Temperature dependence of linewidth in nanocontact based spin torque oscillators: Effect of multiple oscillatory modes

We discuss the effect of mode transitions on the current ($I$) and temperature ($T$) dependent linewidth ($\Delta f$) in nanocontact based spin torque oscillators (STOs). At constant $I$, $\Delta f$ exhibits an anomalous temperature dependence near the mode transitions; $\Delta f$ may either increase or decrease with $T$ depending on the position w.r.t. the mode transition. We show that the behavior of $\Delta f$ as a function of $I$ can be fitted by the single mode analytical theory of STOs, even though there are two modes present near the mode transition, if the nonlinear amplification is determined directly from the experiment. Using a recently developed theory of two coupled modes, we show that the linewidth near mode transition can be described by an “effective” single-oscillator theory with an enhanced nonlinear amplification that carries additional temperature dependence, which thus qualitatively explain the experimental results.

Figure 1

(a) Two-dimensional power spectral density map of $f$ versus $I$ at a magnetic field of ${\mu }_{0}H=1$ T, applied at an angle of ${80}^{\circ }$ to the film plane. Top inset shows two examples of mode transitions at $I=30.2$ mA and 35.3 mA respectively, where the left spectrum has two clearly resolved Lorentzian peaks, and the right spectrum shows a single broader, asymmetric peak that can still be well fitted by two Lorentzian functions. The bottom inset shows the inverse power $1/p$ vs current and a linear fit (solid line). (b) Experimentally measured (red triangles) and calculated $\Delta f$ (blue solid line). The black dashed line represents a linear fit to linewidth using Eq. (1) for subthreshold currents.

Figure 2

Map of frequency of the strongest mode versus temperature and bias $I$, showing the mode transition with temperature. The solid lines are linear fits to the threshold current for the mode transitions $I_1$ and $I_2$ versus temperature. The dotted lines are the positions at which the behavior of the linewidth is discussed in Fig. 3.

Figure 3

Measured linewidth versus temperature at (a) 28.4 mA, (b) 29.4 mA, and (c) 30.3 mA. The solid black circles (respectively the solid blue squares) denote the mode excited below (above) $I_2=30$ mA at room temperature. (d) Integrated power versus temperature at 28.4 mA (solid black circles), 29.4 mA (open symbols), and 30.3 mA (solid blue squares). The dashed lines serve as visual aids.

Figure 4

Temperature dependence of (a) extracted linear contribution of linewidth $\Delta f_{\mathrm{L}}$ (solid symbols) and (b) the nonlinear amplification, $(1+{\nu }^2)$ (solid and open symbols). The solid red lines are calculation based with inclusion of temperature dependence of $M_{\mathrm{s}}$, whereas the dashed blue lines are calculation assuming no temperature dependence of $M_{\mathrm{s}}$.

Figure 5

Map of power (dB) vs frequency ($f$) and temperature $T$ for the three example current values of 28.4 mA, 29.4 mA, and 30.3 mA. The arrows indicate the presence of additional modes, the amplitude of which depends on temperature.