Current noise generated by spin imbalance in presence of spin relaxation

Abstract

We calculate current (shot) noise in a metallic diffusive conductor generated by spin imbalance in the absence of a net electric current. This situation is modeled in an idealized three-terminal setup with two biased ferromagnetic leads (F-leads) and one normal lead (N-lead). Parallel magnetization of the F-leads gives rise in spin-imbalance and finite shot noise at the N-lead. Finite spin relaxation results in an increase of the shot noise, which depends on the ratio of the length of the conductor (L) and the spin relaxation length (ls). For L ≫ ls the shot noise increases by a factor of two and coincides with the case of the anti-parallel magnetization of the F-leads. PACS:The ability to detect nonequilibrium spin accumulation (imbalance) by all-electrical means is one of the key ingredients in spintronics [1]. Transport detection typically relies on a nonlocal measurement of a contact potential difference induced by the spin imbalance by means of ferromagnetic contacts [2,3,4,5,6] or spin resolving detectors [7]. A drawback of these approaches lies in a difficulty to extract the absolute value of the spin imbalance without an independent calibration.An alternative concept of a spin-to-charge conversion via nonequilibrium shot noise was introduced in Ref. [8] and recently investigated experimentally [9]. Here, the basic idea is that a nonequilibrium spin imbalance generates spontaneous current fluctuations, even in the absence of a net electric current. Being a primary approach [10], the shot noise based detection is potentially suitable for the absolute measurement of the spin imbalance. In addition, the noise measurement can be used for a local non-invasive sensing, as recently demonstrated with a semiconductor nanowire probe [11].It is well known, how a relaxation of the electronic energy distribution via inelastic electron-phonon [12] and electron-electron [13,14] scattering influences the shot noise in diffusive conductors and nonequilibrium spin valves [15]. In this letter, we calculate the impact of a spin relaxation on the spin imbalance generated shot noise in the absence of inelastic processes. We find that the spin relaxation increases the noise up to a factor of two, depending on the ratio of the conductor length and the spin relaxation length.Consider the system shown in Fig. 1. It consists of a diffusive wire, one end of which is grounded and the other is attached to a conducting island much larger Fig. 1. The design of the system. A diffusive normal wire of the length L is attached to normal islands on both ends. Nonequilibrium energy distribution on the left hand side of the wire generates the shot noise at a zero net current. The spin imbalance on the left-hand side of the wire is due to the electric current flowing from one ferromagnetic lead (red) to another one with opposite magnetization (blue).than the transverse dimensions of the contact. The spin imbalance in the island is produced by electron tunneling through two junctions connecting it to ferromagnetic leads with antiparallel magneti...

Spatial and energy resolution of electronic states by shot noise

“…The second one requires the much smaller thermal conductance of the TJ compared to that of the studied conductor [33,38,39,57,59], similarly to the analogous electrical requirement for conventional volt meters. To probe low-resistance conductors, these conditions, alongside TJs, are fulfilled for elastic InAs nanowire-based sensors, allowing additionally thermoelectric or spin-to-charge conversion studies [56,57].…”

“…The spatial resolution is virtually unlimited with state-of-the-art noise scanning techniques [6,[53][54][55]. The approach is quite universal and equally suitable for the measurements of the nonequilibrium configurations created by charge, spin [56] and valley, etc. currents, hence paving the way for the realization of existing [26,36,37,57] and various novel local noise probes.…”

Спектральное И Пространственное Разрешение Электронных Состояний Из Шумовых Измерений / Тихонов Е.С., Петруша С.В., Денисов А.О., Храпай В.С.

“…Такой подход не опирается ни на какие спектральные особенности сенсора [6] и применим, поэтому, практически к любой электронной системе. Помимо спектральных исследований, шумовые измерения могут оказаться полезными и для характеризации самого сенсора [7].…”

Spatial and energy resolution of electronic states by shot noise

“…The second one requires the much smaller thermal conductance of the TJ compared to that of the studied conductor, similarly to the analogous electrical requirement for conventional voltmeters. To probe low-resistance conductors, these conditions, alongside with TJs, are fulfilled for elastic InAs nanowire-based sensors, allowing additionally thermoelectric or spin-to-charge conversion studies 42,43 .…”