The theory of the structure of ferromagnetic domains in films and small particles is discussed. The paper presents calculations of domain boundary, magnetic, and anisotropy energies for thin films, small particles, and long needles of ferromagnetic material. For sufficiently small dimensions, the optimal structure consists of a single domain magnetized to saturation in one direction. The paper shows that the normal macroscopic magnetization characteristics of ferromagnetic materials may change radically when one or more dimensions of the test specimen are reduced below a critical length of the order of 10^-5 to 10^-6 cm. Experimental results support this theory. In the absence of an applied magnetic field, the demagnetized state is the stable state in large ferromagnetic crystals. The domains are oriented so that the magnetic flux circuit lies almost entirely within the specimen. Internal flux closure implies a high degree of ordering in the domain configurations, contrary to the usual statement that domains are oriented at random. Theoretical discussions of domain configurations in large crystals were first made by Landau and Lifshitz, and further contributions were made by Kennard, Lifshitz, and Néel. The critical dimensions for transition from a configuration with domain structure to a saturated configuration are estimated as ~3×10^-6 cm in films and ~2×10^-6 cm in particles or grains. These estimates are based on typical values of the relevant material constants. As the dimensions of the specimen are diminished, the relative contributions of the various energy terms to the total energy are changed, and surface energies become more important than volume energies. When very small dimensions are reached, it is favorable energetically to do away with the domain boundaries, so that the whole specimen becomes one domain and acts as a permanent magnet. This was first predicted by Frenkel and Dorfman. Experimental evidence of permanent magnetization in small ferromagnetic particles was discovered by Elmore. The conditions in which the lowest energy state of a specimen represents a structure with a single domain are expected to differ somewhat in films, needles, and powders. In a film one dimension is small; in a needle or wire two dimensions are small, while in a powder particle of the material all three dimensions are small. The energy relationships in ferromagnetic single crystals have been discussed by Landau and Lifshitz and Brown. The results of these papers are used as a starting point for the present treatment. The terms in the free energy of the specimen which are relevant to the present problem may be represented as the sum F = Fw + Fm + Fa, where Fw is the surface energy of the boundary surfaces between domains, Fm is the magnetic field energy of the configuration, and Fa is the anisotropy energy of spin orientation. The paper also discusses the application of these energy relationships to particular configurations, including films, needles, and particles. The results are in agreement with experimental observations, showing that smallThe theory of the structure of ferromagnetic domains in films and small particles is discussed. The paper presents calculations of domain boundary, magnetic, and anisotropy energies for thin films, small particles, and long needles of ferromagnetic material. For sufficiently small dimensions, the optimal structure consists of a single domain magnetized to saturation in one direction. The paper shows that the normal macroscopic magnetization characteristics of ferromagnetic materials may change radically when one or more dimensions of the test specimen are reduced below a critical length of the order of 10^-5 to 10^-6 cm. Experimental results support this theory. In the absence of an applied magnetic field, the demagnetized state is the stable state in large ferromagnetic crystals. The domains are oriented so that the magnetic flux circuit lies almost entirely within the specimen. Internal flux closure implies a high degree of ordering in the domain configurations, contrary to the usual statement that domains are oriented at random. Theoretical discussions of domain configurations in large crystals were first made by Landau and Lifshitz, and further contributions were made by Kennard, Lifshitz, and Néel. The critical dimensions for transition from a configuration with domain structure to a saturated configuration are estimated as ~3×10^-6 cm in films and ~2×10^-6 cm in particles or grains. These estimates are based on typical values of the relevant material constants. As the dimensions of the specimen are diminished, the relative contributions of the various energy terms to the total energy are changed, and surface energies become more important than volume energies. When very small dimensions are reached, it is favorable energetically to do away with the domain boundaries, so that the whole specimen becomes one domain and acts as a permanent magnet. This was first predicted by Frenkel and Dorfman. Experimental evidence of permanent magnetization in small ferromagnetic particles was discovered by Elmore. The conditions in which the lowest energy state of a specimen represents a structure with a single domain are expected to differ somewhat in films, needles, and powders. In a film one dimension is small; in a needle or wire two dimensions are small, while in a powder particle of the material all three dimensions are small. The energy relationships in ferromagnetic single crystals have been discussed by Landau and Lifshitz and Brown. The results of these papers are used as a starting point for the present treatment. The terms in the free energy of the specimen which are relevant to the present problem may be represented as the sum F = Fw + Fm + Fa, where Fw is the surface energy of the boundary surfaces between domains, Fm is the magnetic field energy of the configuration, and Fa is the anisotropy energy of spin orientation. The paper also discusses the application of these energy relationships to particular configurations, including films, needles, and particles. The results are in agreement with experimental observations, showing that small