Spin-Spin Interaction

the interaction between the spin magnetic moments of microparticles (see). A relativistic effect, it contains the factor 1/c², where c is the speed of light. As a result, the spin-spin interaction is small compared with, for example, the electrical interaction of particles, the exchange interaction, and the interaction of the spin magnetic moment with an external field. Nonetheless, the spin-spin interaction leads to a number of important effects in atoms, molecules, and solids.

The interaction of the spin magnetic moments of the electrons and nucleus of an atom makes a contribution to the atom’s energy, which consequently depends on the relative orientation of the total spin of the electrons and the spin of the nucleus. A result of this dependence is the hyperfine splitting of atomic energy levels and the lines of atomic spectra (seeHYPERFINE STRUCTURE). The spin-spin coupling of electrons also makes a contribution to the energy of the atom. Such coupling, however, does not lead to additional splitting of energy levels and is usually small compared with spin-orbit coupling, which basically determines the fine structure of atomic spectra (seeMULTIPLICITY). In molecules, the multiplet structure of spectra is in many cases determined by the spin-spin coupling of electrons (1 levels).

In ferromagnetic materials, the magnetic ordering is due to the exchange interaction of the atomic carriers of magnetic moment. The magnetic interaction between the carriers is less significant. It, however, together with the action of the electric field of the crystal lattice, leads to the dependence of the crystal’s energy on the direction of the crystal’s magnetization—that is, to magnetic anisotropy. Although small compared with the exchange energy, the magnetic-anisotropy energy is reflected in the existence of a direction of easy magnetization in a ferromagnetic material and in the existence of the phenomenon of magnetostriction. The spin-spin interaction in a ferromagnetic crystal is also a relaxation mechanism responsible for the finite width of a resonance line in the ferromagnetic resonance effect (seeRELAXATION, MAGNETIC).

The interaction between the spin magnetic moments of electrons and of nuclei is also manifested in electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). Such coupling accounts for the splitting of the magnetic energy levels of the electron in an external field and is responsible for the hyperfine structure of EPR lines. In metals, the resonance frequency of precession of nuclear magnetic moments in NMR is shifted as a result of the appearance at the nucleus of an effective localized magnetic field generated by conduction electrons magnetized by the external field (the Knight shift). The spin-spin interaction within systems of electrons and nuclei is responsible for relaxation processes in the systems and makes a contribution to the width of resonance EPR and NMR lines.