  We present results of large scale simulations of the spin-1 Heisenberg
antiferromagnet on a tetragonal lattice. The stochastic series expansion
quantum Monte Carlo method is used to calculate equilibrium thermodynamic
variables in the presence of an external magnetic field. In particular, the low
temperature magnetization curve is investigated in the quasi-one-dimensional
(Q1D), quasi-two-dimensional (Q2D), and three-dimensional (3D) limits. Starting
from the 3D limit, the Q1D (Q2D) limit is achieved by reducing the in-plane
(out-of-plane) spin coupling strength towards zero. In the Q1D limit, a Haldane
gap appears in the magnetization curve at low magnetic field. Additionally,
near the saturation field the slope of the magnetization curve increases
substantially, approaching the infinite-slope behavior of a one-dimensional
spin-1 chain. A similar (though less pronounced) effect is seen in the Q2D
limit. We also study the effect of uniaxial single-ion anisotropy on the
magnetization curve for Q1D and Q2D systems. Our results will be important in
understanding the field-induced behavior of a class of low-dimensional Ni-based
quantum magnets.
