (b)–(o). Since the magnetization is saturated at −350 mT, (a) corresponds to an average topography signal that is used to correct all the other MFM images. Yellow hexagons in (a) mark lattice stacking faults.

Figure 8

Normalized moment calculated from the MFM images in Fig. 7 as a function of the applied field. Each solid circle corresponds to one MFM image. The dashed line corresponds to a field range where no MFM images have been performed. The arrow shows the field sweep direction. The red stars correspond to the normalized magnetization extracted from MFM images measured during fields applied after out-of-plane demagnetization of the sample. The inset presents the derivative of the solid circle branch.

Figure 9

1 μm × 1 μm MFM images obtained close to half reversal (−60 mT) after negative field saturation (a) and at remanence after demagnetization (b). The solid red disks correspond to hard switchers, open blue disks to easy switchers, and yellow hexagons to topological defects.

Figure 10

Ground states for characteristic values of first-neighbors magnetic coupling $J_1$ with the unit of coupling coefficient being the dipolar coupling between first neighbors; e.g., (a) holds only dipolar couplings.

Figure 11

1 μm × 1 μm MFM images obtained at remanence after out-of-plane demagnetization (a) and then under −180 mT (b), −210 mT (c), and −250 mT (d), respectively. The red solid disks correspond to hard switchers, blue open disks to easy switchers; the green lines highlight specific switched regions, and the yellow hexagons correspond to stacking defects, as discussed in the text. The white dashed lines mark the region taken into account to calculate the relative magnetization in Fig. 8.

Figure 12

(a) MFM image of a 2 μm × 2 μm array of bumps sample surface. (b) Corresponding 2 μm × 2 μm AFM image with the MFM pattern superimposed on it.

Figure 13

(a) AFM image with additional black filled circles showing structural defaults. The triangles obtained by Delaunay triangulation applied to the bump center coordinates are filtered using criteria from Eq. (1) at τ = 0, 3 level and superimposed on the AFM image. (b) Sketch of an equilateral triangle showing the angles and edges notations.

Figure 14

Postprocessing results after triangles base angle (α) analysis giving rise to three main base angle orientations according to the number of occurrences distribution of the α angle. The three different base angle orientations correspond to different magnetic domains delimited by the structural defects (black filled circles). Domains with orange triangles correspond to α ranging from −30° to −17.5°, from 25° to 30°, the ones with blue triangles correspond to α ranging from −17.5° to 6.5°, and the ones with green triangles correspond to α ranging from 6.5° to 25°. (b) Number of occurrences of a given base angle α ranging from −30° to 30° (Δα = 60°). In the inset, triangle base angle α definition showing the six equivalent triangles (due to hexagonal symmetry) for a given α base orientation relative to the $x$ axis. The angle range for the triangle base is then limited to 60° (360°/6) due to symmetry.