Spin-current mediated exchange coupling in MgO-based magnetic tunnel junctions

Heterostructures composed of ferromagnetic layers that are mutually interacting through a nonmagnetic spacer are at the core of magnetic sensor and memory devices. In the present study, layer-resolved ferromagnetic resonance was used to investigate the coupling between the magnetic layers of a Co/MgO/Permalloy magnetic tunnel junction. Two magnetic resonance peaks were observed for both magnetic layers, as probed at the Co and Ni $L_3$ x-ray absorption edges, showing a strong interlayer interaction through the insulating MgO barrier. A theoretical model based on the Landau-Lifshitz-Gilbert-Slonczewski equation was developed, including exchange coupling and spin pumping between the magnetic layers. Fits to the experimental data were carried out, both with and without a spin pumping term, and the goodness of the fit was compared using a likelihood ratio test. This rigorous statistical approach provides an unambiguous proof of the existence of interlayer coupling mediated by spin pumping.

Figure 1

XTEM image of the $a$-plane sapphire/Mo/Au/Co/MgO/Py/Au MTJ. In the overview on the left-hand side, the layer stack can be seen. In the close-up on the right-hand side, the core of the MTJ is highlighted, consisting of the ferromagnetic Co and Py layers, separated by a continuous, insulating MgO barrier.

Figure 2

VNA-FMR absorption as a function of applied magnetic field (${\theta }_H={45}^{\circ }$) and excitation frequency for the MTJ sample held at 300 K. The brightness of the signal corresponds to the strength of the absorption. As the sample consists of two distinct magnetic layers, two resonance curves are visible. White and red dashed lines indicate the frequencies at which the cavity FMR and XFMR were performed, respectively.

Figure 3

Schematic of the XFMR measurement in transverse geometry. The sample (shown in red) is placed face down onto the central conductor of a coplanar waveguide (CPW), which has a tapered hole at the sample position. This allows circularly polarized x rays to enter onto the sample from below, under an angle of ${55}^{\circ }$ with respect to the surface normal. A microwave signal ${\mathrm{h}}_{\mathrm{rf}}\left(t\right)$ is fed to the CPW and the magnetization $\mathrm{m}\left(t\right)$ precesses about the direction of the applied static magnetic field ${\mathbf{H}}_{\mathrm{ex}}$ (illustrated here for the ${\theta }_H={90}^{\circ }$ in-plane direction). Due to the pulsed nature of the synchrotron radiation, the component of $\mathrm{m}\left(t\right)$ along the beam direction $\widehat{\mathrm{k}}$ can be detected stroboscopically via the measurement of the luminescence yield from the sapphire substrate using the photodiode behind the sample.

Figure 4

Cavity FMR resonance curves as a function of external magnetic field direction (${\theta }_H$) with respect to the surface normal for the Py, Co, and MTJ samples at 80 and $300\mathrm{K}$. Blue and orange dots refer to measurement points for Py and Co, respectively. The black lines represent the theoretical model fits, yielding the fitting parameters summarized in Table 1.

Figure 5

XFMR measurements of the MTJ sample at 80 K. (a) XFMR delay scans for the Co layer with the magnetic field oriented at ${\theta }_H={10}^{\circ }$. For clarity, the data points (circles) obtained at different magnetic field values are shifted by a constant offset. The continuous lines represent the fitted sinusoidal functions. Their amplitude and phase as a function of magnetic field strength is plotted in panels (b) and (c), respectively, for both the Co (orange) and Py (blue) layers. (d) Magnetic field direction dependence of the XFMR amplitude for the Co layer. The in-plane measurement at ${\theta }_H={90}^{\circ }$ corresponds to panel (b).

Figure 6

Comparison of the results for model I (EC only, dashed lines) and model II ($\mathrm{EC}+\mathrm{SC}$, solid lines) for different external magnetic field angles and temperatures: (a)–(c) ${\theta }_H={20}^{\circ }, T=80$ K; (d)–(f) ${\theta }_H={60}^{\circ }, T=80$ K; and (g)–(i) ${\theta }_H={60}^{\circ }, T=300$ K. The experimental data are shown as circles for the Co (orange) and Py (blue) layers. The top row shows the FMR plots in the $(X,Y)$-plane, for the field increasing going counterclockwise along the curves. The middle and bottom row show the corresponding amplitude ($C$) and relative phase ($\psi$) plots, respectively, as a function of field. The red and green vectors in panel (a) relate to the $X$ and $Y$ values in model II for Co and Py, respectively, at a magnetic field of $63.5\mathrm{mT}$. The length of the vectors corresponds to the signal amplitude and the angle with the horizontal axis corresponds to its phase. For comparison, the same value of magnetic field is indicated by red dashed lines in panels (b) and (c).

Figure 7

Cumulative distribution function (CDF) of the simulated likelihood ratio (${\lambda }_{LR}$), plotted together with the CFD of ${\chi }_1^2$.