Angular Dependence of Domain Wall Resistivity in Artificial Magnetic Domain Structures

We exploit the ability to precisely control the magnetic domain structure of perpendicularly magnetized $\mathrm{Pt}/\mathrm{Co}/\mathrm{Pt}$ trilayers to fabricate artificial domain wall arrays and study their transport properties. The scaling behavior of this model system confirms the intrinsic domain wall origin of the magnetoresistance, and systematic studies using domains patterned at various angles to the current flow are excellently described by an angular-dependent resistivity tensor containing perpendicular and parallel domain wall resistivities. We find that the latter are fully consistent with Levy-Zhang theory, which allows us to estimate the ratio of minority to majority spin carrier resistivities, ${\rho }_{\downarrow }/{\rho }_{\uparrow }\sim 5.5$, in good agreement with thin film band structure calculations.

Figure 1

(a1) and (b1) show MFM images of 90° and 45° domain “superlattices” created by Ga-FIB irradiation; (a2) and (b2) show MFM images of the same regions after saturation of the magnetization at 300 Oe. (c) Micrograph of the Wheatstone bridge device consisting of four $\mathrm{Pt}/\mathrm{Co}/\mathrm{Pt}$ wires each $16\mu \mathrm{m}$ long and $1\mu \mathrm{m}$ wide. (d) Schematic of the top pair of $\mathrm{Pt}/\mathrm{Co}/\mathrm{Pt}$ wires of the Wheatstone bridge.

Figure 2

(a) Magnetoresistance (offset vertically for clarity) of bridge structures containing 0, 2, 4, and 8 irradiated strips in CPW geometry at 300 K. (b) Maximum resistance change as a function of number of irradiated strips of various widths, $d$.

Figure 3

(a) Magnetoresistance (offset vertically for clarity) of bridge structures containing irradiated strips patterned at different angles relative to the current flow. (b) Calculated potential profile along the middle of the device channel containing a single patterned strip $1\mu \mathrm{m}$ wide at different angles (lower inset). Also shown are typical static eddy currents induced by the domain wall (DW)—a 30 nm region containing the DW has been expanded horizontally to enable the current lines there to be resolved. (c) Angular dependence of the total domain wall resistivity: diamonds, measured values from (a); circles, calculations such as in (b), using $\delta {\rho }_{\mathrm{CPW}}=23\times {10}^{-3}\mu \Omega \mathrm{cm}$, $\delta {\rho }_{\mathrm{CIW}}=3.5\times {10}^{-3}\mu \Omega \mathrm{cm}$, DW width 15 nm; line, Eq. (2) using the same values.