2004/05/31 by D. M. Apalkov, Dmytro Apalkov, P. B. Visscher · 171 citations
Chemistry · Engineering · Physics and Astronomy · #Advanced Memory and Neural Computing #Chemistry #Computer science #Condensed matter physics #Differential equation #Fokker–Planck equation #Magnetic field #Magnetic properties of thin films #Magnetization #Magnetization dynamics #Noise (video) #Oscillation (cell signaling) #Physics #Quantum and electron transport phenomena #Quantum mechanics #Spin (aerodynamics) #Spin-transfer torque #Thermodynamics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.72.180405
published in Physical Review B 72(18) (American Physical Society) · 11 pages, 8 figures, 1 appendix Original version in Nature format, replaced by Phys. Rev. Letters format. No substantive changes
arxiv created 2004/06/01 · openalex publication_date 2005/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe a general Fokker-Planck approach to understanding and calculating magnetization switching rates and noise in the recently observed phenomenon of spin-torque switching. In this phenomenon, which has possible applications to information storage, a large current passing from a pinned ferromagnetic (FM) layer to a free FM layer switches the free layer. Beginning with Brown [Phys. Rev. 130, 1677 (1963)], switching rates in magnetic systems have been calculated using the Fokker-Planck equation. In the small-oscillation limit, the equations have been solved analytically, giving a first-principles justification for phenomenological effective temperature theories: the spin-torque effect increases the Arrhenius factor exp(\ensuremath-E∕kT) in the switching rate by raising the effective spin temperature T. In the present Rapid Communication we generalize the nonlinear Fokker-Planck equation to the case of a Slonczewski spin torque. As an example, we use a linear approximation to calculate telegraph noise rates, leading to good qualitative agreement with recent experiments. However, our nonlinear formulation is also valid for large precessional oscillations. The method also allows the calculation of current-induced magnetic noise in current perpendicular to plane spin valve read heads.