Spin transport in as-grown and annealed thulium iron garnet/platinum bilayers with perpendicular magnetic anisotropy

We characterize the spin Hall magnetoresistance (SMR), spin Seebeck effect (SSE), and dampinglike spin-orbit torque (SOT) in thulium iron garnet/platinum bilayers with perpendicular magnetic anisotropy by using harmonic Hall effect measurements. By consecutive annealing steps followed by measurements on a single device, we reveal that the spin-dependent effects gradually decrease in amplitude as the annealing temperature increases. We attribute this behavior primarily to the changes in the spin-mixing conductance, which sensitively depends on the interface quality. However, further analysis demonstrates that although the SSE scales closely with the SMR, the dampinglike SOT shows a significantly different trend upon annealing, contrary to theoretical expectations. By comparing the dampinglike SOT with the field-induced Hall effect, we found evidence that scattering from Fe impurities in the Pt at the interface might be responsible for the distinct annealing temperature dependence of the dampinglike SOT.

Figure 1

Spin-dependent effects in the MI/NM bilayer studied in this paper. Left panel shows the spin Hall magnetoresistance. It is the change in the resistance of a normal metal in interfacial contact with a magnetic insulator depending on the magnetization orientation, which governs the SHE-induced spin current absorption/reflection at the interface. Middle panel shows the simplified dampinglike spin-orbit torque mechanism driven by the spin Hall effect. The torque direction depends on the current injection direction due to reversal of the SHE-induced spin polarization at the MI/NM interface. Right panel shows the spin Seebeck effect mechanism. A temperature gradient can generate a pure spin current in a magnetic material along the gradient direction, which can create a voltage across the NM due to the inverse SHE.

Figure 2

(a) Optical microscopy image of the Hall cross device and the measurement scheme. Hall resistance with (b) OOP and (c) IP field sweeps for the as-grown and annealed sample. (d) SMR-driven anomalous Hall resistance vs spin-Hall magnetoresistance (red line is a linear fit to the data). (e) Electrical resistivity of Pt measured on the device as a function of annealing temperature. (f) Left axis: effective perpendicular anisotropy field determined by fitting the data shown in (c) by macrospin simulations; right axis: saturation magnetization measured on reference TmIG(20 nm)/Pt(5 nm) bilayer.

Figure 3

Measurement scheme for the harmonic Hall effect measurements showing (a) SSE-dominant and (b) dampinglike SOT-dominant geometry. Lower panels show the raw second-harmonic signal taken in the as-grown state with an in-plane field sweep between $\pm 4000\mathrm{Oe}$. The current density is set to $j_{\mathrm{rms}}=2.5\times {10}^{11}\mathrm{A}/{\mathrm{m}}^2$. (c) Determination of the dampinglike torque by fitting the second-harmonic signal taken at $\phi ={90}^{\circ }$ (within the hysteretic region).

Figure 4

(a) Spin-Seebeck signal and (b) dampinglike SOT as a function of annealing temperature.

Figure 5

Estimated spin mixing conductance as a function of annealing temperature, based on Eqs. (4) and (5), and two different sets of parameters for the spin Hall angle and spin diffusion length.

Figure 6

Comparison of the measured SSE and dampinglike SOT (left axis) with the theoretical estimations based on Eqs. (6) and (7). To estimate $\mathrm{Re}\left[G^{\uparrow \downarrow }\right]$ the SMR expression given in Eq. (4) is used. The $y$ axes have been chosen to match the rightmost data point corresponding to the as-grown state.

Figure 7

Dampinglike SOT (left axis) and the ordinary Hall-effect slope (right axis) versus the annealing temperature. There is an apparent correlation between these two quantities.