Nonlinear Giant Magnetoresistance in Dual Spin Valves

Giant magnetoresistance (GMR) arises from differential scattering of the majority and minority spin electrons by a ferromagnet (FM) so that the resistance of a heterostructure depends on the relative magnetic orientation of the FM layers within it separated by nonmagnetic spacers. Here, we show that highly nonequilibrium spin accumulation in metallic heterostructures results in a current-dependent nonlinear GMR which is not predicted within the present understanding of GMR. The behavior can be explained by allowing the scattering asymmetries in an ultrathin FM layer to be current dependent.

Figure 1

(a) Micrograph of a device: the DSV is within the active region where the current flows perpendicular to the plane. (b) Low current full resistance vs field loop of a $120\times 190{\mathrm{nm}}^2$ DSV(2,2) device; red and blue lines correspond, respectively, to increasing and decreasing field sweeps as indicated by the direction arrows, and the arrows at the top of the graphs represent the magnetic states of the CoFe (top), Py (middle), and CoFe (bottom). (c) Minor MR loops measured at 0 and $\pm 2\mathrm{mA}$: the black curve (uppermost line in each case) is initial sweep from $+150\mathrm{mT}$ to $-32\mathrm{mT}$; blue and red curves sweep between $\pm 32\mathrm{mT}$ with the direction arrows as above.

Figure 2

(a) Low current full resistance vs field loop of a DSV(1,2) device; red and blue lines correspond, respectively, to increasing and decreasing field sweeps. (b) A series of minor differential resistance vs magnetic field for a DSV(1,2) device for dc currents varying from $-1\mathrm{mA}$ to $+1\mathrm{mA}$. (c) The field-induced change in resistance area product vs current density for DSV(1,2) (blue), DSV(2,2) (red), and DSV(8,2) (magenta).

Figure 3

Measurements of a DSV(1,2) sample: (a) and (b) MR as a function of dc current for magnet field sweep directions as indicated. Low (dark blue) and high (yellow) resistance states are marked [the peaks (red) are discussed in the text]. In both cases, the parabolic background which is due to Joule heating is subtracted. (c) and (d) are the differential resistance vs $I_{\mathrm{dc}}$ at zero external magnetic fields for the magnetic states of (a) and (b), respectively. (e) Black and blue graphs are the differential resistances vs $I_{\mathrm{dc}}$ at $+20\mathrm{mT}$ and $-20\mathrm{mT}$ for the $P^{*}$ and AP states shown using the black and blue arrows, respectively. Joule heating background is not subtracted from graphs (c), (d), and (e).

Figure 4

Experimental values of the zero-current specific MR of the AP ($\uparrow \downarrow \downarrow$) [red (gray) squares] and $P^{*}$ ($\uparrow \downarrow \uparrow$) (black squares) configurations relative to $P$ ($\uparrow \uparrow \uparrow$) as function of the thickness of middle Permalloy layer. Continuous lines are the fits calculated using VF model with parameters given in the text. Black crosses are the AP values at $5\times {10}^6\mathrm{A}/{\mathrm{cm}}^2$ obtained by subtracting the minor loop changes from Fig. 2c from the zero-current AP values.