Microwave-Assisted Switching of Microscopic Rings: Correlation Between Nonlinear Spin Dynamics and Critical Microwave Fields

We have studied the spin dynamics of microscopic permalloy rings at GHz frequencies. Increasing the irradiation power, we observe first nonlinear spin dynamics and second microwave-assisted switching (MAS). We explore the MAS phase diagram as a function of microwave power and frequency $f$ and, in particular, extract the critical microwave field $h_c(f)$. Its frequency dependence reflects characteristic eigenfrequencies from both the linear and nonlinear spin-wave spectrum. By comparing $h_c(f)$ with the different susceptibilities, we gain insight into the microscopic processes which might be the basis of a predictive theory of MAS.

Figure 1

Color-scaled absorption spectra taken on rings with $w=500\mathrm{nm}$ at (a) constant VNA power $P=-10\mathrm{dBm}$ and successively decreasing magnetic field, (b) constant field ${\mu }_{0}H=-11.1\mathrm{mT}$ (initializing the vortex state) for increasing VNA output power $P$. Labels highlight strong absorption (spin wave eigenmodes). In (a), spectra were taken after saturation at ${\mu }_{0}H=+90\mathrm{mT}$. Here, white dotted vertical lines indicate switching fields. Modes $A$’, $I$ ($A$, $B$) are characteristic for the vortex (onion) state. [8] In (b), modes $A^{*}$ and $B^{*}$ indicate that microwave assisted switching into the onion state has occurred beyond $P^s\ge 6.5\mathrm{dBm}$ (vertical dotted line). (c) Individual spectra extracted from (b) at the depicted black vertical lines. Spectra are offset for clarity.

Figure 2

(a) Spectra measured at $P=-10\mathrm{dBm}$ and ${\mu }_{0}H=-9.2\mathrm{mT}$ after two different irradiation experiments performed at ${\mu }_{0}H=-11.1\mathrm{mT}$: full line—$f=2\mathrm{GHz}$, $P=75\mathrm{mW}$, and ${\mu }_0{h}_{\mathrm{rf}}=12.4\mathrm{mT}$, the rings switched to the reversed onion state; dotted line—$f=8.5\mathrm{GHz}$, $P=0.2\mathrm{mW}$, and ${\mu }_0{h}_{\mathrm{rf}}=0.7\mathrm{mT}$, the rings remained in the vortex state. (b) Histogram summarizing all the evaluated peak differences in 8450 MAS experiments performed on sample 1. (c) Phase diagram for switching to the reversed onion state (above) from the vortex state (below the white line) at ${\mu }_{0}H=-11.1\mathrm{mT}$. The magnetization states and orientation of $H$ are illustrated in the inset. The white line indicates the phase boundary (critical microwave field) $h_c(f)$ where more than 10 rings have switched.

Figure 3

(a,b) Inverse critical microwave field $h_{c,\min }/h_c$ (black) compared to magnetic susceptibilities $\chi$ (gray) measured via broadband VNA transmission spectroscopy for (a) 500 nm at $-11.1\mathrm{mT}$ and (b) 700 nm wide rings at $-9.2\mathrm{mT}$. (c) $h_{c,\min }/h_c$ for different static fields $H$ in the vortex state of sample 2, i.e., for different effective energy-barrier heights. Labels are explained in the text.