For a spin-one-half ensemble, spin polarization measures unequal occupation or coherent alignment of spin states. A spin-dependent energy splitting does not alone determine the ensemble's response: occupation, temperature and spin relaxation matter. A spin polarization is distinct from a net change of charge density and from the optical polarization of waves.
For two levels separated by and with the plus label assigned to the upper level, thermal equilibrium gives . The weak-splitting limit is . Labels based on the lower-energy aligned moment reverse the reported sign without changing the population imbalance.
A beam's unequal population of spin projections along a specified axis. For spin-one-half particles the displayed longitudinal polarization uses populations parallel and antiparallel to the momentum. An unpolarized beam has equal populations and requires an initial-spin average in a cross section; a polarized beam weights the corresponding helicity amplitudes differently. This differs from photon linear polarization.
A spin texture describes how a spin expectation value or spin polarization varies with position or wavevector. It specifies a vector field, including its magnitude when that matters; a direction field alone is undefined wherever that magnitude vanishes. A Rashba spin texture is an example in which spin expectation values wind around circles in the plane of wavevectors.
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Spin polarization refers to the distribution of electron spins in a material or a system, which can result in a net magnetic moment due to an imbalance in the populations of spin-up and spin-down states. In quantum mechanics, electrons possess an intrinsic angular momentum known as "spin," which can be thought of as a kind of internal magnetic moment. When a material exhibits spin polarization, it means that there is a preference for one of the spin states over the other.