Relative weight of the inverse spin-Hall and spin-rectification effects for metallic polycrystalline Py/Pt, epitaxial Fe/Pt, and insulating YIG/Pt bilayers: Angular dependent spin pumping measurements

We quantify and compare the relative weight of inverse spin-Hall and spin-rectification effects occurring in metallic polycrystalline (Py/Pt), epitaxial (Fe/Pt), and insulating (YIG/Pt) bilayers. To distinguish the spin rectification signal from the inverse spin-Hall voltage the external magnetic field is rotated in plane to take advantage of the different angular dependencies of the prevailing effects. We prove that in permalloy anisotropic magnetoresistance is the dominant source for spin rectification while in epitaxial iron the anomalous Hall effect has a comparable strength. The rectification in yttrium-iron-garnet/platinum bilayers reveals an angular dependence imitating the one seen for anisotropic magnetoresistance and anomalous Hall effect caused by spin-Hall magnetoresistance.

Figure 1

Experimental setup and coordinate system: $x, y$, and $z$ are the laboratory fixed coordinates. The external field $\vec{H}$ rotates in plane, while the angle ${\mathrm{\Theta }}_{\mathrm{H}}$ is defined as the angle between $z$ and $\vec{H}$. The bilayer films are lying in the $x$ and $z$ plane and $y$ is the out-of-plane coordinate. The microstrip antenna used for excitation with dimensions of $(25\times 0.7\times 0.2) {\mathrm{mm}}^3$ is parallel to $z$ and generates an in-plane dynamic magnetic field $h_x$ and an out-of-plane field $h_y$. Since the microstrip antenna generates a quasi-TEM microwave mode a longitudinal electrical field component $e_z$ rises, which induces an electrical current $j_z$ in the samples in $z$ direction. Eddy currents $j_{\mathrm{eddy}}$ potentially can flow transverse to the microwave electrical field in $x$ direction. The electrical contacts for measuring the dc voltage are either transverse ($V_x$) or parallel ($V_z$) to the microstrip.

Figure 2

Theoretical in-plane magnetization angular dependencies of spin-rectification effects and ISHE with contacts transverse to the microwave antenna ($x$ direction) and different dynamic magnetic field geometries, adapted from Harder et al. [8]. ${\mathrm{\Theta }}_{\mathrm{H}}$ is the magnetic field angle (defined in Fig. 1), $A_{\text{L}}$ and $A_{\text{D}}$ are the amplitudes of the effects contributing to the symmetric voltage (L: Lorentzian) and the antisymmetric voltage (D: dispersive). ISHE can only appear in $A_{\text{L}}$, while SR effects can have contributions in both $A_{\text{L}}$ and $A_{\text{D}}$ with the same angular dependence and eventually the same or opposite sign.

Figure 3

Angular dependent spin pumping measurements of Py(12 nm)/Al(10 nm) (top graph) and Py(12 nm)/Pt(10 nm) (bottom graph) at 13 GHz excitation frequency with contacts transverse to the direction of the microstrip antenna. Black and orange arrows are highlighting the side maxima/minima originating from AMR.

Figure 4

Angular dependent spin pumping measurements of Fe(12 nm)/MgO(10 nm) (top graph) and Fe(12 nm)/Pt(10 nm) (bottom graph) at 13 GHz excitation frequency with contacts transverse to the direction of the microstrip antenna. Through the pronounced magnetocrystalline anisotropy of Fe the abscissa was rescaled from the angle of external magnetic field (${\mathrm{\Theta }}_{\mathrm{H}}$) to the relevant angle of magnetization (${\mathrm{\Theta }}_{\mathrm{M}}$). More specific information about the rescaling and anisotropy can be found in the text.

Figure 5

Angular dependent spin pumping measurements of YIG(100 nm)/Pt(10 nm) at 6.4 GHz excitation frequency with contacts transverse (top graph) and parallel (bottom graph) to the direction of the microstrip antenna.

Figure 6

Theoretical in-plane magnetization angular dependencies of spin rectification effects and ISHE with contacts parallel to the microwave antenna and different dynamic external magnetic field geometries, adapted from Harder et al. [8]. ${\mathrm{\Theta }}_{\mathrm{H}}$ is the magnetic field angle (defined in Fig. 1), $A_{\text{L}}$ and $A_{\text{D}}$ are denoting the amplitudes of the effects contributing to the symmetric voltage (L: Lorentzian) and the antisymmetric voltage (D: Dispersive). ISHE can only appear in $A_{\text{L}}$, while SR effects can have contributions in both $A_{\text{L}}$ and $A_{\text{D}}$ with the same angular dependence and eventually the same or opposite sign.