Effects of spin-orbit torque on the magnon gas

Abstract

Spin orbit torque (SOT) provides the possibility to control the magnetization state of conducting and insulating magnetic materials. Recently, it was shown that the influence of SOT on the spin system of ferromagnets results in either enhancement or suppression of magnetic fluctuations, depending on the polarization, which can be equivalently described as generation or annihilation of incoherent magnons. This mechanism is not specific to certain magnon states, and is expected to change magnon populations throughout the entire spectrum, thus avoiding the non-thermalized transient states inherent to other mechanisms used to drive magnon gases, such as the parametric pumping. Recent theoretical studies suggest that SOT can drive the magnon gas into a quasi-equilibrium state described by the Bose-Einstein statistics with non-zero chemical potential, suggesting the possibility of electrically-driven Bose-Einstein condensation (BEC) of magnons. These theories have been supported by the successful application of the developed theoretical framework to incoherent magnon transport. Variations of the chemical potential of the magnon gas were recently detected in measurements of spin relaxation rates of a nitrogen-vacancy center in diamond coupled to spin waves in a magnetic insulator. However, there was no direct experimental evidence that the magnon gas driven by SOT forms a quasi-equilibrium distribution, and the dependence of the effective thermodynamic characteristics has not been established. We studied the effects of SOT on the magnon distribution over a broad spectral range, by utilizing the micro-focus Brillouin light scattering (BLS) spectroscopy. The studied system comprises a 2 micrometers wide and 5 nm thick Pt strip overlaid by a 1 micrometer wide and 10 nm thick ferromagnetic Permalloy (Py) strip (Fig. 1a). The system is magnetized by the static magnetic field applied along the Py strip. The electric current I flowing in Pt is converted by the spin-Hall effect (SHE) into a spin current injected into Py through the Py/Pt interface. The magnetic moment carried by the spin current is either parallel or antiparallel to the Py magnetization M, depending on the direction of current, resulting in a decrease or an increase of the magnon population, respectively. The BLS spectra reflecting the current-dependent spectral density of magnons (Fig. 1b) allowed us to analyze the spectral magnon population function and determine the thermodynamic characteristics of the magnon gas. Our analysis clearly indicated that the magnon distribution can be described by the Bose-Einstein statistics expected for the quasi-equilibrium state. We determined the current-dependent chemical potential and effective temperature of the magnon gas (Fig. 2), and showed that, for one polarization of the spin current, the effective temperature of the magnon gas becomes significantly reduced, while the chemical potential stays almost constant (Fig. 2a). In contrast, for the opposite polarization, the effective temperature remains nearly unaffected, while the chemical potential linearly increases with current, until it closely approaches the lowest-energy magnon state (Fig. 2b), indicating the possibility of spin current-driven Bose-Einstein condensation. Our experimental results provide direct spectroscopic evidence that the magnon gas is driven by the SOT into a quasi-equilibrium state, which can be described by the Bose-Einstein distribution with current-dependent values of chemical potential and effective temperature. These findings support the theoretically proposed mechanism for the formation of current-induced magnetization auto-oscillations via the Bose-Einstein condensation of magnons. Our results should stimulate further experimental and theoretical exploration of the relationship between the thermodynamics of magnon gases driven by spin currents, and coherent magnetization dynamics.