Magnetic properties of spin-1 Heisenberg antiferromagnet with easy-axis single-ion anisotropy in three dimensions: Linked-cluster series expansion approach

Abstract

The magnetic properties of spin-1 Heisenberg and Ising antiferromagnet with easy-axis single-ion anisotropy are studied in both ordered phase and disordered phase by using the linked-cluster series expansion method. We calculate the seventh-order series for the free energy and staggered susceptibility and the sixth-order series for the staggered magnetization on three-dimensional bipartite lattices. We obtain accurate estimate of the N\'eel temperature, the critical exponent $\ensuremath{\gamma}$, and the staggered magnetization. The effect of quantum and thermal spin fluctuations on the magnetic ordering of the system is discussed.