(a)–(c) Scheme of ferromagnetic (FM) domain configurations appearing in magnetically patterned exchange-bias layer systems. is the initial exchange-bias field direction; is the applied external magnetic field during the ion bombardment and IB denotes the regions subjected to the ion bombardment induced magnetic patterning; is the vector normal to the domain wall plane; , denote the domains' magnetizations; and the long stripe axis orientation of the domains. (a) head-to-head (hh), (b) head-to-side (hs), and (c) side-by-side (ss) configuration of magnetizations in adjacent domains. (d)–(f) illustrate the amount of uncompensated magnetic interface charges within the left domain wall for the domain configurations: (d) (hh), (e) (hs), and (f) (ss). (g)–(i) show the results of the spatial magnetization distribution obtained by the OOMMF simulations. Note that for (g) only one of the two energetically degenerated states obtained by the simulations is shown where the magnetitization can perform either a cw or a ccw rotation inside the domain wall.
Hysteresis loops obtained by vibrating sample magnetometry shown for the (ss) (a), (hh) (b), and (hs) (c,d) configurations. Both (hh) and (ss) were measured along the easy axis, i.e., the external magnetic field was aligned parallel to the initial EB-field direction , whereas (hs) was measured along the easy and hard axes ( ⊥ ), respectively. The indicated saturation fields and for the (hs) configuration ( 40 kA/m) were used for estimating the ferromagnetic uniaxial anisotropy constant .
(a)–(c) Normalized images obtained by MFM measurements for (a) (hh), (b) (hs), and (c) (ss) domain configuration. For (a) and (b), monopolar charge contrast is observed; note that both the signal magnitude and the domain wall width are increased for (hh) configuration due to the higher amount of interface charges, whereas for the uncharged (ss) configuration, dipolar charge contrast is visible. (d)–(f) Calculated MFM charge contrast according to Eq. (2) for the spatial magnetization distribution obtained by the micromagnetic simulations performed with OOMMF for the different domain configurations, i.e., (a) (hs), (b) (hs), and (c) (ss) configuration. Qualitative comparison between experimentally observed and theoretically predicted charge contrast reveals good agreement concerning the relative signal intensities, the domain wall widths, and the observed charge contrast polarity.
(a) Generic MFM-signal as a function of the scan-length in -direction for the (hh), (hs), and (ss) domain configuration. Nonlinear fit functions obtained by the experimental data are added as a guide to the eye. The progressive transition from the dipolar to monopolar charge contrast as a function of the relative interface charge amount from (ss) over (hs) to (hh) domain configuration is clearly evident. (b) Calculated generic MFM-signal as a function of the scan-length in -direction for the (hh), (hs) and (ss) configuration, fitted by nonlinear regression as a guide to the eye, i.e., gaussian functions for the (hh) and (hs) domain configuration and a forth order fourier series expansion for the (ss) configuration. Note that the reletive signal amount of the (ss) configuration was enhanced by two orders of magnitude allowing direct comparison with the (hh) and (hs) data. Besides the transition from dipolar to monopolar charge contrast and the increased domain wall widths, further information is obtained considering the signal symmetry referred to the peakintensity: Due to the inhomogeneous charge distribution in the case of (hs)-configuration, the domain wall width is increased in -direction, related to the center of the domain wall depicted.
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