Spin Hall magnetoimpedance

The recently discovered spin Hall magnetoresistance effect electrically probes pure spin current flow across a ferrimagnetic insulator/normal metal bilayer interface. While usually the dc electrical resistance of the bilayer is measured as a function of the magnetization orientation in the magnetic insulator, here we present magnetoimpedance measurements using bias currents with frequencies up to several GHz. We find that the spin Hall magnetoresistance effect is frequency independent up to frequencies of 3 GHz, corroborating the assumption of a frequency-independent spin Hall angle. Our data therefore show that all interaction time constants relevant for the spin Hall magnetoresistance effect are shorter than about 50 ps. Therefore this technique should allow for the fast readout of the magnetization direction in magnetic insulator/normal metal bilayers.

Figure 1

(a), (b) YIG/Pt bilayer bridging a gap in the Cu center conductor of a coplanar waveguide (CPW) structure shown in (a) a top view and (b) a cross-sectional drawing along the center conductor. The dimensions shown are given in mm. (c) The equivalent electrical circuit model used to describe the YIG/Pt bilayer on the CPW.

Figure 2

Frequency-dependent resistance for the ip, oopj, and oopt rotation planes. (a), (e), and (i) show a sketch of the YIG/Pt bilayer and the external magnetic field relative to the applied bias current direction. (b), (f), and (j) show $\tilde{R}$ [Eq. (8)] from frequencies of dc to 8 GHz for the respective magnetic field rotations. (c), (g), and (k) show the resistance modulation $\Delta R$ with respect to ac current frequency and the corresponding magnetic field rotation angles at a constant external magnetic field of ${\mu }_0\left|\mathbf{H}\right|=0.6\mathrm{T}$. (d), (h), and (l) show $\Delta R$ as a function of the respective rotation angles at different, fixed frequencies: dc (black line), $1\mathrm{GHz}$ (red line), $2\mathrm{GHz}$ (green line), $3\mathrm{GHz}$ (blue line), and $4\mathrm{GHz}$ (light blue line). The $\Delta R$ curves are offset for clarity.

Figure 3

The real and imaginary parts of the complex impedance $Z\left(\omega \right)$ recorded for ${\mu }_0\left|\mathbf{H}\right|=0.6\mathrm{T}$ and $\alpha =-{90}^{\circ }$ in the ip rotation measurement. Both are fitted simultaneously with Eq. (6) (green line), yielding the capacitance $C=0.2\mathrm{pF}$ and inductance $L=1\mathrm{nH}$ of the equivalent circuit of Fig. 1.