Longitudinal Spin Pair Correlation in Ferro- and Antiferromagnets with Uniaxial Anisotropy

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The spin pair correlation in Heisenberg ferro- and antiferromagnets with uniaxial ani-sotropy is studied with the aid of the thermal Green function method introduced by Matsu-bara and applied successfully to magnetic systems by Liu. The correlation is calculated by using the Tyablikov decoupling. The explicit dependence of the longitudinal correlation on temperature T and wave vector q just below the critical point is obtained. It agrees with the result of the spin wave theory at very low temperatures and satisfies the isotropic con-dition above the transition temperature in the absence of anisotropy. (1) In antiferromagnets, < S^0_<q+K_0>S^0_<-q-K_0> > plays the same role as < S_q^0 S^0_<-q> > in ferromagnets, where S_q^0 is the Fourier q-component of spin S^0,0 denoting the z-component, K_0 the half of the reciprocal vector, <・・・> the canonical average. (2) In the absence of anisotropy, < S^0_<q+K_0> S^0_<-q-K_0> > behaves as [q(q+δ)]^<-1> just below the Neel point T_N, δ being a constant depending on T, which is similar to < S_q^0 S^0_<-q> > in ferromagnets obtained by Kawasaki and Mori. Moreover, it is found that this dependence of the correlation is neither restricted to small q nor to spin 1/2. (3) In the presence of anisotropy and just below the critical point, < S^0_<q+K_0> S^0_<-q-K_0> > and < S^0_qS^0_<-q> > behaves [q^2+k_D^2]<-1>, where k_D is the correlation length determined by the anisotropy constant. It is to be noted that the anisotropy plays a decisive role even for D/J~10^<-4>, D and J being the anisotropy constant and the exchange integral, respectively.
理論物理学刊行会の論文
1969-03-25

Longitudinal Spin Pair Correlation in Ferro- and Antiferromagnets with Uniaxial Anisotropy

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