A ferromagnet (or other like materials) exists usually in domains and their polarization makes a loop with varying external polling field. These domains reflect the microscopic symmetry of the systems. The formation of domains is due to long-range interactions, while the intra-domain texture is dominated by short-range behaviors, as expected by the definition. Without long range force, a single domain will be randomly selected, due to spontaneous symmetry breaking. Long range force then modifies this and result in richer structure, with all possible domains occurring conforming to the symmetry. Domains are separated by domain walls, which are usually very thin and allow the order parameter to change gradually from the value of one domain to that of another domain. Domains form randomly (usually think so), in the course of thermal fluctuations, but can be modified by applying external field. The behavior of domains is therefore history dependent. A very quantitative understanding of the dynamics of domains is not easy, especially in the presence of impurities and other factors. A recent study reveals more new aspects of this behavior: Phys. Rev. B 82, 104423 (2010).
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