Spin-Transfer-Driven Ferromagnetic Resonance of Individual Nanomagnets

We demonstrate a technique that enables ferromagnetic resonance measurements of the normal modes for magnetic excitations in individual nanoscale ferromagnets, smaller in volume by more than a factor of 50 compared to individual ferromagnetic samples measured by other resonance techniques. Studies of the resonance frequencies, amplitudes, linewidths, and line shapes as a function of microwave power, dc current, and magnetic field provide detailed new information about the exchange, damping, and spin-transfer torques that govern the dynamics in magnetic nanostructures.

Figure 1

(a) Room-temperature magnetoresistance as a function of field perpendicular to the sample plane. Inset: Cross-sectional sample schematic, with arrows denoting a typical equilibrium moment configuration in a perpendicular field. (b) Schematic of circuit used for FMR measurements. (c) FMR spectra measured at several values of magnetic field, at $I_{\mathrm{dc}}$ values (i) 0, (ii) $150\mu \mathrm{A}$, and (iii) $300\mu \mathrm{A}$, offset vertically. Symbols identify the magnetic modes plotted in (d). Here $I_{\mathrm{rf}}=300\mu \mathrm{A}$ at 5 GHz and decreases by $\sim 50\%$ as $f$ increases to 15 GHz [10]. (d) Field dependence of the modes in the FMR spectra. The solid line is a linear fit, and the dotted line would be the frequency of completely uniform precession.

Figure 2

Comparison of FMR spectra to dc-driven precessional modes. (a) Spectral density of dc-driven resistance oscillations for different values of $I_{\mathrm{dc}}$ (labeled), with ${\mu }_{0}H=370\mathrm{mT}$ and $I_{\mathrm{rf}}=0$. (b) FMR spectra at the same values of $I_{\mathrm{dc}}$, measured with $I_{\mathrm{rf}}=270\mu \mathrm{A}$ at 10 GHz. The high-$f$ portions of the $305\mu \mathrm{A}$, $445\mu \mathrm{A}$, and $505\mu \mathrm{A}$ traces are amplified to better show small resonances. The $I_{\mathrm{dc}}=0$ curve is the same as in Fig. 1c.

Figure 3

(a) FMR peak shape for mode $A_0$ at $I_{\mathrm{dc}}=0$ and different values of $I_{\mathrm{rf}}$: from bottom to top, traces 1–5 span $I_{\mathrm{rf}}=80–340\mu \mathrm{A}$ in equal increments, and traces 5–10 span $340–990\mu \mathrm{A}$ in equal increments. (b) Bottom curve: spectral density of dc-driven resistance oscillations for mode $A_0$, showing a peak with a half width at half $\mathrm{\text{maximum}}=13\mathrm{MHz}$. Top curve: FMR signal at the same bias conditions, showing the phase-locking peak shape. Inset: Evolution of the FMR peak for mode $A_0$ at 370 mT, $I_{\mathrm{dc}}=0$, for $I_{\mathrm{rf}}$ from $30\mu \mathrm{A}$ to $1160\mu \mathrm{A}$. (c) Evolution of the FMR signal for mode $A_0$ in the phase-locking regime at $I_{\mathrm{dc}}=0.5\mathrm{mA}$, ${\mu }_{0}H=370\mathrm{mT}$, for (bottom to top) $I_{\mathrm{rf}}$ from 12 to $370\mu \mathrm{A}$, equally spaced on a logarithmic scale. (d) Results of macrospin simulations for the dc-driven dynamics and the FMR signal [10].

Figure 4

(a) Detail of the peak shape for mode $A_0$, at $I_{\mathrm{dc}}=0$, $I_{\mathrm{rf}}=180\mu \mathrm{A}$, ${\mu }_{0}H=535\mathrm{mT}$, with a fit to a Lorentzian line shape. (b) Dependence of linewidth on $I_{\mathrm{dc}}$ for modes $A_0$ and $B_0$, for ${\mu }_{0}H=535\mathrm{mT}$. For the PyCu layer mode $A_0$, ${\Delta }_0/f_0$ is equal to the magnetic damping $\alpha$. The critical current is $I_c=0.40\pm 0.03\mathrm{mA}$ at ${\mu }_{0}H=535\mathrm{mT}$, as measured independently by the onset of dc-driven resistance oscillations.