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Unformatted text preview: Physics 927 E.Y.Tsymbal 1 Section 16: Magnetic properties of materials (continued) Ferromagnetism Ferromagnetism is the phenomenon of spontaneous magnetization the magnetization exists in the ferromagnetic material in the absence of applied magnetic field. The best-known examples of ferromagnets are the transition metals Fe, Co, and Ni, but other elements and alloys involving transition or rare-earth elements also show ferromagnetism. Thus the rare-earth metals Gd, Dy, and the insulating transition metal oxide CrO 2 all become ferromagnetic under suitable circumstances. Ferromagnetism involves the alignment of an appreciable fraction of the molecular magnetic moments in some favorable direction in the crystal. The fact that the phenomenon is restricted to transition and rare-earth elements indicates that it is related to the unfilled 3d and 4f shells in these substances. Ferromagnetism appears only below a certain temperature, which is known as the ferromagnetic transition temperature or simply as the Curie temperature. This temperature depends on the substance, but its order of magnitude is about 1000K for Fe, Co, Gd, Dy. It might be however much less. For example it is 70K for EuO and even less for EuS. Thus the ferromagnetic range often includes the whole of the usual temperature region. Above the Curie temperature, the moments are oriented randomly, resulting in a zero net magnetization. In this region the substance is paramagnetic, and its susceptibility is given by C C T T = (1) which is the Curie-Weiss law . The constant C is called the Curie constant and T C is the Curie temperature . The Curie-Weiss law can be derived using arguments proposed by Weiss. In the ferromagnetic materials the moments are magnetized spontaneously, which implies the presence of an internal field to produce this magnetization. Weiss assumed that this field is proportional to the magnetization, i.e. E = B M (2) where is the Weiss constant. Weiss called this field the molecular field and thought that this field results from all the molecules in the sample. In reality, the origin of this field is the exchange interaction . The exchange interaction is the consequence of the Pauli exclusion principle and the Coulomb interaction between electrons. Consider for example the system of two electrons. There are two possible arrangements for the spins of the electrons: either parallel or antiparallel. If they are parallel, the exclusion principle requires the electrons to remain far apart. If they are antiparallel, the electrons may come closer together and their wave functions overlap considerably. These two arrangements have different energies because, when the electrons are close together, the energy rises as a result of the large Coulomb repulsion. This is actually an explanation of the first Hund rule according to which the system of electrons tends to have a high possible spin, which is not forbidden by the Pauli principle. As we see from this example the electrostatic energy of an electron forbidden by the Pauli principle....
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This note was uploaded on 03/11/2012 for the course PHYSICS 927 taught by Professor Staff during the Fall '11 term at UNL.
- Fall '11