| spin | |
|---|---|
| Name | Spin |
| Dimension | Dimensionless |
| SIunit | none |
| Introduced | 1925 |
| Introduced by | George Uhlenbeck and Samuel Goudsmit |
spin
Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. It is a fundamentally quantum mechanical property distinct from classical rotation, quantized in units of the reduced Planck constant ℏ and closely tied to the Pauli exclusion principle and the classification of particles as fermions or bosons. Spin underpins many phenomena in atomic physics, condensed matter physics, and quantum information science.
The concept of spin emerged in the mid-1920s to explain anomalous atomic spectra and magnetic moments that could not be accounted for by orbital motion alone. In 1925 George Uhlenbeck and Samuel Goudsmit proposed electron spin to explain the fine structure of the hydrogen atom and the pattern of spectral lines first explored in the era of the old quantum theory. Subsequent developments by Wolfgang Pauli, who formulated the Pauli exclusion principle and the Pauli matrices, and by Paul Dirac, whose Dirac equation predicted spinor behavior and the existence of the positron, established spin as a central element of quantum mechanics. Experimental confirmation arrived via the Stern–Gerlach experiment and precision measurements of magnetic moments at institutions such as the Cavendish Laboratory and laboratories of the American Physical Society community.
In quantum theory spin is described by operators that satisfy the Lie algebra of the rotation group SO(3) or its double cover SU(2). The spin operators S_x, S_y, S_z obey the commutation relations [S_i,S_j]=iℏ ε_{ijk} S_k. Allowed eigenvalues of S^2 are s(s+1)ℏ^2 and of S_z are m_sℏ, where s is the spin quantum number (integer or half-integer) and m_s ranges from −s to +s in integer steps. Common values are s=1/2 for the electron, proton, and neutron; s=1 for many vector bosons; and s=0 for scalar particles such as the Higgs boson. Spinors transform under SU(2) representations and require a 720° rotation to return to the original state, a property formalized in representation theory and used in relativistic quantum field theory frameworks like quantum electrodynamics (QED) and quantum chromodynamics (QCD).
Spin is intrinsic angular momentum, not arising from spatial motion around an axis like classical orbital angular momentum L = r × p. In atoms total angular momentum J combines both contributions via J = L + S and is subject to LS coupling (Russell–Saunders) or jj coupling depending on atomic number and electron configuration. Magnetic moments associated with spin are characterized by the g-factor; for the electron the anomalous magnetic moment is a precision test of QED, measured and computed by collaborations at institutions such as CERN and NIST. Distinctions between intrinsic and orbital contributions are critical in explaining fine structure, hyperfine structure, and phenomena like spin–orbit coupling in solids and atoms. In relativistic theories, spin is tied to representations of the Poincaré group.
The earliest direct evidence for spin came from the Stern–Gerlach experiment, which spatially separated silver atom beams according to their magnetic moment. Modern techniques for preparing and measuring spin include magnetic resonance methods: nuclear magnetic resonance (NMR) and electron spin resonance (ESR or EPR). Spin-polarized beams and spintronic devices employ spin filtering and spin pumping to create non-equilibrium spin populations. Detection technologies include SQUID magnetometers, spin-polarized scanning tunneling microscopy (SP-STM), and optical methods exploiting optical orientation and Kerr effect measurements in condensed matter laboratories at universities like Stanford University and MIT. Precision experiments measuring the electron g-factor and the muon anomalous magnetic moment (g−2) probe physics beyond the Standard Model.
Spin determines quantum statistics: half-integer spin particles obey Fermi–Dirac statistics and the Pauli exclusion principle, while integer-spin particles obey Bose–Einstein statistics and can condense into the same quantum state (Bose–Einstein condensate). In many-body systems spin degrees of freedom give rise to magnetic order (ferromagnetism, antiferromagnetism) described by models such as the Heisenberg model and the Ising model. Spin excitations manifest as magnons in ordered magnets and as quasiparticles in correlated systems studied in condensed matter physics. Spin correlations and entanglement are central to phenomena like superconductivity in unconventional materials, the fractional quantum Hall effect, and the study of quantum phase transitions in cold-atom experiments at facilities like JILA and Max Planck Institute for Quantum Optics.
Spin underlies technologies ranging from magnetic resonance imaging (MRI) in medical imaging to spintronics devices such as giant magnetoresistance (GMR) read heads pioneered by researchers at IBM and elsewhere. Electron and nuclear spins serve as qubits in quantum computing platforms: NV center defects in diamond and donor spins in silicon are prominent implementations pursued by groups at Harvard University, University of Chicago, and companies like Microsoft (Station Q) and Intel (research collaborations). Spin-based quantum control enables quantum sensing with extreme sensitivity to magnetic and electric fields. Research into topological states of matter leverages spin–orbit coupling and spin textures (e.g., skyrmions) for potential low-power information technologies.
Category:Quantum mechanics Category:Particle physics Category:Condensed matter physics