Solving Electron Spin Drift-Diffusion Equations in Presence of Hyperfine Interactions*

Large nuclear fields, induced by the hyperfine interaction, are known to influence spin transport characteristics in n-GaAs [1,2,3]. Nuclear fields are added to the spin drift-diffusion equation and the resulting spin distributions are calculated. Various boundary conditions are assumed in order to model various experimental arrangements. Due to the complicated nature of the nuclear field, the steady state spin drift-diffusion equations are non-linear and must be solved numerically. In this work, we examine solutions for the spin distribution and spin current in the presence of a nuclear field. Lastly, the effect of magnetic field gradients on steady state spin are explored to show how these gradients  affect spin current.

[1] M. Chan et al. Phys. Rev. B 80, 161206, (2009)

[2] N. J. Harmon, T. A. Peterson, C. C. Geppert, S. J. Patel, C. J. Palmstrøm, P. A. Crowell, and M. E. Flatté, Phys. Rev. B 92, 140201(R) (2015).

[3] Y.-S. Ou, Y.-H. Chiu, N. J. Harmon, P. Odenthal, M. Sheffield, M. Chilcote, R. K. Kawakami, and M. E. Flatté, Phys. Rev. Lett. 116, 107201 (2016).