Electrical detection of ferromagnetic resonance in single layers of permalloy: Evidence of magnonic charge pumping

The generation of a DC voltage in single layers of permalloy (${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$) when the magnetization is undergoing ferromagnetic resonance is investigated in a series of samples with thickness varying from 4.0 to 150 nm. By sweeping the external field at a fixed microwave frequency, we measure a DC voltage at the ends of the layer as a function of the in-plane angle for each sample. The asymmetric voltage signal generated at the resonance field is a superposition of symmetric Lorentzian and antisymmetric Lorentzian derivative line shapes. The in-plane dependence of both symmetric and antisymmetric signals cannot be explained as due to spin rectification (SRE) only. The results are well explained by a model that takes into account in addition to the SRE the contribution of the recent discovered effect of magnonic charge pumping that converts magnetization dynamics into charge current by means of the spin orbit coupling.

Figure 1

(a) Field sweep DC voltage measured for the sample with $t_{\mathrm{Py}}=34$ nm and for ${\varphi }_{\mathrm{o}}=0^{\circ }$. The black solid line was obtained by combining symmetric and antisymmetric Lorenztian curves that are shown in the inset. (b) Sketch of the sample setup including the reference frames used to interpret the data.

Figure 2

Angular dependence of the DC voltage amplitudes of the symmetric and antisymmetric Lorentzian curves, for some representative samples. The solid lines were obtained by adjusting the data (symbols) from the equations of the symmetric component, $A_{\mathrm{sym}}({\varphi }_0,H)=a_{\mathrm{sym}}sin{\varphi }_{0}sin\left(2{\varphi }_0\right)+b_{\mathrm{sym}}cos{\varphi }_0$ (red lines) and antisymmetric component, $B_{\mathrm{antisym}}({\varphi }_0,H)=a_{\mathrm{antisym}}sin{\varphi }_{0}sin\left(2{\varphi }_0\right)+b_{\mathrm{antisym}}cos{\varphi }_0$ (blue lines).

Figure 3

(a) DC voltages measured in three different samples for ${\varphi }_0=0^{\circ }$ confirming the effect of the perpendicular anisotropy field on shifting the resonance and increasing the FMR line width. (b) Dependence of the surface anisotropy field as a function of $t_{\mathrm{Py}}$, extracted from the FMR field measured for each sample. The solid line was obtained by fitting with an equation $\propto t_{Py}^{-1}$. (c) Dependence of the FMR line width as a function of the $t_{\mathrm{Py}}$. Solid line was obtained as discussed in the text.

Figure 4

$V_{\mathrm{MCP}}$ data (solid squares) extracted from the measurements by means of the equation $V_{\mathrm{MCP}}=b_{\mathrm{sym}}\left[1-\left(a_{\mathrm{sym}}/b_{\mathrm{sym}}\right)\left(b_{\mathrm{antisym}}/a_{\mathrm{antisym}}\right)\right]$. The solid line was obtained by using Eq. (17) in which we used the experimental data for the effective magnetization ($M_{\mathrm{eff}}$) and the Gilbert damping (α).