Magnetic Materials: From Isolated Moments to Ordered Arrangements
Magnetic Materials: From Isolated Moments to Ordered Arrangements
The magnetic behavior of materials can be quite diverse with a wide range of susceptibilities. All materials exhibit diamagnetism with a very small, negative susceptibility and it is predominant in elements with completely filled shells, ionic and covalently bonded solids, organic compounds, water, and blood. In addition, superconductors expel the magnetic flux (Meissner effect) below the critical temperature and can be treated as ideal diamagnets. Paramagnetism, exhibited by elements with unpaired electrons, can be described classically by the Langevin function or quantum mechanically by the Brillouin function; the Curie law describes their temperature dependence. Ferromagnets are characterized by an internal “molecular” field, proportional to the magnetization, which explains the coupling between atomic magnetic moments and the spontaneous magnetization in regions called domains. The internal field has its origin in the quantum mechanical exchange interaction that is isotropic, short range, but can be of very large magnitudes. The Bethe–Slater curve describes the exchange interaction in terms of interatomic distances and correctly predicts ferromagnetism for intermediate distances; for smaller distance antiferromagnetism (§4) and for larger distances, an absence of order is also predicted. The strength of the exchange interaction determines the Curie temperature; above which the spontaneous magnetization vanishes and the material behaves as a simple paramagnet, as described by the Curie–Weiss law. In the vicinity of the Curie temperature, ferromagnets shows critical phenomena—four exponents characterize the magnetization and susceptibility and describe the order–disorder transition. When nearest and next-nearest exchange interactions are considered, the ground state can be a helical structure, an interesting spin order observed in some rare earth elements with hexagonal unit cells.
Keywords: diamagnetism, superconductors, paramagnets, Langevin function, Brillouin function, ferromagnets, Curie temperature, critical phenomena, exchange, Bethe–Slater curve, critical phenomena & exponents
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