Nonlocal magnon-based transport in yttrium-iron-garnet–platinum heterostructures at high temperatures

The spin Hall effect in a heavy metal thin film allows to probe the magnetic properties of an adjacent magnetic insulator via magnetotransport measurements. Here, we investigate the magnetoresistive response of yttrium iron garnet/platinum heterostructures from room temperature to beyond the Curie temperature $T_{\mathrm{C}}\approx 560\mathrm{K}$ of the ferrimagnetic insulator. We find that the amplitude of the (local) spin Hall magnetoresistance decreases monotonically from $300\mathrm{K}$ towards $T_{\mathrm{C}}$, mimicking the evolution of the saturation magnetization of yttrium iron garnet. Interestingly, the spin Hall magnetoresistance vanishes around $500\mathrm{K}$, well below $T_{\mathrm{C}}$, which we attribute to the formation of a parasitic interface layer by interdiffusion. We confirm the presence of such an interface region with Fe and Pt intermixing by transmission electron microscopy and spatially resolved energy dispersive x-ray analysis. Around room temperature the nonlocal magnon-mediated magnetoresistance exhibits a power law scaling $T^{\alpha }$ with $\alpha \sim 3/2$, as already reported. The exponent decreases gradually to $\alpha \sim 1/2$ at around $420\mathrm{K}$, before the nonlocal magnetoresistance vanishes rapidly at a similar temperature as the spin Hall magnetoresistance. We attribute the reduced $\alpha$ at high temperatures to the increasing thermal magnon population which leads to enhanced scattering of the nonequilibrium magnon population and a reduced magnon diffusion length. Finally, we find a magnetic field independent offset voltage in the nonlocal signal for $T>470\mathrm{K}$, which we associate with electronic leakage currents through the normally insulating yttrium iron garnet film. Indeed, this nonlocal offset voltage is thermally activated with an energy close to the band gap.

Figure 1

(a) The Hall bar used for measuring the local magnetotransport response (SMR). A current is applied along the $\mathbf{j}$ direction and the longitudinal $V_{\ell }$ and the transverse $V_{\mathrm{t}}$ voltage drop are measured along the current and along the transverse direction $\mathbf{t}$, respectively. (b) In the nonlocal device geometry, the current is applied in one Pt wire, while the nonlocal voltage $V_{\mathrm{nl}}$ is measured on a second, electrically insulated Pt wire. The magnetic field is rotated in the sample plane for both measurement types. Local [(c) and (e)] and nonlocal [(d) and (f)] magnetotransport response of the YIG/Pt heterostructure for several temperatures, respectively. As expected from the SMR theory framework, a $sin\left(\alpha \right)cos\left(\alpha \right)$ modulation is observed in the transverse resistivity. The amplitude of this modulation decreases towards higher temperatures and becomes indistinguishable from the background noise and drift above $540\mathrm{K}$. For the nonlocal voltage, a ${sin}^2\left(\alpha \right)$ modulation is observed, where the amplitude increases with temperature until $420\mathrm{K}$ and then drops off sharply above $500\mathrm{K}$. Additionally, for $T>500\mathrm{K}$ a magnetic field orientation independent offset voltage is present in the nonlocal voltage.

Figure 2

(a) SMR amplitude as a function of temperature extracted from $sin\left(\alpha \right)cos\left(\alpha \right)$ fits to the field-orientation dependent measurements (cf. Fig. 1). The magnetization as a function of temperature of a different piece from the same YIG wafer is shown as solid teal line and the magnetization calculated using a mean-field model is shown as dashed yellow line. (b) The amplitude of the nonlocal voltage modulation $\mathrm{\Delta }{V}_{\mathrm{nl}}$ obtained by ${sin}^2\left(\alpha \right)$ fits to the field-orientation dependent measurements. In addition, a field-independent offset voltage emerges (teal and yellow symbols). The data shown with gray squares (yellow triangles) were taken during the first measurement run from 300 to $500\mathrm{K}$, the data shown by red circles (teal pentagons) during the second run from 300 to $600\mathrm{K}$. (c) The amplitude $\mathrm{\Delta }\rho$ (gray and red symbols) shows a strong dependence on temperature and vanishes similarly as $\mathrm{\Delta }\rho /{\rho }_0$. The resistivity ${\rho }_0$ (yellow and teal symbols) of the Pt layer increases linearly as a function of temperature until approximately $470\mathrm{K}$. In the blue shaded region (above $470\mathrm{K}$) the resistivity deviates from the linear fit (black line). Additionally, the resistivity is permanently lowered when the measurement is repeated (teal symbols).

Figure 3

The MMR amplitude $\mathrm{\Delta }{V}_{\mathrm{nl}}$ roughly scales as $T^1$ up to $T\approx 470\mathrm{K}$ for both runs and then decreases sharply, scaling as $T^{-6}$. The trend lines for the two runs have been shifted by the same vertical offset.

Figure 4

(a) High-resolution TEM image of the Pt/YIG interface. [(b) and (c)] Elemental maps of Fe (b) and Pt (c) as obtained from EDS using the Pt-L and Fe-K edge intensities, respectively. (d) EDS profiles of the Pt-L (teal squares) and Fe-K (red circles) intensities together with a Fe-K EELS profile (black line) across the Pt/YIG interface.

Figure 5

(a) A simplified equivalent circuit of the nonlocal device allows to evaluate the impact of a finite electrical conductivity of the YIG layer in between the two Pt electrodes. If the conductivity of the YIG is nonzero, a small leakage current $I_{\mathrm{L}}$ will give rise to an additional magnetic field orientation independent nonlocal voltage $V_{\mathrm{nl}}$. (b) Using this model, the magnetic field-independent offset voltage can be used to determine the resistance $R_{\mathrm{YIG}}$ of the YIG film. The activation energy of the electrical transport is estimated to $E_{\mathrm{A}}\approx 1.9\mathrm{eV}$.