Antiferromagnetism

In this section, in discussing a typical antiferromagnetic crystal like MnO, we suppose as indicated in the last section that each Mn2 + ion has a moment due to its five electrons lined up by Hund s rule, and that the crystal is an insulator. 

The arrangement of moments in a typical antiferromagnetic is shown in Fig. 3.1. Moments on adjacent atoms are, in the simplest cases such as MnO or NiO, coupled so that they are antiparallel. Then at low temperatures the susceptibility depends on whether the field is parallel or perpendicular to the moments. If it is parallel, the susceptibility X goes to zero as T- 0. This is because the coupling prevents any spins from turning over, and no spin waves are excited. On the other hand, if the field is perpendicular to the moments, they will be oriented by the field as shown in Fig. 3.2 and x is independent of temperature. The susceptibilities in the two directions are shown in Fig. 3.3. In practice, a macroscopic sample will usually contain numerous domains, and then the average susceptibility is 

Above a certain temperature TN, known as the Neel temperature, the long-range ordering of the moments disappears and the susceptibility then behaves roughly 

The ground state of an isotropic antiferromagnet is a singlet, the moments shown in Fig. 3.1 rotating in much the same way as the moment on an impurity rotates in the Kondo problem (see Section 8). The time for rotation, however, is very long, according to Anderson (1952) of order 

In a crystalline antiferromagnet the moment on each ion is less than it would be on the free ion. There are two separate phenomena involved here. One is the zero-point energy of the spin waves, which reduces the moment on each ion by a factor (Anderson 1952, Ziman 1952) 

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Wlien 2 g > (Eaa BB binary alloy corresponds to an Ismg ferromagnet (J> 0) and the system splits into two phases one rich in A and the other rich in component B below the critical temperature T. On the other hand, when 2s g < (Eaa+ bb > system corresponds to an antiferromagnet the ordered phase below the critical temperature has A and B atoms occupying alternate sites. 

In 1962 Heller and Benedek made aeeiirate measurements of the zero-field magnetization of the antiferromagnet MnF2 as a fiinetion of temperature and reported a p of 0.335 0.005, a result supporting an experimental parallelism between fluids and magnets. 

The development of neutron diffraction by C G Shull and coworkers [30] led to the detennination of the existence, previously only a hypothesis, of antiferromagnetism and ferrimagnetism. More recently neutron diffraction, because of its sensitivity to light elements in the presence of heavy ones, played a cmcial role in demonstrating the importance of oxygen content m high-temperature superconductors. 

Cheng H S and Wang L S 1996 Dimer growth, structure transition and antiferromagnetic ordering in small chromium clusters Phys. Rev. Lett. 77 51... 

Viitala E, Merikoski J, Manninen M and Timonen J 1997 Antiferromagnetic order and frustration in small clusters Phys. Rev. B 55 11 541... 

Antiferromagnetism Antifoam Antifoam agents Antifoaming agents... 

Parasitic ferromagnetism is a weak ferromagnetism that accompanies antiferromagnetism, eg, in a-ferric oxide [1309-37-1], a-Fe202. Possible causes include the presence of a smaU amount of ferromagnetic impurities, defects in the crystal, and slight deviations in the directions of the plus and minus spins from the original common axis. 

D. P. Landau, M. Krech. Spin dynamics simulations of ferro- and antiferromagnetic model systems comparison with theory and experiment. J Phys Condens Matter 77 R175-R213, 1999. 

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