Magicangle

Magic angle is a term used in spectroscopy and solid-state nuclear magnetic resonance to describe a specific orientation that simplifies measurement of anisotropic interactions. The magic angle is approximately 54.7356 degrees, defined as the angle between the external magnetic field and the axis of a rotating sample in magic angle spinning (MAS) experiments. When a sample is spun rapidly around an axis at this angle, certain dipolar couplings are averaged to zero, yielding narrower, more easily interpreted spectra.

The underlying principle rests on the angular dependence of dipolar interactions, which scale with the factor 3cos^2θ − 1, where θ is the angle between the internuclear vector and the magnetic field. At θ ≈ 54.7356 degrees, cos^2θ equals 1/3, causing 3cos^2θ − 1 to vanish. As a result, first-order dipolar broadening is removed in the averaged spectrum, allowing observation of isotropic chemical shifts and other interactions with reduced line broadening.

Applications of magic angle spinning include high-resolution solid-state NMR of organic compounds, polymers, and biological materials, where it enables structural insights and dynamic information that are difficult to obtain from powders. The technique complements other methods by clarifying resonance positions and coupling patterns, though higher-order effects or non-ideal spinning can leave residual anisotropy. The concept is widely used in materials science and biophysics to study structures and motions in solids.