Spin Wave Theory of Principal Susceptibilities of the Heisenberg Antiferromagnet

The parallel and perpendicular susceptibilities of the Heisenberg antiferromagnet below the Néel temperature are discussed on the basis of the spin wave approximation. It is shown through a new approach that an interplay between the external field and the spin wave interaction makes an important contribution of the order of 1/ S 2 to the temperature dependence of each of the principal susceptibilities. In the case of the perpendicular susceptibility, the contribution is made by the fluctuation of the torque acting on a spin which is expressed in terms of the spin waves as a simultaneous (de-) excitation of three or more magnons. In the case of the parallel susceptibility, a frequency shift of the spin waves induced by the external field through the spin wave interaction is responsible for the contribution. Numerical calculations of the susceptibilities of MnF 2 are carried out on the bases of newly derived expressions in which the terms of the order of 1/ S 2 are taken into account fully. The calculations in good agreement up to 2 T N /3 with the experimental data measured by Trapp and Stout. The terms of the order of 1/ S 2 newly included are essential for the agreement above T N /4.