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In mathematics the spin group, denoted Spin(n), [1] [2] is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2)
English: Dispersion relations of a spin orbit coupled system for different coupling strengths. Box A has no coupling. The dispersion relation shows 2 shifted free space dispersion relations. Box B shows how the gap at k=0 opens for weak coupling.
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence of the mathematics of quantum mechanics.
The spin magnetic moment of the electron is =, where is the spin (or intrinsic angular-momentum) vector, is the Bohr magneton, and = is the electron-spin g-factor. Here μ {\displaystyle {\boldsymbol {\mu }}} is a negative constant multiplied by the spin , so the spin magnetic moment is antiparallel to the spin.
Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons.The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei.
Spintronics emerged from discoveries in the 1980s concerning spin-dependent electron transport phenomena in solid-state devices. This includes the observation of spin-polarized electron injection from a ferromagnetic metal to a normal metal by Johnson and Silsbee (1985) [5] and the discovery of giant magnetoresistance independently by Albert Fert et al. [6] and Peter Grünberg et al. (1988). [7]
[1] [2] They also introduced for the first time the notion of spin current. In 1983 Averkiev and Dyakonov [3] proposed a way to measure the inverse spin Hall effect under optical spin orientation in semiconductors. The first experimental demonstration of the inverse spin Hall effect, based on this idea, was performed by Bakun et al. in 1984 [4]
In particle physics, spin polarization is the degree to which the spin, i.e., the intrinsic angular momentum of elementary particles, is aligned with a given direction. [1] This property may pertain to the spin, hence to the magnetic moment , of conduction electrons in ferromagnetic metals, such as iron , giving rise to spin-polarized currents .