Spin

Spin is a fundamental property of quantum particles that describes intrinsic angular momentum. Unlike classical rotation, quantum spin is not due to a particle physically spinning in space and can exist even for point particles.

The spin of a particle is described by a spin quantum number s, and the component along any chosen direction can take values m_s from −s to +s in integer steps. Particles with half-integer s are fermions (electrons, protons, neutrons); particles with integer s are bosons (photons, many gauge bosons). The electron has s = 1/2, a photon has s = 1.

Measuring spin along a direction yields discrete outcomes; for spin-1/2 these are “up” and “down” states. Spin interacts with magnetic fields through the magnetic moment, leading to phenomena such as Zeeman splitting and Larmor precession.

Spin is coupled to orbital motion (spin-orbit coupling) and participates in the Pauli exclusion principle, which constrains the allowed states of multi-electron atoms. Nuclear spin gives rise to hyperfine structure and underpins techniques such as NMR and MRI.

In condensed matter, electron spin is central to magnetism and the field of spintronics, which studies spin currents and spin-based information processing. Collective spin excitations, called magnons, occur in magnetic materials.

In quantum information, spin-1/2 systems serve as qubits, enabling simple quantum logic and entanglement.