Control of the Bose-Einstein Condensation of Magnons by the Spin Hall Effect

Previously, it has been shown that rapid cooling of yttrium-iron-garnet–platinum nanostructures, preheated by an electric current sent through the Pt layer, leads to overpopulation of a magnon gas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnons depending on the electric current and applied field orientations. Here we demonstrate that the injection or annihilation of magnons via the SHE can prevent or promote the formation of a rapid cooling-induced magnon BEC. Depending on the current polarity, a change in the BEC threshold of $-8\%$ and $+6\%$ was detected. These findings demonstrate a new method to control macroscopic quantum states, paving the way for their application in spintronic devices.

Figure 1

Colored scanning electron microscopy image of the structure under investigation and sketch of the experimental setup. The structure consists of a $2\text{−}\mu \mathrm{m}$-wide and 34-nm-thick YIG stripe. A $3\text{−}\mu \mathrm{m}$-long and 7-nm-thick platinum heater is placed on top and contacted by $\mathrm{Ti}/\mathrm{Au}$ leads separated by a distance of $2\mu \mathrm{m}$.

Figure 2

BLS intensity color coded (log scale) as a function of the BLS frequency and time. The duration of the 100-ns-long heating dc pulse with an amplitude of $|U|=1.5\mathrm{V}$ is marked by the black boxes. (a) Current parallel to the external field, thus no contribution of the SHE-STT effect is expected. The achieved overpopulation after pulse termination due to the rapid cooling effect is sufficiently large to trigger the formation of a magnon BEC. (b) Current is perpendicular to the external field. The STT annihilates magnons during the pulse. The condensation of magnons is suppressed. (c) Reversed current direction in comparison to the situation in (b), the STT injects magnons. After the pulse is applied, the magnon BEC density is enhanced compared to the situation depicted in (a). For the exact geometries, see insets.

Figure 3

(a) Inverse BLS intensity as a function of the voltage for the application of a continuous dc current. The linear fit yields a threshold for the damping compensation of $U_{\mathrm{th}}=-0.95\mathrm{V}$. (b) Integrated BLS intensity at the end of the applied dc pulse (integration interval ${\tau }_P-8\mathrm{ns}<t<{\tau }_P$) as a function of the absolute value of the voltage. The external field of ${\mu }_0{\mathbf{H}}_{\mathrm{ext}}=110\mathrm{mT}$ is aligned perpendicular to the direction of the current. The SHE-STT effect either injects (“$+$” sign data points) or annihilates (“$-$” sign data points) magnons. (c) Integrated BLS intensity after the pulse is switched off (${\tau }_P<t<{\tau }_P+95\mathrm{ns}$) as a function of the absolute value of the voltage. The blue curves correspond to the situation in (b); the black curves show the reference curve for ${\mu }_0{\mathbf{H}}_{\mathrm{ext}}\Vert {\mathbf{j}}_C$, without a SHE-STT contribution. (d) Integrated intensity as in (c), the residual signal caused by the decaying STT-injected magnons is subtracted. Because of the injection or annihilation of magnons via the STT, the thresholds are shifted with respect to the case without a SHE-STT contribution (pink line).