Quantum fluctuations in easy-plane spin-one ferromagnet

The magnetic properties of easy-plane spin-one Heisenberg ferromagnet, H=D∑_i(S_i^x)² - J∑_(i,j)S_i·S_j- h∑_iSi^z, are investigated using the linked cluster series expansion. The results of the linked cluster series expansion method cover the whole range of temperatures, both magnetically ordered and disordered phases. The order parameter is included in correlations of spin fluctuation and solved self-consistently to high orders. The magnetization as a function of temperature for a given value of easy-plane anisotropy is shown. The observed values of magnetization from the linked cluster series expansion are appreciably depressed from their mean-field approximation values due to the quantum and thermal fluctuations. The effects of the quantum fluctuation on the magnetic ordering in three-dimensional (3D) systems are discussed.