Abstract

One of the cornerstones in spintronics is the precession of the magnetization of single-domain ferromagnets under the influence of spin-transfer torque (STT). Conventionally, the STT is derived by assuming an equilibrium distribution function on the nanomagnet, thus neglecting any non-equilibrium effects. In a previous work, the full non-equilibrium dynamics of the problem were treated within the Keldysh formalism, and it was found that no stable precessions of the magnetization were allowed [1].

In this talk, I will discuss an extension of this Keldysh description to include dissipation, using an imaginary Büttiker lead to couple the electron system to a reservoir [2]. I will discuss the resulting magnetization dynamics and will show that we now recover the possibility of stable precessions – thus highlighting the need to include dissipation for a complete description of the problem. Finally, I will show that in the limit of strong dissipation, these results can also be obtained by requiring charge conservation in the conventional derivation of the STT [3].

[1] Tim Ludwig, Igor S. Burmistrov, Yuval Gefen, and Alexander Shnirman, Phys. Rev. B 95, 075425 (2017)
[2] M. Büttiker, Phys. Rev. B 33, 3020 (1986)
[3] Pieter M. Gunnink, Tim Ludwig, and Rembert A. Duine, Phys. Rev. B 109, 024408 (2024)