We have considered magnetic ordered structures in two-dimensional ion lattice with spins and delocalized charge carrier states in such magnetic structures.
Employing field theoretical and topological methods leads to stable global space inhomogeneous magnetic ordered configurations with finite energy. These magnetic structures have short-range ferromagnetic order, and in addition to local ferromagnetic order there is a long-range antiferromagnetic order. We have found that stable inhomogeneous magnetic configurations are described by two scalar fields (which have an interpretation of magnetization vectors) and also by vector fields, which are related to orbital momentum. Each of inhomogeneous magnetic configurations is characterized by their own field topological number q and a finite energy Eq.
Owing to their topological nature, such inhomogeneous magnetic ordered structures are stable under fluctuations, i.e. they do not decay in time. As a result, they can exist at sufficiently high temperatures, for example, in classical (lanthanum, yttrium) high-temperature superconductors and in heterostructures based on diluted magnetic semiconductor.
Moreover, these inhomogeneous magnetic structures are not destroyed through interactions with current carriers. However, the delocalized charge carrier states are determined by the energy and the structure of magnetic configurations. The energy functional of the charge carrier system, as a functional over all the fields (histories) of the stable ion-field configuration with the fixed q, is finite and single-valued only if the charge carrier system is coherent. It has conserved momenta whose symmetry is consistent with the structure of the ion-field configurations. For the stable ion-field configuration with the lowest energy we have found coherent p- and d-states. The coherent electron d-states have superconducting properties.
Coherent charge carrier states and their transport properties in magnetic materials have attracted interest from the physical point of view as well as for the technological application.
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