Spin diffusion length

Shim JH, Raman KV, Park YJ, Santos TS, Miao GX, Satpati B, Moodera JS (2008) Large spin diffusion length in an amorphous organic semiconductor. Phys Rev Lett 100 226603... 

It was aheady mentioned that one of the major advantages for the application of organic semiconductors in spintronics applications is the large spin diffusion length even at room temperature. While most of the spintronics experiments published up to now are performed at very low temperature, it is assumed that applying organics makes this effort non-essential. For this reason SQUID measurements were also carried out at room temperature in order to check if the magnetic behaviour of the contacts still allows spinFET operation. 

The Concepts of Spin Accumulation and Spin Diffusion Length... 

It follows from the above discussion that the spin accumulation decays exponentially away from the interface, on a length scale called the spin diffusion length (A-sd)- This concept is crucial for realizing a link between spin electronics and magnetic nanostructures. In this section, we shall not go further into this concept, but we shall do a rough calculation to see how large Asd is and on what parameters it depends. We use the following expression from [3.90] ... 

Estimates of the upper boundary of domain size of inhomogeneity in ASD from magnetization spin-diffusion length (from H Ti/Tip times) Crystallization monitoring > Tg alternatively by nuclear quadrapole double resontmce ... 

Global AMI.5 sun illumination of intensity 100 mW/cm ). The DOS (or defect) is found to be low with a dangling bond (DB) density, as measured by electron spin resonance (esr) of - 10 cm . The inherent disorder possessed by these materials manifests itself as band tails which emanate from the conduction and valence bands and are characterized by exponential tails with an energy of 25 and 45 meV, respectively the broader tail from the valence band provides for dispersive transport (shallow defect controlled) for holes with alow drift mobiUty of 10 cm /(s-V), whereas electrons exhibit nondispersive transport behavior with a higher mobiUty of - 1 cm /(s-V). Hence the material exhibits poor minority (hole) carrier transport with a diffusion length <0.5 //m, which puts a design limitation on electronic devices such as solar cells. 

It is found that the relaxation parameter T p as a function of temperature does not follow an increase with chain length, as the square of the number of methylene carbons. Nor is it linear with N, the number of methylene carbons, which should be true if relaxation to the lattice were rate controlling. Rather, it shows a temperature-induced increase of the minimum value of Tjp with about the 1.6 of N. So, both spin diffusion and spin lattice coupling are reflected. For a spin diffusion coefficient D of approximately 2 x 10 12 cm.2/sec., the mean square distance for diffusion of spin energy in a time t is the ft1 = 200/T A, or about 15A on a Tjp time scale. 

There have been many investigations of photoinduced effects in -Si H films linked to material parameters. Changes have been observed in the carrier diffusion length, unpaired spin density, density of states in the gap, and infrared transmission. The transition from state A to B seems to be induced by any process that creates free carriers, including x-ray radiation and injection (double) from the electrodes. Because degradation in a solar cell is accentuated at the open-circuit voltage conditions, the A to B transition occurs upon recombination of excess free carriers in which the eneigy involved is less than the band gap. It has been pointed out that this transition is a relatively inefficient one and the increase in spin density takes place at a rate of 10-8 spins per absorbed photon. 

In contrast to the 1D experiment, where steady-state NOEs may be obtained, only the less intense transient NOE.s are measured in the NOESY experiment. ROEs can only be obtained as transient effects in both the ID and the 2D experiment. Furthermore the intensities of the NOESY and ROESY cross peaks depend upon the molecular size as well as the length of the mixing period. In the case of large molecules, e.g. polypeptides, rather short mixing times are usually chosen to avoid spin diffusion. 

By the pulsed field gradient spin echo method (1) it is possible to measure mean diffusion lengths ( /(l2)) for molecules in a given time interval in systems without a concentration gradient. The application of the method is limited to... 

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

Volume 21, Part C, is concerned with electronic and transport properties, including investigative techniques employing field effect, capacitance and deep level transient spectroscopy, nuclear and optically detected magnetic resonance, and electron spin resonance. Parameters and phenomena considered include electron densities, carrier mobilities and diffusion lengths, densities of states, surface effects, and the Staebler-Wronski effect. 

Material Intermolecular distance3 c (nm) Exciton spin multiplicity Lifetime T (s) Diffusion length lA (nm) Diffusion coefficient D (cm2/s) Hopping time th (s) Total distance covered l (nm) l/l a... 

The mean value of the i Vs for each sample was calculated. The calculated mean values of T/ s and the standard deviations are presented in Table 2. It is seen, from Table 2, that the standard deviation in both blends and complex is negligibly small. This indicates that the spin-dilfusion among all protons in the blends and the complex can average out the whole relaxation process and hence the domain size of these samples is smaller than the spin-diffusion path length within the time frame of Ti . From the obtained value of Ti and using the Eq. (1) with 10 m s it is believed that the PAA/PVP blends are intimately mixed on the Ti measurement scale of 32-39 nm. 

As reviewed in the previous section, measurements of Ti and Tip can provide an estimation of the length scale of miscibility of polymer blends. Compared with such kinds of experiments, the results of the spin-diffusion experiments are more quantitative and straightforward. The accuracy of the results of spin-diffusion experiments relies, to a large extent, on the values of spin-diffusion coefficients (7)) employed in calculation of the constituent phase components. Despite efforts that have been made, there still lacks a suitably applicable method of directly measuring the spin-diffusion coefficients, at least for polymers. For rigid polymer below Tg, 0.8 nm /ms has been turned out to be a reliable value of spin-diffusion coefficient. The difficulty left then concerns how to determine the coefficient of the mobile phase, which is very sample dependent. Recently, through studies on diblock copolymers and blend samples with known domain sizes, Mellinger et al established empirical relations between the T2 and D as follows ... 

From these semiquantitative estimations, one can regard that, if the observed Ti values for the component polymers are the same, the size of the domains is small enough for spin diffusion to average polarization gradient among spins A and B created by different intrinsic relaxation rates. Then, the question arises how small the size of the domains should be to realize fast spin diffusion The maximum diffusive path length r by spin diffusion in three-dimensions for a time Ty may be given as [78-81]... 

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