The bond operator representation and the one-loop renormalization group treatment are used to study the spin-1 Heisenberg antiferromagnetic with single-ion anisotropy and transversal magnetic fields in three-dimensional cubic lattices. We start from a disordered spin-liquid phase to an ordered phase, at a critical field Hc 1 above which the system enters an XY-antiferromagnetic phase. This transition is interpreted as belonging to a universality class with a dynamical critical exponent z = 1. In this marginal case logarithmic corrections are found to the physical quantities. These theoretical predictions are compared with the scaling of the magnetization as a function of field and temperature for the organic compound NiCl2 - 4 SC (NH2)2. © 2009 Elsevier B.V. All rights reserved.