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

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 Néel temperature, the critical exponent γ, and the staggered magnetization. The effect of quantum and thermal spin fluctuations on the magnetic ordering of the system is discussed.