Comparison and Discussion of Some Periodic Domain Structures

The energy density of seven periodic domain structures in sheets of uniaxial magnetic materials placed in a magnetic field Hz perpendicular to the sheet is calculated.1 The following periodic structures are considered: I. A hexagonal bubble lattice; within the cylinders the magnetization Ms is reversed with respect to Hz. II. The negative of I; within the cylinders, Ms and Hz have the same directions. III. A similar but square lattice of bubbles and its ``negative'' (IV). V. A honeycomb structure where the prisms are the reversed domains. VI. The negative of V. VII. A strip lattice. The energy density is minimized with respect to two variables. Comparing the structures I-VII it is found that: (1) In a large field region a hexagonal bubble lattice (I) has the lowest energy. At low fields, VII has the lowest energy. (2) The structures where the reversed domains are connected with each other (II, IV, VI) have a higher energy than their negatives (I, III, V). (3) The radius of a bubble in a hexagonal lattice (I) differs at the same magnetic field considerably from the radius of an isolated bubble. (4) The energy of the honeycomb structure V is always higher than the energy of structure I. Comparing VI and II this is not the case: at higher field, structure VI has a lower energy than structure II. (5) Comparing the fields at which for I, III, V, and VII the lattice distance becomes infinite, we found the lowest field for VII and the highest for I and III. The occurrence of the different structures will of course not only be determined by the energy difference between them but also by the number of nucleation points and the possible energy barriers. The occurrence of I in zero field seems to be possible since the lattice distance for I is almost the same at zero field as at the lowest field for which I have the lowest energy. If I can occur at low fields the same holds for II, since it can be formed from I by reversing Hz. For higher fields, II will go over into VI. At a field where the lattice distance of VI becomes infinite, an isolated interconnected reversed domain will appear. This can be a hollow cylindrical domain. Changing the field in such a way that the well-known transitions occur: ring→bubble→strip→strip lattice, a transition from I→VII via different structures has been described above. Such a transition was also found experimentally. Detailed calculations will be published elsewhere.1