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Spatially periodic domain wall pinning potentials: Asymmetric pinning and dipolar biasing
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Image of FIG. 1.
FIG. 1.

(a) Cross-sectional schematic showing the general structure of each sample. The lower continuous soft ferromagnetic film and upper hard multilayer nanoplatelet stacks are shaded in gray. Each array is denoted X/Y with X and Y, respectively, the intended width and edge-to-edge spacing of the nanoplatelets. Zoomed in scanning electron micrographs of the (b) 200/400, (c) 200/200, and (d) 50/100 nanoplatelet arrays. (e) Positive-field-driven switching of the continuous film (sharp transition) and nanoplatelets (gradual transition) following negative saturation measured using the spatially averaged PMOKE microscopy method outlined in Sec. III C .

Image of FIG. 2.
FIG. 2.

(a) Perpendicular component of the stray field beneath positively saturated nanoplatelets ( ) as calculated at the center of the soft layer in the 200/1000, 200/400, 200/200, and 50/100 arrays. The solid line represents the stray field value along a line passing through the center of a row of nanoplatelets. The dotted line corresponds to its value averaged over a moving window in the plane of the continuous layer with a width of 10 nm and a length equal to the array period. The latter allows one to visualize the field experienced by a straight wall moving through the array averaged along its length. (b) Plot of the perpendicular component of the nanoplatelet stray field for the 200/200 array beneath two neighboring nanoplatelets.

Image of FIG. 3.
FIG. 3.

Micromagnetic simulation (400 nm × 2400 nm) of domain walls propagating through an ideal (defect free) Co(0.65 nm) layer towards the location of two nanoplatelets for the (a) P configuration ( and ) and the (b) AP configuration ( and ). The perpendicular component of the field of the nanoplatelets within the calculation region has been superimposed on the image (the blue and red “squares”). The color code for the film's magnetization and the nanoplatelets' perpendicular dipolar fields is +z = blue, −z = red, and +y = green (Bloch domain wall).

Image of FIG. 4.
FIG. 4.

Stabilized domains in the continuous ferromagnetic layer outside (a,h) and beneath the 200/400 (b,c,i,j), 200/200 (d,e,k,l), and 50/100 (f,g,m,n) arrays following wall propagation under fields parallel (P) or antiparallel (AP) to the magnetization of the nanoplatelets. The images in the two columns correspond to approximate wall velocities of 10 nm/s (a-g) and 0.1 m/s (h-n). The dark domains are propagating towards the bottom of each image, which has dimensions of 21.6 μm × 21.6 μm.

Image of FIG. 5.
FIG. 5.

MFM images of the 200/1000 array for driving fields (a) parallel, P ( ), or (b) antiparallel, AP ( ), to the nanoplatelet magnetization ( ), and in the (c) demagnetized D state ( , ) where there are both and magnetized nanoplatelets. The magnetic field used to drive the walls through the array was +130 Oe, −100 Oe, and +80 Oe, for the P, AP, and D configurations, respectively. For the P state, the dark domain is expanding at the expense of the light domain. The inverse applies for the AP and D states. The length of each black scale bar is 4 μm. Magnified images of the regions inside the black squares are shown in the insets.

Image of FIG. 6.
FIG. 6.

Natural logarithm of the velocity, v, of domain walls in the continuous soft layer outside the arrays (bare film) and beneath the arrays for P, AP, and D configurations plotted against for the (a) 200/1000 (data from Ref. 22 ), (b) 200/400, (c) 200/200, and (d) 50/100 arrays. Inset: The P and AP velocity curves can be superimposed on those measured in the absence of the nanoplatelets by plotting versus . Data in (a) are reprinted with permission from Appl. Phys. Lett. 94, 132504 (2009). Copyright 2009 American Institute of Physics.

Image of FIG. 7.
FIG. 7.

Retardation field values, Hret , for the P and AP configurations as deduced from the collapsed versus data sets [insets of Fig. 6 ]. Values are shown as a function of the array period, [see Fig. 1(a) ]. Error bars represent uncertainties in the Hret value, which yields the best data overlap in Fig. 6 .

Image of FIG. 8.
FIG. 8.

(a) To obtain a quasi-static remanent PMOKE hysteresis loop of the continuous layer beneath and outside the array, the system is imaged at remanence and the average PMOKE signal of the soft layer is measured in two regions: one covering a corner of the array and another covering a region directly next to the array. These signals are normalized in order to construct the M–H loops shown in Fig. 9 . (b) A portion of the field application sequence used to obtain the positive branch of a hysteresis loop where a field pulse is applied over a time tstep at each step of the sequence.

Image of FIG. 9.
FIG. 9.

Left hand side: Normalized, spatially averaged, remanent PMOKE hysteresis loops (black dots) of the soft layer measured in a region located underneath the negatively (a), positively (b, c), and demagnetized (d) 200/200 nanoplatelet array. The equivalent loop for reversal limited only by wall pinning is shown as a gray line in (a) (see Appendix D ). The values of tstep are indicated. Right hand side: Corresponding PMOKE images for negative and positive values of the applied field close to the coercive field of the portion of the continuous layer beneath the array. The vertical dotted white line indicates the left boundary of the array [see also Fig. 8(b) ]. The white scale bars are 10 μm long.


Generic image for table
Table I.

Nanoplatelet array characteristics (see Fig. 1(a) ). All lengths and film thicknesses are in nm. The actual nanoplatelet widths, X, and edge-to-edge separations, Y, were measured by scanning electron microscopy [e.g., Figs. 1(b)–1(d) ].


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spatially periodic domain wall pinning potentials: Asymmetric pinning and dipolar biasing