Spinmotive force in the out-of-plane direction generated by spin wave excitations in an exchange-coupled bilayer element

The generation of the spinmotive force (SMF) requires the temporal and spatial variations of the magnetic moments. We explore an approach to satisfy this requirement by creating asymmetry in a thin film structure along the out-of-plane direction, through the use of an exchange-coupled $L{1}_0-\mathrm{FePt}/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ bilayer element. As the spin wave is excited by a rf magnetic field, a continuous dc voltage signal in the out-of-plane direction of the bilayer element appears. The sign of the voltage signal and its microwave power dependency agree with the theoretical framework of the SMF. The corresponding spin wave modes are revealed by carrying out the micromagnetic simulation. Our results demonstrate the generation of the SMF using a vertically structured element in addition to previously reported in-plane structured devices.

Figure 1

(a) Schematic illustration of the device structure and measurement setup. The reference signal of the lock-in amplifier (LIA) is fed into the signal generator (SG) for amplitude modulation (AM). $I_{\text{rf}}$ passes through the short end of the coplanar waveguide (CPW) and generates $h_{\text{rf}}$ to excite the spin wave in the $L{1}_0$-FePt/Py bilayer element. The red arrow indicates the direction of $H$, which is aligned to the $y$ axis. The voltage signal between the top and bottom of the bilayer element is captured by LIA. (b) Microscopic image of the device. Two bilayer elements in two separate measurement circuits with the top and bottom electrodes are placed at the top of the image, facing the short end of the CPW. Magnification of a bilayer element is shown in the inset of (b).

Figure 2

(a) Experimentally measured $U-H$ curves under the microwave power application of 20 dBm with $f=17$, (b) 16, (c) 15, and (d) 14 GHz. (e) The ferromagnetic resonance (FMR) spectra of the bilayer element calculated by micromagnetic simulation under $h_{\text{rf}}$ of 45 Oe with $f=17$, (f) 16, (g) 15, and (h) 14 GHz. The vertical axes of (e)—(h) are inverted for comparison with the $U-H$ curves. The black squares in (g) mark the conditions for the results shown in Fig. 3.

Figure 3

(a) Snapshot of the top Py surface for $m_{\text{x}}$ under $H=1.86\mathrm{kOe}$ along the $y$ axis, and $h_{\text{rf}}=45\mathrm{Oe}$ along the $z$ axis with $f=15\mathrm{GHz}$. (b) Cross sections in the $yz$ plane as indicated by the white dashed line in (a) evolve for half the period of $h_{\text{rf}}$. (c) Plots of $m_{\text{x}}$ along the $z$ axis at the center of the model [indicated by the white dot in (a) and colored arrows in (b)] for half the period of $h_{\text{rf}}$. The black dashed line indicates the interface between FePt and Py. (d) Snapshot of the top Py surface for $m_{\text{x}}$ under $H=1.4\mathrm{kOe}$. (e) Cross sections in the $yz$ plane as indicated by the white dashed line in (d). (f) Plots of $m_{\text{x}}$ along the $z$ axis at the center of the model. (g) Snapshot of the top Py surface for $m_{\text{x}}$ under $H=1\mathrm{kOe}$. (h) Cross sections in the $yz$ plane as indicated by the white dashed line in (g). (i) Plots of $m_{\text{x}}$ along the $z$ axis at the center of the model.

Figure 4

(a) Experimentally measured $U-H$ curves with $f=15\mathrm{GHz}$ and the microwave power of 20, (b) 18, and (c) 15 dBm. (d) The FMR spectra of the bilayer element calculated by micromagnetic simulation under $h_{\text{rf}}$ of 45, (e) 35, and (f) 25 Oe with $f=15\mathrm{GHz}$. The vertical axes of (d)–(f) are inverted for comparison with the $U-H$ curves. (g) The microwave power dependence of $\mathrm{\Delta }U$ at the dips indicated by the black circles in (a)–(c). The black dashed line is a linear fitting through the origin. (h) Schematic illustrations of the SMF generation and measurement in our setup, and the corresponding plots of electrochemical potential ($\mu$) and electric potential ($\phi$) along the $z$ axis.