Modeling Spin-Orbit Torques
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2.3 Spin-Transfer Torque (STT)
Figure 2.3: Schematization of the spin-transfer mechanism. The yellow arrow depicts the electrical current flowing from the right to the left, i.e., electrons flow from left to right. The blue and black arrows depict the flow and
direction of the spin magnetic moment, respectively, while the red arrow depicts the magnetization direction of the FM layer. The purple arrows show the loss of transverse spin magnetic moment and the resulting torque on the
magnetization.
The first applications of GMR and TMR for information storage relied on external magnetic fields to switch the magnetization of the FL; however, this approach severely limited the scalability of the technology and, consequently,
its application in devices that benefit from high densities such as MRAM. In 1996, John Slonczewski and Luc Berger independently proposed a mechanism by which a spin-polarized current could exert a torque on the magnetization
of a FM layer [29, 30], enabling current-induced magnetization switching without the need for external magnetic fields. This phenomenon is known as STT and has since become a fundamental concept in spintronics. Experimental
demonstration of STT magnetization reversal was first reported by Katine et al. in 2000 using a fully metallic spin valve [31]. Later in 2004 Huai et al. demonstrated the same in an MTJ with a Al\(_2\)O\(_3\)
barrier [32]. The discovery of STT opened the door for the development of highly scalable and energy-efficient spintronic devices, such as STT-MRAM, which have the potential to revolutionize data storage technology.
The spin-transfer mechanism can be understood as follows. Consider a stream of electrons entering a FM thin film magnetized along the \(z\) axis. The electrons move in the \(x\) direction with an initial spin projection that is
not collinear with the magnetization. At the interface, they may be either reflected or transmitted. Typically, majority-spin electrons are more easily transmitted than minority-spin electrons. Once transmitted into the FM, the
electrons experience a strong exchange field along the magnetization direction, which drives a rapid spin precession. By the time they leave the FM, the transverse \(xy\)-components of the net spin polarization are fully dephased
due to differences in electron trajectories, while the longitudinal \(z\)-component remains unchanged (assuming there is no spin-flip scattering due to SOC or disorder). Conservation of angular momentum requires that the lost
transverse spin angular momentum be transferred to the FM, which the magnetization experiences as a torque. For thick FM layers, this effect is negligible, but in sufficiently thin films, the torque can rotate the magnetization
towards the net polarization direction of the incoming electrons. The spin-transfer mechanism is illustrated in Fig. 2.3 in terms of spin magnetic moment currents, where the
torque is given by the difference in outgoing and incoming spin currents.
STT switching occurs in spin valves and MTJs when a sufficiently high current density is passed through the structure. When the FL and RL are in an antiparallel configuration, and the current is applied from the FL to the RL
(electrons flow from the RL to the FL), due to the different scattering rates, the majority electrons incident from the RL on to the FL have a higher transmission probability than the minority electrons, resulting in a spin-polarized
current entering the FL carrying a magnetic moment opposite to the FL magnetization. As the spin-polarized electrons enter the FL they quickly align with the FL magnetization, resulting in a STT. If the current density is
sufficiently high, the torque can overcome the energy barrier of the FL, leading to its eventual switching to a parallel configuration with the RL. In the opposite process, when the two layers are in a parallel configuration and a
current is applied from the RL to the FL (electrons flow from the FL to the RL), it is the reflected minority electrons that generate the STT torques on the FL magnetization. Consequently, the two switching processes are
asymmetric, with the antiparallel-to-parallel switching typically requiring a lower current density than the reverse process. One should note that a perfectly collinear alignment of the FL and RL magnetizations would not result in
any torque, as only the transverse spin components are transferred to the FL magnetization. However, due to thermal fluctuations and disorder, the FL magnetization is never perfectly aligned; thus, a torque is always exerted on it.
Due to the initial near collinear configuration, a long incubation time is typically observed before switching occurs, as the initial torques are too weak to initiate the switching process.
