The processes of development and formation of ordered domain structures in low-frequency alternating magnetic field are studied. The possibility of formation of spiral and ring structures of the local magnetic inhomogeneities is experimentally demonstrated. Mechanisms and models for formation of spiral domains under the influence of a gyrotropic force are proposed. In quasistatic approximation a quantitative parameter is introduced and reasonably justified for characterizing the conditions favorable for the occurrence of these ordered structures. The study of the processes of self-organization in open, nonequilibrium thermodynamic systems consisting of randomly moving and interacting elements is one of the urgent problems of modern science. Spatially ordered structures in inanimate objects formed as a result of self-organization represent a particular interest. All considered ordered domain structures are very sensitive to slightest changes in external conditions of energy pumping from alternating magnetic field and, therefore, can be sensitive sensors of external influences.