The interplay between the rapid cooling-induced BEC and SHE-STT-driven bullet mode

Abstract

It has been shown that a rapid cooling of Yttrium-Iron-Garnet (YIG)/Pt nanostructures preheated by a DC electric current pulse sent through the Pt layer leads to an overpopulation of a magnon gas and to the subsequent Bose-Einstein condensation (BEC) of magnons [1]. Hereby, the application of a sufficiently-long DC heating pulse was used to generate a high population of magnons being in equilibrium with the phononic system. The subsequent rapid decrease in the temperature resulted in the break of the equilibrium, in the over-population of magnons over the whole magnon spectrum, and, in the following, in a redistribution of magnons from higher to lower energies. Finally, if the elevated temperature was high enough, and the cooling process fast enough, the chemical potential reached the minimal energy of the system and the BEC was triggered [1].In these experiments, a Pt or Al layer was used to heat the YIG nanostructure. For a Pt heater, in addition to the Ohmic heating effects, one expects the generation of a spin-polarized current transverse to the YIG/Pt interface due to the spin Hall effect (SHE) [2]. The spin current, consequently, is known to act on the magnetization dynamics in the YIG via spin-transfer torque (STT). Whereas in our previous studies the induced disequilibrium was found to be mainly given by the temperature increase and subsequent rapid cooling, we observe a significant contribution of the spin Hall effect (SHE) in a new set of samples. The larger effect of the SHE-STT was reached by a modification of the structures (see Fig. 1) with respect to those in the original study [1], i.e. by a decrease in the YIG thickness, and via using a sputtered Pt layer instead of an epitaxially grown Pt layer studies to enhance the spin Hall angle [3].It was found that SHE-induced STT enhances the BEC formation at the bottom of the magnon spectrum – in the minimum frequency of the fundamental spin-wave mode, and excites a nonlinear magnon mode – the spin-wave bullet, located below the linear magnon spectrum [4]. We investigated the dynamics of these magnon states employing Brillouin light scattering (BLS) spectroscopy. A sketch of the experimental setup and SEM images of the investigated structure is depicted in Fig. 1. The application of a 50-ns-long DC-pulse to a 7-nm- thin Pt layer on top of a 34-nm-thin and 2-μm-wide YIG strip results in the SHE-STT. At sufficiently large amplitudes of the DC-pulse applied, the bullet mode is formed during the DC pulse at a frequency around 1.8 GHz below the frequency of the fundamental mode, see Fig. 2b. The pronounced magnon density peak in the left panel in Fig. 2c (solid orange line), measured at the time just before the current pulse is switched off, clearly demonstrates the bullet mode formation. The SHE-STT nature of the mode is confirmed by the variation of the magnetisation orientation with respect to the current direction. The consequent switching of the DC pulse off results in the rapid cooling-induced BEC of magnons at the frequency around 6 GHz - see Fig. 2c. The results of the control experiment with no SHE-STT contribution under periodically changing polarity of the applied current (Fig. 2d) are in agreement with the original findings presented in Ref. [1].The interplay between the magnon condensate and the SHE-STT bullet mode, after the current pulse was gone, attracts special attention. Initially, in the rapid cooling phase of the process, thermally-induced excess magnons populate both the bullet mode and the condensate, see Fig. 2a. Further, both modes decay slower than expected from their lifteime indicating that they are still pumped from the gas. Finally, about 30 ns after the DC pulse is turned off, a qualitatively new process begins, resulting in the redistribution of magnons from the bullet mode to the condensate. This phenomenon manifests itself in an elevation of the condensate density accompanied by an increased decay of the bullet mode, and apparently occurs when the chemical potential of the magnon gas [1] decreases below the bullet mode frequency. The results suggest a path towards the application of macroscopic quantum states in spintronic devices. **