Magnetotransport properties of ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ films with stripe domains

Magnetotransport properties of ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ films with stripe domains are studied. The anisotropic magnetoresistance dominates the low field behavior, which is extremely dependent on the magnetic domains configuration. The magnetoresistance measured at different temperatures displays qualitatively different behaviors depending on the measurement configuration. When the stripes are oriented along the electric current, the low-field magnetoresistance changes sign with temperature, while when the stripes are perpendicular to the electric current the magnetoresistance curves are nearly temperature independent. A simple model considering parallel (series) conduction along (across) the stripes, plus the temperature dependence of anisotropic magnetoresistance and domains configuration, accounts for these experimental results.

Figure 1

(a) Magnetic force microscopy image of 72-nm-thick ${\mathrm{Fe}}_{0.8}{\mathrm{Ga}}_{0.2}$ film. The image was acquired at room temperature and at zero applied field; the stripes lie along the direction of the previously applied magnetic field. (b) In-plane and (c) out-of-plane magnetization loops measured at 300 K in the same sample. (d) Normalized remanent magnetization obtained from in-plane magnetization loops at different temperatures. The dashed line, $M_r/M_s=0.37$, represents the mean value of the data.

Figure 2

Room temperature $\rho \left(H\right)$ curves measured with the magnetic field applied in the plane (blue and red) and normal to the plane of the sample (green). Schematics of current and field directions are shown at the right of each curve. The zero-field resistivities ${\rho }_{\perp }, {\rho }_{\parallel }$, and ${\rho }_n$ are extrapolated from the high-field linear behavior.

Figure 3

Magnetoresistance measured at different temperatures between 100 and 300 K with the magnetic field applied (a) in the plane of the sample perpendicular to the current, (b) parallel to the current, and (c) perpendicular to the sample. In panel (a), the $r$ and $\mathrm{MR}\left(H_{\mathrm{sat}}\right)$ parameters defined in the text are indicated for the 100-K curve.

Figure 4

(a) Slopes of $\mathrm{MR}\left(H\right)$ curves in Fig. 3 for the different magnetic-field configurations. The high- and low-field slopes correspond to the linear behavior observed above and below the saturation field, respectively. The low-field data in the perpendicular configuration are divided by 10. (b) Hollow symbols: zero-field intercept $r$ of the high-field linear behavior of $\mathrm{MR}\left(H\right)$ curves in Fig. 3; solid symbols: MR evaluated at saturation field, $\mathrm{MR}\left(H_{\mathrm{sat}}\right)$ [see Fig. 3 for an example of $r$ and $\mathrm{MR}\left(H_{\mathrm{sat}}\right)$]. The dashed lines in panel (b) are linear fits to data.

Figure 5

AMR measured at different temperatures between 100 and 300 K. The lines depict ${cos}^2\left(\varphi \right)$ dependencies for in-plane (AMR $<0$) and out-of-plane (AMR $>0$) angular variations. In both configurations, $\varphi =0$ corresponds to the magnetic field parallel to the electric current direction. Continuous lines are ${cos}^2\left(\varphi \right)$ fitting curves for 100-K data.

Figure 6

Resistivity ratios ${\rho }_{\perp }/{\rho }_{\parallel }$ and ${\rho }_n/{\rho }_{\parallel }$ calculated from AMR curves in Fig. 5 as described in the text. The room-temperature ${\rho }_n/{\rho }_{\parallel }$ value was calculated directly from data in Fig. 2. The ${\rho }_n/{\rho }_{\perp }$ ratio was computed from the other ones. The lines are fits to data, a linear fit in the case of ${\rho }_{\perp }/{\rho }_{\parallel }$ and exponential fits for the other two cases.

Figure 7

Simplified magnetic structure consisting of stripe cores (white) with the magnetization in the direction normal to the film, closure domains (dark gray) with the magnetization in the plane of the film and perpendicular to the stripes, and Bloch walls (light gray) with the magnetization along the stripes direction. Once the stripes are formed, the electric current $I$ runs across (a) or along (b) the stripe domains. (c) The areas of stripe cores, $A_s$, closure domains, $A_c$, and Bloch walls, $A_w$, in one semiperiod are indicated.

Figure 8

(a) Temperature dependence of the relative areas of stripe cores $\left(a_s\right)$ and closure domains $\left(a_c\right)$ estimated from $\mathrm{MR}\left(H\right)$ curves as described in the text, by considering a constant value for $a_w$. (b) Volume ratio of stripe and closure domains, $A_s/A_c$. The white and gray regions correspond to negative and positive low-field MR, respectively. The boundary was determined by imposing the condition ${\rho }_{\parallel }^{\mathrm{rem}}={\rho }_{\parallel }^{\mathrm{sat}}={\rho }_{\parallel }$ to Eq. (6) and using resistivity ratios obtained from $\mathrm{AMR}\left(\varphi \right)$ measurements; the hollow circles were obtained using discrete data in Fig. 6 to perform this calculation and the continuous boundary was computed using the fitted curves to those data. $A_s/A_c$ values calculated from relative areas in panel (a) are also plotted (black stars).