Figure 1

Sketch of (a) in-plane and (b) out-of-plane spin valve configuration: the polarizer in blue has its magnetization fixed, whereas the free layer in green can align parallel or antiparallel to it.Reuse & Permissions

Figure 2

(a) ac-resistance variation as a function of the net applied magnetic field ($H_{\mathrm{net}}$) under zero current for an elliptical nanopillar spin valve of 50 nm by 300 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni] with a platinum layer on top. The net applied field is define as the applied field minus the average dipolar field coming from the hard layer ($H_{\mathrm{net}}$ $=$ $H$ − $H_{\mathrm{dip}}$). The red and blue curves correspond to the field increasing and decreasing branches of the hysteresis loop. (b) Corresponding difference of the normalized resistances between the field increasing and decreasing branches of the hysteresis loop. (c) Corresponding half sum of the normalized resistances between the field increasing and decreasing branches of the hysteresis loop. The normalized resistances ($R$ − $R_{\mathrm{P}}$)/($R_{\mathrm{AP}}$ − $R_{\mathrm{P}}$) are plotted to remove the Joule heating contribution for the $R_{\mathrm{sum}}$ curve. These curves highlight three regions of different available magnetic configurations: the parallel (P) or the antiparallel (AP) states only or the bistable region.Reuse & Permissions

Figure 3

State diagrams of an elliptical nanopillar spin valve of 50 nm by 300 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni] with a platinum layer on top obtained (a) from the difference of ac-resistances treatment and (b) from the half sum of the ac-resistances treatment. The applied magnetic field step is 1 mT and the injected current step is 0.1 mA. Data are acquired at a sample ambient temperature unless otherwise specified. The colored scale bar corresponds to the value of the normalized resistance for both ac-resistances treatment. Note that the same scale bars are used in the following figures.Reuse & Permissions

Figure 4

State diagram of an elliptical nanopillar spin valve of 50 nm by 300 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni] obtained from the half sum method along with three characteristic hysteresis loops at $I$ $=$ − 13 mA, $I$ $=$ 0 mA, and $I$ $=$ 11 mA.Reuse & Permissions

Figure 5

Orientation of the magnetization unit vectors m and p, applied field H, and injected current $I$ relative to $x$,$y$,$z$ axis in the case of a purely uniaxial symmetry.Reuse & Permissions

Figure 6

(a) Theoretical state diagram of a nanopillar spin valve with perpendicular magnetizations in the case of a uniaxial, macrospin, and 0 K approach in reduced coordinates ($h=H/H_K$ and $i=\frac{\beta I}{\alpha {\gamma }_0{H}_K}$). (b) Experimental state diagram of a hexagonal nanopillar spin valve of 100 nm by 200 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni]. The blue and red circles are for the measured switching fields and the orange triangles indicates the presence of a peak in the differential resistance measurements. The blue and red lines present what could correspond to the expected evolution of the switching current as a function of the applied magnetic field of our simple modeling. The values of the parameters used here can be found in Ref. 50.Reuse & Permissions

Figure 7

Experimental state diagrams of an hexagonal nanopillar spin valve of 100 nm by 200 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni] measured at (a) $T$ $=$ 290 K and at (b) $T$ $=$ 20 K. The blue and red lines present what could correspond to the expected linear evolution of the switching current as a function of the applied magnetic field.Reuse & Permissions

Figure 8

Experimental state diagram of an elliptical nanopillar spin valve of 50 nm by 300 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni] for various sweeping rate of 100 mT (background and black line), 10 mT/s (red line), and 1 T/s (blue line).Reuse & Permissions

Figure 9

Experimental state diagram of a rectangular 100 nm by 100 nm spin valve with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni]. Blue and red correspond to the parallel or antiparallel states. The symbols (cross) indicate the zero temperature switching current extrapolated from short-time measurements.[91] As this extrapolation eliminates the thermal excitations, the switching current is significantly larger than during the quasistatic measurement.Reuse & Permissions

Figure 10

Experimental state diagrams of an hexagonal nanopillar spin valve with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni] of (a) 100 nm by 200 nm and of (b) 50 nm by 100 nm. The blue and red lines present what could correspond to the expected evolution of the switching current as a function of the applied magnetic field of our simple modeling.Reuse & Permissions

Figure 11

Experimental state diagrams of an elliptical nanopillar spin valve of 50 nm by 300 nm with a hard layer made of [Co/Pt]/[Co/Ni] and a free layer made of [Co/Ni]. The magnetic field is applied at an angle $\Psi$ toward the perpendicular axis. (a) $\Psi$ $=$ 40° and (b) $\Psi$ $=$ 0°. The blue and the red lines present what could correspond to the expected evolution of the switching current as a function of the applied magnetic field of our simple modeling.Reuse & Permissions

Figure 12

Orientation of the magnetization unit vectors m and p, applied field H, and injected current $I$ relative to $x$,$y$,$z$ axis in the case of a nonuniaxial symmetry.Reuse & Permissions

Figure 13

Stability diagrams in the applied magnetic field and injected current plane in reduced coordinates. The colored areas correspond to the unstable regions and the lines to the theoretical evolution of the switching currents with the applied magnetic field. (a) Case of the parallel state. (b) Case of the antiparallel state.Reuse & Permissions

Figure 14

(a) Theoretical state diagram of a nanopillar spin valve with perpendicular magnetizations in the case of a nonuniaxial (Ψ $=$ 20°), macrospin, and 0 K approach. (b) Theoretical evolution of the critical currents as a function of the angle of application of the magnetic field.Reuse & Permissions

Figure 15

Theoretical state diagram for uniaxial system calculated using numerical simulations. The new reduced coordinates $h=H/H_K$ (bottom) and $i=\frac{\beta I}{\alpha {\gamma }_0{H}_K}$ (right) have been added using the new parameters (see text).Reuse & Permissions

Figure 16

Theoretical state diagrams in the case of a tilted applied field of (a) $\Psi =5^{\circ }$ and (b) $\Psi ={20}^{\circ }$.Reuse & Permissions

Figure 17

Theoretical state diagrams in the case of a tilted anisotropy field of (a) ${\Psi }_{\mathrm{ani}}=0.5^{\circ }$ and (b) ${\Psi }_{\mathrm{ani}}=5^{\circ }$.Reuse & Permissions

Figure 18

Theoretical state diagrams in the case with an added in-plane $K_p=1\times {10}^4\mathrm{J}/.{\mathrm{m}}^3$ and second-order $K_2$ anisotropy constant. (a) $K=K_1=4\times {10}^5\mathrm{J}/.{\mathrm{m}}^3$ and (b) $K_1=3\times {10}^5\mathrm{J}/.{\mathrm{m}}^3,K_2=1\times {10}^5\mathrm{J}/.{\mathrm{m}}^3$. The value of the total anisotropy constant $K$ is chosen to be the same in both cases.Reuse & Permissions

Figure 19

Energy landscape of the free layer as a function of the angle $\theta$ for an applied field of 200 mT and without injected current. The parameters used here are $K_p=1\times {10}^4\mathrm{J}/.{\mathrm{m}}^3$, $K_1=3\times {10}^5\mathrm{J}/.{\mathrm{m}}^3$. The red curve is plotted for $K_2=0$, the green one for $K_2=1\times {10}^5\mathrm{J}/.{\mathrm{m}}^3.$Reuse & Permissions