Solid-state nuclear magnetic resonance (ssNMR) is a spectroscopy technique used to characterize atomic-level structure and dynamics in solid materials. ssNMR spectra are broader due to nuclear spin interactions which can be categorized as dipolar coupling, chemical shielding, quadrupolar interactions, and j-coupling. These interactions directly affect the lines shapes of experimental ssNMR spectra which can be seen in powder and dipolar patterns. There are many essential solid-state techniques alongside advanced ssNMR techniques that may be applied to elucidate the fundamental aspects of solid materials. ssNMR is often combined with magic angle spinning (MAS) to remove anisotropic interactions and improve the sensitivity of the technique. The applications of ssNMR further extend to biology and medicine.

The resonance frequency of a nuclear spin depends on the strength of the magnetic field at the nucleus, which can be modified by isotropic (e.g. chemical shift, isotropic J-coupling) and anisotropic interactions (e.g. chemical shift anisotropy, dipolar interactions). In a classical liquid-state NMR experiment, molecular tumbling coming from Brownian motion averages anisotropic interactions to zero and they are therefore not reflected in the NMR spectrum. However, in media with no or little mobility (e.g. crystalline powders, glasses, large membrane vesicles, molecular aggregates), anisotropic local fields or interactions have substantial influence on the behaviour of nuclear spins, which results in the line broadening of the NMR spectra.

Chemical shielding is a local property of each nuclear site in a molecule or compound, and is proportional to the applied external magnetic field. The external magnetic field induces currents of the electrons in molecular orbitals. These induced currents create local magnetic fields that lead to characteristic changes in resonance frequency. These changes can be predicted from molecular structure using empirical rules or quantum-chemical calculations.

In general, the chemical shielding is anisotropic because of the anisotropic distribution of molecular orbitals around the nuclear sites. Under sufficiently fast magic angle spinning, or under the effect of molecular tumbling in solution-state NMR, the anisotropic dependence of the chemical shielding is time-averaged to zero, leaving only the isotropic chemical shift.

Nuclear spins exhibit a magnetic dipole moment, which generates a magnetic field that interacts with the dipole moments of other nuclei (dipolar coupling). The magnitude of the interaction is dependent on the gyromagnetic ratio of the spin species, the internuclear distance r, and the orientation, with respect to the external magnetic field B, of the vector connecting the two nuclear spins (see figure). The maximum dipolar coupling is given by the dipolar coupling constant d,

where γ₁ and γ₂ are the gyromagnetic ratios of the nuclei, ${\displaystyle \hbar }$ is the reduced Planck constant, and ${\displaystyle \mu _{0}}$ is the vacuum permeability. In a strong magnetic field, the dipolar coupling depends on the angle θ between the internuclear vector and the external magnetic field B (figure) according to

D becomes zero for ${\displaystyle \theta _{m}=\arccos {\sqrt {1/3}}=\arctan {\sqrt {2}}\simeq 54.7^{\circ }}$. Consequently, two nuclei with a dipolar coupling vector at an angle of θ_m = 54.7° to a strong external magnetic field have zero dipolar coupling. θ_m is called the magic angle. Magic angle spinning is typically used to remove dipolar couplings weaker than the spinning rate.

Nuclei with a spin quantum number >1/2 have a non-spherical charge distribution and a quadrupole moment. The quadrupole moment is a second rank tensor that couples to the surrounding electric field gradient, another second rank tensor. Nuclear quadrupole coupling is typically the second largest interaction in NMR, comparable in size to the largest interaction called Zeeman interactions. When the nuclear quadrupole coupling is not negligible relative to the Zeeman coupling, higher order corrections are needed to describe the NMR spectrum correctly. In such cases, the first-order correction to the NMR transition frequency leads to a strong anisotropic line broadening of the NMR spectrum. However, all symmetric transitions, between ${\displaystyle m_{I}}$ and ${\displaystyle -m_{I}}$ levels are unaffected by the first-order frequency contribution. The second-order frequency contribution depends on the P₄ Legendre polynomial, which has zero points at 30.6° and 70.1°. These anisotropic broadenings can be removed using DOR (DOuble angle Rotation) where you spin at two angles at the same time, or DAS (Double Angle Spinning) where you switch quickly between the two angles. Both techniques were developed in the late 1980s, and require specialized hardware (probe). Multiple quantum magic angle spinning (MQMAS) NMR was developed in 1995 and has become a routine method for obtaining high resolution solid-state NMR spectra of quadrupolar nuclei. A similar method to MQMAS is satellite transition magic angle spinning (STMAS) NMR developed in 2000.