Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

/pdf/spintronics-fundamentals-and-applications-2dx38n6phu.pdf

Spintronics: Fundamentals and applications

A derivation is given of the effect of a time‐dependent magnetic field gradient on the spin‐echo experiment, particularly in the presence of spin diffusion. There are several reasons for preferring certain kinds of time‐dependent magnetic field gradients to the more usual steady gradient. If the gradient is reduced during the rf pulses, H1 need not be particularly large; if the gradient is small at the time of the echo, the echo will be broad and its amplitude easy to measure. Both of these relaxations of restrictions on the measurement of diffusion coefficients by the spin‐echo technique serve to extend its range of applicability. Furthermore, a pulsed gradient can be recommended when it is critical to define the precise time period over which diffusion is being measured.The theoretical expression derived has been verified experimentally for several choices of time dependent magnetic field gradient. An apparatus is described suitable for the production of pulsed gradients with amplitudes as large as 100 ...

/pdf/spin-diffusion-measurements-spin-echoes-in-the-presence-of-a-6hwz49rcqz.pdf

Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient

https://www.cell.com/biophysj/pdf/S0006-3495(94)80775-1.pdf

MR diffusion tensor spectroscopy and imaging.

A spin echo method adapted to the measurement of long nuclear relaxation times (T2) in liquids is described. The pulse sequence is identical to the one proposed by Carr and Purcell, but the rf of the successive pulses is coherent, and a phase shift of 90° is introduced in the first pulse. Very long T2 values can be measured without appreciable effect of diffusion.

/pdf/modified-spin-echo-method-for-measuring-nuclear-relaxation-2b6u7j2zc8.pdf

Modified Spin‐Echo Method for Measuring Nuclear Relaxation Times

High Resolution Nuclear Magnetic Resonance

The phenomenological Bloch equations in nuclear magnetic resonance are generalized by the addition of terms due to the transfer of magnetization by diffusion. The revised equations describe phenomena under conditions of inhomogeneity in magnetic field, relaxation rates, or initial magnetization. As an example the equations are solved in the case of the free precession of magnetic moment in the presence of an inhomogeneous magnetic field following the application of a 90\ifmmode^\circ\else\textdegree\fi{} pulse with subsequent applications of a succession of 180\ifmmode^\circ\else\textdegree\fi{} pulses. The spin-echo amplitudes agree with the results of Carr and Purcell from a random walk theory.

Bloch Equations with Diffusion Terms

Transient nutations of the resultant nuclear magnetic moment vector are set up by applying radiofrequency power in the form of pulses in the neighborhood of resonance ($\ensuremath{\omega}=\ensuremath{\gamma}{H}_{0}$). The nutations have an initial amplitude depending on the state of magnetization at the start of a pulse and on the proximity to resonance, and are damped by spin-spin and spin-lattice interaction. The thermal relaxation time can be directly found by observing the dependence of initial amplitude on the time between pulses. The spin-spin time constant ${T}_{2}$ can be found from the rate of decay even in the presence of normally disturbing inhomogeneity in magnetic field. Sensitivity is in many cases comparable to that obtained in the modulation method with narrow band amplifiers. The fast response due to the relatively wide band widths used can be applied to a rapid search for unknown resonances. The effects observed are in qualitative accord with predictions based on the Bloch theory.

Transient Nutations in Nuclear Magnetic Resonance

The general theory of Bloembergen, Purcell, and Pound of nuclear spin relaxation has been extended to a more quantitative study of relaxation by translational diffusion. It has been found necessary to treat the problem by the theory of random walk. In the case of isotropic diffusion two cases have been studied: one in which the flight distance has a probability distribution, and the other in which it is constant. The problem of random walk to nearest neighbor sites in a lattice is also treated and quantitative results are obtained for a face-centered cubic lattice.

Nuclear Spin Relaxation by Translational Diffusion

A model is developed to describe nuclear relaxation and spin pumping caused by sparsely distributed electronic spins. It is assumed that the nuclei which are outside the interaction sphere of the paramagnetic centers are influenced indirectly via a fast diffusion process. Nuclei close to the electron spins are assumed to combine with these to form spin pairs of finite lifetime $\ensuremath{\tau}$. Spin pumping and relaxation in these pairs is described phenomenologically. The coupling with a radio-frequency power source is described in terms of a spectral distribution function with Lorentzian shape. Simultaneous spin flips, made possible by the static part of the spin-spin interaction, are included. The equations for two-spin relaxation are generalized to account for the fluid motion and electron spin relaxation as two independent sources of randomness. The results for relaxation and spin pumping are adapted to various special cases and compared with experiments. In particular, qualitative changes in the pumping process are shown to take place when the constant external magnetic field is changed from low to high values.

Theory of Spin Pumping and Relaxation in Systems with a Low Concentration of Electron Spin Resonance Centers

Theory relating spin-lattice relaxation times to diffusion rates has been extended to include the relation of spin-spin relaxation times to diffusion rates. Certain tables presented earlier have been corrected to bring them into agreement with presently accepted theory.

H. C. Torrey

Papers

Bloch Equations with Diffusion Terms

Transient Nutations in Nuclear Magnetic Resonance

Nuclear Spin Relaxation by Translational Diffusion

Theory of Spin Pumping and Relaxation in Systems with a Low Concentration of Electron Spin Resonance Centers

Nuclear Spin Relaxation by Translational Diffusion. III. Spin-Spin Relaxation