Electric field induced parametric excitation of exchange magnons in a CoFeB/MgO junction

Inspired by the success of field-effect transistors in electronics, electric field controlled magnetization dynamics has emerged as an important integrant in low-power spintronic devices. Here, we demonstrate electric field induced parametric excitation for CoFeB/MgO junctions by using interfacial in-plane magnetic anisotropy (IMA). When the IMA and the external magnetic field are parallel to each other, magnons are efficiently excited by electric field induced parametric resonance. The corresponding wavelengths are estimated to be tuned down to exchange interaction length scales by changing the input power and frequency of the applied voltage. A generalized phenomenological model is developed to explain the underlying role of the electric field torque. Electric field control of IMA is shown to be the origin for excitation of both uniform and parametric resonance modes in the in-plane magnetized sample, a crucial element for purely electric field induced magnetization dynamics. Electric field excitation of exchange magnons, with no Joule heating, offers a good opportunity for developing nanoscale magnonic devices and exploring various nonlinear dynamics in nanomagnetic systems.

Figure 1

(a) Schematic showing the orientation of the perpendicular magnetic anisotropy field $H_p$ and in-plane magnetic anisotropy field $H_k$. Magnetization $M$ is taken parallel to magnetic field $H_{\mathrm{ex}}$ applied at an elevation angle θ and azimuthal angle ϕ. A microwave voltage is applied at the CoFeB/MgO junction using an input power $P_{\mathrm{in}}$. Spin current $J_s$ is pumped and then converted into charge current $J_c$ due to inverse spin Hall effect of the Ta layer. (b) Optical image of the sample used in this paper. The top electrode on MgO is marked as T, and the bottom electrodes of the Ta layer are marked as B. The rectified voltage from $J_c$, i.e., $V_{\mathrm{ISHE}}$, is detected across the Ta/Ru/Ta underlayer.

Figure 2

(a) Inverse spin Hall voltage $V_{\mathrm{ISHE}}$ as a function of external magnetic field $H_{\mathrm{ex}}$ for different input powers $P_{\mathrm{in}}$ at a frequency $f=3\mathrm{GHz}$, when $H_{\mathrm{ex}}$ is applied along $\theta =\varphi =0{}^{\circ }$. (b) Resonance field $H_{\mathrm{res},1}^{}$ of the ferromagnetic resonance mode as a function of $P_{\mathrm{in}}$ at $f=3\mathrm{GHz}$. (c) $V_{\mathrm{ISHE}}$ spectra, at high power $P_{\mathrm{in}}=0.3\mathrm{W}$, for $f=2–5\mathrm{GHz}$. (d) $f$ as a function of $H_{\mathrm{res}}$ (for $H_{\mathrm{res},1}^{}$ and $H_{\mathrm{res},2}^{}$). The experimental data are fitted with the Kittel equation (lines).

Figure 3

(a) Threshold power of parametric excitation modes as a function of $H_{\mathrm{ex}}$ for $f=2–4\mathrm{GHz}$. (b) Corresponding magnon wavelengths, calculated using Eq. (1), as a function of $H_{\mathrm{ex}}$ for $f=2–4\mathrm{GHz}$.

Figure 4

Amplitude of $V_{\mathrm{ISHE}}$ as a function of input power $P_{\mathrm{in}}$, for different $H_{\mathrm{ex}}$, at frequencies (a) 2 GHz and (b) 3 GHz. Gray and red lines are linear fits to $P_{\mathrm{in}}$, while blue and green lines are quadratic fits to $P_{\mathrm{in}}$.

Figure 5

(a) Dependence of $V_{\mathrm{ISHE}}$ amplitude on azimuthal angle ϕ, at ${\mu }_0{H}_{\mathrm{ex}}=36\mathrm{mT}$, for input power $P_{\mathrm{in}}=0.001\mathrm{W}$ and $f=2\mathrm{GHz}$. The experimental data are fitted with Eq. (4). (b) Dependence of $V_{\mathrm{ISHE}}$ amplitude on azimuthal angle ϕ, at ${\mu }_0{H}_{\mathrm{ex}}=11.5\mathrm{mT}$, for input power $P_{\mathrm{in}}=0.280\mathrm{W}$ and $f=2\mathrm{GHz}$. The experimental data are fitted with $\mathrm{co}{\mathrm{s}}^3\varphi$.

Figure 6

(a) Inverse spin Hall effect voltage $V_{\mathrm{ISHE}}$ spectrum at $f=3\mathrm{GHz}$ for an in-plane $H_{\mathrm{ex}}$ along $\varphi =40$ degree. The experimental data are fitted with Lorentzian function (line) to obtain $H_{\mathrm{res},1}^{}$. (b) Azimuthal angle ϕ dependence of $H_{\mathrm{res},1}^{}$ for $f=3\mathrm{GHz}$. Sinusoidal dependence shows the presence of an in-plane anisotropy in addition to the perpendicular magnetic anisotropy. The experimental data are fitted with Eq. (A1) (line) to obtain $H_k^{}$ and $H_p^{}$.

Figure 7

(a) Experimental setup used for detecting rectified voltage across heavy metal underlayer. A $z$-axial microwave field $h_{\mathrm{rf},z}$ is generated by a coplanar waveguide near the multilayer strip, and a magnetic field $H_{\mathrm{ex}}$ is applied in the in-plane direction. (b) Rectified voltage spectra (circles) obtained for a microwave frequency of 8 GHz. Lines are fits to the experimental data using the Lorentzian function. (c) Amplitude of the Lorentzian $L$ component (circles) as a function of in-plane azimuthal angle ϕ, fitted (line) using cosϕ. (d) Typical $V_{\mathrm{ISHE}}$ spectra for different input power $P_{\mathrm{in}}$ ranging from 0.001 to 0.631 W ($f=2\mathrm{GHz}$). (e) $V_{\mathrm{ISHE}}$ amplitudes and (f) resonance field $H_{\mathrm{res}}$ as a function of the input power. Linear fit (gray line) to the experimental data in Fig. 7 implies a linear excitation regime, and the arrow in Fig. 7 indicates the transition from linear to nonlinear excitation regime.

Figure 8

(a)–(f) Typical $V_{\mathrm{ISHE}}$ spectra at $f=2\mathrm{GHz}$ for different values of input power $P_{\mathrm{in}}$ ranging from 8.5 to 11.5 dBm. Magnetization is oriented along the $x$ axis by applying $H_{\mathrm{ex}}$ along $\theta =\varphi =0{}^{\circ }$.

Figure 9

Schematic to show the quantities described in the derivation. In the experiment, the external magnetic fields $H_{\mathrm{ex}}$ are applied in the film plane (elevation angle $\theta =0{}^{\circ }$). Due to voltage controlled magnetic anisotropy (VCMA) or Oersted fields, there will be a torque τ on the magnetization. As a result, it will oscillate $m_{\mathrm{ac}}$ around $H_{\mathrm{ex}}$ during resonance, with a cone angle ${\theta }_c$. Spin current $J_s$ with a polarization $s$ is pumped into the Ta layer from the CoFeB layer, which decays as it enters deeper inside the Ta layer. This decay (dashed orange curve) is characterized by the spin diffusion length ${\lambda }_{\mathrm{sd}}$.

Figure 10

(a) 20 nm $\mathrm{Ta}/2\mathrm{nm} \mathrm{CoFeB}/2\mathrm{nm} \mathrm{MgO}/10\mathrm{nm} {\mathrm{Al}}_2{\mathrm{O}}_3$ multilayer structure with size $1\times 0.1\mu {\mathrm{m}}^2$ discretized into triangular mesh elements of size $\sim 10\mathrm{nm}$. (b) Electric field distribution in the multilayer structure when a power of 10 μW is applied on the top surface is color coded as a function of thickness, while the corresponding magnetic field is shown as arrows. Normalized Oersted field distribution (arrows) is shown for samples with $l:w=$ (c) 1:1, (d) 1:5, and (e) 1:10. (f) The microwave field direction (arrows) and amplitude of $h_{\mathrm{rf},y}$ (color scale) in case of a sample with same $l:w$ as the experimental device, i.e., 1:12.

Figure 11

(a) Typical $S_{11}$ spectra of the sample in this paper. Lines are fits to the experimental data using $S_{11}=\frac{Z-50\mathrm{\Omega }}{Z+50\mathrm{\Omega }}$. (b) Schematic of the equivalent circuit of the sample in this measurement. (c) Normalized efficiencies calculated for the electric field torque and the Oersted field toque as a function of frequency of $P_{\mathrm{in}}$.

Figure 12

(a) Rectified voltages for 2 and 4 GHz at $\varphi =0{}^{\circ }$ and 40 °. (b) Dependence of normalized $V_{\mathrm{ISHE}}$ on ϕ for 4 GHz. The experimental data are fitted using Eq. (4).