spinaxis

Spin axis is the orientation of the angular momentum vector associated with a particle's intrinsic spin or with the spin of a rotating body. In quantum mechanics, spin is an intrinsic form of angular momentum carried by elementary particles and by composite systems, and its projection is defined with respect to a chosen quantization axis.

For a spin-1/2 particle, measuring the spin along any axis yields one of two eigenvalues, ±ħ/2; the state is described by a two-component spinor, and the probabilities depend on the overlap with the eigenstates of the chosen axis. Rotation of the coordinate system rotates the eigenstates; the components Sx, Sy, Sz are represented by Pauli matrices.

When a spin is placed in a magnetic field, the torque causes precession of the spin around the field direction; the instantaneous spin axis traces a conical path with Larmor frequency ωL = γ B (for a gyromagnetic ratio γ). In ensemble treatments, the Bloch equation describes the time evolution of the magnetization vector, including relaxation toward equilibrium.

Classically, the spin axis of a rotating rigid body is the axis about which most of its angular momentum is oriented; in a symmetric top in the absence of external torques, the angular momentum vector aligns with the symmetry axis, a situation that underpins gyroscopic stability.

Understanding and controlling spin orientation along a chosen axis is central to technologies such as magnetic resonance imaging and spectroscopy, electron-spin resonance, and spintronic devices, where information is stored and manipulated through spin alignment along specific axes.