The Neumann and Curie Principles

The Neumann and Curie principles have long been the dominating symmetry principles in condensed-matter physics. Both can be formulated in a number of different ways. For instance, the Neumann principle may be stated as follows the symmetry elements of an intrinsic property must include the symmetry elements of the medium . This formulation stresses that every physical property may and often does have higher symmetry, but never less than the medium. 

The symmetry elements to the right mmm) contain a center of inversion, but those to the left (oo/ji) do not. Therefore, if Eq. (94) should be satisfied (i.e., the Neumann and Curie principles together), K must not have a center of inversion, i.e.. 

The symmetry principles of Neumann and Curie can be recast in the language of irreducible representations. The requirement that physical properties be invariant under the symmetry elements of the point group simply means that they should transform as the totally symmetric irrep. For the dipole moment, the components... 

The principles of Neumann and Curie are of course based on classical physics. They remain valid for quantum systems but do not include typical quantum phenomena, such as the existence of electronic degeneracy or transitions between quantum states. A proper quantum description of molecular symmetry is thus required. 

Like other physical objects, as, for example, elementary particles, atoms and molecules, crystals are characterized by their symmetry which, as has been known now for more than a century, has a determining influence on their physical properties. The underlying symmetry principle, often called Neumann-Minnigerode-Curie principle can, for our purposes, be written as ... 

Curie understood that under stress, or in the presence of external electric or magnetic fields, the symmetry of a system is changed. The Neumann principle still applies but should no longer be based on the symmetry of the isolated crystal, but on that of the combined system of crystal and external field, as we have considered in Sect. 3.9. In the case of ammonia, application of an electric field has the Coov symmetry of a polar vector. The symmetry that results from the superposition of the field with the molecular point group 3 depends on the orientation (see Appendix B). In the coordinate frame of Fig. 3.1 one has ... 

Once the spatial group determined, from the structure determination, this structure can be further characterized following all the correlated properties with the existing symmetry elements and operations (in accordance with the so-called Neumann s principle, se also the Curie Principle of Section 2.5.8.2). Consequently, there is again emphasized the importance of the accuracy with which the structure is determined or the method is refined. 

When we are dealing with the question of whether a material can be spontaneously polarized or not, or whether some external action can make it polarized, there are two principles of great generality which are extremely useful, the Neumann principle and the Curie principle. Good discussions of these principles are found in a number of books, for instance [24, 36, 89]. The first of... 

This is the Neumann-Curie principle, developed by Franz Neumann in 1833 and Pierre Curie in 1894 see, e.g., in J.F. Nye, Physical Properties o/ Crystals, Oxford University Press, Oxford (1957). 

Piezo is derived from the Greek piezein, which means to squeeze or press. The piezoelectric effect is the phenomena where some materials generate an electric potential in response to an applied mechanical stress. Piezoelectricity was discovered by Pierre and Jacques Curie in 1880. Based on crystal symmetry and Neumann s principle, it is known that the piezoelectric effect only exists in crystals that do not have a center of symmetry. There are 20 classes of crystal point symmetry groups that exhibit the piezoelectric effect. The piezoelectric effect can be described by [2] ... 

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