Spin torque and interactions in ferromagnetic semiconductor domain walls

The motion of domain walls due to the spin torque generated by coherent carrier transport is of considerable interest for the development of spintronic devices. We model the charge and spin transport through domain walls in ferromagnetic semiconductors for various systems. With an appropriate model Hamiltonian for the spin– dependent potential, we calculate wavefunctions inside the domain walls which are then used to calculate transmission and reflection coefficients, which are then in turn used to calculate current and spin torque.

Starting with a simple approximation for the change in magnetization inside the domain wall, and ending with a sophisticated transfer matrix method, we model the common π wall, the less–studied 2π wall, and a system of two π walls separated by a variable distance.

We uncover an interesting width dependence on the transport properties of the domain wall. 2π walls in particular, have definitive maximums in resistance and spin torque for certain domain wall widths that can be seen as a function of the spin mistracking in the system — when the spins are either passing straight through the domain wall (narrow walls) or adiabatically following the magnetization (wide walls), the resistance is low as transmission is high. In the intermediate region, there is room for the spins to rotate their magnetization, but not necessarily all the way through a 360 degree rotation, leading to reflection and resistance. We also calculate that there are widths for which the total velocity of a 2π wall is greater than that of a same–sized π wall.

In the double–wall system, we model how the system reacts to changes in the separation of the domain walls. When the domain walls are far apart, they act as a spin–selective resonant double barrier, with sharp resonance peaks in the transmission profile. Brought closer and closer together, the number and sharpness of the peaks decrease, the spectrum smooths out, and the domain walls brought together have a transmission spectrum with many of the similar features from the 2π wall.

Looking at the individual walls, we find an interesting interaction that has three distinct regimes: 1) repulsion, where the left wall moves to the left and the right wall to the right; 2) motion together, where the two walls both move to the right, even at the same velocity for one special value of separation; and 3) attraction, where the left wall moves to the right and the right wall moves to the left. This speaks to a kind of natural equilibrium distance between the domain walls. This is of major interest for device purposes as it means that stacks of domain walls could be self–correcting in their motions along a track. Much experimental work needs to be done to make this a reality, however.