The foundations for understanding the electronic structure of many-electron atoms are introduced. We start from the discovery of the spin and introduce spin operators. The spin existence is shown to “upgrade” the state of single particles into a product space with the spin subspace, and to impose constraints on states of identical particles, which must be symmetric (bosons) or antisymmetric (fermions) under particle transpositions. The many-electron state in the atom is therefore approximated as an antisymmetrized products (Slater determinant) of single-electron states (spin-orbitals). The variationally optimal orbitals are shown to be solutions to the Hartree–Fock equations, and the assignment of electrons to these orbitals in the atomic ground state reflects the Pauli exclusion and Aufbau principles, thus explaining the trends in the periodic table of the elements in terms of their electronic configurations. Special attention is given to two-electron systems, demonstrating the exchange stabilization of triplet versus singlet states (Hund’s rule).

The quantum mechanical exchange interaction gives rise to magnetic moments and their interactions in materials, which give rise to patterns and structures in the orientations of magnetic moments at low temperatures. With increasing temperature, pressure, and magnetic field, magnetic structures are altered, and Chapter 21 describes several trends that can be understood by thermodynamics. The critical temperature of magnetic ordering, the Curie temperature TC, is calculated. Compared to chemical ordering, the strengths and alignments of magnetic moments have more degrees of freedom, allowing for diverse magnetic structures. These include ferrimagnetism, frustrated structures, and spin glasses. The vectorial character of spin interactions can give rise to localized spin structures such as skyrmions. An electromechanical phase transition can occur when the energy for a displacement of positive and negative ions in a unit cell is comparable to thermal energies. This ferroelectric transition has some similarities to the ferromagnetic transition, but is described by Landau theory. Domains in ferroelectric and ferromagnetic materials can reduce the energy in surrounding elastic and magnetic fields, andthe width of a boundary between two magnetic domains is estimated.

We shall first outline the types of interactions of spins, which are most important for solid polarized targets: the magnetic dipole interaction, the quadrupole interaction, the spin-orbit interaction and the hyperfine interaction. Other direct and indirect spin interactions are described: these give rise to the chemical shift, the Knight shift, molecular spin isomers and to the exchange interaction of electron pairs. These, and in particular the dipolar interaction, are then used in the discussion of the magnetic resonance phenomena, such as the resonance line shape and saturation. The magnetic resonance absorption and the transverse susceptibility are discussed starting from the first principles, and Provotorov's equations are derived. The relaxation of spins, which is phenomenologically introduced already for the saturation, is then overviewed in greater depth, before closing with sudden and adiabatic changes of spin systems in the rotating frame.