Charge and Spin Noise in Magnetic Tunnel Junctions

Abstract

Manipulation of magnetization by electric current lies in the mainstream of the rapidly developing field of spintronics. The electric current influences the magnetization through the spin-torque effect. Entering a magnet, spin-polarized current exerts a torque on the magnetization, which aligns the magnetization parallel or antiparallel to the spin polarization of the current. The spin-torque effect can be used for fast magnetization switching in magnetic tunnel junctions (MTJ) that consist of two magnetic layers separated by a tunnel barrier. Moreover, applying external magnetic field and passing electric current simultaneously, one can induce a wide variety of nonequilibrium dynamical regimes, ranging from hysteretic switching between two static orientations of magnetization to steady nonequilibrium magnetization precession. Theoretical description of nonlinear nonequilibrium magnetization dynamics is given by the Landau–Lifshitz–Gilbert (LLG) equation. In this approach, the magnetization is treated on a classical level, resulting in a deterministic dynamics, which can exhibit crossover from periodic to chaotic orbits. In presence of spin-polarized current, there are nonequilibrium fluctuations of magnetization – the spin shot noise – that distort the classical dynamics of magnetization. Those fluctuations originate from the discrete nature of spin and, in this respect, they are similar to the well-known shot noise in the charge transport that stems from the discreteness of charge.

A particular feature of the nonequilibrium spin noise is its dependence on the angle between the magnetizations of the magnetic layers forming the junction. This peculiarity leads to the appearance of so-called “hot” and “cold” spots with different noise strengths in the deterministic trajectory of magnetization. Due to the tunnel magnetoresistance effect, the distortion of deterministic magnetization dynamics by the spin shot noise transforms into fluctuations of electric current that are registered experimentally. Peculiar features of the spin shot noise are thereby reflected in the frequency spectrum of electric current fluctuations.

At present time, there are two theoretical approaches to the treatment of the nonequilibrium spin shot noise and the complementary charge shot noise in MTJs. One is based on the extension of Landauer–Büttiker formalism to magnetic junctions, the other one uses the introduction of stochastic Langevin terms into the LLG equation with subsequent derivation of the Fokker–Planck equation for the distribution function of magnetization. In this review, we discuss both approaches with an emphasis on the second one. In addition, a general review of theoretical and experimental works concerning equilibrium and nonequilibrium noise in magnetization dynamics is given. In particular, we discuss the effects of noise in different regimes of magnetization dynamics, such as switching of magnetization between two static orientations and steady state nonequilibrium magnetization precession.