Nonresonant spin rectification in the absence of an external applied magnetic field

A spin rectification effect due to the nonresonant magnetization motion has been found, which differs from the previously known spin rectification effect caused by the resonant magnetization precession at ferromagnetic resonance. A phase-resolved electrical detection technique has been used to measure the phase lag between the magnetization response and the driving microwave magnetic field, which demonstrates unambiguously the distinction between the resonant and nonresonant rectification effects.

Figure 1

(a) The schematic diagram of the experimental setup, where the microwave power is split into two parts and forms a spintronic Michelson interferometer.[18] (b) Magnetoresistance for several orientations ${\theta }_H$ of $H$ relative to the current direction. Arrows indicate the anisotropic field $H_A$. The open symbols are experimental data and solid curves are calculated using $R(0)=121.53$ $\Omega$, $\Delta R=0.66$ $\Omega$, and $H_A=8.0$ mT. (c) A typical PV spectrum at ${\theta }_H=75$ deg and $\omega /2\pi =4.8$ GHz. Two kinds of motion have been indicated by the diagrams: magnetization rotation (MR) and magnetization precession at the FMR.

Figure 2

(a) Typical spectra of PV for several ${\theta }_H$ at $\omega /2\pi =4.8$ GHz. For $\omega /2\pi =45$ deg open symbols and the solid curve are experimental data and fitting results, respectively. (b) The frequency of FMR as a function of $H$ at ${\theta }_H=45$ deg. The solid curves are the calculation according to $\omega {}^2=\gamma {}^2\left|H_r\right|(M_0+|H_r|)$. (c) The deduced contribution of symmetric Lorentz line shape (circles) and antisymmetric Lorentz line shape (squares) as a function of ${\theta }_H$ at $\omega /2\pi =4.8$ GHz, and the solid and dashed curves are $\sin (2{\theta }_H)\cos {\theta }_H$ functions.

Figure 3

(a) PV spectra at $\Phi =-90$, $0$, and $90$ deg. The orientation of $H$ is fixed at ${\theta }_H=75$ deg. (b) Two-dimensional PV amplitude mapping by varying both $H$ and $\Phi$. (c) The normalized PV spectra as a function of $\Phi$ for several $H$. For clarity, the phase shift is indicated by the arrows. (d) Measured (symbols) and calculated (solid curves) ferromagnetic resonance phase $\Theta$, that is, phase lag of the dynamic magnetization response relative to the driving $h$ field, as a function of $H$.

Figure 4

Magnetization switching detected by (a) resistance and (b) PV at ${\theta }_H=0^{°}$. Arrows indicate the sweeping direction of the $H$ field. The inset shows the angular dependence of the switching field from $R$ data (open triangles), PV data (open circles), and theoretical results based on the Kondorsky model (solid line) (i.e., $1/\cos {\theta }_H$ dependence).