## Past Project: Spin Transfer Torques

*Related report*: Exploring Low-Frequency ST-FMR: Simulation & Experiment. CCMR REU Final Report, August 2016.

*Related page*: Plotting sequences of data using colorbars in matplotlib.

During the summer of 2016 I participated in the Cornell Center for Materials Research (CCMR) REU program at Cornell University. I worked in the Ralph group, performing measurements and micromagnetic simulations of spin transfer torques in magnetic bilayers.

The spin Hall effect is a conversion of longitudinal charge current into transverse spin current via spin-orbit coupling that occurs in certain semiconductors and heavy metals. It is a promising mechanism for the generation of spin-polarized currents for use in spintronics technologies such as nano-scale microwave oscillators and magnetic memory devices. The figure of merit for the spin Hall effect is the spin Hall angle, defined as the ratio of the spin current density to the charge current density: Θ_{SH}≡J_{s}/J_{c}.

Spin transfer torque-driven ferromagnetic resonance (ST-FMR) is a very common and robust method for measuring the spin Hall angle in magnetic multilayers. In ST-FMR, rf charge current is passed through the spin Hall metal layer (lower layer in the figure above). This in-plane charge current results in an rf spin current traveling out-of-plane. The spin current is injected into the magnetic layer, exciting resonant precession of the magnetization due to the spin transfer and Oersted torques.

The resistance of the magnetic layer oscillates due to the precession of the magnetization and the anisotropic magnetoresistance of the material. These rf resistance oscillations mix with the rf charge current, resulting in a dc voltage signal. The magnetization dynamics due to spin transfer torques are modeled by the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. Analytical solutions to this equation rely upon the macrospin approximation, which assumes that the magnetization of the entire layer can be described by a single vector. Solutions to the LLGS equation predict a dc mixing signal that is a sum of symmetric and anti-symmetric Lorentzians, due to the spin transfer and Oersted torques, respectively. Parameters such as Θ_{SH} can be extracted by fitting the dc mixing signal to the form predicted by theory (see, for example, Liu, *et al.*, Spin-Torque Ferromagnetic Resonance Induced by the Spin Hall Effect. *Phys. Rev. Lett.*, **106**, 036601 (2011).)

Prior to my project, the low frequency (i.e. < 5GHz) behavior of ST-FMR had not been thoroughly studied, but it had been observed that the determined value of the spin Hall angle diverged at low frequencies, an effect that is not predicted by theory. One possible explanation for this behavior is a breakdown of the macrospin model at low frequencies, where spatial variations in the magnetization dynamics may become important. In order to investigate this hypothesis, I performed experimental ST-FMR measurements on devices with a wide range of dimensions at frequencies from 2-8GHz.

ST-FMR is widely used because it is possible to perform measurements with very high signal-to-noise. However, ST-FMR is not spatially or temporally resolved, so it is effectively only sensitive to the average magnetization dynamics of the device. In order to better understand the ST-FMR in areas of parameter space where the microscopic magnetization dynamics may differ significantly from the average magnetization dynamics (i.e., where the macrospin approximation may not hold), I performed micromagnetic simulations of ST-FMR in thin magnetic films. Using MuMax3 GPU-accelerated micromagnetics running on AWS servers through MuCloud, I was able to model both spin transfer and Oersted torques and explore the trends in the determined spin Hall angle as a function of frequency, sample dimensions, and other experimental parameters.

I developed a set of tools in Python for analyzing and visualizing the results of these simulations. If you are interested in performing micromagnetic simulations of ST-FMR or similar measurements, feel free to contact me.

[Updated: 8/2016]