DC voltage generated by the unidirectional spin Hall magnetoresistance in the spin torque ferromagnetic resonance spectrum

Abstract

Spin torque ferromagnetic resonance (ST-FMR)1 has widely been used for evaluation of the spin Hall effect (SHE) of the nonmagnetic metal (NM) in an NM/ferromagnetic metal (FM) bilayer structure. Figure 1 shows a schematic of the measurement setup of the ST-FMR. DC voltage, VDC, is monitored under a microwave irradiation with sweeping the external magnetic field, Bext. VDC-Bext curve in the ST-FMR measurement is composed of symmetric and anti-symmetric Lorentzian functions. In the simplest case, efficiency of the SHE, which is especially called spin Hall angle (SHA), can be estimated by taking the amplitude ratio between two Lorentzian functions. However, unwanted effects such as the spin pumping, the anomalous Nernst effect, and non-uniform flow of the charge current impede a precise estimation of SHA. Therefore, a cross-check of the obtained SHA by using another methodology is desired.In this study, we found an additional signal related to the SHA in the ST-FMR spectrum2. Figure 2 shows the ST-FMR spectrum of a tantalum (Ta)/cobalt (Co) sample, where the microwave frequency, f, was 12 GHz and the microwave power, P, was 5 dBm. l, w, and q defined as shown in Fig. 1 were 5 μm, 5 μm, and 45°, respectively. In addition to the conventional Lorentzian functions which correspond to the ST-FMR, a magnetization-dependent background (BG) signal was also observed. From the Bext, P, f , temperature and NM material dependences, we conclude that the BG signal is mainly generated by the spin-dependent unidirectional spin Hall magnetoresistance (SD-USMR)3, the origin of which is the spin-dependent electron mobility in the FM. From the magnitude of the BG signal, SHA of Ta was estimated to be -0.042±0.006, which is consistent with the previous works. The ST-FMR spectrum is produced by the spin orbit torque, whereas the BG signal is produced by the spin accumulation. Therefore, our finding provides an effective cross-check of the SHA, which are obtained from two different physical origins by using only one ST-FMR spectrum.  A schematic of the device and the electrical circuit used in the ST-FMR measurement  ST-FMR spectra with the BG signal originating from the SD-USMR for Ta/Co.