Abstract

Spins in an antiferromagnet subjected to an external field perpendicular to the preferred axis of antiferromagnetic magnetization are not exactly aligned parallel and antiparallel to this axis. It is shown that a better approximation to the spin wave theory can be worked out, if one takes the equilibrium directions of the spins as the axes of quantization. One obtains the field·dependent resonance frequency of a microwave, which the usual spin wave theory fails to give, and also a higher approximation to the perpendicular susceptibility. The value of the latter in the limit of vanishing field strength agrees with the one obtained by Kubo. § l. Introduction Since Anderson1> has shown that the spin wave theory is a good approximate method for the ground state of antiferromagnetics, several authors2> have applied this method to the calculation of thermodynamic properties of these substances. The perpendicular susceptibility X..L calculated in the first approximation of the spin wave theory has the same value as that obtained on the basis of the molecular field theory, namely, it depends neither on temperature nor on field strength. However, Kubo3> has shown, by calculating the con­ tribution from terms neglected in the first approximation by the perturbation method, that X..L deviates at absolute zero from its classical value and also depends on temperature. On the other hand, Ziman•>, through a different approach, attained the result that X.1. in a higher approximation is still constant. Nak.amura5> discussed antiferromagnetic resonance absorption, and according to his results, for the case of perpendicular field, only one field-independent resonance frequency is obtained under the assumption of a uniaxial anisotropy. The classical theory developed by Nagamiya6> and Keffer and KitteF> yielded, however, two resonance frequencies, of which one corresponds to the frequency given by the spin wave theory and the other is a frequency which is field-dependent. Nakamura attributed this discrepancy to an insufficient approximation made in his spin wave theory. We propose here another method of treating these problems. Kubo8> suggests a similar method, but his statement is not so specific as ours. By this method the terms neglected in the usual spin wave theory can be taken into account to a certain extent and accordingly the discrepancy concerning the resonance frequency can be removed. We shall also derive X.1. and discuss the discrepancy between two conclusions attained by Kubo and Ziman. We are led to believe that Kubo' s result is more reasonable. We always confine ourselves to the case of two sublattices and to external field applied perpendicularly to the preferred axis. The spins on one sublattice are, in this case, not exactly antiparallel to the spins on the

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