Autonomous and forced dynamics in a spin-transfer nano-oscillator: Quantitative magnetic-resonance force microscopy

Using a magnetic-resonance force microscope (MRFM), the power emitted by a spin-transfer nano-oscillator consisting of a normally magnetized Py$|$Cu$|$Py circular nanopillar is measured both in the autonomous and forced regimes. From the power behavior in the subcritical region of the autonomous dynamics, one obtains a quantitative measurement of the threshold current and of the noise level. Their field dependence directly yields both the spin torque efficiency acting on the thin layer and the nature of the mode which first auto-oscillates: the lowest energy, spatially most uniform spin-wave mode. From the MRFM behavior in the forced dynamics, it is then demonstrated that in order to phase lock this auto-oscillating mode, the external source must have the same spatial symmetry as the mode profile, i.e., a uniform microwave field must be used rather than a microwave current flowing through the nanopillar.

Figure 1

Phase diagram of the STNO autonomous dynamics measured by MRFM.

Figure 2

(a) Determination of the threshold current $I_{\mathrm{th}}$ and noise power $\eta$ at $H_{\mathrm{ext}}=10$ kOe, from the inverse MRFM signal in the subcritical regime. Dependencies of the threshold current (b) and noise power (c) on the perpendicular magnetic field.

Figure 3

MRFM measurement of the STNO dynamics forced by (a) the uniform field $h_{\mathrm{rf}}$ at 8.1 GHz and (b) the orthoradial Oersted field produced by $i_{\mathrm{rf}}$ at 9.2 GHz, as a function of $I_{\mathrm{dc}}$ and $H_{\mathrm{ext}}$. The black traces show the MRFM signal vs $I_{\mathrm{dc}}$ at $H_{\mathrm{ext}}=8.8$ kOe. The pink solid lines show the location of the threshold current determined in Fig. 2b. The dashed lines are guides to the eye.

Figure 4

(a) Magnetic field dependence of the STNO frequency in the free and forced regimes (the external source at 8.1 GHz is $h_{\mathrm{rf}}$). (b) Comparison between the STNO frequency shift deduced from (a) and the MRFM signal.