Spin

What is spin?  

In classical physics, a rotating object possesses a property known as angular momentum. Angular momentum is a form of inertia, reflecting the object's size, shape, mass, and rotational velocity.  It is typically represented as a vector (L) pointing along the axis of rotation.  

Atomic and subatomic particles posses a corresponding property known as spin or spin angular momentum. Protons, neutrons, whole nuclei, and electrons all possess spin and are often represented as tiny spinning balls. Although inaccurate, this is not a terribly bad way to think about spin as long as you do not take the analogy too far. Several key differences should be recognized: 

• The particle is not actually spinning or rotating.
• Spin, like mass, is a fundamental property of nature and does not arise from more basic mechanisms.
• Spin interacts with electromagnetic fields whereas classic angular momentum (L) interacts with gravitational fields.
• The magnitude of spin is quantized, meaning that it can only take on a limited set of discrete values. 

Angular momentum (L) vector points along axis of rotation.

Representation of a "spinning" nucleus with non-zero quantum spin (I)

Quantum mechanics is the branch of modern physics explaining how phenomena like spin operate at the atomic level including its restriction to discrete values. This is a "bizarro" world to be sure, and many of the results are unexpected and non-intuitive. 

Unlike macroscopic angular momentum, spin can only be measured discrete integer or half-integer units (0, 1/2, 1, 3/2, 2, 5/2, ...)  Protons, neutrons, and electrons all have spin = ½. Although exactly the same property, nuclear spin is traditionally denoted by the letter I, while electron spin is denoted by the letter S. Electron spin has only one value (S = ½, always), but nuclear spin values ranging from I = 0 to I = 8 in ½-unit increments can be found across the entire periodic table.  ¹H, the nucleus most commonly used for NMR and MRI, has I = ½, the same spin as the single proton of which it is composed. Only nuclei with non-zero spins (I ≠ 0) can absorb and emit electromagnetic radiation and undergo "resonance" when placed in a magnetic field.

Advanced Discussion (show/hide)»

A few additional comments about spin. . .

Particles with half-integer spin like protons and electrons are called fermions. Particles with integer spin are called bosons.

Any particle with non-zero spin can undergo resonance. So it is possible to have electron paramagnetic resonance (EPR) and even muon paramagnetic resonance (μPR).

Protons and neutrons are no longer considered elementary particles, each being composed of 3 quarks held together by by the strong force mediated by gluons. Quarks are elementary particles that have spin ½. The proton is composed of 2 "up-quarks" and one "down quark". Generally two of the three quark spins cancel leaving the proton with a spin ½, At very high temperatures, however, the three quark spins may align, giving the proton a spin of 3/2. This high-energy, high-spin proton is called a Δ⁺ particle.

In addition to spin angular momentum, electrons also have angular momentum from their orbital motion around the nucleus. The total electron angular momentum is the sum of spin and orbital momentum.

Whole molecules also acquire rotational angular momentum when they collide with other molecules. At absolute zero, molecular motion ceases and so does molecular angular momentum. However, spin angular momentum possessed by subatomic particles persists even at absolute zero.

Although considered "dimensionless" quantum numbers, the angular momenta associated with I and S, like conventional angular momentum (L), do have SI units of Joule-sec when multiplied by the reduced Planck's constant (ħ = h/2π).

In most diagrams, nuclear spin (I) is denoted by an arrow resembling a vector in classical physics similar to L. Like a classical vector, spin does have a specific magnitude (½, 1, etc.). However, its "direction" is not so simply defined because it does not behave as a conventional vector under certain rotations. Spin is therefore considered a spinor, an element of a complex vector space governed by rules of advanced group theory.

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References
     "Introduction to Angular Momentum". Wikipedia, The Free Encyclopedia.
     "Spin (Physics)". Wikipedia, The Free Encyclopedia.
     Weiss M. Spin (website). 2001.

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Related Questions
     You seem to use MR, MRI and NMR interchangeably.  Are there any differences among these terms?
     What is the difference between "spin" and "spin state"?

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