Magnetotransport through magnetic domain patterns in permalloy rectangles

We study the influence of multidomain configurations on the magnetoresistance of rectangular permalloy microstructures with various thicknesses. The anisotropic magnetoresistance (AMR) is the dominating resistance contribution in these systems. Reversible and irreversible magnetization reversals lead to complex AMR signals. Appropriate positioning of the voltage probes allows the local detection of the magnetoresistance. Two methods for calculating the local AMR, the uniform-current model and diffusive transport calculations, are described. The latter takes potential differences and inhomogenous current paths into account. By comparing magnetoresistance measurements, micromagnetic simulations, and images of magnetic-force microscopy for various film thicknesses, we can exactly link the transitions between magnetic configurations to changes observed in the magnetoresistance.

Figure 1

Array of $4\times 2\mu {\mathrm{m}}^2$ permalloy rectangles, three of them contacted. The current contacts are labeled with ${\mathit{I}}_{+}$ and ${\mathit{I}}_{-}$. The in-plane angle $\phi$ between the magnetic field $\mathit{B}$ and the current $\mathit{I}$ is illustrated. The inset shows the $40\mathrm{nm}$ thick element with its current and voltage probes. The voltage probes are $l=1\mu \mathrm{m}$ apart and reach $w=500\mathrm{nm}$ across the sample.

Figure 2

(Color online) Magnetoresistance measurements of the $20\mathrm{nm}$ (red), $40\mathrm{nm}$ (green), and $70\mathrm{nm}$ (blue) permalloy element at $T=50\mathrm{K}$. The AMR is measured in magnetic fields parallel and perpendicular to the principal direction of the current.

Figure 3

(Color online) Minor loops of the $40\text{−}\mathrm{nm}$-thick element at $T=2\mathrm{K}$. The traces 2 to 11 are successively shifted upwards by $5\mu \mathrm{V}$.

Figure 4

(Color online) Simulated and experimental traces of the AMR of a $4\times 2\mu {\mathrm{m}}^2$ large and $20\text{−}\mathrm{nm}$-thick permalloy structure with two different initial magnetic configurations. (a) Top curves show the simulated AMR for the initial $c$-state, with the upper one offset by $+10\mu \mathrm{V}$ for clarity. The bottom curves are two corresponding measured AMR signals, the lower one offset by $-10\mu \mathrm{V}$. (b) Simulated sweep for the initial $s$-state (top curve) and measurements (bottom) akin to the simulation. Between configurations $A$ to $E$ irreversible changes occur. The small outlined boxes represent the regions in which the AMR is measured (see voltage probes in Fig. 1) and simulated.

Figure 5

(Color online) Comparison of measurements at $2\mathrm{K}$ and simulations for $20\text{−}\mathrm{nm}$- (blue), $40\text{−}\mathrm{nm}$- (yellow), and $70\text{−}\mathrm{nm}$- (red) thick rectangles.

Figure 6

(Color online) (a) $2\times 1\text{−}\mu {\mathrm{m}}^2$-large and $70\text{−}\mathrm{nm}$-thick permalloy rectangles, measured by MFM (top row). The middle and lower rows show simulated MFM images according to Ref. 26. The gray scale of the lower row ranges from white (magnetization along the long axis) to black (magnetization perpendicular to long axis). (b) Three consecutive AMR measurements (lower curves) performed at $2.0\mathrm{K}$ on a $4\times 2\text{−}\mu {\mathrm{m}}^2$-large and $70\text{−}\mathrm{nm}$-thick rectangle and an AMR curve simulated for the rectangle in (a).

Figure 7

(Color online) Current distribution just below the surface of the $20\text{−}\mathrm{nm}$-thick permalloy rectangle. The current contacts are attached on the left- and right-hand sides, while the voltage probes lie in the lower part of the figure, on top of the structure. The bright lines illustrate five current paths. Colors represent absolute values of the current density between $0\mathrm{A}∕{\mathrm{m}}^2$ (blue) and $2.0\times {10}^9\mathrm{A}∕{\mathrm{m}}^2$ (red).

Figure 8

(Color online) Comparison of the AMR of the two simulation models with experiments: Bottom three curves (blue) are measured AMR signals for the $4\times 2\text{−}\mu {\mathrm{m}}^2$-large and $20\text{−}\mathrm{nm}$-thick permalloy rectangle at $2\mathrm{K}$, the top curve (black) shows the results of the uniform-current approach and an initial $s$ state, and the middle curve (red) results from the diffusive-transport calculation. Curves 2 to 4 are shifted upwards by 6, 12, and $21\mu \mathrm{V}$.

Figure 9

(Color online) Temperature-dependent AMR measurements of the $70\text{−}\mathrm{nm}$-thick permalloy element. The curves are successively shifted upwards by $2\mu \mathrm{V}$ for clarity.