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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)
That is, the resulting spin operators for higher spin systems in three spatial dimensions, for arbitrarily large j, can be calculated using this spin operator and ladder operators. They can be found in Rotation group SO(3) § A note on Lie algebras. The analog formula to the above generalization of Euler's formula for Pauli matrices, the group ...
The spin Hall effect (SHE) is a transport phenomenon predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel in 1971. [1] [2] ...
The superscript three (read as triplet) indicates that the multiplicity 2S+1 = 3, so that the total spin S = 1. This spin is due to two unpaired electrons, as a result of Hund's rule which favors the single filling of degenerate orbitals. The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total ...
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]
The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, and that does not require the application of a large magnetic field.
In the Rashba–Edelstein effect the spin current is a consequence of the spin accumulation that occurs in the material as the charge current flows on its surface (under the influence of a potential difference and, therefore, of an electric field), while in the inverse Rashba–Edelstein effect the spin current is the quantity injected inside ...
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 .