Influence of interlayer coupling on the spin-torque-driven excitations in a spin-torque oscillator

The influence of dynamic interlayer interactions on the spin-torque-driven and damped excitations are illustrated for a three layer macrospin model system that corresponds to a standard spin-torque oscillator. The free layer and a synthetic antiferromagnetic (SyF) pinned layer of the spin-torque oscillator are in-plane magnetized. In order to understand experimental results, numerical simulations have been performed considering three types of interlayer interactions: exchange interaction between the two magnetic layers of the SyF, mutual spin torque between the top layer of the SyF and the free layer and dipolar interaction between all three magnetic layers. It will be shown that the dynamic dipolar coupling plays a predominant role. First, it leads to a hybridization of the free layer and the SyF linear modes and through this gives rise to a strong field dependence of the critical current. In particular, there is a field range of enhanced damping in which much higher current is required to drive the modes into steady state. This results in a gap in the excitation spectrum. Second, the dynamic dipolar interaction is also responsible for the non-linear interaction between the current driven steady state mode and the damped modes of the system. Here one can distinguish: (i) a resonant interaction that leads to a kink in the frequency-field and frequency-current dispersions accompanied by a small hysteresis and a reduction of the linewidth of the steady state mode and (ii) a non-resonant interaction that leads to a strong frequency redshift of the damped mode. The results underline the strong impact of interlayer coupling on the excitation spectra of spin-torque oscillators and illustrate in a simple three mode model system how in the non-linear regime the steady state and damped modes influence each other.

Figure 1

(a) Magnetoresistance loop of the device measured at low current. (b) Experimental state diagram where blue color represents static antiparallel state and red color represents large angle dynamic excitations. Green color corresponds to a region of low power excitations in the transition region around the critical current. (c) Frequency field dispersions at $j_{\mathrm{app}}=0.15\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ (black curve) and $j_{\mathrm{app}}=0.22\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ (red curve), obtained for an elliptical pillar with axis dimensions of 140×70 nm at room temperature. (d) Range of field where excitations vanish (gap size) as a function of the applied current for positive (green symbols) and negative (red symbols) current polarities.

Figure 2

(a)–(c) (top) Frequency-field dependence of the three linear modes of the coupled system (red, green, and violet symbols, respectively) at different positive currents. Full symbols represent frequencies of the linear eigenmodes (i.e., negative attenuation), while continuous lines in (b) and (c) are guides to the eye to highlight the modes that are in steady state (note that the real frequency of the steady state mode will be redshifted). Dashed black and blue lines in (a) represent the frequency of the free layer and the SyF in the uncoupled (independent) picture. (a)–(c) (bottom) Field dependence of the attenuation of the three linear modes. Dashed black and blue lines in a represent attenuation of a single noninteracting free layer and a SyF in the uncoupled (independent) picture. (d) The FFT of the simulated $M_y$ component of the FL (1–3) and SyF (4–6) upon increasing field for $j_{\mathrm{app}}=0$, numerically solving the three layer coupled LLG equation at $T=400\mathrm{K}$.

Figure 3

(a)–(c) (top) Frequency-field dependence of the three linear modes of the coupled system (red, green, and violet symbols, respectively) at different negative currents. Full symbols represent frequencies in the linear regime (i.e., negative attenuation), while continuous lines in (c) are guides to the eye to highlight the modes that are in steady state (note that the real frequency of the steady state mode will be shifted). (a)–(c) (bottom) Field dependence of the attenuation of the linear modes. (d) Numerical state diagram obtained by linearization of the LLG equations. Gray color represents stable static state, and red color represents instability of the static state (numbers indicate which mode is excited in each region). Yellow lines represent critical current of our three coupled layers system, and white lines represent critical current when dynamic dipolar field is not taken into account.

Figure 4

(a) Experimental steady state frequency-field dispersion at $j_{\mathrm{app}}=0.32\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ and (b) experimental spectra at $H=300\mathrm{Oe}$.

Figure 5

Evolution of the simulated frequency field dispersion of the steady state at 400 K upon increasing current for $j_{\mathrm{app}}=0.4$, 0.7, and $0.9\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ (black, blue, and red symbols, respectively).

Figure 6

(a), (b) Detail of the frequency behavior around the kink/jump effect for $j_{\mathrm{app}}=0.8\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$, obtained (a) at $T=0\mathrm{K}$ in both sweeping directions of the applied field and (b) at $T=400\mathrm{K}$. (c) Simulated FFT spectra obtained at $j_{\mathrm{app}}=0.9\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ at different fields in the low (left) and high (right) frequency range. (d), (e) Variation of the trajectories at a constant field of $H=1250\mathrm{Oe}$ upon increasing current, just before and after the jump: (d) corresponds to the lower frequency branch $(j_{\mathrm{app}}=0.88\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2)$ and (e) to the upper frequency branch $(j_{\mathrm{app}}=0.86\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2)$.

Figure 7

Frequency-time spectrogram obtained from the $M_y$ of the FL at $T=400\mathrm{K}$.

Figure 8

Frequency-field dispersion of the damped mode 1 at $j_{\mathrm{app}}=0\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ (red line) and under application of positive current $j_{\mathrm{app}}=0.7$, 0.8, and $0.9\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$ (color dot symbols).