Parametric Harmonic Generation as a Probe of Unconstrained Spin Magnetization Precession in the Shallow Barrier Limit

We study the parametric excitation of high orders of magnetization precession in ultrathin films having perpendicular magnetic anisotropy. We observe that for a given driving field amplitude the harmonic generation can be increased by lowering the barrier with the application of an in-plane magnetic field in the manner of the Smit-Beljers effect. In this effect, the magnetic stiffness is reduced not by lowering the magnitude of the magnetic field upon which the spins precess, but rather by effectively releasing the field’s “anchoring” point. This results in a shallow energy barrier where the electrons’ spin is locally unconstrained. While the observation is unveiled in the form of nonlinear high harmonic generation, we believe that the physics whereby the barrier is suppressed by an external magnetic field may apply to other phenomena associated with ultrathin films. In these cases, such unconstrained motion may serve as a sensitive probe of the torques associated with proximate spin currents. Moreover, our approach may be used as a model system for the study of phase transitions in the field of nonlinear dynamics.

Figure 1

(a) Experimental setup. Inset illustrates a scanning electron microscope micrograph of the microwire and the patterned magnetic island. (b) Magnetization response versus magnetic field at 10.5 GHz and microwave power of 20 dBm. (c) Temporal magnetization traces across black, blue, and red lines of (b). (d) Measured and calculated frequency dispersion relation.

Figure 2

(a) Magnetization response for $H_0=H_{\text{keff}}$ at 1 GHz and microwave power of 20 dBm. (b) Magnetization response vs magnetic field at 1 GHz and power of 29 dBm. (c) Magnetization responses corresponding to black, blue, and red lines of (b). Calculated response for the field of 1400 Oe is marked by the black dashed line. (d) Spectra of the temporal responses presented in (c). Traces are normalized to peak value. (e) Magnetic field dependence of the spectra. Spectra are normalized to value at the peak. (f) ${\eta }_z^2$ (blue) together with the measured (red circles) and calculated (black dashed line) resonance frequency dispersion relation. (g) Potential energy. Inset indicates the angle $\mathrm{\Delta }\theta$.

Figure 3

Conversion efficiency at different frequencies (green). Red crosses indicate the operating points at which this measurement was performed. Red circles and dashed black line are the previously measured and calculated dispersion relation of Fig. 1, respectively.

Figure 4

(a) Power-dependent temporal magnetization responses. (b) Dependence of fundamental and second harmonics on microwave field amplitude. (c) Efficiency as a function of microwave field amplitude.