Spin-Current-Driven Permeability Variation for Time-Varying Magnetic Metamaterials

We study permeability ($\mu$) variation of a lithographically prepared magnetic meta-atom consisting of $\mathrm{Ta}$/Py/$\mathrm{Pt}$ trilayers by means of spin-torque ferromagnetic resonance (ST FMR). With an injection of a direct current up to $\pm 20\mathrm{mA}$ together with an alternating current in GHz frequencies, the meta-atom under external magnetic fields shows significant changes in position and width of ST FMR signals due to a massive spin-current injection. This leads to the spin-current-driven $\mu$ variation, which is verified by analytical calculation based upon the experimentally obtained resonance field and Gilbert-damping parameter. The present study paves a way to time-varying spintronic metamaterials with a high modulation frequency for realizing microwave sources toward the post-fifth-generation mobile-communication system.

Figure 1

Schematic illustration of the magnetic meta-atom of the $\mathrm{Ta}$/Py/$\mathrm{Pt}$ trilayer with spin-torque ferromagnetic resonance measurement setup. Inset: photograph of the lithographically prepared magnetic meta-atom.

Figure 2

(a) Measured spin-torque ferromagnetic resonance signal, $V_{\mathrm{AMR}}$, as a function of external magnetic field, ${\mu }_0{H}_{\mathrm{ext}}$, at 6 GHz without direct electric current (red circles). Green and blue solid lines represent fitting results with symmetric ($V_S$) and antisymmetric coefficient ($V_A$), respectively. The black solid line corresponds to the sum of $V_S$ and $V_A$. (b) Red circles: microwave frequency plotted as a function of resonance magnetic field, ${\mu }_0{H}_{\mathrm{FMR}}$. Solid line: fitting curve by the Kittel equation [Eq. (2)]. Inset: trilayer’s saturation magnetic flux density, ${\mu }_0{M}_s$, measured by VSM plotted as a function of Py thickness.

Figure 3

Spin-torque ferromagnetic resonance signals with 6-GHz alternative electric currents measured at various direct electric currents, $I_{\mathrm{dc}}$ from $-20$ to $+20\mathrm{mA}$ with intervals of 2 mA.

Figure 4

Ferromagnetic resonance signal line width, ${\mu }_0{\mathrm{\Delta }}_{\mathrm{FMR}}$, at various direct electric currents, $I_{\mathrm{dc}}$, from $-20\mathrm{mA}$ to $+20\mathrm{mA}$ as a function of $\omega /2\pi$. Solid and dashed lines are fitting curves.

Figure 5

(a) $\alpha$ (open circles, left axis) and ${\mu }_0{H}_{\mathrm{FMR}}^{\mathrm{shift}}$ (open squares, right axis) are plotted as a function of $I_{\mathrm{dc}}$. (b) ${\mu }_0{H}_{\mathrm{intrinsic}}^{\mathrm{shift}}$ (open triangles) is plotted as a function of $I_{\mathrm{dc}}$.

Figure 6

Two-dimensional (2D) plot of (a) ${\mu }_r^{\prime }$ and (b) ${\mu }_r^{″}$ evaluated using experimentally obtained $\alpha$ and ${\mu }_0{H}_{\mathrm{FMR}}$ of meta-atom under dc magnetic field of 58.4 mT as a function of $\omega /2\pi$ and $I_{\mathrm{dc}}$. Black dashed lines indicate $\omega /2\pi =5.74\mathrm{GHz}$. (c) $I_{\mathrm{dc}}$ versus ${\mu }_r^{\prime }$ (red solid line) and ${\mu }_r^{″}$ (blue solid line) at 5.74 GHz indicated by black dashed lines in (a),(b).