The Spin-Wave Theory of Antiferromagnetics

The spin-wave theory of antiferromagnets, recently studied by Anderson for the absolute zero of temperature, is examined here for finite temperatures to derive the thermodynamic properties of antiferromagnets at low temperatures. Somewhat differently from Anderson's semiclassical treatment, the present theory has used the formulation devised by Holstein and Primakoff, upon which the thermodynamic quantities are derived quantum-statistically. The parallel susceptibility is shown to be proportional to T², while the perpendicular susceptibility is independent of the temperature in the first approximation but decreases with increase in temperature if calculated in the second approximation. A tentative discussion is given of the nature of the divergences which arise in the simple formulation of spin-wave treatments in the absence of any kind of anisotropy.