Magnetoresistance in ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ thin films with magnetic stripes: The role of the three-dimensional magnetic structure

In this work we show the existence of closure domains in ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ thin films featuring a striped magnetic pattern and study the effect of the magnetic domain arrangement on the magnetotransport properties. By means of x-ray resonant magnetic scattering, we experimentally demonstrate the presence of such closure domains and also estimate their sizes and relative contribution to surface magnetization. Magnetotransport experiments show that the behavior of the magnetoresistance depends on the measurement geometry as well as on the temperature. When the electric current flows perpendicular to the stripe direction, the resistivity decreases when a magnetic field is applied along the stripe direction (negative magnetoresistance) in all the studied temperature range. Transport calculations in the Ohmic regime indicate that the main source is the anisotropic magnetoresistance. In the case of current flowing parallel to the stripe domains, the magnetoresistance changes sign, being positive at room temperature and negative at 100 K. An intrinsic magnetoresistant contribution arising from the domain walls appears as the most plausible explanation for the observed behavior. We have put in evidence the importance of using x-ray resonant magnetic scattering for the determination of thin-film properties related with the magnetic structure.

Figure 1

(a) Schematic view of domains that compose the stripe pattern after the saturating field was applied. (b) MFM image of the stray field generated by the stripe pattern. (c) $M$ vs $H$ loop along the saturating field previously applied, where the characteristic linear behavior of the stripe domains at lower fields is observed in the experimental data (red line) as well as in the oommf calculations (blue circles).

Figure 2

($a$) Measurement geometry. (b) and (c) images of the spots corresponding to the specular, first (marked in red) and second order (marked in green) diffracted peaks for C+ and C- respectively. At an incidence angle $\omega$ = $16.3^{\circ }$, the $q_x$ and $q_y$ ranges covered by the detector are approximately $q_x$ = $\pm 0.045 {\mathrm{nm}}^{-1}$ along the $q_y$ = 0 line and $q_y$ = $\pm$ 0.175 ${\mathrm{nm}}^{-1}$ along the $q_x$ = 0 line. ($d$) Peaks transverse section.

Figure 3

(a) Scattered intensity vs $q$ calculated from the magnetization structure calculated by oommf. The doublet present in the scattering peak for the 84-nm-thickness sample is due to simulated disorder included in the simulation. Had perfect stripes been simulated, the scattering peaks presented would have taken the form of delta functions. (b) Calculated asymmetry ratio and out-of-plane magnetization component as a function of the domain wall width. At either very thin or very thick domain walls, the magnetization distribution is either out of plane or in plane, giving rise to only polar or transverse MOKE components, respectively. In order to produce an asymmetric scattering pattern when illuminated with circularly polarized x rays, constructive interference is required between the polar and transverse MOKE components, and such interference is greatest at intermediate values of the domain wall width.

Figure 4

(a) Geometries used for magnetotransport measurements. (b) MR ratio in both measurement geometries (CPW and CIW) at 300 and 100 K. The lines with squared symbols indicate the AMR calculated from simulations.

Figure 5

Cross-sectional view of the stripe domains. Three top panels: color maps for the three components of the magnetization and domain volume ratios calculated by oommf package. Bottom panel: magnetization vector along the sample.