Magnetic Ordering: Some Structural Aspects

An overview of some structural aspects of magnetic ordering is presented. Magnetic symmetry operations, point groups, and Bravais lattices will be utilized to describe the magnetic symmetry of various magnetic materials. Throughout the talk, the utilization of the theory of magnetic symmetry will be emphasized. The magnetic space groups of Fe, Co, Ni, α’-FeCo, CoPt, CrPt3, and Cu2MnAl will be examined. Introduction One of the most interesting and perhaps most neglected phase transformations in the solid state is the paramagnetic to ferromagnetic transformation. One of the reasons for this is that for many years in the metallurgical community, the transformation was not thought to be a transformation at all! Indeed the paramagnetic β phase in Fe was removed from the iron phase diagrams and replaced with the symbol used for ferromagnetic α-Fe. This confusion amongst metallurgists arose from a faulty understanding of symmetry and its relationship to “structure” and the definition of “phase”. A common definition of phase is “...a portion of the system whose properties and composition are homogeneous and which is physically distinct from other parts of the system”. If we accept this definition it alone, demonstrates that that paramagnetic to ferromagnetic “change” is indeed a phase change, since a paramagnetic phase has different magnetic properties than a ferromagnetic phase. In older definitions, a phase was said to have a distinct “structure” and it is here where the problem arose. As far as could be determined by x-ray diffraction, the structure of ferromagnetic Fe was the same as that of paramagnetic Fe. Thus no change of phase was thought to have occurred when Fe lost its magnetism at the Curie temperature. A good definition of a phase includes the fact that each phase has a set of order parameters, (η1, η2, η3, ...) which specify its physical properties. Such order parameters include composition, structure, atomic order parameter, magnetization, etc. By including “order parameters” in the definition of a phase it becomes clear that a discontinuous change in order parameter occurs at a phase change. If the change is from a zero value to an infinitesimal one, the transformation is of higher order thermodynamically. Such is the case for most paramagnetic to ferromagnetic transformations. Revised Version of paper in Phase Transformations and Evolution in Materials, pages 121-137, edited by P.Turchi and A. Gonis, The Minerals , Metals and Materials Society, 2000 Even if the word “structure” is included explicitly in the definition, the paramagnetic to ferromagnetic transition should be classified as a phase transformation. This is because there is a change in symmetry during the paramagnetic to ferromagnetic transition. For the case of Fe, this transformation causes a change from paramagnetic cubic β-Fe to ferromagnetic tetragonal α-Fe. The changes in symmetry during magnetic transformations are the topic of this paper.