Figure 1

(Color online) (a) Definition of the coordinate system. The $z$ axis is defined as the equilibrium direction of the precessing-layer moment $m_{\text{free}}$. (b) Schematic of the free-layer precession. The precession axis may be slightly misaligned from the $z$ axis when the last term in Eq. (1) is considered. (c) Schematic geometry for our samples with $RA=12\Omega \mu {\text{m}}^2$. The free layer is etched into a rounded rectangle while the bottom pinned layers are left extended. (d) Schematic geometry for our samples with $RA=1.5\Omega \mu {\text{m}}^2$. The synthetic antiferromagnetic pinned layers are etched, as well as the top free layer.Reuse & Permissions

Figure 2

(Color online) (a) Measured ST-FMR spectra from sample 1 at negative, zero, and positive biases for offset angles of $\theta =115°$ and $58°$, with fits to sums of symmetric and antisymmetric Lorentzians. (b) Measured ST-FMR spectra from sample 2 at zero bias with magnetic fields of various magnitudes applied in the $\phi =130°$ direction. The spectra for sample 2 show two closely spaced peaks, suggesting the existence of precessional dynamics in both the free magnetic layer and the etched synthetic antiferromagnet pinned layer.Reuse & Permissions

Figure 3

(Color online) Bias dependence of the uncorrected (a) in-plane and (b) out-of-plane torkances for sample 1 and uncorrected (c) in-plane and (d) out-of-plane torkances for sample 2 at several different offset angles $\theta$, respectively (see the text). The different offset angles are achieved by different combinations of applied field magnitude and direction. For sample 1, for $\theta =131°$, $H=0.38\text{kOe}$ with $\phi =120°$, giving $\beta =142°$; for $\theta =120°$, $H=0.40\text{kOe}$ with $\phi =110°$, giving $\beta =133°$; for $\theta =104°$, $H=0.75\text{kOe}$ with $\phi =130°$, giving $\beta =142°$; for $\theta =82°$, $H=1.00\text{kOe}$ with $\phi =120°$, giving $\beta =129°$; for $\theta =58°$, $H=1.00\text{kOe}$ with $\phi =90°$, giving $\beta =96°$. For sample 2, for $\theta =143°$, $H=0.25\text{kOe}$ with $\phi =150°$; for $\theta =135°$, $H=0.25\text{kOe}$ with $\phi =140°$; for $\theta =108°$, $H=0.30\text{kOe}$ with $\phi =125°$; for $\theta =87°$, $H=0.20\text{kOe}$ with $\phi =85°$; for $\theta =57°$, $H=0.30\text{kOe}$ with $\phi =55°$. The value of $\beta$ is not needed in the calculations for sample 2 because its cross section is circular.Reuse & Permissions

Figure 4

(Color online) Estimated contribution to the ST-FMR signal for sample 1 from (a) the term in Eq. (2c) and (b) the term in Eq. (2d), relative to the frequency-symmetric part of the direct mixing signal, Eq. (2b). The angles in the legends are the initial offset angles $\theta$. In both (a) and (b), we assume for simplicity that the in-plane torkance is a constant $d{\tau }_{\parallel }/dV=0.10\left(\hslash /2e\right)\text{k}{\Omega }^{-1}$ and the perpendicular torkance has a constant slope $d^2{\tau }_{\perp }/d{V}^2=0.16\left(\hslash /2e\right)\text{k}{\Omega }^{-1}/\text{V}$.Reuse & Permissions

Figure 5

(Color online) Determinations of the (a) in-plane and (b) out-of-plane components of the spin-transfer torkance for sample 1 and the (c) in-plane and (d) out-of-plane components of the spin-transfer torkance for sample 2 from an analysis that includes all of the contributions to the ST-FMR signal in Eq. (2). The angles in the legend are the initial offset angles $\theta$. The corresponding values of $H$, $\phi$, and $\beta$ are listed in the caption of Fig. 3. At the largest values of $\left|V\right|$ for some angles there is no real-valued solution for $d{\tau }_{\parallel }/dV$ based on Eq. (2) and our ST-FMR data, and we have marked these regimes with bars along the top or bottom axes in (a) and (c). (e) Uncorrected and corrected determinations of the in-plane component of the torkance for sample 1 for two values of the initial offset angle between the electrode magnetizations, $\theta =58°$ and $131°$. Note that there is better consistency between the measurements for the two angles after the correction.Reuse & Permissions

Figure 6

(Color online) In-plane and perpendicular torkances for a $RA\approx 14.5\Omega \mu {\text{m}}^2$ Fe/MgO/Fe tunnel junction calculated in Ref. 15 using an ab initio multiple-scattering Green’s function approach. The points are determined by numerical differentiation of the data in Fig. 4(a) of Ref. 15. We have converted to the units we use in describing the experiments assuming that the device area is the same as for sample 1 $\left(3.9\times {10}^3{\text{nm}}^2\right)$.Reuse & Permissions

Figure 7

(Color online) (a) Bias dependence of the effective damping for various initial offset angles $\theta$ for sample 1. The corresponding values of $H$, $\phi$, and $\beta$ are listed in the caption of Fig. 3. Dashed lines represent the effective damping predicted by Eq. (6), with the Gilbert damping constant $\alpha =0.010$ and a fit to the measured in-plane spin-transfer torkance. Shaded regions reflect a $\pm 15\%$ uncertainty in the value of $M_{S}Vol$. (b) The bias dependent change of the resonance frequency ${\omega }_m$ for various initial offset angles $\theta$ for sample 1. Lines show the bias-dependent changes predicted by Eq. (3) using the measured value of the perpendicular component of the spin-transfer torkance. The measured bias dependence is much greater than the small variation expected from Eq. (3), suggesting that other effects (e.g., heating) may dominate the bias dependence of ${\omega }_m$ rather than spin torque being the only significant effect. The measured resonance frequencies at zero bias are 9.47 GHz for $\theta =58°$, 9.68 GHz for $\theta =82°$, 8.93 GHz for $\theta =104°$, 5.81 GHz for $\theta =120°$, and 5.91 GHz for $\theta =131°$.Reuse & Permissions

Figure 8

(Color online) (a) Bias dependence of the effective damping for various initial offset angles $\theta$ for sample 2. Dashed lines represent the effective damping predicted by Eq. (6), with the Gilbert damping constant $\alpha =0.014$ and a fit to the measured in-plane spin-transfer torkance. Shaded regions reflect a $\pm 15\%$ uncertainty in the value of $M_{S}Vol$. (b) The bias dependence of the resonance frequency ${\omega }_m$ for various initial offset angles $\theta$ for sample 2.Reuse & Permissions